1、2000FTM4 I Parametric Influences in the IS0 Project Concerning Worm Gear Rating by: M. Octrue, Centre Technique des Industries Mecaniques TECHNICAL PAPER COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling Servicesr O Parametric Influences in the IS0 Project Conce
2、rning Worm Gear Rating Michel Octrue, Centre Technique des Industries Mecaniques The statements and opinions contained herein are those of the author and should not be construed asan official action or opinion of the American Gear Manufacturers Association. Abstract The author analyses the influence
3、 of different parameters taking into account in the CD IS0 14521 for worm gear ratting for the different criteria such as: efficiency, wear load capacity, surface durability (Pitting) deflection tooth root strength The influencing parameters are divided in different categories, like intrinsic parame
4、ters to the worm gear like geometry or materials, environmental parameters like lubricants and temperature, external parameters like loading conditions, and driving and driven machines. Some criteria are compared to analytical methods and experimental results. Copyright O 2000 American Gear Manufact
5、urers Association 1500 King Street, Suite 201 Alexandria, Virginia, 22314 October, 2000 ISBN: 1-55589-765-7 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling Servicest PARAMETRIC INFLUENCES IN THE IS0 PROJECT CONCERNING WORM GEAR RATING By Dr Michel OCTRUE - CET
6、IM - France 1-Introduction In the framework of IS0 Technical committee TC60, a new work item concerning the calculation of load capacity of worm gear is in Focess since 4 years. The future reference of the standard IS0 14521: load capacity calculation of worm gear. This standard is based on DIN 3996
7、 which has been adopted in Germany in September 1998. The following conditions that can limit the rated load capacity : o wear: such damage usually appears on the tooth flanks of bronze wormwheels pitting : this form of damage may appear on the flanks of wormwheel teeth. Its development is strongly
8、influenced by the load transmitted and the loadsharing conditions. tooth breakage : shear failure of wormwheel teeth or worm threads can occur when teeth become thin due to wear or overload. Worm thread and worm shaft breakage: shaft breakage can occur as a result of bending fatigue or overload. wor
9、m shaft deflection : excessive deformation under load modifying contact pattern between worm and worm wheel. o scuffing : this form of damage often appears suddenly. It is strongly influenced by transmitted load, sliding velocities and the conditions of lubrication. working temperature : when excess
10、ively high working temperature leads to accelerated degradation of the worm gear lubricant. Among this, IS0 14521 defines criteria for: wear, pitting, tooth breakage of worm wheel, worm shaf deflection. Table 1 indicates the rdationship between different forms of capacity limits in combination with
11、speed and torque. In order to illustrate the behaviour of IS0 14521, this paper : presents result calculations based on 3 worm gears sets which are those used in our laboratory for testing, o presents synthesis of influencing parameters for each criteria calculation, with comments, and an identifica
12、tion of the best choice for some parameters. 2Principles of calculations in IS0 14521 As it has been introduced, the calculation of load capacity is based on 4 criteria, which are linked together as follows : criteria for pitting and criteria for worm shaft deflection are independent of others, crit
13、eria for wear and criteria for tooth breakage of worm wheel are dependent because the reduction of worm wheel tooth thickness by wear is taken into account for the calculation of shear stress at tooth root. criteria for wear is function of oil film thickness, which depends on oil film temperature, s
14、o the calculation of different type of power losses in order to determine the wheel bulk temperature, is the first step for wear calculation. Note: This concept of wheel bulk temperature calculation is very important in IS0 14521. It must be considered by new users of this standard. At design stage
15、it is not always easy to evaluate all data for such calculation. 3-Definition of gear data Since more than IO years CETIM undertook endurance tests for worm gears in order to check their behaviour according to wear. Three bench tests have been setup, with a centre distance of 125 mm, for 3 different
16、 gear ratios: 1/40, 3131, 5/24 (see Table 2 and Table 3). 1 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling ServicesCSensitivity of IS0 14521 to geometry In order to isolate the influence of geometry on the zone of contact and the lines of contact, it has defi
17、ned nondimensional parameters (see Table 4): p, for the mean Hertzian stress, h, for the mean lubricant film thickness s, for the mean slip path. IA Worm surface B I C Table 2-Geometrical data of worm gears Gear ratio u=zl/z2 Axial module mm Normal pressure angle I Worm PROFILE Lead angle I 1/40 3/3
18、1 5/24 4.95 6.45 8.36 5.4375 21.1369 40.2592 21.81 20.65 25 A A A Worm material Worm wheel Lubricant Worm wheel face width mm I 45 I 45 I 45 External diameter of worm wheel mm I 220 I 220 I 220 Case hardened steel Bronze with 12 % of tin an x% of Nickel. Synthetic Oil : Polyglycol SHELL TIVELA A - 1
19、22 Cst at 40C p, parameter for the mean Hertzian stress si parameter for the mean slip path h, parameter for the mean lubricant film thickness Geometry p, (Type of profile, q, z, x, hjrnfl, u) s (Type of profile, y, u) h (Type of profile, q,. z, x, WQ, 9 u) 2 COPYRIGHT American Gear Manufacturers As
20、sociation, Inc.Licensed by Information Handling Services. These parameters are defined by formulae (method C) in the standard but they can be determined numerically with a detailed study in each point of the lines of contact (method B) of Hertzian stress, lubricant film thickness, slip path. For the
21、 type of profile IS0 14521 considers C profile (known commercially CAVEX) and other profiles A, I, N, K, C which are considered in the same category. Note: The pressure angle and the external diameter of worm wheel are not taken into account by IS0 14521. In order to show the sensitivity it is possi
22、ble to establish that: the allowable torque for pitting resistance is proportional to p,*, the oil film thickness is proportional to h*, the life for a given expected wear (increase of backlash) is proportional to *.(p*).(h*)- the allowable torque for a given expected wear (increase of backlash) is
23、proportional to *.(p*).(h*).* + 0.5) O ( with 0.7912 = 2.24*0.13 The simulation on the 3 gear sets gives the results presented in Table 5. Note: IS0 14521 gives a strong advantage for C Profile with +30% on allowable torque for pitting and wear criteria. This tendency has been checked on different g
24、eometry. So, with IS0 14521, it will be strongly influenced to use C Profile for worm gears Sensitivity : For normal used, it is preferable to use Cu Sn 12 Ni bronze ( sHhmT = 520 MPa) than Cu Sn 12 (sIMT = 425 MPa). For low sliding velocities ( 1,l is recommended. No considerations of thermal excha
25、nge of the housing are considered. This calculation can be used in reverse to determine the flow and the difference of oil temperature in the cooling system. 8.2-Bulk temperature of worm wheel tM; For splash lubrication (Table 9), it is determined by adding to the oil sump temperature, the elevation
26、 of oil temperature A due to power loss in the mesh P, distributed on the surface of the reference cylinder of worm wheel. P, is dependent of the type of ax ia1 adjustment of wormwheel bearing: defined axial clearance or locatechon located bearing . Table 9- Bulk temperature cal 5 COPYRIGHT American
27、 Gear Manufacturers Association, Inc.Licensed by Information Handling Services. Oil film thickness h Equivalent E-module Pressure viscosity exponent Dynamic viscosity Table IO- Bulk temperature Sub Geometry Oil Working Cooling Factor Conditions Conditions k(a, h*) h-(q, Tj Eres! Ca Cdoii type) tloM
28、T)OM (OM) The Formulae are: 0, =o, +A0 ” and 8.4-Wear load capacity The first step is to determine the minimum oil film thickness h, which takes into account bulk Sensitivity : If worm wheel is immersed AO will temperature of worm wheel. hmi, , will be used to calculate the base wear intensity which
29、 depends on worm wheel materials For spray lubrication (Table IO), it is same and lubricant type. process, with another method to distribute power Formulation in IS0 14521 (Table 12) is based on loss in the mesh P, based on experimental results. experimental tests, of 300 hours, with measurement of
30、wear each 24 hours. These are The Formula is: rather short tests. be 20% lower. The Formulae are: &fl = Jw . S, 8.30i1 film thickness (Table II). and &limn =As -COSY, The Formula is: The criteria is : Cw=&imn/aJvn with %min c:“ 770, 0.7 . n, 0.7 .a 1.39 1 .I = 21.h*- TY3 Table 12- Wear load capacity
31、 calculation I Sub I Geometry I Oil Working I Material i 6 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling ServicesThe predicted wear takes into account the wear path of teeth in contact during the life of gear set. This value is than compared the allowable we
32、ar, which is converted to an equivalent reduction of tooth thickness of the wheel. This last value is fixed by the designer (as an increased of backslash). %Tooth root strength The calculation method is based on a nominal shear stress assumption at the tooth root of worm wheel Fable 13). The Formula
33、e are: - and FG =FlirnT “NL Note: This calculation is very basic and considers a uniform trapezoidal section for worm wheel teeth. The influence of radius in the fillet of teeth is not explicit The enveloping effect of worm wheel teeth is not considered. Sensitivity : A Cu AI 10 Ni bronze has a shea
34、r stress endurance limit 28% better than a Cu Sn 12 Ni A Cu Sn 12 bronze has a shear stress endurance limit 8% greater than a Cu Sn 12 Ni For Cu Sn bronze the life expectancy factor Y, is given in function of the permissible accuracy grade deterioration of worm wheel based on pitch error. 1 O-Conclu
35、sions This new standard for load capacity of worm gear introduces new concept of calculation based on more scientific approach of gear mesh study, but it is not enough precise on several points: 0 the excessive optimistic values given on for C profile, the lack of differentiation between A, I, N & K
36、 profiles, the incomplete field of application for materials (except for Cu Sn bronzes but their structure or elaboration mode is not enough considered). the incomplete field of application for lubricants (ex: PA0 are not considered), some implicit recommendation given by this standard must be check
37、ed, concerning the interpretation of the mixed phenomena wear and pitting, generally found in worm gearing. 0 This standard should stay experimental for the moment and an additional work is necessary to compare it with industrial experience. Bibliography: /I/ AGMA Standard 6022C93 Design manual for
38、cylindrical worm gearing 12i AGMA Standard 6034-892 Practice for enclosed cylindrical worm gear - Speed reducers and Gearmotorc BS 721 - 1963/Confirmed 1984 Specification for worm gearing DIN 3996 -1996 Calculation of load capacity of cylindrical worm gear pairs with shaft angle Z=90 131 141 7 COPYR
39、IGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling Services151 M. OCTRUE A new method of designing J71 M. OCTRUE Relations beiween wear and 161 M. OCTRUE - M. GUINGAND Experimental AGMA FTM 1997 worm gears - AGMA FTM 1988 characterization of surface durability of 181
40、M. OCTRUE - Evolution of methods for load materials for worm gears - AGMA FTM 1992 capacity calculation for worm gears : Pitting and WEAR qTh CMETP PARIS 1999 pitting phenomena in worm gears bni Effective wheel facewidth coil specific heat capacity of the oil (for temeerature calculation with spray
41、lubrication) ANNEXE A: Notations mm Ws/( kg“K) I Symbols Description I Units I &I worm reference diameter d, worm wheel reference diameter h* Il Ill, Il2 parameter for min. mean lubricant lm thickness spacing of the worm chaf bearings bearing spacing of the worm shaft mx 1 axial module Am material l
42、oss n1 rotational speed of the worm shaf rotational speed of the wheel n, I a centre distance I mm I mm mm mm mm mg min-1 min1 Is facewidth of the wheel as specified in DIN 3975 I mm I q1 diameter factor SR2 SK tooth rim thickness mean tooth root thickness of the wheel teeth in the spur section mm m
43、m I G proximity value for the viscosity pressure exponent a A5 tooth thickness loss U aear ratio mg I Pm parameter for the mean hertzian stress 1-1 x2 21 z2 A, AR Er& equivalent E-module worm wheel profile shift coefficient number of threads in worm number of teeth in worm wheel free surface of the
44、gear housing total flank surface of the worm wheel rn2 mm2 Nltllm2 S ST* parameter for the mean clip path Darameter for the mean sliD Dath of the standard reference aear 8 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling ServicesF, Fnle Fhl, FblQ L life expecta
45、ncy NL P, axial force to the worm, shaft axial force to the worm wheel circumferencial or tangential force to the worm shaft circumferencial or tangential force to the worm wheel number of ctiesc cycles of the worm wheel input Dower to the worm shaft L N N N N h W - PZ Qd spray quantity R arithmetic
46、 mean rouahness output power from the worm wheel shaft - W m3/s um Ti T2 Z Velocity factor I pitting a pressure viscosity factor input torque to the worm shaft output torque from the worm wheel c6 pressure angle W/( m2K) heat transition coefficient for immersed wheel teeth Nm Nm m2/N reference lead
47、angle of worm I -o -1 I Ynll VZ gear efficiency vm dynamic viscosity of lubricant at ambient pressure and bulk temperature I v- total efficiency of worm drive where the worm drives the wheel 1-1 Nsld O e, oil sump temperature Unr base coefficient of friction “C eo ambient temperature e-:, SDrav teme
48、rature VY pa15 kinematic viscosity at bulk temperature lubricant density at 15 “C “C I “C I mm2/s kddm 3 1% wheel bulk temperature I “C I km V1 ve mean tooth coefficient of friction cross sectional contraction factor of the worm shaft kinematic viscosity at oil temperature kinematic viscosity at 40 “C I I p- material density of the wheel I malmm3 I I A%, temperature difference 9 COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling Services0 O c COPYRIGHT American Gear Manufacturers Association, Inc.Licensed by Information Handling Services
