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Interactive Spur Gear Generation Using Parametric Programming with CNC End Milling N K Mandal1, N K Singh2 and UC Kumar3 1, 3 National Institute of Technical Teachers’ Training and Research Block- FC, Sector-III, Salt Lake City, Kolkata-700106 2 Indian School of Mines, Dhanbad-826004, Jharkhand Phone Number: +91-033-66251973 *Corresponding Author's E-mail: [email protected] Abstract he development of computer technology brings new opportunities in all sphere of manufacturing. Traditional methods of gear manufacturing with conventional machines have many T disadvantages. The traditional methods are basically two types: Gear forming and Gear generation. Gear forming uses form cutters that are normally bought off-the-shelf and one cutter can be used repeatedly in machining many similar gears provided they are of the same module. Moreover, if the demand of the gear is very few, then buying a gear cutter for that purpose only may not be economical. In addition to that, all types of form cutter may not be available at all times. In this research work, an interactive program called MACRO is developed by which almost all types of gear can be manufactured by a simple end mill cutter in a CNC vertical milling machine only by changing some parameters. In this MACRO program, an algorithm describes the point to point movement of the cutting tool of the machine resulting generation of gear tooth profile more accurately which ensures minimum mechanical losses during power transmission.
Keywords: Parametric Programming, CNC VMC machine, gear module, gear generation, Accuracy, CAD/CAM
1. Introduction It is often required to transmit power from one component to another component to increase the speed of the output component. Any power transmission system consists of one input devices, one- output devices and component, that is connected the two. Generally, the input device is a power source or prime mover. Input devices may be an engine, electric motor, PTO shaft of a tractor, etc. The output device or driven device receives the power and does productive work. Output device may be a pump, a conveyor belt etc. Connecting devices exist between the input device (power source) and the output device (point of use of the power). Couplings are used to connect sections of shafts or to connect the shaft of driving machine to the shaft of a driven machine. Clutch is used in between the input and output devices. Chains can be used for comparatively larger distance (5-8 meter) for parallel shafts and has high efficiency (98%). It has a high production cost, the operation is noisy and the design is complicated. Gear is one of the most efficient mechanical power transmission device. Advantages of power transmission by gear over other conventional power transmission system may be summarized as i) It transmits exact velocity ratio ii) It may be used to transmit larger power iii) It may be used for small centre distance of shafts iv) It has high efficiency iv) It has reliable service iv). It has compact layout.
3172 Article History: Received Date: Mar. 14, 2016 Accepted Date: Oct. 21, 2016 Available Online: Dec. 02, 2016
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There are many types of error encountered in conventional gear manufacturing. These includes:
Profile Shifting: In normal practice of gear cutting by hobbling, one gear cutter is used to cut a range of number of teeth per gear like from 35 to 54 numbers of teeth. For big range of gear tooth number, error may occur in tooth profile. It is observed that in one of the tooth there is a tendency for the thickness to reduce at the tip. This is because the involute curve tends to shift inwards as the number of teeth reduces, thus reducing the base circle. Undercutting at root surface: When the number of gear teeth to be cut becomes small, the generating tool sweeps out its path, remove some of the profile and produces an undercut tooth form. To prevent under cut some correction must be introduced. Runout error of gear teeth: This error defines the runout of the pitch circle. It is the error in radial position of the teeth. Most often it is measured by indicating the position of a pin or ball inserted in each tooth space around the gear and taking the largest difference. Alternately, particularly for fine pitch gears, the gear is rolled with a master gear on a variable centre distance fixture, which records the change in the centre distance as the measure of teeth or pitch circle runout. Runout causes a number of problems, one of which is noise. The source of this error may have a detrimental effect on accuracy and ruggedness of the cutting arbour and tooling system. Lead error of gear: Lead error is the deviation of the actual advancement of the tooth profile from the ideal value or position. Lead error results in poor tooth contact, particularly concentrating contact to the tip area. Modifications, such as tooth crowning and relieving can alleviate this error to some degree. Tooth profile error: Tooth profile error is the summation of deviation between actual tooth profile and correct involute curve which passes through the pitch point measured perpendicular to the actual profile. The measured band is the actual effective working surface of the gear. However, the tooth modification area is not considered as part of profile error. Spur gear teeth profile may be either of cycloidal or involute. A cycloid is the curve traced by a point on the circumference of a circle which rolls without slipping on a fixed line. Cycloid form may be of two types, one is epicycloids and another is hypocycloid (Fig. 1). When a circle rolls without slipping on the outside of a fixed circle, the curve traced by a point on the circumference of a circle is known as epicycloids. On the other hand, if circle rolls without slipping on the inside of a fixed circle, then the curve traced by a point on the circumference of a circle is called hypocycloid. An involute of a circle is a plane curve generated by a point on a tangent, which rolls on the circle without slipping or by a point on a taut string, which is unwrapped from a reel. In Fig. 2 being the starting point of the involute. The base circle is divided into number of equal parts. The tangents are drawn and the lengths equal to the arcs are st off. Joining the points, A, A1, A2, A3 etc. we obtain the involute curve AR.
Fig. 1 Construction of Cycloidal Teeth of a Gear
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Fig. 2 Construction of Involute Teeth
In actual practice, the involute gears are more commonly used as compared to cycloidal gears, due to some advantages. The most important advantage of the involute gear is that the centre distance for a pair of involute gear can be varied within limits without changing the velocity ratio. This is not true for cycloidal gears which require exact centre distance to be maintained. In involute gears, the pressure angle, from the start of the engagement of teeth to the end of the engagement, remains constant. It is necessary for smooth running and less wear of gears. But in cycloidal gears, the pressure angle is maximum at the beginning of engagement, reduces to zero at pitch point, starts increasing and becomes maximum at the end of engagement. This results in less smooth running of gears. The face and flank of involute teeth are generated by a single curve whereas in cycloidal gears, double curves (i.e. epicycloids and hypocycloid) are required for the face and flank respectively.
2. Conventional Methods of Spur Gear Cutting Conventional gear manufacturing are two types: i) gear forming and ii) gear generation methods. In forming method, the tooth spaces are produced on the blank by a formed tool. The tool profile is regenerated on the machined surface. The gear teethes are milled consecutively with a formed cutter of disk. The gear milling is done with form cutters having the profile of the tooth space of the same module. The production of the gears by the generating method reproduces the meshing of a pair of the gears; here, one component of the pair is the gear blank while the other is the cutting tool. The spur gears may be generated by hobs, gear shaper cutters, and rack-type generating cutters. This is further classified as i) gear hobbing and ii) gear shaping. In gear hoboing, i) hob rotates at the cutting speed, (b) interacting rotation of the blank (generation), and (c) hob feed along the axis of the blank. The hob, in rotation, cuts metal continuously with its teeth and all the teeth of the gear are consecutively cut, without interruptions in cutting for advancing and withdrawing the hob. In gear shaping, gear shaper cutter is applied for producing both external and internal spur gears. A gear shaper cutter is shaped like a gear of the same module as the gear to be cut. The shaper cutter and the gear blank rotate together as if they were two gears in mesh. The teeth of the shaper cutter are relived to obtain the geometrical form required by a metal-cutting tool. Kibet et. al. [3] have investigated that there is a problem of accurately machining gears by conventional means. This is due to inaccurate positioning of the blank and cutter. They have found the appropriate way of producing quality and accurate gears most economically through the use of a circle as a substitute to involute profile in gear cutting. Reyes et. al. [11] have proposed an algorithm to describe the ideal spur gear profile. The goal was to describe the point to point movement to be used within a CNC machine. Skoczylas et. al. [4] have introduced two variants of making spur gears by using universal CNC machine tools with universal shank cutter. The measurement of the chosen parameters of geometric structures of gear tooth surface is carried out as well as their comparison was done. Özel [4] have proposed cutting of spur gear by the end mill in the computer numerically controlled (CNC) vertical milling machine differently from the conventional manufacturing methods. Parametric
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equations of tool paths for cutting the spur gear were derived. Tolvaly-Roşca [1] et. al. have proposed a pure CAD modeling solution to universally generate surfaces and solid models of gears, which are intended to be used in contact and FEA studies in virtual environment. Uzun [13] et. al. have observed that spur gears can be manufactured by vertical-spindle CNC milling machines unlike conventional manufacturing methods. Deogade [10] et. al. have described how the parametric programming is applicable in CNC machining. Sheth [12] et. al. have observed that despite the tremendous development in CNC programming facilities, linear and circular cuts parallel to the coordinate planes continues to be the standard motions of modern CNC machines. Wang [14] et. al. have described that work efficiency can be improved by using macro program in the practical processing according to the real parts. Oladejo [8] et. al. have described how the design of efficient and reliable gearing mechanism is governed, among other factors, by its ability to withstand the frictional contact condition and high bending stresses experienced at the tooth root. Yahaya [15] have described that an involute curve (or known as an approximated curve) is mostly used in designing the gear teeth especially in spur gear. He has redesigned the spur gear teeth using the transition (S transition and C spiral) curves (also known as the exact curves) with curvature continuity (G2) as the degree of smoothness. Mallesh [6] have generated asymmetric spur gear tooth geometry for different pressure angles on drive and coast side using computer programme. Litecka [5] have described that spur gears with a true involute profile are the most wide parts of machines. Jeon [2] developed automatic gear design program to create three dimensional model and gear profile of the spur and helical gear with involute tooth profile by using user developed program named Visual LISP on the AutoCAD. Nieszporek [7] et. al. have described that Spur involute gears may be manufactured using one of the shaping methods or by hobbing. Manufacturing process needs special tools and machine tools. They have used step-by-step method for generating gear on universal CNC machine tools.
3. CAD/CAM Modeling and Machining of Spur Gear Modeling of a gear needs detailed specification of the gear like number of teeth, module, pressure angle etc. Then, an involute or cycloid profile of the gear teeth is to drawn with AutoCAD or similar software from the principle of involute. Complete gear profile is to be drawn and CAD model is to be prepared (Fig. 3 and Fig. 4). The generated CAD model is to be imported to Delcam or similar software for generation of CNC part program. CNC machines run this part program. We select three basic parameters, module, number of teeth and pressure angle as 8,16 and 20º respectively.
Fig. 3 Mirror of Approximated Ccircle Fig. 4. Polar Command to Generate, Complete Involute Gear
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Fig. 5 Gear Machining in VMC
Selection of a suitable cutting tool like end mill is important in order to cut spur gear teeth in the vertical machining center (VMC). Diameter of the end mill cutter is to be calculated by considering the point wideness of bottom land and fillet radius of root of tooth of considered gear. The radius of the end mill cutter should be less or equal to the maximum root fillet radius. The CAD model is imported in Delcam POWER MILL software to prepare a CNC part program. This CNC part program is fed into the memory of the CNC milling machine through the memory card slot in the control panel. After feeding the part program in the memory of CNC machine a dry run is performed to check feasibility of the program and then final cut machining is conducted.
4. Gear Generation by Parametric Programming There are some common steps which needs to be done before commencing the actual work. This includes, i) selection of various parameters for gear generation ii) development of algorithm of spur gear to be manufactured iii) Generation of parametric programming code (MACRO) using this algorithm iv) Machining of spur gear using this MACRO in a vertical machining center. An involute curve is mostly used in designing the gear teeth (profile) in spur gear as this ensures no sliding at least theoretically, as it follows the tangency along contact line. The choice of the involute to describe the portion of contact allows to avoid friction as much as possible. The formal definition of involute curve is the curve traced by a point on a straight line which rolls without slipping on the circle. The circle is called the base circle of the involute. In vector form the curve is described by the following equations according to Fig. 6.
Fig. 6 A Tooth Portion
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Fig. 7 Head Thickness
Fig. 8 Complete Tooth Profile
x cos(θ+ ) sin( θ ) 1 = rb (1) y sin(θ− ) cos( θ ) θ
It is described in a polar way in equation 1 as x2 + y2 = r 2 (2)
rr22=(1 +θ2 ) Putting equation 1 into equation 2 we get b (3)
For a general radius, it is easy to get the angle and vice versa.
rr22− θ= b r 2 b (4)
From Fig. 2, we get the following relations of equations 5, 6 and 7
tg()β=θ (5)
θβ=α- re re re (6)
α =tg() β −β =θ − atg () θ rere re re re (7)
The connection point between the involute and the external radius provides
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rr22− θ= eb re r 2 b (8) θ In equation 8, re is the angle where the involute stops. Putting equation 8 into equation 9 and the angle that contain the involute descriptions appears as
α=θ−atg() θ re re re (9)
θ=θ An arc concentric to base circle continues the tooth profile. It starts at re over the involute or starts α α +ξ at re over the external circle and finishes in re . Profile generation follows its way at the top of the tooth and the actual point would be controlled by the Boolean operation to stop the head arc.
y (αre +ξ ) x cos(α+re step ) = re ysin(α+ step ) where re (11) As in equation 9, the angle from the beginning and the end of the involute can be expressed as: 22 22 rrpb−− rr pb α−= atg rp rr22 bb (12) π m Ec= = rp γ Circular thickness, 2 π γ= m 2r Circular thickness angle, p The relations given in equations 13, 14, and 15 ε=α −α re rp (13) ξ=γ−2 ε Head angle, (14) Finally circular head thickness can be written as, Ht =ξre (15) Now the mirrored involute is described xr=cos( θ+ ) r θ sin( θ ) bb (16) 3178 International Journal of Mechatronics, Electrical and Computer Technology (IJMEC) Universal Scientific Organization, www.aeuso.org PISSN: 2411-6173, EISSN: 2305-0543 N K Mandal et al. / Vol. 6(22), Oct. 2016, pp. 3172-3187 yr=−sin( θ+ ) r θ cos( θ ) bb (17) But this curve must be rotated counterclockwise using the rotation matrix by the following angle. σ=ξ+2 α Mirrored curve rotation angle, re (18) ξ+2 α re x' cos(θθ ) sin( ) 1 = rb y'− sin( θ+ ) cos( θ ) θ (19) Equation 19 can be transformed as xx cos(σ− ) sin( σ ) ' = rb yysin(σ+ ) cos( σ ) ' (20) θ=θ The curve in equation 20 starts from re and decreases to θ=0 . The tooth profile starts in rc at the point p1 of Fig. 8. p1 and p2 are connected by a straight line. Coordinates of point p2 are: x = rb; y = 0; p2 and p3 are connected by the involute of the base circle. Using equation 1, coordinates of point p3 can be derived as: xr=b cos( θ ) +θ r sin( θ ) b b re b re re yr=sin( θ ) −θ r cos( θ ) bbb re b re re θ Where (5.8) give re , p3 and p4 are connected by the arc of the external radius, coordinates of p4 are: xr=cos( α +ξ ) e re yr=sin( α +ξ ) e re p4 and p5 are connected by the mirrored involute, coordinates of p5 are: xr=cos( σ ) b yr=sin( σ ) b p5 and p6 are connected by a straight line. Coordinates of point p6 are: xr=cos( σ ) r yr=sin( σ ) r 3179 International Journal of Mechatronics, Electrical and Computer Technology (IJMEC) Universal Scientific Organization, www.aeuso.org PISSN: 2411-6173, EISSN: 2305-0543 N K Mandal et al. / Vol. 6(22), Oct. 2016, pp. 3172-3187 σ is the angle that contains the tooth without root, the total amount of use depends of Z. The total pattern to be repeated is defined by the profile joining points pi, i = 1,2,..,16. Define then τ as the sector angle of the pattern. 360 τ= Z (21) It is clear that the number of teeth is equal to the number of roots. Thus, p6 and p7 are connected by the arc of the root circle. Coordinates of point p7 are: xr=cos( τ ) e yr=sin( τ ) e ψ=τ−σ C = ψr Where root angle will be and the circular root thickness rt rc Algorithm for MACRO Program: Sector I: p1 -p2 step ← x0; x ← rrc; y ← 0; do x ← rrc + s0; y ← 0; while ( x < rb ); Sector II: p2 - p3 step ← θ0 ; θ ← 0; x←rb; y = 0; rr22− θ= eb re r 2 b do xr←cos( θ+ ) r sin( θ ) bb yr←sin( θ− ) r cos( θ ) bb θ←θ+θ 0 x (a tan<αre ) y while Sector III: p3 - p4 θ step = 0 ; θ←θ re ; xr←cos( θ+ ) r θ sin( θ ) bb yr←sin( θ− ) r θ cos( θ ) bb do 3180 International Journal of Mechatronics, Electrical and Computer Technology (IJMEC) Universal Scientific Organization, www.aeuso.org PISSN: 2411-6173, EISSN: 2305-0543 N K Mandal et al. / Vol. 6(22), Oct. 2016, pp. 3172-3187 xr←θcos( ) e yr←θsin( ) e θ←θ+θ 0 ; (θ< ( ξ+α )) while re Sector IV: p4 -p5 step ←θ 0 ; θ←α re ; σ←ξ+2 α re ; xr←cos( ξ+α ) e re ; yr←sin( ξ+α ) e re ; do xr←( cos( θ+ ) r θ sin( θ ))cos( σ−− ) ( r sin( θ+ ) r θ cos( θ ))sin( σ ) b b bb yr←( cos( θ+ ) r θ sin( θ ))sin( σ+− ) ( r sin( θ+ ) r θ cos( θ ))cos( σ ) b b bb θ←θ−θ 0 ()θ>σ while Sector V: p5 - p6 step← x 0 ; xr←σcos( ) b yr←σsin( ) b do x←− xx 0 ; yx←σtan( ) ; r←+ xy22 ()rr> while c Sector VI: p6 - p7 step ←θ 0 ; θ←σ; xr←σcos( ) r yr←σsin( ) r 3181 International Journal of Mechatronics, Electrical and Computer Technology (IJMEC) Universal Scientific Organization, www.aeuso.org PISSN: 2411-6173, EISSN: 2305-0543 N K Mandal et al. / Vol. 6(22), Oct. 2016, pp. 3172-3187 xr←θcos( ) do r yr←θsin( ) r θ←θ+θ 0 ; (θ< ( τ )) while ; Until now, just one tooth has been described. The aim is to describe the point to point movement to be used in a CNC machine, but a gear has Z no of teeth. Rotation matrices are useful for repeating circular patterns. After analyzing the algorithm for Involute tooth of spur gear a FANUC Macro Program is developed and the same program is used to run a FANUC controlled Vertical Machining Centre. Main Part Program O0002; M06 T01; G0 G90 G40 G21 G17 G94 G80; …………. G65 P0001 X0 Y0 R80 Z0 F100 I56.0 A0 B22.5 H16; G0 Z10; M30; Sub Program O0001; G0 X#18 Y0; N20 ; ………. G01 G42 X#10 Y#14; #5=#5+#3; GOTO 8; N9; #1=#1+#2; #11=#11-1; GOTO 20; N21; G69 M99; Sample Part Program (MACRO) In this experiment, commercially PVD coated solid carbide and inserted end mill cutters are used since coated carbide tools are found to perform better than uncoated carbide tools. Two cutting tools are used. Surface facing is performed by a 16mm diameter carbide inserted face mill cutter. Then a 4mm diameter solid carbide end mill cutter is used for profile milling. Details of the cutters are given below 5. Machining of Spur Gear in Vertical Machining Centre The milling machine used for this generating method is ‘GOURAV Series BMV 35 TC 20’ CNC Vertical Machining Centre having ‘FANUC-Series Oi-MD’ control system with vertical milling head manufactured by Bharat Firtz Werner Ltd. For generating the gear tooth profile, FANUC macro programme have been developed and run on this machine. The Macro Program generated using algorithm of gear profile is now fed to the memory of Vertical Machining Center. Simulation of CNC part program is done to check feasibility of the CNC code generated. A block of aluminium alloy of 3182 International Journal of Mechatronics, Electrical and Computer Technology (IJMEC) Universal Scientific Organization, www.aeuso.org PISSN: 2411-6173, EISSN: 2305-0543 N K Mandal et al. / Vol. 6(22), Oct. 2016, pp. 3172-3187 3 dimension 150 × 150 × 16 mm is drilled of diameter of 14 mm so as to hold it centrally by a bolt which is fastened in the T-slot provided in the table of CNC machine by a tenon. Face milling is done to make the block perfectly flat and parallel to the machine bed. The position of the center bolt is taken as zero offset i.e. machine zero. After face milling is done with a end mill cutter (Fig. 9(a), 9(b), 9(b)) final profile milling is done by solid carbide end mill running the CNC part program inserted in the machine memory (Fig. 10). Fig. 9 a) 5.5 Solid Carbide Fig. 9 b) Tool Holder with 6 mm dia. Fig. 9 c) Tool Holder with End Mill Solid End Mill Cutter Inserted End Mill Cutter After machining burrs are removed by filing it with a second cut file so that no sharp edge remains on the gear. Now it is ready for measurements. 6. Experimental Results and Analysis In this research work, spur gears are produced by both CAD/CAM technique and by MACRO programs. A comparative study of both the methods are performed based on the accuracy and surface roughness of the produced gear. Metzer-M profile projector is used for rapid inspection and measurements (linear and angular) of small to medium size components such as gears, tools, rubber components, miniature electronic assemblies, and so on. Its best quality high resolution optics provides accurate, bright clear and sharp images. The special front and back surface coated mirror are highly polished and lobbied distortion and reproduction. Three elements condenser system and high intensity Halogen Lamps provide brilliant images even in day light condition commitment to ensure the quality at the highest levels of precision, quality reliability and performance. Measurement of an involute profile is based on its geometric property (A line normal to an involute curve is a tangent to the base circle). The actual involute profile of the spur gear tooth is printed on a transparent tracing paper with a magnification of 10 X. The gear is then placed on the table of the profile projector and tooth profile projected on the screen under a magnification of 10 X using a profile projector shown in Fig. 10 and Fig. 11. The gear is then checked for consistency with the actual involute profile printed on the tracing paper. Fig.10 Machining of Spur Gear in VMC 3183 International Journal of Mechatronics, Electrical and Computer Technology (IJMEC) Universal Scientific Organization, www.aeuso.org PISSN: 2411-6173, EISSN: 2305-0543 N K Mandal et al. / Vol. 6(22), Oct. 2016, pp. 3172-3187 Fig. 10 Checking of Gear Tooth Profile Fig. 11 Tooth Profile Dimension Measurement Using profile projector, the dimensions of the two machined gears are measured and compared with those of the actual involute profile. Table 1 compares the values of the machined gear by both the methods against the ideal that is expected. The tip of the tooth is taken as the datum, then the vertical reading set to allow for the desired horizontal measurement to be read and recorded. This process is repeated till all the seven measurements got as shown in the table 1. It should be noted that for the MACRO machined gear, the deviations are within the allowable backlash allowance of 0.2 mm while for the CAD modeled is not lying within the limit. The graph in Fig. 14 shows that tooth dimensional thickness for a CAD modeled gear is thinner at the addendum and thicker at the dedendum. The deviation of MACRO generated gear is minimum. The circle involute profile of MACRO generated gear is found to be exactly as the true involute profile though error of 0.06 mm was observed in some sections of the profile. At the tip of the tooth there was a profile shift to the left side only, this give the impression that is an asymmetric tooth, Fig. At the region of the addendum, an inward profile shift is noted, which has an effect of reducing the top landing of the tooth drastically. During CAD modeling, it is very difficult to draw accurate profile and as such, the tooth was thinner at the tip but thicker towards the root. 7. Measurement and Comparison of Gears Tooth Roughness Surface roughness of the gear tooth is measured using the ‘Mar Surf PS1’ surface profilometer manufactured by Mahr GmbH Gottingen. The arithmetic average roughness value Ra is measured by this instrument. The surface finish of the tooth flank of gears generated by two methods is measured using the profilometer. Set up for roughness testing is illustrated in Fig. 15. Gears are held in a machine vice rigidly so that gear tooth flank, root surface remains perfectly parallel to the stylus of the surface profilometer. Then, surface profilometer is placed on flat surface of vice so that stylus can reach the surface to be measured. Finally legs of profilometer is adjusted and switched ON for required measurement. 3184 International Journal of Mechatronics, Electrical and Computer Technology (IJMEC) Universal Scientific Organization, www.aeuso.org PISSN: 2411-6173, EISSN: 2305-0543 N K Mandal et al. / Vol. 6(22), Oct. 2016, pp. 3172-3187 Fig. 12 Profile of MACRO Generated Gear Fig. 13 Profile of CAD Generated Gear Actual involute Vertical distance Fig.14 Dimensionsf of the h Actual Involute Profile Fig. 15 Roughness Measurement along Root of Tooth For measurements four teeth from each gear are chosen randomly. The measurement is repeated five times on every chosen tooth. Two points along the gear profile at the addendum and the dedendum are measured and the average is worked out, given in Table 2. The average roughness level Ra is found to be 1.352 µm for the CAD modeled gear and 1.272 µm for the MACRO generated gear. 3185 International Journal of Mechatronics, Electrical and Computer Technology (IJMEC) Universal Scientific Organization, www.aeuso.org PISSN: 2411-6173, EISSN: 2305-0543 N K Mandal et al. / Vol. 6(22), Oct. 2016, pp. 3172-3187 Table 6.1: Comparison of Tooth Thickness Vertical distance Actual involute Macro generated gear CAD generated gear where measurement Measurement Deviation Measurement Deviation measurement is taken 0.5 5.84 5.72 - 0.12 5.26 - 0.58 2.0 7.58 7.56 - 0.02 7.24 - 0.34 4.0 9.58 9.6 + 0.02 9.66 + 0.08 6.0 11.22 11.2 + 0.02 11.44 + 0.22 8.0 12.42 12.4 - 0.02 12.74 + 0.32 10.0 13.18 13.18 0.00 14.4 + 0.61 12.2 13.56 13.52 - 0.04 14.76 + 0.60 Table: 6.2 Comparison of Roughness Level CAD modeled gear MACRO generated gear (µm) (µm) Addendum roughness level 1.462 1.232 Dedendum roughness level 1.242 1.312 Average 1.352 1.272 Conclusion In the present study, we have developed an algorithm for interactive parametric program which may be used to manufacture spur gears, of different shape and sizes from the same program. Although, many commercial packages like Delcam, Edgecam, NCcam etc. is used to generate NC codes from a 3D model and these codes are sent directly to a CNC machine through a network to manufacture the gear, the user has no control over the generated shape, since he does not have access to the code that generates it. Therefore, it can be concluded that only one type of gear which is already modelled can be manufactured through CAD/CAM technique. On the other hand, the interactive gear generation method has three distinct advantages. Firstly, no commercial software is needed for interactive parametric programming technique. Secondly, spur gears of different specification may be produced from the same program just by altering some numerical data. Only one MACRO program is able to generate spur gear from a small to very big one. The main result of the study can be concluded as the spur gears can be manufactured very accurately under standard and non-standard pressure angles and module values by parametric programming Thirdly, it has been experimentally proved that the spur gear manufactured using interactive parametric program are more accurate than the same produced by CAD/CAM technique. The measured values gear profile is found to be consistent with the calculated values whereas the profile made by CAD modelling is somehow differs from the actual profile due to rough approximation of involute curve during drawing of the same. On the other hand, there is a possibility of human error during drafting as it requires much skill. The experiments also showed that MACRO cut gear is of finer surface finish as compared to the CAD modeled gear which had a higher roughness level. A finer surface finish is desired in gear surface to reduce wear, noise and non-uniform motion transmission. Therefore, there is no need of special cutters or machines only a standard end mill cutter with a CNC machining centre is sufficient for machining a spur gear with standard or non- standard parameters i.e module pressure angle, number of teeth. 3186 International Journal of Mechatronics, Electrical and Computer Technology (IJMEC) Universal Scientific Organization, www.aeuso.org PISSN: 2411-6173, EISSN: 2305-0543 N K Mandal et al. / Vol. 6(22), Oct. 2016, pp. 3172-3187 References [1] Ferenc Tolvaly-Roşca, Zoltan Forgo. Mixed CAD Method to Develop Gear Surfaces Using the Relative Cutting Movements and NURBS Surfaces, vol.19, no. 5, pp.20-27, 2015. [2] Jeon Eon-Chan, Lee Su-Yong, Song Ho-Bong, Chun Jung-Do, Kim Soo-Yong. “Study for the Verification of the Tooth Profile Accuracy of the Automatic Gear Design program.” Global Journal of Technology & Optimization, vol. 2, no.1, pp. 97-103, 2011. 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