1、95FTMll I Feature-B ased Definition of Bevel Gears by: Robert E. Brown, Caterpillar, Inc. TECHNICAL PAPER COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling ServicesFeature-Based Definition of Bevel Gears Robert E. Brown, Caterpillar, Inc. The statements and opin
2、ions contained herein are those of the author and should not be construed as an official action or opinion of the American Gear Manufacturers Association. Abstract Bevel gears for many appiications are subject to mcreasing levels of perfomance but with reduced cost. These factors have driven bevel g
3、ears toward sophisticated CMM control techniques. The complex shape of abevel gear tooth surface must be defned mathematically for the CMM, but the maihematical definition tends to be Wicult for direct use in gear design and manufacture. The mathematical definition may be condensed into a“featmbased
4、“ definition which is more convenient for gear design and manufacture. The featurebased definition may easily be described on the engineering drawings and subsequently toleranced to describe “fitness-for-use“ boundaries. Development and appiication of the feam it will be treated minimally. Caterpill
5、ar Gear Application Caterpillar makes a wide variety of earthmoving machinery including tractors, wheel loaders, motor graers, off highway trucks, wheel tractor scmpen, etc. Modern products of this type are continuously subject to demands for higher reliability, longer durability, improved performan
6、ce, ya lower cost. The track type tractor. for example (Figure 1). competes in the market only if within stringent cost limits, it can provide reliable service and durability levels demanded by the customer. Such machines are further subject to government noise restrictions that routinely grow in se
7、venty. This means that ail components must constantly improve, gears mcluded. Figure 1. Modern rack-type tractor 1 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling ServicesSTD-ALMA 75FTMLL-ENGL 1775 I Ob87575 OOOLi772 878 = Vhy Develop CMM Techniques? ligher de
8、mands on the bevel gears eventually led into field life and ioise problems. Enough problems were dg, along with the xpcnse of warrany. that a joim team of enginee, man- only a brief ddption of the contact p8“m was provided /lanufaaunng control was hstrated by the inevitable presence of eat treat dis
9、tonion; settings and cutter geometry were changed at the inction of the manucming forman to obtain the “correct“ contact attem. The entire process was, of course, highly subjective. ariable geometry was produced with limited understanding of the eometry and its effct on gear set stress and life. lie
10、 problems that surfaced were difficult to resolve. These appeared i the form of some parts that bad difficulties for reasons that were not lear (Figure 2). A sporadic element was present as well; sometimes good jobs drifted to “bad“ and others oscillated in and out of roblmi status. Generally, exper
11、imenting by persons with onsiderable experience was the only resolution technique and this :as not always successful. he team agreed that the best solution was to provide analytical ispection techniques for bevel gears. This was not without recedent: involute spur and helical gears were inspected wi
12、th the naiyticai equipment of the familiar variety, and had been for many - VI- inial CMM Experience he early experiments with CvM of bevel gears showed, for the fim me, that routine shop adjustments caused significant geometry hang-. Also, these showed considerable variation from heat treat ffects.
13、 From these experiments, the following conclusions were raw. 1.Analyticai measurement was mandatory to allow management of bevel gear design and manunicnUe with modem tschnology. 2.W was in hammy with the nst of CaterpiIWs c. *gopaatiorc noothercomponaitwould evcn be considered for niamifiirnm witho
14、ib the use of modan produaion technology. decisians. coiild be qlaiocd with CMM iaspeaion (Figura 3). 3.ROblcm jobs, and assuckd nianunuhinn gproceJs u that time, no commd CMM systems wem avaabie :o a decision wps reached to proceed with CMM bevel gear Ievciopment was Wiatcd for powerful FEA-based a
15、naiysis ools. uraiyticai dtvdopment at csterpillar. s-wly, :MM Application Philosophy ZMM methodology was a wry big change from the long tanding practice of contact paaem inspeaion. One could iot expect just to “drop in“ CMM inspection and have it go nto em; it was too different and no one knew exac
16、tly PARTS LEX TROUBLEMAKERS WITH PATTERS CAUSE: COXTROL ONLY: SCRAP Dorn KNOW WHY ADJumtm TROUBLE- SOME PARTS CAUSE TROUBLEMAKERS Figure 2. Parts with unclear reasons for difficulties what to expect from a CMM system in the open manufacturing environment. To devise a system that would, in fact, be e
17、ffective in the actual production mode required some planning. To meet the dual needs of design and manwg was, initially, a matter of establishing CMM application philosophy. Fim was agreement of the specific application goals. CMh4 bevel gear inspection intentions would be to: A. Enhance design acc
18、uacy for the required loads in the vehicle operation. B. Provide man- g the ability to identify the process to meet the required tooth acaracy. C. Enable process control with SPC. D. Equate cause and effect. Next was the establishment of a method approach for modem production technology requinmeats
19、2: A. Conformance to an objective standard. B. Capability based tolrranccs. c. Manufachinng * process cantrol. And then a method approach for process control: A. Evaluate the actual level of confonnance. B. Compare this actual level with the standard. C. Take corrective action if required BACK TO TH
20、E PARTS LIST: WHYTBOUBLXMAICERS? 1. PROCESS COULD BE DRIFTING - DATA HELPS MONITOR -must PROCESS VIA SPC 2. DESIGN INAPPROPRIATE FOR PROCESS -OPTIONS: a. REDESIGN *TROUBLEMAKERS Figure 3. Paro with difficulties explained by CMM inspection b. MWE TO BETTER PROCESS 2 COPYRIGHT American Gear Manufactur
21、ers Association, Inc.Licensed by Information Handling ServicesSTD-ALMA 95FTMZL-ENGL 1995 I b87575 0004773 724 I DEFINE PROCESS - ESTABLISH CAPABILITY CAPABILITY BASED TOLERANCES l I ESTABLISH TOLERANCE CLASSES FOR EACH PROCESS 8 1 I AS-HEAT i X X X X 1 TREATED i I l LNPL i IUNPL GROUND X X X X 1 1 F
22、igure 4. SPC application to specific features by tolerance class How to Display the Data? Conseasus was reached that, if CMM techniques were to be successful, there must exist a single and a clear method of bevel gear quality assessment. This was agreed to be possible oniy if analysis of bevel gear
23、inspection was broken down into components. in other words, to measure a complex 3-D tooth bevel gear surface shape and apply SPC, one must condense the measurements into srecific featurrs. A “feature“ is the general term applied to a physical part or tooth 3. Features of bevel gears or pinions are
24、bores, pinion bearing journals, splines, etc. Features of the teeh, such as profile modification, are described later in this paper. Matching of process capability and design requirements was also recognized to be important. Some process methods, such as CBN grinding, are more accurate than others.
25、Likewise, some gear designs require higher accuracy than others. By breaking down the tooth surface shape into specific features and applying SPC. matching of specific design needs to the process capability is enhanced (Figure 4). Furthemore, potential for improved design robustness and process impr
26、ovements are made more readily possible. CMM Features to be Measured Manufacturing and engineering design, it was to be found, had different conceptions of the specic feanires of most interest. The points of view were not the same: engineering design concerns predominantly rested with the end produc
27、t inside the vehicle in a field application, and manufacturing concerns primarily addressed the need for efficient process flow. Each group desire maximum allowance for variations, both the variations of manukture and the variations of loading from differences in machine applications. Each group als
28、o desired a well defined, constant description of target geometry and the associated tolerance boundaries. Mer numerous meetings on the subject, the iist of features was condensed to those shown in Table 1. Display of the CMM data was an important issue in itself. So many features were to be derived
29、, each with a good reason, that efficient display of the data required carel thought. A method which allowed the same interpretation by ail persons had existed for many years in the form of the familiar tooth profile measurement system for involute gears (Figure 5) 4, S. 61. This system is successfu
30、l because it breaks down a complicated mathematical shape into a form that is readily understood. This fonn is a simple deviation fmn a reference line. Experience with the involute measurement system had shown high value in making deviations hm conjugate visible 171. The deviations normaiiy are disp
31、layed graphidly but may also readily be condensed into numerical values. Many of the modem commercial CMM involute inspection systems display both the graphical and numerical output ali on the same chait (Figure 6). It was agreed by the team at caterpillar to devise a similar output system for bevel
32、 gears. The Coordinate System All CMM systems for gears are similar in operation; each measures coordinates by one or mother of the common mathematical frameworks 8, 91. The differences are in the choice of points to be meanired (number, location, etc.) and in the analysis method of the resulting me
33、asured data The system devised by Caterpillar measures the normal emr of a specific point identified by X, Y, and Z coordinates and the associated direction cosines. The coordinates chosen for the feature-based definition describe the coniueate refei.ence IO ,I i. For a bevel gear, this is the shape
34、 of a perfect part with no machining errors or heat treat distoaion. For a bevel pinion, this is the tooth surface shape that would tmsmit a constant velocity at zero torque running with a perfect gear. The conjugate reference forms the baseline for bevel gear measurements in a fashion similar to a
35、perfect involute and lead for cylindrical gears. Measurements of actuai bevel gears show the variations from the conjugate reference and, in most cases, these are intentional. 3 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling Services STD-AGHA 75fTMLL-ENGL 177
36、5 Ob87575 OOOl774 bbO Table I. Bevel gear features to be measured (condensed list) SIDE PROFILE4 CROWN ACTUAL - CONVEX SIDE PROFILE CROWN ACTUAL - CONCAVE SIDE THREE TEEi“ EQUALLY SPACED; TOE, MIDFACE, TOE, MIDFACE, for this purpose, the given pm plot may be “overlaid“ on the reference part plot. Th
37、e numerical output is also used for a variety of puposes such as direct comparison to tooth control data as shown on the engineering drawing and for compilation of SPC data. Application of Feature-Based Definition Feature-based definition is oriented towd “Customer First;“ the purpose is to ensure t
38、he delivey of accurate gears to the customer who buys the machine and subjects it to loads. The focus is therefore on conformance to the tooth contour specified on the engineering dtawing. Production efficiency is also a practical necessity, of course, and the entire design and man-g process is addr
39、essed as a joint effort. 10% FRC“ MIDFACE 10% FROM HEEL ROOT (SAP) Figure 11. Standard (default) tooth contour measurement positions 7 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling ServicesSTD-AGMA 75FTMLl-ENGL 1775 - Ob87575 0004778 20b 05140. arc TOOTH BEV
40、EL GEAR 05-AUG-93 E/C# O HARD COMPUTER 00,*2a/aa CHO: o cm a GHGCMH. K PROFILE AT HEEL MIDFACE TOOTH THICKNESS 1 0.000 57- 0.000 R - 0.000 TIP I TIP I ROOT HEEL ALIGNMENT ROOT CONCAVE TOE 1 ROOT SIZE HEEL TOE TOE -o. 100 -O. SOG TIP SIZE 1 HEEL TOE o. O00 o. O00 BACKFACE WAS MOVED MASTER TOOTHW1 0,0
41、00 BORE SI ZE o. O00 TOOTH HEEL 1 EH6CMH. K PROFILE AT MIDFACE TIP I CONVEX TOE TIP I ROOT ROOT HEEL ALIGNMENT TOE SCAL: .lIN.l.OO1O IN (0.025 MM) 1 MM-0.010 MM (.O004 IN.) Fgiue 12. Graphical output - typical hard master gear 8 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Info
42、rmation Handling ServicesPINION 12-AUG-93 HARD COMPGTER E/C# o CONVEX TOE D500C1. INP TOOTH ASLCMH. i. o.i.*2s/es et* o COR: 7 PROFILE AT MIDFACE TIP TIP 1 HEEL I 1 I ROOT ROOT SIZE HEEL TOE -0. io0 -0.100 TOE HEEL ALIGNMENT TOOTH THICKNESS 1 -0.489 TIP SIZE TOE o. O00 o. O00 - x - -.4es R - 0.000 B
43、EARING DIAS. LOWER UPPER CSLJCMH. K PROFILE AT MIDFACE CONCAVE TOE HEEL TOCTH TIP TIP 1 I 1 1 1 ROOT ROOT TOE HEEL ALIGNMENT Toom THICKNESS (ADJUSTED0.308FOR BACKLASH AT MIDFACE) I -o.le% SCALE: -1IN.-.0010 IN (0.025 MM) 1 MM-0.010 MM (.O004 IN.) Figure 13. Graphical output - typical hard master pin
44、ion 9 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling Services12-my-94 08:12:14 HARD PINION FILE NAMES:(concave or top) (convex or bottom) CJ1PAL.Kl AJ1PAL.Xl Identification: ADIT 35-93-7 DATA SAVED Why checked: kXh.riPLc Eng- data: D5112.ING 04/11/89 CHG:O CO
45、R-mR 3 SUMKARY AND AVERACES TDOTH PROFILE AND ALIGIJHENT . * CONCAVE OR TOP SIDE * PROFILE MODIFICATI ON PROFILE CROWN AYGWHENT TOO= HEEL MIDF TOE REEL MIDF TOE MOD CROWN 1 0.115 0.043 -0.085 0.071 0.057 0.051 0.252 0.135 2 0.131 0.070 -0.052 0.072 0.061 0.045 0.288 0.129 3 0.074 0.023 -0.065 0.070
46、0.052 0.045 0.263 0.126 AVG 0.107 0.045 -0.074 0.071 0.057 0.047 0.268 0.130 * CONVEX OR BTTOM SIDE * PROFILE MODIFICATION PROFI= CROWN WG“T TOOTH HEEL MIDF TOE HEEL MIDF TOE MOD CROWN 1 -0.038 0.042 0.155 0.036 0.047 0.075 -0.113 0.115 2 -0.069 0.022 0.157 0.024 0.055 0.087 -0.123 0.130 3 -0.080 0.
47、010 0.129 0.027 0.050 0.093 -0.100 0.123 AVG -0-062 0-025 0.147 0.029 0.051 0.078 -0.112 0.123 TIP, ROOT, AHD TOOTH THICIWESS ERROR . TOOTH ROOT NORWAL ERROR TIP NORMAL ERROR T“S TOOTH HEEL TOE HEEL TOE ERROR 1 -0.172 -0.107 -0.043 o. 002 -0.336 2 -0.317 3 -0.355 AVG -0.336 Figure 14. Numerical outp
48、ut - typiul routine production pinion Mamhmhg applies fraaabbased CMM methods as follows: 1. Roioint CMM inspeaion of mnchined (not ya cat mated) paru 2.Atmiysb of SPC dam to cW;atam consistency and id- 3.Routiw rmbits of heat tread parts with CMM inspeaion with with colhaion of fsrtim dara for SPC.
49、 mechining pioceos capability (Figure 15). nnther coliection of data for SPC. pinions. 4.Approval of inproceos (not heat tnated) master gears and 5. Jod mi with mdg Of =-heat tnated part SPC data to dmrmine draw compliance and establish capability of the complete proceas. 6. Development with mginaring of new parts with understanding 7.Und- of questions arising from contact pattern roil 8.Combined it das not make sets. Bevel sets and heat tnat these exist at the proceps control output where one cari daea, but not correct, outsf-specifica
