1、d 2 98FM7 Checker of 3D Form Accuracy of Hypoid Gear, Hypoid gear, Bevel gear, Checker, Accuracy, Quality, Quality control 1. Introduction The geometrical accuracy of 3 dimensional tooth flank form is one of the most important items to insure the performance of gears. For cylindrical involute gears,
2、 tooth form checker is widely used to fulfill this techno-industrial demands. For bevel and hypoid gears although, the development of tooth form checker is still not well done. The conventional measurement was carried out usually at 9 x 5 matrix points on a tooth flank, and it is not easy to estimat
3、e the gear performance from that measured results. The lack of the number of measuring points makes it difficult to get necessary information, for instance, about heat-treatment distortion and about the state of lapping removal. The measuring technology of the curved figure of tooth flank, accuratel
4、y in position and in absolute value of measurement, is therefore strongly demanded for the quality control of those gears. The first attempt of the development of hypoid gear checker to fulfil the industrial demand mentioned above began in the later years of 1970s. This report explains how the curve
5、 measurement of the tooth flank of beyel and hypoid gears is realized through the continuous work of the development based on the original work and the accuracy of the measurement is discussed. The example of * 1 730-2 Mikunya, Hiaashi Osaka 577-0032; Fax.(J)-6-782-0649 O *2 1 Toyotacho,Toyoda City
6、471-8572; Fax.(J)-565-23-5757 *3 3-45 Akatsukicho, Seto City 489-0071; Fax. (J)-561-48-0115 *4 Dept.Frec.Eng, Kyoto 606-8501; Fax.(J)-75-771-7286 utilization of this checker for quality control of hypoid gears in mass-production in Japanese automotive industry to realize quiet5nal hypoid gear drive
7、is introduced. ._ vj 2. Measurement of tooth flank form deviation The form accuracy of machine parts is described on the design drawing and tooth flank form accuracy of gears is defined on the coordinate system fixed to the gear. When we measure the form deviation of gear tooth flank by using 3D coo
8、rdinate machine or by gear checker, the displacement of the center of the contacting ball at the tip of probe stylus is obtained as the corrective value of the soll- position that is controlled by the scales of the checker, that is, the measured values are obtained on the coordinate system of the ch
9、ecker. 4z measured tooth flank Ref e ren ce of form accuracy Coordma te system of A: Point at which the form deviation is defined B: Corresponding point of A on the aCNd surface AB: Fomi deviation measured on the checkers scale coordinates Fig. 1 What is form accuracy of gear tooth flank ? COPYRIGHT
10、 American Gear Manufacturers Association, Inc.Licensed by Information Handling ServicesConversion of Gear coordinates 10 Scale Tooth fink form is defined on ihe individual Gear coordinates or on design drawing Application software for production, quality control and for L Dejnied on the cwrdnates of
11、 the scales of checker Dejnied on the CoordinarCF of tinaviohi gear piece Fig.2 Measurement of form accuracy of gear tooth flank by CNC gear checker and conversion of data inside For the quality control of the geometrical form accuracy of gear teeth, it is necessary to convert these positional value
12、s of tooth flank in 3D space of gear checkers scales into the form accuracy or form deviation of the tooth flank, that is to convert these values into the values on the coordinate system of the objective gear. For this purpose, the zero point adjustment of checker scales is first done by measuring t
13、he datum surface of the objective gear by the same probe of the checker. Form deviation is the deviation of the position of the actual tooth flank to be measured from the reference tooth flank for the definition of form accuracy, i.e. in Fig.1. In case of CNC gear checker, this reference tooth flank
14、 is given by the numerical data. For example, at the measurement of cylindrical involute gear teeth, the 3D coordinate values of involute helicoid are converted to the gear checkers scale values to drive the probe along the reference surface for the definition of the form accuracy of gear tooth flan
15、k. Fig.2 illustrates the relation between hardware and software to measure form accuracy of tooth flanks by CNC gear checker. 3. Nature of hypoid or bevel gear tooth measurement It is interesting that so much percentage of gear engineers and gear researchers knows only cylindrical involute gears and
16、 hardly knows the fundamental about hypoid or bevel gears. They usually extrapolate their thought about cylindrical involute gears to the hypoid or bevel gears and sometimes that extrapolation is not correct. To measure the tooth flank form accuracy of hypoid or bevel gears, the first difficulty is
17、that the reference tooth flank for the definition of form accuracy is not uniquely approved: This is the main difference from the case of cylindrical involute gears and the reason why the tooth form accuracy of hypoid or bevel gears is not defined in any national or international Standards. The Glea
18、son and Klingelnberg companies propose to use the trajectory surface of cutter blade to the work piece at gear cutting for the reference of the definition of form accuracy. The main trouble is that the reference surface becomes the function of setting parameters or summary data of each type of gear
19、cutting machine and it is not expressed by explicit mathematical formulae. Compare this fact with the case of cylindrical involute gears whose reference for the definition of tooth flank form deviation is involute helicoid that is a well known mathematical function. carried out by observation of con
20、tact pattern of tooth flan The quality control of hypoid or bevel gears is usually and this brings another difficulty. The operator of gear cutting machine or lapping machine changes machine settings according to their experience to obtain the specified 0. -2113- COPYRIGHT American Gear Manufacturer
21、s Association, Inc.Licensed by Information Handling Services2, contact pattern, where the record of machine setting parameters the operator used is usually not stored. * That means the information to establish the reference for the definition of tooth flank form accuracy is lost. a - Hypoid or bevel
22、 gears are usually heat treated after tooth cutting and lapped. Distortion or deformation of the gear through heat treatment process is considerably large, and the datum surface of the work piece at the gear cutting loses its position. After the heat treatment, the datum surface of the wor!; piece i
23、s regenerated by holding the distorted tooth flank. Gear lapping is then carried out on this new datum surface that is different datum from that of the gear cutting. The reference surface for the definition of tooth flank form accuracy is obtained on the old datum and the conversion of the measured
24、data of objective tooth flank stored as the gear checkers scale data to the data defined on the coordinate system fixed to the objective gear to evaluate the form accuracy becomes therefore less accurate. For the case of cylindrical involute gears, such problem also exists, but for hypoid or bevel g
25、ears this problem becomes serious because of its complexity in three dimensional figure. a I e Dimensions of miml Dinsnsions of pinion Fillet stress, Contact stress, Fig.3 Algorithm to calculate hypoid gear performance, when the nominally generated tooth flank form of pinion is incorporated as the r
26、eference of the form accuracy of pinion L_ Final niachine setting sumnary of pinion (for genarate method) A :Analysis withwt muring tooth flank form A :Analysis with neasuring tooth flank form B :Detailed stress analysis Fig.4 Algorithm to calculate hypoid gear performance, when the conjugate pinion
27、 tooth flank form to the gear tooth flank is incorporated as the reference of the form accuracy of pinion The tooth flank form of the bevelhypoid gears is complicated 3D figure and its measurement with the CNC machine has to be carried out by the synchronous control of multi-axes. For some kind of g
28、ear dimensions, it is impossible to avoid the quadrant change of NC scales of the checker during the measurement. Some inevitable influence such as lost motion and other non linearity are getting in the measurement. To minimize the data discontinuity at the quadrant change, very precise machine hard
29、ware is necessary. h c To measure the tooth flank of bevelhypoid gears, the contacting position on the surface of ball at the tip of probe stylus is not a fixed point: it moves over the surface of the bail. This brings difficult problem to compensate the influence of the radius of the ball from the
30、measured data for the form accuracy of gear tooth. The maintenance of probe stylus of the checker is very important. Hypoid or bevel gear wheel and pinion is cut with quite different machine. The conventional measurement of 3 -3113- COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by
31、Information Handling Servicesmating wheel and pinion is then carried out quite separately based on the reference for the tooth setting parameters of each tooth cutting machine and the form deviation is evaluated flank form accuracy that is the function of 3 Fig.5 Contact lines on gear tooth flank an
32、d and on the mating coniugate Dinion tooth flank (Contact lines on the reference tooihfiaks for the definition of form deviation) independently and the measured form deviation of tooth flank of each gear is fed back to each gear cutting procedure. Because the reference for the wheel and that for its
33、 mating pinion is different and they are not conjugate, these measured tooth flank form deviation has no direct correlation with the state of tooth contact nor with the prediction of the gear performance. To use these data of tooth flank form deviation for the prediction of the gear performance, som
34、e complicated procedure is necessaryr2, cf. Fig.3. It is also very difficult to estimate the tooth flank form deviation of pinion and wheel from the observed tooth contact pattern. The requirement for the measurement of tooth flank form accuracy is considered as the following four cases: (1) at desi
35、gning It is necessary to determine the dimensions, tooth flank form corrections and tolerance for the gear set to meet the requirements for the performance and reliability of the products. It is then necessary to evaluate the stresses and operating perfonnance It is necessary to calculate the machin
36、e settings in order to cut the designed beveihypoid gears. It is demanded to know tooth flank form deviation of manufactured gears and the calculating method for the corrective (2) at production control machine settings to minimize the tooth form deviation. It is necessary to predict the change in t
37、he performance, if some results, such as contact patterns or tooth flank form deviation, are different from those specified. Provide aid for trouble shooting. It is necessary to predict the stress values and vibrational excitation, if there is failure during the operation. It is convenient if those
38、values can be predicted from the design drawing and the measured tooth flank form deviation or observed bearing pattems. (3) at performance prediction (4) at insurance of operation To meet the demands at designing, performance prediction and problems during operation, the virtual surface that is con
39、jugate to the reference tooth flank of wheel is propos Using this conjugate reference, it becomes easier to incorporate measured data of tooth flank form deviation to predict gear performance f2. The relation between measured gear tooth form accuracy and gear performance becomes very resemble to tha
40、t of cylindrical involute gears. Intuitional supposing from the relation for cylindrical for the reference of the tooth form accuracy of pinion. o Fig6 Conventional expression of form deviation of hypoid gear tooth flank by matrix points measurement, where the the reference of form accuracy for pini
41、on is the nominally generated tooth flank form obtained as function of the summary data of pinion cutting machine. -4113- a COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling Services*. .,- c -i- *- Fig.7 Tooth flank form and pitch checker HyB-35 for hypoid and b
42、evel gears involute gears to that of bevelhypoid gears becomes possible, because there exist contact lines on the mating conjugate reference tooth flanks of pinion and wheel as shown in Fig5 4. Configuration of the checker The importance of quality control of form accuracy of hypoid gear teeth has b
43、een recognized by Toyota Motor Corporation since long time to realize silent hypoid gear drive for personal cars and also to reduce total production cost. The conventional method for measuring tooth form accuracy of bevel and hypoid gears is carried out usually at 9 x 5 matrix Tooth omfe Fig.8 Measu
44、rement of hypoid wheel Fig9 Measurement of hypoid pinion i Fig.10 The axes of gear checker HyB, and measurement of tooth profile deviation and tooth lead form deviation of hypoid gears -5113- COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling Services. PINION GEA
45、R 1 1 mm) 2.Number of teeth 01 3. Face Width 4. Pinion Offset 5. Sum of Pressure Angle 6. Pressure Angle Pin. Concave 7. Shaft Angle a 8. Outer Cone Distance (mm) 9. Pitch Diameter (m) 10. Pitch Apex Beyond Cross Pt. (mm) 11.Face Apex Beyond Cross Pt. (m) 12.Root Apex Beyond Cross Pt. (-) 13.Crmn to
46、 Cross Pt. 14.Front Crown to Cross Pt. 16. Face Angle 17.Root Angle 18.Hand of Spiral Oui ORH 19.Mean Spiral Angle 20. Inner Spiral Angle 22. Genr Finishing Blade Angle (Concave Side) (Convex Side) 23. Finishing point Width 15.Pitch Angle (W (W (d%) 6:Z- 21. Cutter Diameter (inch)- 25.achine Center
47、to Back 24. achine Root Angle (da) 26. 27. Horizontal Vertical (-9 (-) p9 28. bad (Formate dHReAATF8E: O) (h) FE: O) (dcg) GEAR PINION 31. OMfset Angle on Hy-35 -1 30. bunting Distance II Il (mm) -1 (mm) i-Pinion 71%. - Re (%wliihg)maRLILk 1 5 3 Fig.12 Input data sheet for HyB-35 -11.1 :fl 16.4 -2.1
48、 2.1 1.1 -11.1 -0.7 :q 1.6 1.0 1.3 -11.1 ;,R 11.1 11.1 -1.1 2.6 O.* 1.1 43.1 T -;,;!7 :(j 4.1 14.1 14.1 1.1 i 14.4 1.1 1.1 8.1 um um T 1.4 -1.1 1.1 -1.1 1.1 4.5 M.O 4.1 1.1 1.1 *.O 1.1 M um -11.1 4.1 11.1 -1.6 1.4 1.1 u.4 LI 1.1 8.4 maau. ar t.1 ar 1.1 -.am7 I Fig.13 Output sheet of.the tooth flank
49、form checker HyB-35 ( formate pinion after case hardening and lapping) -7113- COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling Servicesalready fairly widely used in gear industry. Many comparison measurements of these three machines have been carried out for pinion and wheel of different dimensions. The results are almost same as that of Fig. 1 1. The data repeatability of the HyB machine for the acceptance of machine at the beginning of its delivery was 5 pm for 25 times of measurements. Now the repeatability
