School of Industrial Engineering and Management Department of Production Engineering Relation between Process Capability Indices and Geometric Errors of Machine Tool Harikishan Veluru Ramanaiah M.Sc. Thesis KTH Royal Institute of Technology Stockholm November 2016 1 SAMMANFATTNING Högsta kvalitet, har blivit det viktigaste kravet från kunder oavsett segment och kravet på att ha högsta kvalitet har ökat oerhört inom tillverkningssektorn. För att hålla jämna steg med de ständigt ökande kraven från kvalitetsstandarder, måste industrier använda olika tekniker och metoder som stöd för att producera den tillverkade delen med högsta precision. Detta beror på flera faktorer såsom maskinverktyg, skicklighet och kunskap hos operatören, skärande bearbetning och parametrar, noggrannhet och precision hos mätutrustning. Trots att ingenjörer är väldigt noggranna med att säkerställa att den tillverkade delen är av bästa kvalitet med högsta precision, kommer det alltid att finnas slumpmässiga faktorer som kommer att resultera i en viss avvikelse i artikel dimensionerna vilket påverkar den slutliga produkten vid montering. För att övervinna detta, har industrier valt att tillämpa kapacitets index för att möjliggöra regelbundna kontroller av hur väl en process kan producera delarna. Studie av duglighets faktorer är kända för att vara mycket effektiv. I kombination med detta, övervakar industrier noga eventuella fel som uppstår antingen från maskinverktyg, process eller arbetsmiljö, detta för att kunna studera dessa fel och deras orsakande faktorer, som elimineras och minimeras för att uppnå högsta möjliga noggrannhet hos produkterna. Det har skett en omfattande forskning kring fel som påverkar produkt noggrannhet och olika metoder för kompensering har utformats för att minimera effekterna av dessa fel. Diskussioner kring dessa två ämnen ledde till frågeställningen, "finns det någon koppling mellan kapacitets index och maskinverktygs fel" och "om det finns ett samband, vad är det och hur kan det bidra till att uppnå en bättre noggrannhet. För att bedöma genomförbarheten av denna frågeställning, har denna forskning bedrivits. Kärnan i detta examensarbete är att studera realtidsdata av kapacitetsindex och kontrollera om det finns låga index värden för någon process. Sedan associera teoretiska överväganden om eventuella fel som orsakar ett lågt värde av kapacitetsindex. Vilket i sin tur kommer att bidra till identifieringen av relationen mellan kapacitetsindex och fel i maskinverktyg. Detta teoretiska övervägande kommer att valideras via simulationstester i MATLAB. Detta kommer att genomföras med stöd från företaget Leax, Falun. Kapacitets data som testerna baseras på kommer att förses från Leax, och avser maksinverktyget Mazak VMC. 2 ABSTRACT Appropriate quality, has become the most important requirement of a customer from any segment and the demand to have the highest quality has tremendously increased for a manufacturing sector. To keep up with the ever-rising demands of quality standards, industries must employ various techniques and methodologies which assist them in producing the manufactured part with the highest accuracy. This depends on several factors such as machine tool, skill and knowledge of the operator, cutting process and parameters, accuracy and precision of measuring equipments. Although the engineers take at most care to make sure the manufactured part is of the best quality with highest part accuracy, there will always be some random factors which will add some amount of the deviation in the part dimensions and this might affect the final product during assembly. To overcome this, industries have known to follow the application of capability indices in order to have regular check on how well a process can produce the parts. Study of the capabilities have known to be very effective. Along with this, industries closely monitor for the possible errors arising either from the machine tool, process or working environment, to study these errors and their causes, which will be eliminated and minimized to have the highest part accuracy. There has been an extensive research done on the errors affecting the part accuracy and various compensation methods have been devised to minimize the impact of these errors. Discussions about these two topics led to the thought, ‘is there any link between the capability indices and the machine tool errors’ and ‘if there is a link, what is it and how can it help in achieving a better accuracy’. To assess the feasibility of this thought, this research has been carried out. The core of this thesis research is to study the real-time data of capability indices and check for the presence of any low capability indices for any process. Then, associate the theoretical considerations of possible errors causing a low value of capability indices. Which in turn will help in identification of relation between capability index and the errors of machine tool. This theoretical consideration will be validated by carrying out simulation runs in MATLAB. This research will be carried out with the support from industry Leax, Falun and the data related to capability study is also collected from the same industry. The data of capability study that has been obtained is recorded for the machine tool Mazak VMC. 3 ACKNOWLEDGEMENT This thesis research would not have been possible without the able support and guidance of my supervisor Dr. Andreas Archenti and I extend my sincere thanks and gratitude to him. Also, this thesis would not have shaped up in a good way without the help of Ph.D. student, Theodoros Laspas. He has always been my reliable support and was always available to guide me during the entire thesis phase and it was Theodoros Laspas, who was responsible to help me setup the LDBB testing equipment and carrying out the tests in the industry. I would like to extend my gratitude to Mr. Björn Johansson, production engineer at Leax, Falun, for giving me the opportunity to visit the Leax industry and for helping me in understanding about their current methods employed to carry out capability study and for providing me all the relevant data required regarding the capability study. I, humbly thank all the faculty of Leax, Falun, for helping me carry out the testing in one of their machine tool. Lastly, I would like to thank my parents and friends who have always been of high motivational support all through the thesis research. 4 Nomenclature and Abbreviations Cp Process capability Cpk Adjusted process capability Cpm Process capability, when target is of essence Cm Machine Capability Cmk Corrected machine capability USL Upper specification limit LSL Lower specification limit μ Process mean σ Standard deviation T Target value n Sample number N Sample number N-1 Bessel’s correction S Standard deviation for sample 푥̅ Mean xi Value in the population 5 Table of Contents 1. Introduction .............................................................................................................................. 11 1.1. Research Background ....................................................................................................... 11 1.2. Research Objective ............................................................................................................ 11 1.3. Research Scope ................................................................................................................. 11 1.4. Research Motivation .......................................................................................................... 11 2. Literature Research ............................................................................................................... 12 2.1. Capability ............................................................................................................................. 12 2.1.1. Capability Definition ....................................................................................................... 12 2.2. Literature on Capability index ........................................................................................... 12 2.2.1. History of Capability Index ............................................................................................ 12 2.2.2. Process Capability ......................................................................................................... 13 2.3. Quality Tools Associated with Cp .................................................................................... 15 2.3.1. Control Charts ................................................................................................................. 15 2.3.1.1. Control Limit Choice ................................................................................................... 16 2.3.2. Histograms ...................................................................................................................... 16 2.4. Capability index for Varying Distributions ....................................................................... 17 2.5. Calculation of Standard Deviation ................................................................................... 18 2.6. Machine Capability ............................................................................................................. 19 2.7. Applications of Capability Indices .................................................................................... 21 2.8. Limitations of Capability Indices ....................................................................................... 21 2.9. Process Capability