Application of Dynamic Programming for Multiple Cutter Selection in Optimizing Machining Time of Sculptured Surface

APPLICATION OF DYNAMIC PROGRAMMING FOR MULTIPLE CUTTER SELECTION IN OPTIMIZING MACHINING TIME OF SCULPTURED SURFACE

By Jovian Agathon ID No. 004201400026

A Thesis presented to the Faculty of Engineering President University in partial fulfillment of the requirements of Bachelor Degree in Engineering Major in Industrial Engineering

2018 THESIS ADVISOR RECOMMENDATION LETTER

This thesis entitled “Application of Dynamic Programming for Multiple Cutter Selection in Optimizing Machining Time of Sculptured Surface” prepared and submitted by Jovian Agathon in partial fulfillment of the requirements for the degree of Bachelor Degree in the Faculty of Engineering has been reviewed and found to have satisfied the requirements for a thesis fit to be examined. I therefore recommend this thesis for Oral Defense.

Cikarang, Indonesia, February 22nd, 2018

Anastasia Lidya Maukar, ST., MSc., M.MT.

DECLARATION OF ORIGINALITY

I declare that this thesis, entitled “Application of Dynamic Programming for Multiple Cutter Selection in Optimizing Machining Time of Sculptured Surface” is, to the best of my knowledge and belief, an original piece of work that has not been submitted, either in whole or in part, to another university to obtain a degree.

Cikarang, Indonesia, February 22nd, 2018

Jovian Agathon

APPLICATION OF DYNAMIC PROGRAMMING FOR MULTIPLE CUTTER SELECTION IN OPTIMIZING MACHINING TIME OF SCULPTURED SURFACE

By Jovian Agathon ID No. 004201400026

Approved by

Anastasia Lidya Maukar,S.T., M.Sc., M.MT. Thesis Advisor

Ir. Andira Taslim, M.T. Head of Industrial Engineering Study Program

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ABSTRACT

Many kinds of manufacturing companies can be found in this era of industrialization, especially the make-to-order industry such as mold maker industry in fulfilling the demand of customer. As the trend keeps changing, the sculptured surface product is introduced and has been used for object design. Optimal machining time is the main concern that will affect the production cost and customer satisfaction. Many researchers have invented methods in finding the best strategy using the Computer Numerical Control (CNC) machine in the process. Thus, this research focuses on implementing one of the research algorithm, Chen’s Dynamic Programming model using the real data. A research object is designed and asked to several respondents to simulate in particular software by their own process planning. The information from the simulation is used as the input for the calculation using Chen’s Dynamic Programming algorithm. Through the calculation, the feasible tools can be revealed, machining plane can be determined, and the optimal machining time can be obtained using the algorithm model. Chen’s model reduces the machining time to 23% in average. Lastly, the calculated time using Chen’s algorithm and simulated machining time by the respondents are compared for case study.

Keywords: Mold Maker Industry, Sculptured Product, Machining Time, Computer Numerical Control (CNC) Machine, Dynamic Programming, Algorithm

ACKNOWLEDGEMENT

This thesis is hardly to be done without blessing from God and big motivation and tremendous support from the others. Therefore, I would like to express my gratefulness to: 1. Jesus Christ, as the source of inspiration and all blessing that I have gained. The only shelter to protect me from the storm 2. My beloved family, Mom, Grandma, Aunty, and Uncle. Thank you for your never ending support, prayers, and motivation to me. 3. My thesis advisor, Mrs. Anastasia Lidya Maukar, S.T., M.Sc., M.MT. and Mrs. Ineu Widaningsih, S.T., M.T. Thank you for your guidance, motivation, and advices in doing and accomplishing this thesis. 4. My academic advisor and Head of Industrial Engineering Study Program, Mrs. Ir. Andira Taslim, M.T. Thank you for your guidance, advice, and everything from the beginning until the completion of this thesis. 5. Betinsss squad: Nico, Aberson, Julius and Michael who always be a place to share the happiness and problems together in any time and many ways in rent house. 6. WW Gombel squad: Shella, Santi, Vero, Rika, Nico, Julius, Aberson, and Michael as my brother and sister in Cikarang. 7. My best closest female friend, Shofa Ramadhina, who always encourage me to keep striving finishing all that should be finished. The best place for the process to be myself. 8. My classmate, Industrial Engineering 2014 and Engineering Family. Thank you for always sharing, reminding, supporting each other, and all the memories that we had made together in the university life. 9. Others that I cannot mention one by one but keep supporting and motivating me. Thank you for make my life meaningful.

TABLE OF CONTENT

THESIS ADVISOR ...... i

DECLARATION OF ORIGINALITY ...... ii

LETTER OF AGREEMENT ...... iii

ABSTRACT ...... iv

ACKNOWLEDGEMENT ...... v

LIST OF TABLES ...... ix

LIST OF FIGURES ...... x

LIST OF TERMINOLOGIES ...... xi

CHAPTER I INTRODUCTION ...... 1

1.1 Problem Background ...... 1

1.2 Problem Statement ...... 2

1.3 Objectives ...... 2

1.4 Scope ...... 3

1.5 Assumption ...... 3

1.6 Research Outline ...... 3

CHAPTER II LITERATURE STUDY ...... 5

2.1 Manufacturing System ...... 5

2.2 Machining Process ...... 6

2.2.1 Sculptured Surface ...... 8

2.2.2 Computer Numerical Control (CNC) Machine ...... 9

2.2.3 Tool Selection for 3D Sculptured Cavities ...... 11

2.3 Operation Research ...... 12

2.3.1 Integer Programming ...... 13

2.3.2 Dynamic Programming ...... 13

2.4 Chen’s Algorithm using Integer and Dynamic Programming ...... 14

2.5 Questionnaire Design ...... 17

2.4.1 Convenience Sampling ...... 20

2.4.2 Purposive Sampling ...... 21

2.6 State of the Art ...... 22

CHAPTER III RESEARCH METHODOLOGY ...... 25

3.1 Research Methodology ...... 25

3.1.1 Problem Identification ...... 25

3.1.2 Literature Study ...... 26

3.1.3 Data Collection ...... 27

3.1.4 Data Analysis ...... 28

3.1.5 Conclusion and Recommendation ...... 28

3.2 Research Framework ...... 28

3.2.1 Data Collection ...... 29

3.2.2 Data Analysis ...... 31

CHAPTER IV DATA COLLECTION AND ANALYSIS...... 32

4.1 Data Collection ...... 32

4.1.1 Research Object ...... 32

4.1.2 Questionnaire ...... 34

4.2 Collecting Data Result ...... 35

4.3 Calculation using Chen Dynamic Programming Model ...... 36

4.3.1 Respondent A ...... 39

4.3.2 Respondent B ...... 43

4.3.3 Respondent C ...... 45

4.4 Summary of the Research...... 47

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4.4.1 Calculation Summary ...... 47

4.4.2 Implementation of Chen’s Algorithm in Real Work Environment ...... 50

CHAPTER V CONCLUSION AND RECOMMENDATION ...... 51

5.1 Conclusion ...... 51

5.2 Recommendation ...... 51

REFERENCES ...... 52

APPENDICES ...... 54

Appendix 1 – Questionnaire Sheet ...... 54

Appendix 2 – Filled Questionnaire ...... 57

Appendix 3 – Calculation using Chen’s Algorithm ...... 65

Appendix 4 – Documentation of Collecting Data Phase ...... 75

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LIST OF TABLES

Table 2.1 Previous Research Optimizing Sculptured Surface Machining Process24 Table 4.1 Target Population ...... 34 Table 4.2 Prominent Collected Data ...... 35 Table 4.3 Tools Used by Respondent A ...... 39 Table 4.4 Feasible Tool Matrix for Respondent A ...... 40 Table 4.5 Machining Time Matrix for Respondent A ...... 41 Table 4.6 Process Planning by Respondent A ...... 42 Table 4.7 Comparison of Simulated and Calculated Respondent A Machining Time ...... 42 Table 4.8 Comparison of Simulated and Calculated Respondent A Process Planning ...... 43 Table 4.9 Tools Used by Respondent B ...... 43 Table 4.10 Process Planning by Respondent B ...... 44 Table 4.11 Comparison of Simulated and Calculated Respondent B Machining Time ...... 44 Table 4.12 Comparison of Simulated and Calculated Respondent B Process Planning ...... 45 Table 4.13 Tools Used by Respondent C ...... 45 Table 4.14 Process Planning by Respondent C ...... 46 Table 4.15 Comparison of Simulated and Calculated Respondent C Machining Time ...... 46 Table 4.16 Comparison of Simulated and Calculated Respondent C Process Planning ...... 47 Table 4.17 Machining Time Comparison ...... 47 Table 4.18 Relative Machining Time Calculation ...... 49

LIST OF FIGURES

Figure 2.1 Machining Process Method by Lee et al...... 7 Figure 2.2 Product Development Cycle and Sculptured Surface Machining ...... 9 Figure 2.3 3-Axis CNC Machine ...... 11 Figure 2.4 Decision Stages in Dynamic Programming (DP) Method ...... 16 Figure 3.1 Research Methodology ...... 25 Figure 3.2 Research Framework ...... 29 Figure 4.1 Research Object in 3D view ...... 32 Figure 4.2 Holes Dimension in the Object ...... 33 Figure 4.3 Research Object Technical Drawing ...... 33 Figure 4.4 Ball Mill and Bull Nose Mill Cutter ...... 36 Figure 4.5 Dynamic Programming Model Flowchart ...... 38

LIST OF TERMINOLOGIES

Cavity : Unit of the molded parts

CNC machine : A machine tool that generally used in manufacturing (Computer industries to perform the works automatically based on Numerical Control) the programmed commands as the results from converting the designed product on the software into the coordinates, movement of the cutter, speed of the machine, and the other settings.

Dynamic A general algorithm design for solving multivariable Programming problems by breaking it down into simpler sub problems.

Hunting plane : The intersection of sculptured surfaces which perpendicular to the tool axis to extract the geometric constraints of machining.

Machining plane : Desired cutting depth level of an object to be machined.

Roughing : An activity of removing the excess material from a raw stock to create the desired shape.

Sculptured Surface : Also called freeform surface, the irregular surface shape which made from joined different patches together.

Solidworks : A 3-dimension design software which is able to make a solid modeling and categorized as computer-aided design (CAD) and computer-aided engineering (CAE) computer program.

CHAPTER I INTRODUCTION

1.1 Problem Background In the era of industrialization, many improvements have been made to accomplish and satisfy the customer needs. The technology keeps integrating, same as the growth of the industries. There are many kinds of manufacturing companies based on their kinds of products and the strategy in dealing with their customer. One of them is make-to-order strategy. The customer will order by giving the information related to the product to the company who will create the product. As the response, the company should give the order response in the shortest time with the detail of the duration of machining time and production cost in producing it.

The advance of all the aspects in life and the changes of the interest of customers result the changes of the product design nowadays, particularly the sculptured or freeform surfaces. Chen et al. (2003) claims the sculptured parts can be found most applied in the aeronautical, automotive, and many other industries. Because of the asymmetrical shape, the complex surface parts are difficult to be machined. According to Chen, among the advanced technologies, the computer numerical controlled (CNC) machines are commonly used to machine the complex surfaces parts, however, it needs the preparation in weeks for the NC program machine. According to Hatna et al. (1998), the time spent on rough machining is usually five to ten times that spent on finishing, which is the reason of most research focusing on the roughing process.

Same problem that always faced by manufacturing company, especially the mold maker manufacturing industries is the efficiency of machining process. The process of machining will take much time when the surface of the object is more complex, the sculptured product. Specific coding with planned strategy will be made as the input for CNC machine which takes enough time for the preparation. Despite of other factors, the tools selection and machining plane determination will affect the

1 entire process to runs well. Moreover, the experts in the companies are mostly only using their experiences in doing the process planning.

There has been some research done focusing on the cutter selection. Domaze (1990) proposed a ruled matrix method for cutter selection in turning process. There are some techniques were also presented in Lee et al. (1996) to determine the cutter sizes based on effective cutting shapes for three-axis and five-axis sculptured- surface finishing. Chen et al. (1998) developed a model using integer and dynamic programming to get the best decision of cutter and helping the determination of machining plane for numerical controlled machining of complex surfaces.

In optimizing a condition using the calculation of numbers, a study named Operation Research is used by most people particularly in the industrial scope, for example the linear programming, sensitivity analysis, transportation and network models. Along with this idea, it is a challenge and opportunity for the manufacturing company to apply the algorithm and deal with the complexity of the product. This research will try to propose the Chen algorithm using dynamic programming to get the optimal cutter selection and machining time and get to be acquainted with the situation in the real work environment in purpose.

1.2 Problem Statement Based on the problem background that has been explained above, the problem statement of this research is: How does the implementation of Chen algorithm using dynamic programming to find the optimal cutter and machining time in real work environment?

1.3 Objectives The objective of this research based on the problem statement above is implementing the dynamic programming to optimize machining time in real work environment.

1.4 Scope Due to limited time and capability, there is a scope in this research: 1) The model object for the research is only single cavity. 2) The research is focusing only on the roughing process. 3) The model is for products made by CNC machine. 4) The data is obtained from the Jababeka industry area. 5) The calculation is done in the Microsoft Excel software.

1.5 Assumption There is an assumption made for this research which are: 1) The material composition for making the object is Carbon Steel (S50C). 2) The tools for this research is made from Carbide.

1.6 Research Outline Chapter I Introduction This chapter explains the details of problem background, problem statement, research objectives to answer the problem statement, scope and assumption of research as well as the research outline. Chapter II Literature Study This chapter consist of basic theoretical framework those taken from books, journals, and expertise works related with manufacturing system and machining process, details and history of sculptured surface, the explanation of CNC machine and tool selection for 3D cavities, operation research, questionnaire design technique and surely the Chen’s optimization technique. Chapter III Research Methodology This chapter contains the general and detail process flow procedure from problem identification to literature study, continued with collecting data process by designing the research object and questionnaire, then field study. Furthermore, the collected data will be used and compared with calculated number using Chen’s algorithm. Lastly, the result will be analyzed and conclusion is made.

Chapter IV Data Collection and Analysis This chapter will elaborate the implementation calculation of Chen’s Dynamic Programming algorithm using the obtained real data from the field study. The calculated data is compared by inputting the obtained strategic planning by the respondents using software to acquaint the effectivity of the method.

Chapter V Conclusion and Recommendation This chapter contains the result of the research calculation and also some consideration of Chen’s algorithm implementation in the real work environment to answer the problem statement. Moreover, the conclusion and recommendation is also made for further research.

CHAPTER II LITERATURE STUDY

2.1 Manufacturing System Fogarty et al. (1991), defines manufacturing system as a system that connecting the production function with the other function in purpose of reaching the optimal performances, such as production time, production cost and machine utility. There are many classifications of manufacturing system and Bertrand et al. (1990) divides the system into 4 types based on the production types, includes Make to Order (MTO), Make to Stock (MTS), Assemble to Order (ATO) and Engineering to Order (ETO) which are explained below. 1) Make to Order (MTO) is a production type which performed when the order from the customer comes in. Customer will give their product specification to be accomplished and the company will give the quotation/ offer in the form of production cost, production time and other specific things as the response. Sheikh (2002) claims the demand changes overtime and cannot be forecasted due to various/ customized product. 2) Make to Stock (MTS) is a production type that focusing on the upcoming order by producing finish goods and store it as the inventory. The variety of this type is small and mostly the demand can be forecasted. The examples are food and beverage industry and toys industry. 3) Assemble to Order (ATO) is a production type that prepares the subassembly which will be assembled into finish product whenever the order comes. This type of production is used by company that has modular product that can be easily assembled into some finish products. The variety is large and the product has competitive prices, in example the computer and sound system. 4) Engineering to Order (ETO) is a production type that similar with MTO, no stock as inventory, but the company should develop the product design and give it to the customer with the production cost and time before the production begin.

If the deal is done, the production can be started. Typically, it is performed when making a new product that never be launched before. Based on the four classification types of manufacturing system above, MTO and ETO are categorized as job order production, which is the process of manufacturing custom or unique products requested by specific customer. According to Toha (2000) MTO and ETO are categorized as job order manufacturing system, which means that an order is needed to trigger the production activity. These type of manufacturing system are divided into repetitive and non-repetitive type, where the repetitive type is easier than the non-repetitive type because the company can repeat the production process that has been performed before. The non-repetitive type has high variety of product causing the process is more complex.

2.2 Machining Process Creese (1999) defines the machining is a process of shaping part through removal of material. By using the tool, which known as machine tool that made of harder material than the part being formed, it is forced against the part which results cut by the tool. Machining is both primary as well as secondary manufacturing process. It is the most accurate and precise manufacturing process because of its competence to produce different types of part geometries and geometric features. According to Creese, almost all the manufacturing process require machining to get the desired three-dimensional final shape or surface characteristics. The removed material is usually in the form of “chips”, but may also as fine particles or powder (in grinding or polishing process), or after dissolved or vaporized form (such as electrochemical machining) that all of them are hard to recycle.

According to Groover (2010) there are many kinds of machining operations in setting up a particular part geometry and surface texture, but there are three mostly used types which are turning, drilling, and milling. The turning activity uses a cutting tool which has the single cutting edge to remove the material in generating a cylindrical shape from a rotating work piece. Same as its name, drilling is literally used for making a round hole on the object by using a cutting tool, moves by doing

6 the rotation movement with two cutting edges. In milling, the plane or straight surface will be generated using rotating tool with multiple cutting edges tools.

Moreover, there are two categories divided based on the purpose and cutting condition, the roughing and finishing. The first step is roughing, the process of removing the big amount of material as fast as possible close to the desired form, although there is still some left material on the piece which can be done through the finishing activity. The finishing cuts is used for completing the part fitted to the desired shapes and features for the final dimensions. There are some constraints generally for the sculptured object to be produced. Based on Lee et al. (1992), the method for the sculptured surface machining process with constraints appears in the Figure 2.1.

Figure 2.1 Machining Process Method by Lee et al.

In the proposed method, the first phase is using a set of hunting planes to intersect the object to obtain the geometric information, which includes the size and depth of the cavity, the cutting area on each hunting planes, and also the height and cross- section of islands inside. After that, the second step is executing and making decision in machining processes, choosing the cutters to be used, and merge the selected processes which will be practiced in this research. The implied cutters and hunting planes are merged by considering the machining constraints to decide the final cutting planes and cutter selection. The last step in the process is generating the cutter path for roughing and finishing process.

There are many advantages using the machining in shaping process, either as the primary or secondary operation. It can improve the dimensional tolerances and the surface finish. Not only that, because of the lower setup times and the ability to produce complex geometry could be the consideration to be selected. Despite of many advantages provided by the process, machining processes produce large amounts of chips as waste which means the poor material utilization, longer cycle time because of several needed cuts, and also consume high energy to produce a product. The speed, feed, and depth of cut of the cutter are the cutting conditions.

2.2.1 Sculptured Surface Byung (1998) explains that before the beginning of high-speed computation, sculptured or could be also called freeform surfaces were made by the expertise artisan who created a master model in an easily formed material like clay. After then, there was numerical coded (NC) machines made and developed in the 1950s which globally changed the process. The master model was still made by artisans, but it was stored in digital form through data sampling done by a coordinate measuring machine (CMM) which using more functions of the computer. With the advance of high speed computers with bigger capacity of memory and disk space, many past methods are simple to be implemented now. The demand of sculptured surface products is increasing as many companies and manufacturing industries try to keep enhancing their aesthetic appeal to satisfy the customer.

The efficient machining process of sculptured surfaces, particularly in mold maker industry has become critical in various manufacturing industries which results the sculptured surface machining (SSM) technology has become a vital technology to be used in those industries. Choi (1998) claims that information processing technology made of the three technologies, which are sculptured surfaces, machine tools, and numerical controls. According to Choi, the SSM process is an important part of the non-machining processes, such as plastic injection molding since it is applied mainly to the manufacture of dies and molds. A typical product usually has the development cycle consist of styling, part-design, die-making, tryout, and production which shown in Figure 2.2. There are some related technological developments such as machine tool technology and the numerical control technology in the process.

Source: Choi et al., 1998, Sculptured Surface Machining: Theory and Applications Figure 2.2 Product Development Cycle and Sculptured Surface Machining

2.2.2 Computer Numerical Control (CNC) Machine Geng (2004) defines CAM is the acronym of “computer-aided manufacturing in the use of leveraging the product design information in the format of CAD data to drive manufacturing functions. It allows the manufacturing and tooling engineers to control the machine tool operations by only writing the computer programs and it has brought a great improvement linked with the CAD technology. The computer numerically controlled (CNC or NC) machine has inside programs that contains thousands of commands as the instruction to move the machine tool precisely to any position. It symbolizes the changes of using the traditional method to the modern one and has been giving the long-lasting impact on the reliability and quality of manufacturing environment these days. Nowadays, the CAM systems is

9 capable to import 3D solid models and develop it to be CNC computer code which required to control the manufacturing operations.

There have been many evolvements in the CNC machine tool industry, from the earliest numerically controlled machines with expensive price to the rapid adoption of high-end 3D CAM systems which have been introduced with the affordable prices. According to Geng, CAMs itself were added to machine tools during the Civil War to speed weapons production since the mid-1800s. Nowadays, the three- axis CNC milling machines and two-axis lathes are common. The combination of conventional like tooling milling operations with the turning operations is revolutionizing the machining industry and the complex parts can now be completely machined as part of a totally automated manufacturing process.

There are various types of CNC machines, such as milling machine, lathe and CNC plasma cutter. In designing the CAM systems to be able to operate with different types of machine tools, a machine-specific translator is utilized to convert the generic CAM instruction to the low level that the machine controller can understand. Through this way, once using the same CAM program, it can be used to run different types of machine tools. Because of the use of CNC machine tools, almost all products on store is more reliable and less expensive both manufactured and bought.

CNC machine can be operated in multi axis machining centers based on the preferences and shape of the product to be created. Geng (2004) classifies the multi axis types into three-, four-, or five-axis machine for 3D object. The three-axis machine features three linear usual axes, X, Y, and Z. A four-axis machine features a rotary table, when the five-axis machine features the additional of tilting table or head, for example three linear axes and two rotary axes. Mostly used and invented first, the three-axis CNC milling machine accurately used for automatic operation, milling, drilling holes, and cutting sharp edges. It is able to create the same products as four-axis and five-axis machines, but cannot delivers the same level detail or efficiency as the other using axes, although it will cost lower. Chen (2003) explains

10 three-axis CNC machines are frequently used in manufacturing which can be used to machine sculptured parts of simple shape because of its lower cost.

Source: Chen et al., 2003, Automated Surface Subdivision and Tool Path Generation for 31 1 axis 2 2 CNC Machining of Sculptured Parts p. 320 Figure 2.3 3-Axis CNC Machine

2.2.3 Tool Selection for 3D Sculptured Cavities Sculptured surfaces are difficult to deal with and need the effective correct action in the machining process. The complexity of the surfaces makes difficult at the programming stage to produce the desired quality of the actual operation. Supported by the computer-aided design, there are still some tasks to be focused on, such as the cutter selection, cutter path generation, and NC programming.

Meng et al. (2014) clarify the optimal size selected cutter is critical in the process of machining 3D cavities using a single number or more than one cutters. There have been many researches made in deciding the optimal choice of multiple tools and toll sequence selection. Lasemi et al. (2010) proposed a method of tool selection based on the geometry to do the roughing until cleaning up process. Jensen et al. (2002) explained the method in selection tools based on curvature of the object that matched the machining process; the radius, corner radius and length of tool

11 were identified to know the possibility of errors in machining and total material removed after a process has done. Moreover, Zhang et al. (2008) developed a method using algorithm to get the accessible information regarding to the all available tools in a tool library and feasible tools those to be identified. If there are multiple tools to be used in machining process, the set of tools with minimum machining time will be chosen in each different regions of sculptured surface. Chen et al. (1998) also developed an algorithm for determining the optimal cutter to be used and machining plane for complex surfaces.

Lee et al. (1992) affirm the difficulty of the cavity machining process depends on the geometric complexity and the constraints in machining the cavity of part surface. Indeed, a shallow with not-so curved cavity is simpler to be machined than a complex and deep cavity, when a very curved sculptured surface needs smaller cutter to do more movements on the surface. Theoretically, cavity can be divided into many types by considering the machining information and cost. The machining procedure itself is based on the type of cavity to be machined.

2.3 Operation Research Optimization can be defined as the act of obtaining the best result by giving the maximum or minimum of a function under given circumstances. A company has to find the best way to minimize the cost and maximize the profit to optimize the operation. There are many methods to get the optimum point which also known as mathematical programming techniques and generally studied as operation research. According to Miller and Starr, Operation Research is an applied decision theory using any mathematical or logical calculation in dealing with decision problems, when Ackoff and Arnoff define it as the application of scientific method, techniques and tools to provide the optimum solution of problem. In conclusion, operation research is a branch of mathematics concerned with finding the best or optimal solutions using the application of scientific method and techniques in decision making. The well-known operation research technique is linear programming, usually used for solving the problems with linear objective and having some constraint functions. The other algorithm methods that will be explained in the next

12 subchapters are integer programming (the variables assumed integer values) and dynamic programming (the model of the problem can be break up into more sub problems).

2.3.1 Integer Programming Integer programming or usually called integer linear programs (ILP) are linear program models with the variables have the number of integer or discrete values. There are two main algorithms of ILP, which are branch and bound (B&B) and cutting plane in solving the problems. B2B algorithm is considered to be more efficient computed. Then, in finishing the ILP algorithms successfully, there are three steps in doing the strategy. Step 1. Change the solution space of ILP by removing the integer restriction on all integer variables and replacing any binary variable y with the continuous range 0≤y≤1. The obtained result is a regular Linear Programming. Step 2. Solve the LP model and identify its continuous optimum. Step 3. After finishing the second step, add the special constraints that constantly modify the LP solution space in a manner that will eventually render an optimum extreme point satisfying the integer requirements.

2.3.2 Dynamic Programming Dynamic programming is used for determining the optimal solution of a multivariable problem by elaborate it into sub problems which consists of a single- variable sub problem. The advantage of it is the optimization process at each level will involve only one variable, which much simpler to be calculated than dealing with all the variables simultaneously. Generally, in applying the dynamic programming to obtain the solution, it should be solved backward toward the beginning from a problem, separate the large, unhandled problem into smaller, more plot able problems. Based on those process, there are some characteristics of dynamic programming applications which are listed below.  The problem can be separated into phases with a decision required at each phase.  Each phase has a number of states associated with it.

 The decision chosen at any phase describes the changes of how the state at the current phase is transformed into the state at the next phase.  Given the current state, the optimal decision for each of the remaining phases could be obtained and must not depend on previously reached states or previously chosen decisions.  If the states for the problem have been divided into one of T phases, there must be a recursion that relates the cost or reward earned during stages.

2.4 Chen’s Algorithm using Integer and Dynamic Programming Chen (1998) introduced the algorithm of using integer and dynamic programming to get the best selection of cutter and determined machining plane for optimal machining time. It is applied on sculptured surface object using CNC milling machine. In the process, Chen made the algorithm and used MATLAB software to support the research. The integer programming model will be used to retrieve the feasible cutter for each hunting plane and machining plane determination information, complete with the result of machining plane determination and calculated machining time. Although the result has been obtained, but it is still not optimal because the machining plane is not merged. Hence, the dynamic programming model will be used to get the optimal solution. Started with the feasible cutter for machining process, it can be defined from feasible tool matrix. The formulated formula is shown below.

푚 푛 min 푓 (푥) = ∑푖=1 ∑푗−1 푐푖푗푥푖푗 (2-1) subject to: 푚 푛 (2-2) ∑푖=1 ∑푗=1 푑푖푥푖푗 ≥ ℎ 푚 (2-3) ∑푖=1 푎푖푥푖푗 ≤ 푏푗 j=1, 2, …, n 푚 ∑푖=1 푥푖푗 = 1 j=1, 2, …., n (2-4)

Xij = 0 or 1, for Ɐ and j (2-5)

Equation 2-1 shows the feasible cutter selection formula without determining the machining plane at first. Variable of m shows the number of cutter used and n shows the number of hunting planes in the object. Cij represents the cutting time required

14 of hunting plane j using cutter i in the process and variable Xij is the decision variable obtained from the calculation, either 0 or 1 to discover a cutter is feasible or not in a particular hunting plane. The formula is restricted by constraints from Equation 2-2 until Equation 2-5. Equation 2-2 restricts the depth of cutter i for all cutters used and current number of hunting plane should be more than or equals the total depth of cavity. According to Geng (2004), depth of cut can be interpreted as the radial movement or engagement of lathe tools and drills, with the axial engagement for milling cutters. In simpler way, it is the depth that can be reached by the movement of the tools in each one-time movement to the bottom before ramping up. The total depth of cavity value is the total depth of the object cavity. In this research, it is focused on the single cavity. Next, Equation 2-3 ensures the diameter of cutter i should be less than or equals to critical distance of boundary on hunting plane j. Each contour or step has its critical distance which is the smallest distance in a boundary. After finishing with the first two constraints clarify only one cutter is allowed to be assigned to a hunting plane. Then Equation 2-4 and 2-5 ensure the obtained decision variables either 0 or 1 only.

Finished considering the feasible cutter to certain hunting plane, using the obtained machining data for each hunting plane and the feasible cutter matrix the machining plane will be determined and the machining time is retrieved. There are two steps in doing that, first is Primal Improvement and second step is Dual Improvement. Primal Improvement focusing on detailed cutter i assignment to the hunting plane. A certain cutter i will be assigned to certain hunting plane when the cutter is feasible and having the minimum marginal cost of machining time with certain depth of cut among all feasible cutters. Dual Improvement continues with machining plane determination with considered cutter to each hunting plane. The result of machining time is obtained with the detail of each component, but the hunting planes are not considered to be merged two or several planes into one, which means it is still not optimal. Therefore, the Dynamic Programming model is used to assist the calculation of optimal solution for both tools selection and machining plane resolve.

In applying the dynamic programming model, the data of choice of cutter and machining time of the selected cutter, all of the possible combinations can be made. Explaining the process, the distance between two adjacent hunting planes could be symbolized as ∆Z. An object is separated by hunting planes with certain distance ∆Z to determine the machining plane. The figure below shows each level of hunting plane symbolized by s, divide the object of each level with the highest level S. Figure above is named decision stages which used to decide how many hunting plane down from the s to be machined. In optimizing the machining time, several hunting planes s will be merged, which variable is x.

Source: Chen et al., 1998, Optimal Cutter Selection and Machining Plane Determination for Process Planning NC Machining of Complex Surfaces p.381 Figure 2.4 Decision Stages in Dynamic Programming (DP) Method

The x hunting planes will be merged and machined by one particular selected cutter q (s, xs) in one cut. Although there are some hunting planes to be merged, the crucial distance is still considered with the cutter diameter 퐴푞(푠̅, 푥̅푠) ≤ 퐵푠̅, 푥̅. The stage 푠̅ with the given state 푥̅s means that the position is 푠̅th hunting plane from the bottom of the cavity and 푥̅s hunting planes are planned to machine in one cut by one particular cutter. Next, The minimum machining time to remove 푥̅s hunting planes down from hunting plane 푠̅ by using one cutter, the cutter q(푠̅, 푥̅) can be formulated as below.

(Dq(푠̅, 푥̅푠) ≥ 푥̅s●∆Z, (2-6 ׀ 퐶푞̅(푠̅, 푥̅s) = min{Cq(푠̅, 푥̅s 퐴푞(푠̅, 푥̅푠) ≤ 퐵푠̅, 푥̅, 1 ≤ q(푠̅, 푥̅푠) ≤ m}

Equation 2-6 is the formula to get the optimal machining time 퐶푞̅(푠̅, 푥̅s) by getting the minimum value of it. Some statement and constraint included in the formula above. The first statement means that the selected cutter depth should be more than or equal to total depth required for machining the 푥̅s hunting planes. Second statement explains that the diameter of cutter should be less than or equal to the critical distance and the last constraint means the particular selected cutter value is between 1 and the cutter used. In special case, if there is any tie, any one achieving minimum value can be selected to be the tiebreaker. It can be defined as f(푠̅) which is the minimum machining time to remove the 푥̅푠 hunting planes by using the optimal combination of different cutters and hunting planes. The f(푠̅) variable is formulated by Equation 2-7. Equation 2-8 implies the variable 푠̅ only has the value of integer number 1,2 until S.

ꬵ(푠̅) = min {[ 퐶푞̅(푠̅, 푥̅s)(1) + f(푠̅-1)], (2-7) [퐶푞̅(푠̅, 푥̅s)(2) + f(푠̅-2)], …, [퐶푞̅(푠̅, 푥̅s)(푠̅) + 푓(0)] for 푠̅ = 1, 2, …, S. (2-8)

2.5 Questionnaire Design Human are forced to make decision every day from the simple until the hard-made decision in their life. Sometimes, there are some decision those need to be analyzed in detail and even requiring the opinion from a group people. Therefore, there is an instrument called questionnaire with the function to collect data, validating data, gaining the opinion from a group for a decision for all people, or even the preparation before launching a product and more on. Based on Bell (1999) a questionnaire is a structure technique consists of written questions to collect the primary data where the respondents have to give the response to it. A questionnaire should be well designed to motivate the respondents to give the accurate and detail information those reliable and relevant. There are three types of question which are open-ended, dichotomus and multichotomus (close-ended). Close-ended questions only require the simple answers and provides a range of possible answers, when open-ended question require a deeper thought response for it.

According to Brancato et al. (2005), there are three steps in making a good questionnaire design, those are developing the conceptual framework of the questionnaire, how to do the writing and sequencing questions in the right order, and making the questionnaire is visually satisfying for the respondent. All of the components are used in designing the questionnaire presently. a) Conceptual frame Before a questionnaire could be made, it is suggested to review the relevant literature and analyses from other surveys related with the topic at first. The designer should read it first before going to the next step. Afterwards, the objectives and concepts of the research are needed to be made specific and conceptualized. The made concept will be used to create the suitable indicators and observable variables. When doing the conceptualization, it requires the involvement of the users, the expert in the subject of the questionnaire, the questionnaire designer and of course, the respondents Brancato et al. (2005). By involving all the subjects, the concepts and definition can be known whether the designed questionnaires are comprehensible to the respondents and suit to the user’s requirements. As the output, a proper description of the survey concepts, the list of indicators which affecting the questionnaire and variables in the decision making, and a preliminary order of variables replacing in the future the questions. b) Writing questions The quality of gained data during the collecting process really depends on the quality of the questionnaire. It should be made easy to be understood by the respondent and they could give the best required information. Thus, the main concern in writing the questions for a questionnaire is providing a set of questions those minimalize the errors in the questionnaire provided, the respondent and the interviewer. In minimalizing the errors, there should be principle focusing on the relevance of each question, the type of questions to be used, the logical sequence and also wording of questions. Generally, when the respondent is given the questionnaire, they should:  Aware and clearly understand the questions of being asked  Be able to answer the list of questions attached in the questionnaire, and

 Understand how the answer has to be answered as the user needs Through this way, it allows to gain the optimal cooperation from all targets of population rather than only the “optimal respondents”. Based on the information or data that can be attained, there are four types of survey questions, which listed below.  Factual Questions The questions would require the fact based information rather than the opinion of the respondent  Behavioral Questions The questions will ask about the activity, routine, situation of the respondent, business or any other related habitual.  Opinion Questions Different than the factual questions, the opinion questions seek for the subjective opinions rather than the facts.  Hypothetical Questions Hypothetical questions are made by making the hypothetical statement of a certain condition or situation and generally much easier to agree with a statement than to go against it. Because of that, this type of question should be avoided than the others or at least used only when referring to a hypothetical occurrence of a situation.

The types of questions are not only classified based on the required data, but also the answer formats. There are open questions and closed questions. As mentioned before, rather than asked to select from the options, the open questions grant the respondents to answer the question using their words. Reverse from it, the closed questions prepare the respondents with a range of possible answers to be chosen. c) Visual Design Elements The visual design components consist of the elements related to layout of the questionnaires, the fonts, and structure of the tasks required in the questionnaire. It is related with the visual of the questionnaire in guiding the filling answer process. The main point of visual design elements is the obvious in self-answering

19 questionnaires (PAPI or as CASI instruments). Well visual designed of a set of questions will make the answering process more effective.

Not only designing questionnaire, the sampling technique to be used should be considered based on the needed data and target respondents. Battaglia (2008) said that there are two sampling techniques, they are probability sampling and nonprobability sampling. In the probability sampling, the sample will be randomly selected from a population. Differently, the nonprobability sampling will use subjective methods to decide which elements are included in the sample. Hence, it is crucial for a researcher to determine which sampling technique to be applied in the study.

Focusing on the nonprobability sampling, the technique can be divided again into two types, convenience sampling and purposive sampling. A convenience sampling will be conducted when the subjects are having the close proximity to the researcher. For purposive sampling, it is purposely done sampling because of the certain characteristics that suit the purpose of the study.

2.4.1 Convenience Sampling Dornyei (2007) defines convenience sampling (also familiar as Accidental Sampling) as a nonrandom sampling technique where the target respondents fit to certain criteria of condition, such as availability time, easy accessibility, and geographical proximity. Lisa (2008) explains this type of sampling is assigned to the subjects of the population that are easily accessible by the researcher. The convenience sampling is easy for the practice and affordable. Its main objective is collecting the information from participant who are easily accessed by the researcher and homogeneous population. Because of its character that results in the high possibility of self-selection by the researcher in non-probability sampling, the convenience sampling is not recommended to be used as the representative of the population.

2.4.2 Purposive Sampling In gathering the data, there are some occasion that the information should be recorded from specified qualified respondent to fulfill the requirements. The purposive sampling technique or could be called judgement sampling intentionally choose certain participant due to the qualities the participant possesses. The researcher decides what will be the needed data and find the people who can and willing to provide the information with enough experience or knowledge. There are some purposive sampling ways, which are mentioned below. a) Maximum Variation Sampling This method uses all the available types of respondent in a population, which also known as “Heterogeneous Sampling” to get the better understanding. b) Homogeneous Sampling Dissimilar with the MVS (Maximum Variation Sampling) method, the homogeneous sampling only focuses on candidates who have the specific characteristics. Etikan (2016) gives the example of a researcher wants to do a research on the long-term side effect of working with metallic component environment, the only people worked with metallic component for 20 years or longer are included. c) Typical Case Sampling Etikan (2016) interprets the typical case sampling is usually used when a researcher is dealing with large scope programs and the candidates are commonly chosen based on their possibility of behaving like everyone else. For instance, a researcher is studying the reactions of 9th grade students that will be graduated and directed to a job placement program, the respondents will be classes from similar socio-economic regions. d) Extreme/ Deviant Case Sampling According to Etikan (2016), extreme case sampling is used for gaining the information from individuals that are unusual or typical. The example will be a study of cancer patients. There will be patients who recovered faster, and there will be other slower patient than the average. The focus will be on the variation and the reasons of the atypical recoveries.

21 e) Critical Case Sampling This method emphasizes the critical cases to be selected and examined. In example, it comes up with the statement: “If it happens there, will it happen in other places?”. f) Total Population Sampling According to Etikan (2016), Total Population Sampling (TPS) is a method which includes all the elements of population that fit with the criteria (e.g. experience) in the research being conducted by the researcher. It is more generally used for small number of cases that being investigated. g) Expert Sampling Referring to its name, the Expert Sampling is only conducted for the experts in the peculiar field in certain subjects of the purposive sampling. It is usually useful for a long time taken research or where there is a lack of observational evidence.

2.6 State of the Art There are three invented methods by the researchers in optimizing the machining process for sculptured product, which are Chen et al. (2003), Chen et al. (1998), and Lee et al. (2010). Each three researcher has different strategy and focus on finding the optimal way on machining time of sculptured surface.

Chen et al. (2003) come up with a method to divide the sculptured surface of an object into a series of simple-shaped patches according to the surface features. The subdivision can be known by grid points through two steps, rough subdivision and fine subdivision. Rough subdivision divides the surface into many regions with several major shape categories based on the geometrical calculation and machinability parameters, which are convex, concave, and saddle as the variables. Finishing fine subdivision is done by making more details on the regions divided from previous rough subdivision. Afterwards, each patch can be conveniently approached in part construction and efficiently machined through 3-axis machining. The function of 3-axis CNC machining on each patch in the part build up is to

22 ensure the maximum tool path generated and machining efficiency in the process. There are also Gaussian curvature and mean curvature as the additional variables for further calculation to acquaint the types of the shapes.

Different method with the same first name, Chen et al. (1998) found the algorithm of using integer programming (IP) and dynamic programming (DP) model to determine the optimal cutter choices and machining plane for the process planning. The information of the available tools and details of the object is needed. The IP algorithm grants the upper bound for the problem, the feasible tool and machining time without the possibility of merging the hunting planes. Then, DP algorithm gives the optimal solution but costs longer computational time. Focusing on the Dynamic Programming model, there are several variables as the input and decision for the calculation. The diameter, depth, and number of cutter values are obtained from the strategy process by the performer. Critical distance variables are the values of the smallest boundary for each hunting plane from the object. The distance between two hunting planes is defined later by the performer also, where the number of the distance is smaller the number of hunting planes is bigger and more details on calculation. Last variable is number of hunting planes to be removed in one cut defines the strategy when using the Chen’s Dynamic Programming model to optimize the machining time by combining several hunting planes in one cut. It emphasizes the maximum depth of cut to be utilized. The advantage of using this method than others is the optimal solution both for cutter selection and machining plane determination.

Lee et al. (2010) introduced the method that almost the same steps with Chen in the previous explanation, but different calculation method and algorithm and result. As the first step, the sculptured surface object will be intersected using a set of hunting planes to get the geometric information. Next, the cutters and machining planes will be determined. At last, the cutter path planning in the process for both roughing and finishing will be generated. In this case, the machining time will be obtained by calculate the material removal rate (MMR) with the needed data of feed, diameter of cutter, number of teeth, spindle speed, and cutting speed as the variables used.

Table 2.1 Previous Research in Optimizing Sculptured Surface Machining Process No. Name Title Description Variables  Convex shapes The sculptured or complex surfaces is Automated Surface Subdivision and  Concave shapes Zezhong C. Chen 1 1 divided into simple shaped patches based 1 Tool Path Generation for 3 axis CNC  Saddle shapes et al. (2003) 2 2 on grid points through rough subdivision machining of sculptured parts and fine subdivision  Gaussian curvature  Mean curvature  Number of hunting planes to be removed in one cut Optimal Cutter Selection and  Diameter of cutter Defining the suitable cutter and best Yen-Hung Chen et Machining Plane Determination for  Critical distance 2 machining planes using integer and al. (1998) Process Planning NC Machining of  Depth of cutter dynamic programming model Complex Surfaces  Number of cutter  Distance between two adjacent hunting planes  Diameter of cutter  Feed rate Cut Distribution and Cutter Selection Determination of optimal selected cutter Y. S. Lee et al.  Number of teeth 3 for Sculptured Surface Cavity and cutter path to get the optimal (2010)  Spindle speed Machining machining time  Cutting speed  Volume of object

CHAPTER III RESEARCH METHODOLOGY

3.1 Research Methodology Kothari (2006) defines research is an activity in revealing the truth and searching for knowledge by conducting study, observation, comparison and experiment through objective and systematic method of finding the solution to a problem. The research methodology for this research can be seen in Figure 3.1.

Problem Identification: Problem - Identify current existing problem Identification - Define research objective - Define research scope and assumption Literature Study: - Manufacturing System Literature Study - Machining Process - Operation Research - Chen’s Integer and Dynamic Programming Model - Questionnaire Design Data Collection Data Collection: - Object Research - Details of Tools Used - Software CAM used - Simulated Machining Time Data Analysis Data Analysis: - Machining Time Calculation using Chen’s Algorithm - Comparison of Current and Chen’s Algorithm Conclusion and Conclusion and Recommendation: Recommendation - Conclusion of the calculation and analysis - Recommendation for further research Figure 3.1 Research Methodology

3.1.1 Problem Identification First step of the research starts with the problem identification that needed to be solved or having the opportunity for improvement of the current system. In this case it is related with the optimal cutter selection and reducing machining time topic to be analyzed. A problem statement is made, questioning “How does the

25 implementation of the Chen theory using dynamic programming to find the optimal cutter and machining time in the real work environment?” that needs to be answered in this research. The objective set is to know and compare the implementation of Chen’s theory using the dynamic programming study with the real work environment regarding to the optimal cutter selection and reduction of machining time for sculptured surface numerical coded machine. Because of the limited time and capability of the researcher, the research will be focused on only the sculptured product which produced using CNC machine in a single cavity and will be only simulated until the roughing process. The data is obtained in Jababeka area near the researcher and because of limited time, the calculation will be done using Microsoft Excel software. There is some assumption made, the object material is made from Carbon Steel and the tools material made from the general material, Carbide. It is defined to make the same situation for the respondent to simulate the object.

3.1.2 Literature Study After identified the problem, the literature is studied to support the research process. The literature study is the theoretical explanation and guide based on the chosen topic which contains the detail explanation of the subject or the research that had done by the researchers. In this research, there are some literature study to be used as the guidance in the process.  Manufacturing system. According to Bertrand et al. (1990), there are four types of manufacturing system based on the production types, which are Make to Order (MTO), Make to Stock (MTS), Assemble to Order (ATO), & Engineering to Order (ETO).  Machining process. Machining process is the process of shaping part through removal of material (Creese,1999). The machining process is mostly used in the manufacturing company nowadays. There are two categories of machining tasks, based on the purpose and cutting condition which are roughing, for the first process and finishing, for the last process. Sculptured or could be called freeform surface product is more interesting for the customer as the trends changes. In fulfilling the demand with also prioritizing the quality, there have been lots of inventions invented and improvements made, include Computer

Numerical Controlled (CNC) machine. The CNC machine are widely used by the company to manufacture the product in this era since it is more precise and practical. There are also many methods invented to improve the process in some concern to meet the effective and efficient way, such as the tool path generation and tool selection for the 3D cavities.  Operation Research: This study is identical in optimize the current condition using the current available resources. Chen et al. (1998) introduces the method using integer and dynamic programming which represented by algorithm for optimal tools selection and machining plane resolve to optimize the machining process for complex surfaces. Integer programming is linear programs with the variables that has the value of integer or discrete numbers, when Dynamic programming used for optimizing the result. In the Chen’s algorithm to produce the best choice, an extra variable called Lagrange Multiplier is used for the calculation of constrained problems.  Questionnaire Design. The questionnaire is made and target respondent is defined. The respondents will be experts with minimum 3 years of work experience working in Jababeka area. There are convenience and purposive sampling, and there are still many choices of questionnaire design according to the researcher’s need.  Chen’s algorithm to optimize the machining time. The method is learnt and tried to be implemented in this research using real data to know the possibility of the implementation in the manufacturing process.

3.1.3 Data Collection Subsequently, the data required regarding to the topic is collected for a certain duration of time. It can be short because of less parameter, constraints, and variables to be identified, otherwise for such a long time depends on the problem to be solved. An object research is made to be tested by the respondents, simultaneously recorded in the questionnaire. By doing the collecting data phase, the details of tools used, software, and simulated machining time by the respondents are retrieved. The collected data will be analyzed thoroughly in the next step.

3.1.4 Data Analysis Collected data will be sorted and analyzed to be applied the chosen method, Chen’s Dynamic Programming in gaining the solution for optimal result. There are several steps in the process referring to the journal by finding the feasible tool, recording and making the machining time matrix for each hunting plane, and applying the dynamic programming algorithm for many iterations to get the best solution. The result of the calculation is the acquired number of machining plane as the strategy planning in doing the machining process of the object and the predicted optimal time in doing the process. The calculated time will be compared to the simulated machining time by the respondents and elaborated in detail.

3.1.5 Conclusion and Recommendation After retrieving the result, the conclusion is made to summarize all parts of the research from the beginning until the result. It will show the result of the calculation both using Chen algorithm and simulation software and concludes whether the Chen’s algorithm is eligible and suitable to be applied. In addition, recommendations are provided for the future research and study.

3.2 Research Framework Figure 3.1 only shows the general framework of the process conducted in the research. The collecting data and analysis phases are elaborated more and explained in Figure 3.2 below.

Figure 3.2 Research Framework

3.2.1 Data Collection The first step to be explained is data collection. A research cannot be conducted without data for the analysis. In some occasion, an experiment should be held to support the research. In this case, the main topic of the research is cutter selection and machining time for sculptured surfaces machining process. Hence, a research object, sculptured product is provided, made in the form of 3D using Solidworks software. The dimension of the object is 30*30*35 mm with a hole in the middle,

29 shaped sculptured with different critical distance for certain step. Later, the object will be used for simulation by the respondent and calculation in doing the field study. Questionnaire is made to support the collecting data. The questionnaire consists of questions regarding to the needed information and also additional questions for the background profile, brand of machine in the company, advantages and disadvantages of the current simulation software, and the difficulties faced by the respondent frequently in the machining process. After the questionnaire is designed based on the needed data, it is tested on a respondent from a mold maker company in ensuring the clearance on it. There is some revision for several questions to make them easier to understand and the others still remains. After then, the collecting data is conducted by doing the field study. There are 3 respondents from different companies willing to help and spare the time for the research in Jababeka area. The respondents are from PT. Cahaya Sukses Mandiri, PT. Meiwa Mold Indonesia, and PT. Twintech Precision, which have different experience and level of education. The researcher accompanies the respondents in doing the simulation to get the same understanding, which could be several documented and seen in Appendix 4. The drawing of the object is included in the questionnaire, which also consists of some general questions regarding to respondent’s background profile, the habit done by them related to the topic, and the questions regarding to the needed information. The main information to be obtained from the questionnaire are:  Detail Tools used for simulating the research object Diameter of the tools, maximum depth of cut of tools, cutting speed used and feed rate information are obtained in the first question. The brand of the tools data is obtained as the additional information. The collected data above will be used for making the feasible tool matrix in Chen’s algorithm.  Total machining time required during the simulation The object will be divided into many hunting planes based on the chosen distance between two adjacent hunting planes. Each hunting plane will be tested to be machined using the simulator and the data will be recorded to fill up the machining time matrix of cutters in Chen’s algorithm. Total machining time for the process is also recorded to compared the result from each respondent.

 Common software used by the respondent in the company There are many types of software could be used for simulating object in machining process. Each company has their own strategy and bought software in supporting the daily tasks. The data recorded to know the variability of used software to be compared on the result of each respondent. There is some additional question to be included such as the predicted percentage of residual, the advantages and disadvantages of using the current software, and difficulty in using it. The questionnaire is made in Indonesian language and the respondent is scoped only in Jababeka industry.

3.2.2 Data Analysis Finish collecting the data, the analysis with the collected data will be made. The obtained information of details tools used and machining time for each hunting plane is used for calculation using Chen’s algorithm. Chen proposed algorithm using dynamic programming to get the optimal tools selection and resolving machining plane for complex surfaces. At first, the algorithm made by Chen is simplified into flowchart to be easily understood. The feasible cutter and machining planes to be defined info could be retrieved. The hunting planes are divided based on the defined distance between two adjacent hunting plane. After that, the feasible matrix calculation requires the information of diameter and maximum depth of cutter chose during simulation, and the critical distance of each hunting plane that could be seen in the research object using 3D view software. Machining time matrix is also made for each tool and hunting plane. The data is obtained during the simulation by the respondent. The infeasible tool for certain hunting plane will be excluded to optimize the simulating process.

Designed feasible cutter and machining time matrix are used as the input for Dynamic Programming (DP) model solution directly to get the machining plane and the calculated required machining time. The result of calculated machining time will be reduced from the previous one. After calculating and retrieving the result, the simulated machining time data by the respondent and calculated data are compared and analyzed.

CHAPTER IV DATA COLLECTION & ANALYSIS

4.1 Data Collection In data collecting phase, there are several things to be prepared and collected. As mentioned before, regarding to the topic of sculptured surface machining process, an object research is designed for the project. After designing the object, the questionnaire is made since the help from respondent to simulate the machining process of the object is needed. By using the questionnaire, the general and core information is obtained. The previous object research will be simulated by the respondent and there is several information that used for the own calculation using Chen’s algorithm. The detail explanation of the components is explained below.

4.1.1 Research Object A research object is designed using Solidworks to be used for collecting the data. The object is made of S50C (Carbon Steel) material in a form of block with a hole in the middle. The object in 3D view can be seen in Figure 4.1.

Figure 4.1 Research Object in 3D view

The object is designed with the dimension of 30*30*35 millimeters with scale 1:1. A hole is grinded in the middle of the object, with some stepping contour to create a model of sculptured object. The details of hole dimension are explained below.

Figure 4.2 Holes Dimension in the Object

The outer diameter is made 10 mm with the total depth 30 mm. Each 5 millimeters depth, the diameter will be reduced by 1 mm to make it step. The last diameter in the bottom uses radius of 5 mm. Moreover, the design of the object from different views can be seen below.

Figure 4.3 Research Object Technical Drawing

Figure 4.3 shows the design of research object from many views, consists of top view, front view, right view, and isometric view. After finishing the object designed, the questionnaire is used for collecting core information for the research.

4.1.2 Questionnaire Questionnaire is used for retrieving the information or opinion regarding to anything for research. It usually used for preparation of the future planning and knowing the current situation or habit. In this chance, the questionnaire will be needed to get the important needed information based on each respondent’s taken action. The respondent is specified to ensure the result is reliable. Respondent with the minimum 3 years working experience in the machining process programming is defined. More details of the target population are explained in Table 4.1 below. Table 4.1 Target Population Criteria Target Population Sampling technique used Purposive Sampling Minimum years of experience 3 years Size of company Middle sized-large companies

In the process, the respondent will be asked for help to simulate the machining process of the provided research object by using their own company’s software. After the simulation is success, they will be asked to fill in the questionnaire regarding to the result of what they did. Refer to Table 2.1, there are some variables to be included in the questionnaire for calculation data, which are diameter of cutter to be used, depth of cutter, and number of cutter. The information of distance between two adjacent hunting planes variable can be retrieved from the intersection of hunting planes on the object and the critical distance value is informed in the drawing of the object. There are also some general questions related to the background profile of the respondent, the selected software for machining simulation by the respondent, and the benefits and disadvantages of using it. The result is 3 respondents are acquired since the limitation time of doing the research and the availability of the target respondent. The details of the questionnaire can be seen in Appendix 1.

4.2 Collecting Data Result After the process collecting data is finished, all the information is gathered to be compared and analyzed. There are 3 filled questionnaire by 3 different respondents from different company. In simplifying the pictured data and focused on the important information, only the total machining time, chosen software, brand of machines that used in daily works, and required tools to be compared also some background information of the company is included in the table below. The complete filled questionnaire is attached in Appendix 2. Table 4.2 Prominent Collected Data Respondent A Respondent B Respondent C Company Origin Indonesia Japan China Number of Workers >100 160 40 Selected software Hypermill WorkNC Mastercam Total Machining Time 1 min 26 s 1 min 52 s 1 min 16 s Required Tools 4 3 5 Brand of Machine Makino and Quaser Okk and DMG Quaser and Akira

Respondent A works in a large Indonesian mold maker industry with more than 100 number of workers. He requires 4 tools to do the simulation using Hypermill software, which results 1 minute and 26 second to be done. The second respondent, Respondent B comes from Japan industry with 160 workers. He uses WorkNC as the simulator to do the practice. Three tools with different diameter are chosen and 1 minute 52 second of time required to finish the process. The third respondent uses the different software and more tools in the simulation. Respondent C uses Mastercam software and total 5 tools, which generates 1 minute and 16 second total time in the system. He works in a China company with the total only 40 workers.

Furthermore, there are two types of cutter that chosen to be used by all the respondents. Those are ball mill and bull nose mill. Ball mill cutter has the rounded shape with radius on the edge, when bull nose mill cutter is almost similar with flat end cutter, but has some radius on both end edges. The example of the pictures can be seen in Figure 4.4 below.

Figure 4.4 Ball Mill and Bull Nose Mill Cutter

Not significantly affected by the chosen software, the strategic process planned by each respondent will affect most in the result, such as feeding rate, chosen tools, cutting depth, and many more factors. As additional information, when fulfilling the demand and producing the real object, the brand of machines in the companies will also affect the performance since it has various capabilities. All the possibilities acquired from the questionnaire will be explained in the next subchapter.

4.3 Calculation using Chen Dynamic Programming Model Chen et al. (1998) invented the algorithm for optimal cutter selection and machining plane determination to get the optimal machining time. The process requires the data of machining time each hunting plane and the selected cutter to proceed to the calculation steps. In this research, after obtaining the data from the respondent using the designed object to be tested, the feasible cutter will be considered and continues directly to the Dynamic Programming with the constraints in retrieving the optimal solution. The Integer Programming model will not be used since it will be needed to work twice from integer to dynamic model, but all the constraints are included. There are 3 respondents contributed to the research with experience minimum 3 years in their field in machining process and having each of their own strategy in dealing with the research object. This research will not only focus on the result of calculated time using Chen’s Dynamic Programming and compare it with the simulated time, but also comparing of many aspects includes the process planning for the same object research for each respondent. There are three steps in the calculation process, first is making the feasible cutter matrix, next is obtaining the

36 information and making the matrix of machining time for each hunting plane, and the last step is doing the dynamic programming model to get the optimal solution.

First step is done to get the feasible cutter for each hunting plane. An object is intersected into a number of desired hunting planes to get the detail of geometry boundary. After defines the number of hunting planes, a matrix is made with the objective function of minimum machining time for the consideration of merging layers in applying the dynamic programming algorithm later. There are several constraints as the concern from Equation 2-2 until Equation 2-5. The matrix will be first filled in with the diameter and maximum depth of cut to be used with also the critical distance value for each hunting plane. In the calculation using Microsoft Excel Software, the formula includes all the constraints where the depth of cutter for number of cutter to be used and hunting planes to be defined should be more or equals to depth of the cavity, which is the depth of the hole on the object, and also the diameter of cutter to be used on the particular hunting plane should be less than or equal the critical distance on the current hunting plane. If one of the constraint is not fulfilled the result is 0, otherwise 1.

Second step is retrieving the machining time of each hunting plane. It is not obtained from the calculation but getting the information by simulating it on the software, accompanied by the respondent. The respondent is asked to simulate the machining process for each hunting plane to get the machining time, but only for the feasible tools for certain hunting plane, referring to the feasible tool matrix. The unfeasible tools for particular hunting plane cells will be left unfilled.

The third step is implement the Chen Dynamic Programming algorithm to get the optimal solution. The algorithm made by Chen to do the dynamic programming model is shown below.

Figure 4.5 Dynamic Programming Model Flowchart

The input values in the model are the variables that will be obtained in the process.

푋̅s represents the number of hunting planes planned to be removed in one cut by one particular cutter, a represents the diameter of cutter, b is the variable of critical distance on hunting plane j, d is depth of cutter i, m is the number of cutter, and ∆Z defines the distance between two adjacent hunting planes. By using the data from the first and second step, the dynamic programming algorithm is conducted with the objective value of 퐶푞̅(푠̅, 푥̅푠), machining time for particular cutter 푞̅ for the desired number of hunting planes 푥̅푠 to be removed in one cut from hunting plane 푠̅. Backward planning is done by doing the optimization from the lowest level of hunting plane until the highest level.

Referring to the machining time matrix recorded, the chosen cutter for each hunting plane is based on the minimum value to get the fastest process. After that, the maximum depth of cutter is utilized to get the optimal merging layer process. Same as the objective, the chosen combination is the smallest value of machining time in the result for specific used tools. Machining time for each machining plane and total machining time for each cutter are recorded. Output of the model is the total minimum value of machining time calculated using dynamic programming

38 algorithm. The data from each respondent is calculated separately and compared to the simulated time. The explanation and analysis that has made is explained below.

4.3.1 Respondent A Respondent A is a manager of engineering CNC milling of a company with 10 years of experience. After seen the research object in 3D dimension technical drawing, he decided to use 4 tools for roughing process, 3 bull nose mill and 1 ball mill tools. The element of information shown in the Table 4.3 below. Table 4.3 Tools Used by Respondent A Diameter Maximum Depth Depth of Cut Feed Rate Types of Tools (mm) of Cut (mm) (mm) (rpm) Tools T1 4 2 0.2 1400 Ball mill T2 4 2 0.2 1400 Bull Nose mill T3 6 3 0.2 1400 Bull Nose mill T4 8 4 0.2 2400 Bull Nose mill

Respondent A uses the 6 mm diameter bull nose mill tool as the biggest diameter and 3 mm diameter to machine the object. All of the tools are set 0.2 mm depth of cut and the feeding rate is set 1400 rpm, except T4 use the 2400 rpm. As mentioned before, the respondent uses the Hypermill software to do his daily work and the result of simulating the research object machining time is 1 min and 26 second.

Data that can be acquainted in the beginning is the parameter of the tools that will be used by the respondent and filling the feasible tool matrix. The feasible tool matrix consists of information regarding to the number of hunting plane defined, the diameter and maximum depth of cut for the cutters that will be operated. Moreover, there is the number of critical distance as the constraint for tools usage for particular hunting plane. Each hunting plane has the number of critical distance and differs based on the design of the object. As explained before, it is the smallest distance in a boundary. The research object in this part has the critical distance ranged from 5-10mm for each step. Next, after all the information has filled in the matrix, each cell can be filled in based on number of tools used, either 0 or 1 with several constraints. The result is 1 when all the constraint is fulfilled and vice versa for the 0 value. The feasible tool matrix for Respondent A can be seen in Table 4.4.

Table 4.4 Feasible Tool Matrix for Respondent A Feasible Tool Matrix Diameter 4 4 6 8

Max. Depth of Cut 2 2 3 4 Hunting Plane Critical Distance T1 T2 T3 T4 HP59-60 10 1 1 1 1 HP57-58 10 1 1 1 1 HP55-56 10 1 1 1 1 HP53-54 10 1 1 1 1 HP51-52 10 1 1 1 1 HP49-50 9 1 1 1 1 HP47-48 9 1 1 1 1 HP45-46 9 1 1 1 1 HP43-44 9 1 1 1 1 HP41-42 9 1 1 1 1 HP39-40 8 1 1 1 1 HP37-38 8 1 1 1 1 HP35-36 8 1 1 1 1 HP33-34 8 1 1 1 1 HP31-32 8 1 1 1 1 HP29-30 7 1 1 1 0 HP27-28 7 1 1 1 0 HP25-26 7 1 1 1 0 HP23-24 7 1 1 1 0 HP21-22 7 1 1 1 0 HP19-20 6 1 1 1 0 HP17-18 6 1 1 1 0 HP15-16 6 1 1 1 0 HP13-14 6 1 1 1 0 HP11-12 6 1 1 1 0 HP9-10 5 1 1 0 0 HP7-8 5 1 1 0 0 HP5-6 5 1 1 0 0 HP3-4 5 1 1 0 0 HP1-2 5 1 1 0 0

Table 4.4 shows the feasible tool matrix for Respondent A. Afterwards, there is machining time matrix for each hunting plane in Table 4.5.

Table 4.5 Machining Time Matrix for Respondent A

Machining Time Matrix ( in second)

Hunting Plane T1 T2 T3 T4

HP59-60 22 14 10.4 8 HP57-58 22 14 10.4 8 HP55-56 22 14 10.4 8 HP53-54 22 14 10.4 8 HP51-52 22 14 10.4 8 HP49-50 15 12.6 9 8 HP47-48 15 12.6 9 7 HP45-46 12 12.6 9 7 HP43-44 12 12.6 8 7 HP41-42 12 12.6 8 7 HP39-40 9.5 9 8 6 HP37-38 9.5 9 8 6 HP35-36 9.5 9 7 6 HP33-34 9 8.6 7 6 HP31-32 9 8.6 7 6 HP29-30 7 6 5 HP27-28 7 6 5 HP25-26 7 6 5 HP23-24 7 6 5 HP21-22 7 6 5 HP19-20 6.6 5 4.5 HP17-18 6.6 5 4.5 HP15-16 6.6 5 4 HP13-14 6.6 5 4 HP11-12 6.6 5 4 HP9-10 5.5 4.8 HP7-8 5.5 4.5 HP5-6 5.5 4.5 HP3-4 5 4 HP1-2 5 4

Continuing the previous matrix, the feasible tools machining time for each hunting plane will be recorded. The information is obtained from the machining simulation using the software in each hunting plane for each tool. Information of the machining simulation is more detail and ready to be used as the calculation using Chen’s

41 algorithm. As the additional information to be compared later, process planning strategy by the respondent is also recorded that can be seen in the Table 4.6. Table 4.6 Process Planning by Respondent A Tools Cutting Depth (mm) T4 10 T3 20 T2 29 T1 30

Referring to the table above, the machining process will be started from the surface using T4 with the cutting depth 10mm. After that, the process will continue with T3 to cut 20 mm of the object. T2 will cut around 29 mm depth of the object and at last T1 will finish the roughing process. The process will not include the finishing process due to the limited time and availability of the respondent. Next, using the obtained data, the dynamic programming model process will be tried to solve and get the optimal solution by doing many iterations (hunting planes) to be calculated.

The dynamic programming model takes longer computational time but generates the optimal solution for cutter selection and machining plane determination. There are many iterations done to get the optimal one. Using Microsoft Excel as the software to solve the model and considering the constraints, there are 60 hunting planes (iterations) to get the optimal value. Implementation of the Dynamic Programming model is started from the lowest to the highest hunting planes of the object as the backward planning strategy is used. Each hunting plane is assigned with the tools with minimum machining time than the other tools to get the optimal value in the result. The focus in merging the layer is optimizing the maximum depth of cutting cutter to minimize the objective value. There will be several occasions with several combinations as the consideration. The chosen combination will be the optimal value for specific cutter with minimum needed machining time. The result is 10 machining planes as the recommended strategic cutting planning with total machining time 1.03 minutes. Details of the calculation can be seen in Appendix 3 for Respondent A. Table 4.7 Comparison of Simulated and Calculated Respondent A Machining Time Simulated Machining Time Chen’s Algorithm Calculated Machining Time 1 min 26 s 1 min 2 s (61.8 s)

By using Chen’s Dynamic Programming model, an optimal solution for machining the object by using the current strategy, the machining time can be reduced from 1 minute 26 second to around 1 minute and 2 second, which the detail in second is 61.8 second. The guidance for optimal process planning is also included and explained in the obtained solution, shown by the machining planes for each selected cutter. The comparison of current process planning by respondent and the result using Chen’s algorithm is shown in Table 4.8. Table 4.8 Comparison of Simulated and Calculated Respondent A Process Planning Simulated Depth of Calculated Depth of Tools Cutting (mm) Cutting (mm) T4 10 15 T3 20 25 T2 29 28 T1 30 30

Same to the number of tools planned by the Respondent A, the process will use 4 tools. The fourth tool or T4 with biggest diameter will cut 15 mm, deeper than the planned before. Then T3 will be used for cutting 25 mm depth, T2 until 28 mm and T1 will cut until 30 mm depth. T1 is used for finishing the roughing since it is a ball mill tool, suitable to shape the radius on the bottom of the object. Based on the comparison, the significant difference is only in using the tools to cut deeper than planned before.

4.3.2 Respondent B Respondent B is a staff from molding company with 10 years of experience in machining process as the programmer. He uses his experiences to make the process planning for the object and decided to use three tools only to do the machining process, two bull nose end mill and one ball mill. The software used is WorkNC for the simulation, same as the daily use software in his company. Table 4.9 Tools Used by Respondent B Diameter Maximum Depth Depth of Cut Feed Rate Types of Tools (mm) of Cut (mm) (mm) (rpm) Tools T1 4 2 0.18 1200 Ball mill T2 4 2 0.2 1400 Bull Nose mill T3 6 3 0.2 1400 Bull Nose mill

Different than the previous respondent, Respondent B uses WorkNC software to simulate the object machining process with 3 tools, the biggest diameter tool sized 6 mm, followed with 4 mm bull nose mill, and 4 mm diameter of ball mill. Depth of cut for the smallest diameter tool is set 0.18 mm and 0.2 mm for the remaining tools. The feeding rate is also set differently where the first Tool (T1) is set 1200 rpm, when T2 and T3 set in 1400 rpm feeding rate. After simulated the machining process in the software, the result shows that the predicted required time is 1 minute and 52 second. Then, the process planning strategy by the respondent is also recorded which described as follow. Table 4.10 Process Planning by Respondent B Tools Cutting Depth (mm) T3 20 T2 28 T1 30

The programmer uses third tool (T3) to cut 20 mm depth in the object, T2 to cut 28 mm depth and T1 for 30 mm depth. After the total simulated machining time has been mentioned and the strategy process planning has been explained, Respondent B is asked to show machining time of each hunting layer that divided into 60 layers by hunting planes. The obtained data will be recorded in machining time matrix. There are two matrixes to assist the calculation process, the feasible tool matrix and machining time matrix, following the required data. After collecting the data, it will be input to the Chen’s dynamic programming model calculation. In the end, there are also 60 hunting planes used to intersect the object, the obtained machining time is reduced to 80.5 second or 1 minute 21 second and there are 12 machining planes to be recommended from the result. Table 4.11 Comparison of Simulated and Calculated Respondent B Machining Time Simulated Machining Time Chen’s Algorithm Calculated Machining Time 1 min 52 s 1 min 21 s (80.5 s)

Compared to the simulation machining time, the required time is significantly reduced in number of seconds. To doing so, the process planning strategy is also shown to know how to get the optimal condition using the current tools specifications.

Table 4.12 Comparison of Simulated and Calculated Respondent B Process Planning Simulated Depth of Calculated Depth of Tools Cutting (mm) Cutting (mm) T3 20 25 T2 28 28 T1 30 30

T3 will cut 25 mm depth into the object, deeper than the planning by respondent, when T2 and T1 will remain the same for the cutting depth. The details of calculation using dynamic programming for Respondent B can be seen also in Appendix 3. The process is more complicated by defining the machining time of each hunting layer than only rely on the software to simulate it, but by using this method the machining time could be reduced which affect many important aspects in manufacturing.

4.3.3 Respondent C Respondent C is a programmer CNC milling of a company with experience of 5 years. He chose 5 tools to help him in the machining process of the object. There are 4 end mill tools and 1 ball nose end mill tools for the deepest sculpture. The important specification information of the tools is elaborated below. Table 4.13 Tools Used by Respondent C Diameter Maximum Depth of Depth of Cut Types of Tools Feed Rate (mm) Cut (mm) (mm) Tools T1 3 1.5 0.5 1200 Ball mill T2 4 2 0.5 1200 Bull Nose mill T3 5 2.5 0.5 1200 Bull Nose mill T4 6 3 0.5 1200 Bull Nose mill T5 8 4 0.5 1000 Bull Nose mill

The table above shows Respondent C uses 5 tools with the biggest diameter bull nose mill tool 8 mm and the smallest diameter tool, ball mill 1.5 mm. All of the tools used in the Depth of Cut 0.5 mm. The total machining time required for the process is 1 minute 12 second. Using the information of tools used and the critical distance of each step that can be seen on the object, the feasible tool matrix is made. The result of the calculation can be seen in Appendix 3 for Respondent C. The output of the matrix will be used on the dynamic programming model to select the best cutter combined with the machining plane of each hunting plane. Machining

45 time information for each hunting plane for feasible tools is also recorded for machining time matrix. Next, the respondent also asked to explain the strategy of his process planning. Table 4.14 Process Planning by Respondent C Tools Cutting Depth T5 10 mm T4 20 mm T3 25 mm T2 29 mm T1 30 mm

The machining process started from the surface of the object. The actual process starts with T5 that will be used for cutting process until 10 mm depth of the object, continues with T4 for 20 mm depth of cutting. The process will be continued following the steps above until T1 for the last roughing process. There will be no finishing process since it will take much longer time to finish it. After finishing the general simulation, the respondent asked to do the tools trial to each hunting plane level based on the feasible cutter to know the machining time of each hunting plane, which shown in details in the appendix.

The last step is doing the dynamic programming model with the constraints in it. Using the Microsoft Excel software, the calculation is conducted manually until get the optimal solution. The defined number of hunting planes is 60 into the object to get the optimal selection with 12 machining planes and total calculated optimal machining time 65.6 seconds. The comparison of machining time is shown in Table 4.15 below. Table 4.15 Comparison of Simulated and Calculated Respondent C Machining Time Simulated Machining Time Chen’s Algorithm Calculated Machining Time 1 min 16 s 1 min 6 s (65.6 s)

As seen above, the calculated total machining time is less than the simulated machining time. Chen’s Dynamic programming algorithm offers the smaller value of machining time. It means that the strategy machining plane by the respondent could be more optimal with different machining plane.

Table 4.16 Comparison of Simulated and Calculated Respondent C Process Planning Simulated Depth of Calculated Depth of Tools Cutting (mm) Cutting (mm) T5 10 15 T4 20 25 T3 25 28 T2 29 - T1 30 30

Applying the Chen’s algorithm using dynamic programming model, there are only 4 tools to be used. It is considered that the deepest 2 mm depth of the object from hunting plane 0 until hunting plane 4 should be machined using the ball nose end milling tool because the curvature shaped radius started from hunting plane 4. From the top surface of the object, T5 will be used to cut 15 mm depth of the object, continues with T4 to cut 25 mm from the surface, T3 used for cutting 28 mm depth, and T1 for the radius shaped deepest curvature.

4.4 Summary of the Research 4.4.1 Calculation Summary Chen et al. (1998) introduced the algorithm to get the optimal cutter selection and machining plane determination, and this research try to implement the theory using real data with the help from the experts. Three respondent from different companies are willing to help the research. Through the simulation, the chosen tools and machining time information can be recorded to be used in the calculation model. The calculation takes some steps from filling the feasible tool matrix, recording the machining time matrix for each hunting layer, and calculated using Chen’s Dynamic Programming model. By compute and doing many iterations, the optimal solution is retrieved for each obtained simulated machining time. Table 4.17 Machining Time Comparison Machining Time using Respondent Simulated Machining Time Chen’s Algorithm A 1 min 26 s 1 min 2 s B 1 min 52 s 1 min 21 s C 1 min 16 s 1 min 6 s

The outcome of the calculation is reduced amount of machining time for the research object. The first predicted machining time reduced from 1 minute 26

47 second to 1 minute 2 second, followed by Respondent B the machining time is reduced from 1 minute 52 second to 1 minute 21 second. The last recorded simulated machining time reduced from 1 minute 16 second to 1 minute 6 second through the dynamic programming calculation. Several main point can be concluded, either from the data collecting process or the calculation method.

The first point is the collected data may differ because of many factors. Respondent A, B, and C have their own strategy and experience in dealing with the design object in daily life. When asked to simulate the machining process of the object, they choose different number of tools and diameter, feeding rate, and other settings. Respondent A use the Hypermill software, when Respondent B use WorkNC and Respondent C use Mastercam. Their companies are also using the different brand of machine which can also affect the process in the actual situation. For example, Company A uses Makino machine and Company B uses Okk machine. Refer to the respondent for the practice in the field, it can affect the result process. In this case, it is deduced that the collected data may differs because of the strategy and equipment used by the respondent.

Afterwards, the second point is Chen’s Dynamic Programming Model takes longer time to solve, but offers the optimal value. Nowadays, as the technology keeps integrating the manufacturing companies are racing to produce the customer demand in high quality but also low cost. By reducing the machining time through accurate cutter selection and machining plane determination, the cost of machining process can be reduced and satisfying the both company and customer. But in another side, by implementing the correct method to get the optimal value it needs longer time to execute. Hence, it depends on each company to deal with the request from the customers and optimizing the process.

The third point is Chen’s algorithm implementation using the real data is quite effective, although it is not implemented and applicable enough for companies. The relative machining time is the value calculated from the differences between both

48 of them to know the effectivity and reduction made for the machining time using Chen’s algorithm. The calculation formula is shown as follow.

퐶푎푙푐푢푙푎푡푒푑 푚푎푐ℎ𝑖푛𝑖푛푔 푡𝑖푚푒 푢푠𝑖푛푔 퐶ℎ푒푛′푠 푎푙푔표푟𝑖푡ℎ푚 푅푒푙푎푡𝑖푣푒 푀푎푐ℎ𝑖푛𝑖푛푔 푇𝑖푚푒 = 푂푏푡푎𝑖푛푒푑 푚푎푐ℎ𝑖푛𝑖푛푔 푡𝑖푚푒 푠𝑖푚푢푙푎푡푒푑 푏푦 푡ℎ푒 푟푒푠푝표푛푑푒푛푡

Using the formula, the three obtained values of machining time is calculated to get the relative machining time. Table 4.18 Relative Machining Time Calculation Machining Time Relative Average of Simulated Respondent using Chen’s Machining Relative Machining Time Algorithm Time Machining Time A 1 min 26 s 1 min 2 s 0.72 B 1 min 52 s 1 min 21 s 0.72 0.77 C 1 min 16 s 1 min 6 s 0.87

The result in Table 4.18 above shows the difference of each calculate machining time for each respondent by using relative machining time calculation. From the result, Respondent A has the value of 0.72, respondent B has 0.72, and respondent C has 0.87 from the comparison between simulated machining time and using Chen’s algorithm. The average number of relative machining time is 0.77. It means that the simulated machining time manually by the respondent using the software has reduced to 0.77 from the beginning by using Chen’s algorithm. In simpler explanation, by using the algorithm it could reduce 0.23 of machining time which planned by the programmers before.

Machining Time Comparison

112 86 62 81 76 66

A B C Simulated Machining Time Calculated Machining Time using Chen's Algorithm

Figure 4.6 Machining Time Comparison

Figure 4.6 records the machining time comparison between the simulated machining time by respondents and calculated machining time using Chen’s Algorithm in seconds. The graph bar for simulated machining time is blue colored and the calculated machining time using Chen’s Dynamic Programming algorithm is orange colored. Objective of the research is reached by the optimized machining time. Although the objective is accomplished, the Chen’s algorithm is not purely applicable and implemented to the real environment because of some consideration in the actual situation for the other aspects. The summary explanation by respondents is described in the next subchapter below.

4.4.2 Implementation of Chen’s Algorithm in Real Work Environment Following the reduced machining time and changing suggested process planning, the respondents are asked again directly whether Chen’s algorithm is used in their companies and acquainting the possibility of implementing Chen’s method by merging the hunting planes to get the optimal machining time. The result was 2 main reasons from all the respondents that rejecting the algorithm.

The first reason is the cutting tools will be faster worn out than it should be, even broken because of deeper cutting depth. By merging the potential hunting planes into one and cutting it using the same feed rate, it will result the same machining time as the hunting plane before merged which considered to be optimal, but indirectly wearing the cutting tools faster. It should be avoided to prevent the purchasing of cutters several times.

Thereafter, Chen’s algorithm only focusing on optimizing the machining time, not includes the other aspect to be considered, particularly the cost. Implementing the Chen’s algorithm earns optimal machining time, shorter machining time for roughing process considerably improves the efficiency of the process, on the other hand results the higher production cost. Cost spent in the process includes electricity and manufacturing cost. The manufacturing cost could increase as the cutting depth is deeper which results faster worn out and the potential of broken tools.

CHAPTER V CONCLUSION & RECOMMENDATION

5.1 Conclusion The conclusion of this research is Chen algorithm using Dynamic Programming algorithm is rarely implemented to find the optimal cutter and machining time in real work environment. The phase of the Chen’s Dynamic Programming algorithm consists of defining the feasible tools, recording the machining time of each hunting layer, and calculating the optimal solution using dynamic programming. The detail information of the designed object, tools for machining, and machining time should be obtained.

A design of sculptured product is made for this research and the experts asked to give their strategy in the simulation process. By implementing Chen’s algorithm, the calculated machining time is successfully reduced around 23%. It can deliver the optimal selection of tools and machining plane determination as the recommended strategy for the process planning for focusing on optimize the machining time, although it takes longer computational time than only using the simulation software. However, the manufacturing industries, particularly the mold maker industry in Jababeka doesn’t implement the Chen’s algorithm since there are several risk of broken tools and increasing cost in the process, despite of reducing the machining time in roughing process.

5.2 Recommendation The recommendation for further research are: 1) Chen’s algorithm should be improved involving cost aspect as the other consideration in optimizing the machining process. 2) Due to limited time, the research should involve more respondent to make the result more valid. 3) Expand the scope, including the finishing process and outside Jababeka area. 4) Develop the software for more accurate and faster calculation.

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APPENDICES

Appendix 1 – Questionnaire Sheet FORM KUESIONER

Dengan hormat, Sehubungan dengan penyelesaian tugas akhir atau skripsi yang sedang lakukan dengan judul “Aplikasi Dynamic Programming untuk Pemilihan Alat dalam Optimasi Proses Permesinan Permukaan Kompleks” di President University, saya meminta kesediaan Bapak/ Ibu dan Saudara/i untuk mengisi kuesioner ini sebagai data yang akan dipergunakan dalam penelitian. Untuk itu, diharapkan para responden dapat memberikan jawaban yang sebenar-benarnya demi membantu penilitian ini. Atas waktu dan kesediaannya, saya ucapkan terima kasih.

Cikarang, Januari 2018

Jovian Agathon

Nama Perusahaan Kota Jabatan Lama Bekerja Asal Perusahaan Jepang Korea Selatan China Lainnya………… Jumlah Karyawan Pendidikan Terakhir S3 S2 S1 SMA/ SMK SMP SD Usia ≥51 41-50 31-40 21-30 ≤20 Pertanyaan yang diajukan mengacu pada gambar 3D dengan ukuran tertentu yang telah diberikan N.B.: Tooling terbuat dari material Carbide dan objek yang akan diuji terbuat dari S50C Carbon Steel. Riset ini dibatasi sampai dengan proses roughing saja.

1) Peralatan yang dipakai Kedalaman Tools Diameter Feed Rate Pengikisan (DoC) I II III IV V

2) Berapa total jumlah lapisan pada objek yang akan diproyeksikan untuk dipotong/ “termakan”? 60-51 50-41 40-31 30-21 20-11 ≤10

3) Berapa total waktu yang dibutuhkan dalam proses permesinan objek yang diuji?......

4) Apa software yang selama ini digunakan untuk melakukan simulasi proses permesinan? SolidCAM PowerMILL VoluMILL WorkNC TopSolid Lainnya……….

5) Jelaskan kelebihan dan kekurangan software simulasi proses permesinan yang digunakan selama ini, Kelebihan: 1) 2) 3)

Kekurangan: 1) 2) 3)

6) Apakah pernah mencoba menggunakan software yang berbeda? Jika ya, sebutkan nama software tersebut. ………………………………………………………………………………… …………………………………………………………………………………

7) Sebutkan jenis/ brand mesin yang dipakai selama ini! 1) 2) 3)

8) Apa saja kesulitan dalam proses permesinan selama ini? Fitur permukaan yang kompleks Peralatan yang terbatas Lainnya…………

Appendix 2 – Filled Questionnaire Respondent A

Respondent B

Respondent C

Summary of Recorded Data

Items Respondent A Respondent B Respondent C Name of PT. Cahaya Sukses PT. Meiwa Mold PT. Twintech Precision company Mandiri Indonesia Age 41-50 31-40 31-40 Last S1 S1 SMA/SMK education Company Indonesia Japan China origin Manager of Position Engineering CNC Staff Programmer CNC Milling Milling Length of 10 years 10 years 5 years work Number of >100 160 40 workers Software used Hypermill WorkNC Mastercam

Advantages: - A layer in Mastercam can Advantages: be made 2D and 3D design - Detailed simulation Advantages: - Able to make wear of collision checking - Easy to use programme (tool for 3 axis and 5 axis compensation) - Easier to use - Complete with curve, Advantages & solid, and surface design Disadvantages Disadvantages: Disadvantages: - Need to make the Disadvantages: - Undetailed cam boundaries at the beginning - Longer time for tool simulation (between of designing 3D object path generation the finished surface - The result of 3D calculation and not finished) machining simulation is rougher than other software

Diameter used: Diameter used: Diameter used: - Bull nose: 8mm, - Bull nose: 4mm - Bull nose: 8mm, 6mm, 6mm, and 4mm and 6mm 5mm, and 4mm - Ball mill: 4mm - Ball mill: 4 mm - Ball mill: 3mm Depth of Cut: Depth of Cut: Depth of Cut: - Bull nose: 0.2mm, - Bull nose: 0.2mm - Bull nose: 0.5mm, 0.5mm, Tools used 0.2mm, and 0.2mm and 0.2mm 0.5mm, and 0.5mm - Ball mill: 0.2mm - Ball mill: 0.18 -Ball mill: 0.5mm Feed Rate: Feed Rate: Feed Rate: - Bull nose: 2400rpm, - Bull nose:1200rpm, -Bull nose:1400rpm 1400rpm, and 1200rpm, 1200rpm, and and 1400rpm 1400rpm 1200rpm -Ball mill: 1200rpm - Ball mill: 1400 rpm - Ball mill: 1200rpm

Summary of Recorded Data (cont.)

Number of hunting 60 60 60 planes Total Machining 1 min 26 sec 1 min 52 sec 1 min 16 sec Time Other Powermill and Space-E NX/UG and Cimatron software used Camtool Mikron Agie Brand of Chairmill, Makino, Quaser, Robot Drill, and Okk and DMG Machine Yasda, Wole, and Akira Quaser Machining process in Difficulty in the programme, tools Machining used, process - Complex surface Process planning, and machines

Appendix 3 – Calculation using Chen’s Algorithm Respondent A

DP Model Solution for Respondent A Max. Cutter Selected Cutter Original Ti for HPj Merged Machining Ti for MPk Machining Total Machining Hunting Max. Plane MPk Selected Time of Using Machining Depth of Time on MPk Plane HPj Ti Depth by DP Model Ti Cutter Ti Time Cut cut HP59-60 T4 4 HP57-58 T4 4 MP11 T4 3 8 HP55-56 T4 4 HP53-54 T4 4 HP51-52 T4 4 MP10 T4 4 8 HP49-50 T4 4 HP47-48 T4 4 HP45-46 T4 4 29 61.8 HP43-44 T4 4 MP9 T4 4 7 HP41-42 T4 4 HP39-40 T4 4 HP37-38 T4 4 HP35-36 T4 4 MP8 T4 4 6 HP33-34 T4 4 HP31-32 T4 4 HP29-30 T3 3 MP7 T3 2 5 18.5

DP Model Solution for Respondent A (cont.)

HP27-28 T3 3 MP7 T3 2 5 HP25-26 T3 3 HP23-24 T3 3 MP6 T4 3 5 HP21-22 T3 3 HP19-20 T3 3 18.5 MP5 T3 2 4.5 HP17-18 T3 3 HP15-16 T3 3 61.8 HP13-14 T3 3 MP4 T3 3 4 HP11-12 T3 3 HP9-10 T2 2 MP3 T2 1 4.8 HP7-8 T2 2 9.3 MP2 T2 2 4.5 HP5-6 T2 2 HP3-4 T1 2 MP1 T1 2 5 5 HP1-2 T1 2

Respondent B

Feasible Tool Matrix

Diameter 4 4 6

Max. depth of 2 2 3 Cut Hunting Critical T1 T2 T3 Plane Distance HP59-60 10 1 1 1 HP57-58 10 1 1 1 HP55-56 10 1 1 1 HP53-54 10 1 1 1 HP51-52 10 1 1 1 HP49-50 9 1 1 1 HP47-48 9 1 1 1 HP45-46 9 1 1 1 HP43-44 9 1 1 1 HP41-42 9 1 1 1 HP39-40 8 1 1 1 HP37-38 8 1 1 1 HP35-36 8 1 1 1 HP33-34 8 1 1 1 HP31-32 8 1 1 1 HP29-30 7 1 1 1 HP27-28 7 1 1 1 HP25-26 7 1 1 1 HP23-24 7 1 1 1 HP21-22 7 1 1 1 HP19-20 6 1 1 1 HP17-18 6 1 1 1 HP15-16 6 1 1 1 HP13-14 6 1 1 1 HP11-12 6 1 1 1 HP9-10 5 1 1 0 HP7-8 5 1 1 0 HP5-6 5 1 1 0 HP3-4 5 1 1 0 HP1-2 5 1 1 0

Machining Time Matrix (in second)

Hunting Plane T1 T2 T3

HP59-60 22 14 11 HP57-58 22 14 11 HP55-56 22 14 11 HP53-54 22 13 11 HP51-52 20 13 11 HP49-50 18 12.4 10 HP47-48 18 12.4 10 HP45-46 16 12 9 HP43-44 16 12 9 HP41-42 14 12 8 HP39-40 12 9 7 HP37-38 12 9 7 HP35-36 11 9 7 HP33-34 10 8.6 6.4 HP31-32 10 8.6 6.4 HP29-30 9 6.5 5.5 HP27-28 9 6.5 5.5 HP25-26 8 6.2 5.3 HP23-24 7.5 6 5 HP21-22 7.5 6 5 HP19-20 6.8 5.4 4.6 HP17-18 6.8 5.4 4.6 HP15-16 6.4 5 4.4 HP13-14 6.4 5 4.4 HP11-12 6.4 5 4.4 HP9-10 6 4.5 HP7-8 6 4.5 HP5-6 5 4.4 HP3-4 5 4 HP1-2 5 4

DP Model Solution for Respondent B

Max. Cutter Merged Selected Cutter Original Ti for HPj Machining Ti for MPk Machining Machining Total Hunting Plane MPk Time on Time of Using Machining Max. Plane HPj Selected by DP Depth MPk Cutter Ti Time Ti Depth Ti Model of Cut cut HP59-60 T3 3 HP57-58 T3 3 MP12 T3 1 11 HP55-56 T3 3 HP53-54 T3 3 HP51-52 T3 3 MP11 T3 3 11 HP49-50 T3 3 HP47-48 T3 3 HP45-46 T3 3 MP10 T3 3 10 HP43-44 T3 3 66.5 80.5 HP41-42 T3 3 HP39-40 T3 3 MP9 T3 3 8 HP37-38 T3 3 HP35-36 T3 3 HP33-34 T3 3 MP8 T3 3 7 HP31-32 T3 3 HP29-30 T3 3 MP7 T3 3 5.5 HP27-28 T3 3

DP Model Solution for Respondent B (cont.) HP25-26 T3 3 MP7 T3 3 5.5 HP23-24 T3 3 HP21-22 T3 3 MP6 T3 3 5 HP19-20 T3 3 66.5 HP17-18 T3 3 MP5 T3 3 4.6 HP15-16 T3 3 HP13-14 T3 3 MP4 T3 3 4.4 80.5 HP11-12 T3 3 HP9-10 T2 2 MP3 T2 1 4.5 HP7-8 T2 2 9 MP2 T2 2 4.5 HP5-6 T2 2 HP3-4 T1 2 MP1 T1 2 5 5 HP1-2 T1 2

Respondent C

Feasible Tool Matrix

Diameter 3 4 5 6 8

Max. depth 1.5 2 2.5 3 4 of Cut Critical Hunting Plane T1 T2 T3 T4 T5 Distance HP59-60 10 1 1 1 1 1 HP57-58 10 1 1 1 1 1 HP55-56 10 1 1 1 1 1 HP53-54 10 1 1 1 1 1 HP51-52 10 1 1 1 1 1 HP49-50 9 1 1 1 1 1 HP47-48 9 1 1 1 1 1 HP45-46 9 1 1 1 1 1 HP43-44 9 1 1 1 1 1 HP41-42 9 1 1 1 1 1 HP39-40 8 1 1 1 1 1 HP37-38 8 1 1 1 1 1 HP35-36 8 1 1 1 1 1 HP33-34 8 1 1 1 1 1 HP31-32 8 1 1 1 1 1 HP29-30 7 1 1 1 1 0 HP27-28 7 1 1 1 1 0 HP25-26 7 1 1 1 1 0 HP23-24 7 1 1 1 1 0 HP21-22 7 1 1 1 1 0 HP19-20 6 1 1 1 1 0 HP17-18 6 1 1 1 1 0 HP15-16 6 1 1 1 1 0 HP13-14 6 1 1 1 1 0 HP11-12 6 1 1 1 1 0 HP9-10 5 1 1 1 0 0 HP7-8 5 1 1 1 0 0 HP5-6 5 1 1 1 0 0 HP3-4 5 1 1 1 0 0 HP1-2 5 1 1 1 0 0

Machining Time Matrix (in second)

Hunting Plane T1 T2 T3 T4 T5

HP59-60 24 12 10.8 9.6 8 HP57-58 24 12 10.8 9.6 8 HP55-56 24 12 10.8 9.6 8 HP53-54 24 12 10.8 9.6 8 HP51-52 24 12 10.8 9.6 8 HP49-50 12 10.8 9.6 8.4 7 HP47-48 12 10.8 9.6 8.4 7 HP45-46 12 10.8 9.6 8.4 7 HP43-44 12 10.8 9.6 8.4 7 HP41-42 12 10.8 9.6 8.4 7 HP39-40 10.8 9 8.4 7 5 HP37-38 10.8 9 8.4 7 5 HP35-36 10.8 9 8.4 6 5 HP33-34 10.8 9 8.4 6 5 HP31-32 10.8 9 8.4 6 5 HP29-30 9 7.5 7.2 4.8 HP27-28 9 7.5 7.2 4.8 HP25-26 9 7.5 7,2 4.8 HP23-24 9 7,5 7,2 4 HP21-22 9 7.5 7,2 4 HP19-20 7 6.6 6 3 HP17-18 7 6.6 6 3 HP15-16 7 6.6 6 3 HP13-14 7 6.6 6 3 HP11-12 7 6.6 6 3 HP9-10 6.6 5.4 4.8 HP7-8 6.6 5.4 4.8 HP5-6 6.6 5.4 4.8 HP3-4 6.6 5.4 4.8 HP1-2 6.6 5.4 4.8

DP Model Solution for Respondent C Selected Max. Cutter Ti Merged Cutter Ti for Machining Original for HPj Machining Total MPk Machining Time of Hunting Plane MPk Machining Max. Time on MPk Using Cutter Plane HPj Selected by Depth Time Ti Depth Ti Ti DP Model of Cut cut HP59-60 T5 HP57-58 T5 4 MP12 T5 3 8 HP55-56 T5 HP53-54 T5 HP51-52 T5 4 MP11 T5 4 8 HP49-50 T5 HP47-48 T5 HP45-46 T5 28 HP43-44 T5 4 MP10 T5 4 7 65.6 HP41-42 T5 HP39-40 T5 HP37-38 T5 HP35-36 T5 4 MP9 T5 4 5 HP33-34 T5 HP31-32 T5 HP29-30 T4 HP27-28 T4 3 MP8 T4 3 4.8 14.8 HP25-26 T4

DP Model Solution for Respondent C (cont.) HP23-24 T4 3 MP7 T4 2 4 HP21-22 T4 HP19-20 T4 3 MP6 T4 2 3 HP17-18 T4 14.8 HP15-16 T4 HP13-14 T4 3 MP5 T4 3 3 HP11-12 T4 65.6 MP4 T3 0.5 4.8 HP9-10 T3 2.5 9.6 HP7-8 T3 2.5 MP3 T3 2.5 4.8 HP5-6 T3 2.5 MP2 T1 0.5 6.6 HP3-4 T1 1.5 13.2 MP1 T1 1.5 6.6 HP1-2 T1 1.5

Appendix 4 – Documentation of Collecting Data Phase