1、STI).AGMA bFTM9-ENGL Lb Is Ob87575 0004929 489 96FTM9 The Development of a Practical Thermal Rating Method for Enclosed Gear Drives by: Allyn E. Phillips, Rockwell Automation - Dodge I I TECHNICAL PAPER STD-AGHA SbFTMS-ENGL LSSb W Ob87575 OUUY73U IT0 9 The Development of a Practical Thermal Rating M
2、ethod for Enclosed Gear Drives Aiiyn E. Phillips, Rockwell Automation - Dodge fThe statements and opinions oonaincd herein are those of the author and should not be construed as an official action or opinion of the American Gear Manufacturers Association. Abstract This thed rating method balances th
3、e sum of the load-independent iosses and the load-dependent losses against the heat dissipation capability of the gear case. Empirical fctors are determined which calirate the calculations against the test muits for assembled gear reducers. The resuits of this calculation method are compared to the
4、test dts from 251 gear reducer tests. in addition, since loses are caiculatd, this method can be used to caidate the efficiency of the gear drive for the operating conditions. copyright o 19% American Gear Manufacturers Association 1500 King Street, Suite 201 Alexandria, Vigjnia, 22314 October, 1996
5、 ISBN: 1-55589-676-6 STD-AGMA SbFTMS-ENGL LS7b b87575 0004933 037 The Development of a Practical Thermal Rating Method for Enclosed Gear Drives Ailyn E. Phillips Senior Development Engineer Rockwell Automation - Dodge Greenville, SC 1. NOMENCLATURE lhe symbols used in this paper are defined in table
6、 1. These symbols may be unique to this paper and are therefore not necessarily the same as the symbols and definitions used in other AGMA papers or standard practices. 2. INTRODUCTION The present AGMA method for calculating the thermal rating of enclosed gear drives is presented in AGMA 601-E88, Pr
7、actice for Endosed Speed Reducers or Increasers Using Spur, Helical, Hemngbone and Spiral Bevel Gears l. This present practice is an empirical method developed more than 30 years ago from tests run on offset parallel shaft reducers using through hardened gear sets. Modem gear reducers are usually de
8、signed with carburized and hardened gear sets and with power densities far exceeding those of 30 years ago. Consequently, the present thermal rating practices can no longer be used for modem gear reducers. Therefore, it is necessary to develop a method to calculate the thermal rating of a gear reduc
9、er which recognizes the tooth pressures and power densities of todays designs. The thermal rating method presented in this paper is an empirical method that was developed from 251 tests run on a family of gear reducers using carburized gear sets. It involves calibrating the equations which represent
10、 the individual items contributing to heat generation to match the test recuits. It is not intended to be used to calculate each component of the power loss independently. This empirical procedure should be used in its entirety. Do not use other methods for calculating the power loss of individual c
11、omponents without adjusting the calibrating constants and exponents. 3. PRODUCT TESTED The reducers tested were concentric shaft reducers. Gears and pinions were carburized and hardened with the tooth flanks either honed or profile ground. All shafts were supported on tapered roller bearings. A phot
12、ograph of one of the reducers is shown in figure 1 and a cr0s.s section showing the typical design and construction is shown in figure 2. All reducers were two stage reducers with total ratos ranging from 5:l to 25 :I. The reducers ranged in size from 10x1012” and 125 Ib. to 36x32”x33 and 4000 Ib. T
13、est bads rangedfrom no-load to 200 hp and input speeds were 1750, 1450, 1170 and 870 rpm. The oil used in all of the tests was Exxon Teresstic 220. A complete description of the range of test parameters can be found in table 2. A total of 251 tests were run under the following load conditions: 84 at
14、 no-load, 83 at mid load and 84 at maximum load. No-load was the load required to rotate the test equipment without applying any additional load through the dynamometer. Maximum load was defined as the lesser of the following: - the reducer mechanical capacity. - - test stand horsepower capability.
15、Mid load was defined as a load approximately half way between the no-load and the maximum load test points. Since the mload tests did in fact have some load applied to the reducer, the no-load temperatures were determined by plotting the no-load. mid-load and maximum load temperatures versus their r
16、espective loads and extending the plot back to zero transmitted load. The data from all tests was included. No test data was thrown out. The purpose for performing these tests was to determine the thermal horsepower ratings to use in the catalog for the Dodge MAXUM concentric shaft reducer. a sump t
17、emperature of approximately 210 OF. 1 sY!m ?3 a b D Cl e F 9 H Y Ht h K k L M Mo Ml mg NG NP n Table 1 Symbols and Definitions J Unh Area of Gear Case ft2 Arrangement Constant for Gearing - Load Modiing Exponent - Diameter Modifying Exponent - Mesh Coefficient of Friction Constant OD of Element for
18、Gearing Windage and Churning in. Bearing Diameter Over Rolling Elements in. Oil Seal Diameter in. Mean Diameter of the Bearing mm Viscosity Modiing Exponent - Total Face Width of Gear or Pinion in. Face Width of Gear in Contact with its Mate in. Gear Dip Factor - Mesh Coefficient of Friction - Beari
19、ng Dip Factor - Coefficient of Friction for Bearings Load Intensity Modifying Exponent - Specific Sliding Velocity at End of Recess Action Pitch tine Velocity Modifying Exponent Load Intensity Psi Heat Transfer Coefficient hpM2 OF Length of Element for Gearing Windage and Churning in. Mesh Mechanica
20、l Advantage - Load-Independent Toque Moment for Bearings Ibh. Load-Dependent Toque Moment for Bearings Ib.in. Gear Ratio - Number of Teeth on Gear Number of Teeth on Pinion Ratation Speed for Element being Calculated Pinion Rotating Speed rpm Bearing Frictional Power Loss hP Bearing Windage and Chur
21、ning Power Loss hP Power Dissipated by Gear Case hP Power Generated by Total of all Losses hP Gear Windage and Chuming Power Loss hP Load-Dependent Power Loss hP Load-Independent Power Loss hP Gear Mesh Frictional Power Loss hP OU Seal Power Loss hP Transmitted Power hP Transverse Diametral Pitch in
22、- Laad Determining Frictional N Torque Moment for Bearings Roughness Factor for Gear Teeth Outside Radius of Gear in. Operang Pitch Radius of Gear in. Outside Radius d Pinion in. m. - - Depth that Bearing Rolling Element Dips in Oil Specific Sliding Velocity at Start of Approach Action in. - - - I -
23、 wm - Operating Ptch Radius of Pinion Temperature Daferential OF Pitch Line Velocity fPm Operating Pressure Angle deg- Eficiency Percent Generated Hel“ Angle deg. Operating Helix Angle deg. Applied Toque to Pinion Ib.in. Oil Seal Toque Ibh. Kinematic Viscosity of the oil ai Operating Temperature cSt
24、 Concentric Speed Reducer Figure 1 Typical Reducer Cross Sectinn Figure 2 Table 2 Range of Parameters Teed 2 . II INCRE4SER REPUER I- - TEST ARRANCEMENT FIGURE 3 4. TEST PROCEDURES The test Set-up was a load absorption test and is shown in figure 3. Two similar test Set-ups were used. A 60 horsepowe
25、r motor driving a 100 horsepower dynamometer was used for the six smallest reducers in the product line and a 200 horsepower motor driving a 400 horsepower dynamometer was used to test the six largest sizes. Two gear drives were operated at one time. Both gear drives had identical ratios and were co
26、nnected to each other at the slow speed shafts through a toque sensor. One gear drive operated as a reducer and the other gear drive operated as a speed increaser. The high speed shaft of the reducer was coupled to a second torque sensor which in turn was coupled to a jack shaR The jack shaft was dr
27、iven by an electric motor with the input speed to the reducer varied by changing the V-belt ratio beween the motor and the jack shaft. The high speed shaft of the increaser was connected to the dynamometer by another V-belt set. Themiocouples were installed in the oil sump both at the high speed gea
28、r stage and at the low speed gear stage. These thermocouples were located to avoid contact with the gear case and also to avoid the hot oil stream out of the mesh. In addition, thermocouples were installed at Variaus places on the exterior of the gear case. Although both the reducer and the increase
29、r were monitored and recorded, only the data from the reducer has been used to develop this thermal rating practice since the oil level in the increaser was not adjusted for differing operating conditions and the increaser was frequently force cooled by the use of portable fans. The test procedure c
30、alled for each reducer tested to be operated under light bad for a period of 24 hours in each direction of rotation for break-in. The reducer was then operated in both the clockwise and counterclockwise mtatns under a nommai load to determine the rotation that ran the hottest. The hottest running ro
31、tation was then tested to determine the thennal ratings. The reducer was considered to be in thermal equilibrium when the temperature change was less than one degree Fahrenheit per hour. 5. ELEMENTS CONTRIBUTING TO A THERMAL RATING The thermal rating of a gear drive is defined as the power that can
32、be transmitted through that gear drive which will cause the oil temperature in the sump to rise a predetemined amount above ambient for the particular operating conditions. In other words, the reducer is in thermal equilibrium where the heat generated by the sum of the various losses is equal to the
33、 heat dissipated by the gear case. See equation (1). The thermal rating of a gear drive is the transmitted load that causes equation (1) to be satisfied. P, =PD Heat generated in a gear reducer is the total of the bad-independent and the Wependent losses. See equation (2). P, =Pu +Pu, The bad-indepe
34、ndent losses are those losses that do not vary with the magnihide of the applied load. They consist of the sum of the oil seal losses, the total bearing windage and churning losses, and the total gear windage and churning losses. See equation (3). (3) The loaddependent losses are those losses that v
35、ary depending upon the magnitude of the applied load. They consist of the sum of the bearing frictional losses and the gear mesh frictional lasses. See equation (4). 6. ANALMIC PROCEDURE USED (4) The procedure used to develop this thermal rating practice consisted of two basic steps each with severa
36、l substeps. First, the loadindependent loss equations were determined. It was necessary to determine the load-independent loss equations before working on the load-dependent equations as the load-independent losses are a part of the total losses for the loaded test runs. 3 STD*AGMA SbFTMS-ENGL 1796
37、Ob87575 0004934 84b D Oil seal Wes were calculated in accordance with the procedures outlined in AGMA 6023-A88, Design Manual for Endosed Epicydic Gear Drives 121. Bearing windage and churning losses were determined using the methods outlined in SKFs catalog 4000 US, 1991 3 with a procedure devebped
38、 to evaluate the factor f,. Several procedures were tried for calculating the gear windage and churning losses. A modifcation to the equatiwrs givw in section 12.5.2 of Dudleys Gear Handbook, second edition, 141 best represented the test condiiions. These loadindependent losses were combined and com
39、pared to the mload test results to determine the validsr of the load-independent equations. Second, the loaddependent loss equations were determined. Bearing bad losses were determined by the methods outlined in SKF 131. Various values for the bearing coefficient of fridion were evaluated. Gear set
40、bad loss equations were developed based on equations found in AGMA 602SA88 p and chapter 12 of Dudley 141. These baddependent lasses were combined along with the bad- independent losses to evaluate their accuracy by comparing the prediied results to the test results. Mi load test resuits were evalua
41、ted separately from the maximum bad test results to eliminate any skew when comparing the calculated results to the test results. In th instance, skew is defined as the situation where the mid bad calculated results are less than the test results and the maximum bad calculated results are greater th
42、an the test results, or vice versa. Addiinal infomiation on bearing losses can be found in Ball and Roller Bearings, Theory, Design and Application, by Eschmann Hasbargen and Weigand, Second Edition 151 and Roller Bearing Analysis, by Tedric A. Hams, Third Edition q. 7. HEAT DISSIPATION The ability
43、of a gear case to dissipate heat depends upon the surface ama, the heat transfer coefficient and the temperature differential. See equation (5). PD = A,* k* AT (5) Gear case surface areas were calaiiated from the projected area of the top. sides and the ends. The area of the base was not considered
44、as it was not exposed to the air. Bolt heads or other minor asperities were not considered. The surface area of the shai extensions was not used although the area of the shaft end was included in uie projected area of the ends of the reducer. A value of 0.0012 HPm OF was used for the heat transfer c
45、oeffiasnt when evaluating the formulas in this dowment against the test results. This value is representative of the condi which existed m the bb where these reducers were tested. The lab contrdled the ambient air temperature between 70 and 76 OF. Air movement. drafts or breezes, were minimal. The h
46、eat transfer coesficient indudes the combgied effects of convection, conduction and radiation. Table 3 piwides heat transfer coefficient values that may be used for mer conditions. Temperature differential is defined as the steady state oil sump temperature minus the ambient temperature. 8. OIL SEAL
47、 LOSSES All the reducers tested had a single nitrile (Buna N) spring loaded double lip oil seal at each shai extension. AGMA 602SA88 Z provides a graph to determine the toque on an oil seal. This graph .- Candiion Air Vebaty. FPM HPfi OF 4275 0.0007 - 0.0010 0.0011 - 0.0014 275 0.0012 - 0.0015 OUtdO
48、OrS 725 0.0014 - 0.0017 Small Confined Space , Lame Indoor Space Large Indoor Space e275 can be represented by equation (6) for Buna N oil seals and by equation (7) for Vion oil seals. The power loss for each oil seal can then be calculated by equation (8). T,*n 63025 ps =- 9. BEARING WINDAGE and CH
49、URNING LOSSES Bearing windage and churning bsses are based on the methods described in SKF 3. The load-independent frictional moment, Mo. is given by equations (9) and (IO). Please note that the bearing mean diameter, 0.5(OD+ID, is expressed in millimeters. The kinematic viscosity, v, is a function of sump temperature. The factor 113 in the equations converts the toque from Nmm to Ib.in. If: Pcn2000 16 * d,“ MI = 113 Ml*n 63025 P, =- D DEPENDENT LOSSES Mesh losses are a function of the mechanics of tooth action and the caefficient of friction.
