1、13FTM11 AGMA Technical Paper Striving for High Load Capacity and Low Noise Excitation in Gear Design By Dr. K. Stahl, Dr. M. Otto and M. Zimmer, Gear Research Centre (FZG)2 13FTM11 Striving for High Load Capacity and Low Noise Excitation in Gear Design Dr. K. Stahl, Dr. M. Otto and M. Zimmer, Gear R
2、esearch Centre (FZG) The statements and opinions 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 In the design process of gearboxes, common requirements are high load capacity and low noise
3、 excitation. Reaching both goals is laborious and normally requires a trade-off. Detailed analyses of contact conditions and deformations are necessary. These should take place in an early design stage to realize a mostly straightforward design approach and prevent late design changes. Focused on cy
4、lindrical gears, the paper covers an approach starting at the first draft of a gearbox. Defining the macrogeometry of the teeth regarding load capacity calculation according to standards leads to a reasonable gear design. On that basis, the micro geometry of the teeth is specified and load distribut
5、ion as well as noise excitation is calculated. The design parameters are interdependent so provisions have to be made to adjust each step on the remaining ones. Effects resulting from changing profile contact ratio under load and contact patterns not covering the whole flank have to be regarded. The
6、 beneficial effect of a modified microgeometry is dependent on the ability to precisely account for contact conditions and meshing clearances. To find an optimal solution for the competing goals of capacity and excitation, detailed calculation methods are required. To be able to apply latest researc
7、h results, these are implemented in highly specialized software. The task described above is handled by using the software that was developed at the Gear Research Center (FZG) with funding by the German Research Association for Gears and Transmissions (FVA). The underlying calculation methods and an
8、alyzed phenomena are covered. Copyright 2013 American Gear Manufacturers Association 1001 N. Fairfax Street, Suite 500 Alexandria, Virginia 22314 September 2013 ISBN: 978-1-61481-068-1 3 13FTM11 Striving for High Load Capacity and Low Noise Excitation in Gear Design Dr. K. Stahl, Dr. M. Otto and M.
9、Zimmer, Gear Research Centre (FZG) General method In the early stage of gearbox design, elements have to be dimensioned by simple methods that dont require many input data, because only few values are already determined and fixed. Using these rough design methods is efficient and provides a fast ear
10、ly design process. In this stage many dimensions of the gears and the toothing are determined that have significant influence on load capacity and noise excitation. Though a detailed analysis is not in focus yet, the final goal of optimization has to be kept in mind. The last step of optimization us
11、ually is an adequate design of flank modifications. The possibility to improve the gear mesh behavior by flank modification is closely dependent on the selected main geometry of the toothing. A different approach, e.g., starting with a detailed FE-Simulation of the whole gearbox, is not efficient. C
12、omplexity of the model and number of necessary parameters are so big so that it severely limits the flexibility that is needed in the early stage of the design process. A fast approach to flank microgeometry for low noise excitation is described by Houser and Harianto 9. A variation of microgeometri
13、es is analyzed by an analytical method and an interactive selection allows the identification of a desired result. The modifications are designed to also account for the influence of manufacturing deviations. For increasing normal module, that influence gets less significant, since other parameters
14、(clearances, deformations) amount to most of the resulting deviations in contact. A method with focus on load distribution is discussed in 7 by Thoma et al., the tooth contact analysis includes the influences of bearings and shafts. The load distribution resulting from the calculation is used to eva
15、luate load distribution factors according to ISO 6336-1. Pears et al. 15 describes an evaluation method for the contact stiffness in the mesh that is used for an analysis of transmission error. The influences of further elements like shafts and bearings are included. The process described in this pa
16、per starts with rough design methods and successively proceeds to more detailed methods. Necessary calculations are carried out by several specialized software programs. The programs from early design stages provide data for latter, more complex steps and programs. By this approach flexibility stays
17、 high and necessary design changes can be realized even late in the design process. The resulting data are passed on to the more complex analyses without obstacles between the different programs. Data management is controlled by a unified User Interface for all programs (FVA Workbench 4, see Figure
18、1). Figure 1. Interaction of programs in design process Key GEAS Gearbox Analysis System determines torque moments and rotational speeds STplus Calculates cylindrical gear geometry and load carrying capacity according to standards RIKOR Performs tooth contact analysis and determines load distributio
19、n 4 13FTM11 Succession of design steps: - Define gearbox structure; - Distribute the ratios of the different stages to reach the gearbox ratio (GAP 1); - Design main geometry of the gears (STplus 8) according to load capacity requirements ; - Dimension shafts and bearings, perform detailed calculati
20、on of shaft deformation and bearing lifetime (RIKOR/WELLAG 16,18), include housing elasticity and further influences ; - Determine load distribution by tooth contact analysis (RIKOR 16); - Design flank modifications to reach high load capacity, check for noise excitation; - Optimize flank modificati
21、ons for low noise excitation (DZP 5). Finally, the goals high load capacity and low noise excitations are reached by designing flank modifications. The goal high load capacity leads to a detailed definition of the flank modifications to ensure even load distribution, usually at high loads. Noise exc
22、itation behavior may require a different microgeometry, because the noise relevant operating range is related to lower torque moments. A trade-off between the two goals is required to determine the final flank modifications. Gear main geometry As an example, a gearbox structure with two helical gear
23、 stages and one planetary gear stage will be used (see Figure 2). The focus in this paper will be the high speed stage. For this given structure, the ratios of the stages have to be determined. The goal here is to reach a design that is compact and light. The ratio is an important factor for the mas
24、s of the gears. The torque moment transmitted in the mesh is the main influence for the dimension of the teeth. With given power, low speed shafts transmit a higher torque moment than high speed shafts. This leads to bigger teeth and wider gears on low speed shafts and ultimately a higher mass of th
25、e respective stages. Therefore a planetary stage with the advantage of internal power split is used for the low speed stage and helical stages are selected for the higher speeds. Determining the ratios of the stages is an optimizing task that is performed by the program GAP according to suggestions
26、by Winter 14 or Linke 13. Figure 2. Sketch of example gearbox 5 13FTM11 It is necessary to rate the load capacity of the gear meshes in the optimization process. This can be done by simple methods like K* value for flank load capacity and U value for tooth root capacity. *1t1F uKbd u (1) ttFUbm (2)
27、where K* is flank load capacity; Ftis load in transverse plane, N; b is face width, mm; d1is reference diameter, mm; u is gear ratio; U is tooth root capacity; mtis transverse plane module. Since the final geometry has to be rated according to ISO 6336 10, ISO 6336 is used in the basic step as well.
28、 For this purpose, many default values are assumed, e.g., for the K-factors of ISO 6336, tool data and further values. This has the advantage that the default values can be determined in more detail during the design process without leaving the framework of ISO 6336. With the ratios defined, the tor
29、que moment and speed of every stage is determined. Table 1 shows the main geometry of the high speed shaft. The detailed tooth geometry can be defined including manufacturing and heat treatment. A geometry calculation with respect to cutting and grinding tool geometry is necessary. The final geometr
30、y includes backlash and detailed tooth root contour. On that basis, a full load capacity calculation according to ISO 6336 is performed. This is easily accomplished with the STplus-suite 8 that includes the geometry calculation and the standard calculation as well. To cover pitting resistance and ri
31、sk of tooth root breakage, ISO 6336 is adequate. Further limiting factors can be taken into account e.g., by ISO TR 13989 (scuffing) 11, ISO TR 15144 (micropitting) 12 and further standards like API or ABS. Being available in direct connection to the geometry calculation makes the application of the
32、se additional methods easy and the process straightforward. Figure 3 shows the tooth form in the mesh and the range of standards that are available for rating the gears in the mesh. Shafts and bearings Dimensions of shafts and bearings are covered only by rough estimate at first. A detailed calculat
33、ion has to follow to ensure sufficient load capacity. To determine the influence on the contact conditions in the mesh, the deformation of the shaft-bearing system has to be calculated. Table 1. Main gear data High speed stage Pinion GearNumber of teeth, z 35 138Gear ratio, u 3.943Normal module, mn,
34、 mm 7.5 Center distance, a, mm 695.0 Normal pressure angle, n, degrees 20.0 Helix angle, , degrees 13.0 Profile shift coefficient, x 0.4020 0.2267 Tip diameter, da, mm 292.809 1082.518 Face width, b, mm 235.0 220.0 Transverse contact ratio, 1.833Overlap ratio, 2.005Total contact ratio, 3.8386 13FTM1
35、1 Figure 3. Geometry plot and range of available standard calculations in STplus The shaft deformation is well handled by using linear beam theory. The common approach neglects the shear forces on the deformation which is reasonable for slender shafts. Gearbox shafts have a length to diameter ratio
36、that may be below two and cannot be considered as slender. The equations are used including the effects of shear stress 16, 17. To cover roller bearings sufficiently, bearing clearance and the contact deformations between rollers and raceways have to be included (Eschmann 3). In roller bearings the
37、load is distributed between the rollers that transmit the contact loads. Dependent on the type of bearing, the analysis may have to cover up to five degrees of freedom (three linear axes, two rotational axes). A taper roller bearing, that is widely used for high load capacity, transmits not only rad
38、ial and axial forces but reacts with a bending moment on shaft inclinations. A result in this detail is computed by covering each contact between roller and raceway. The line loads in the contacts are determined in respect to the position of raceway, roller and profile of the contact partners. When
39、not all of these detailed information is available, reasonable assumptions are made (e.g., logarithmic profiles of rollers). With calculation methods for shaft and bearing (WELLAG/LAGER2 16) the elements can be considered in detail. On the basis of these results, contact pressures in the bearing can
40、 be calculated and an advanced bearing lifetime calculation according to DIN 26218 (DIN ISO 281 add. 4) 2 is performed. The shaft deformation and the bearing deformation are closely coupled and have to be determined in respect to each other (Figure 4). To account for the close coupling, equilibrium
41、between shaft and bearing forces has to be achieved. This is performed by an iteration, because the function of inner ring dislocation in respect to the outer ring of the bearing may be highly non-linear (however, more linear behavior is supposed for taper roller bearings under axial preload), see F
42、igure 5. A valid result has been found when forces and deflections of shaft and all bearings on the shaft are compatible. Important influences on the position of the shafts and on the contact conditions in the gear meshes may result from housing deformations. Since the housing is of complex geometry
43、, a FE approach is encouraged. The resulting deflections of the bearing positions in the housing are transferred to the gear calculation. 7 13FTM11 Figure 4. Effects of shaft deformations and of bearing clearance Figure 5. Example roller bearing, the left part shows the contact pressure for every ro
44、ller with inner raceway. The roller is divided in slices, width of slices decreases at the edges to ensure accurate results (RIKOR/LAGER2) 16 18 The results of these efforts not only yield the load capacity of shaft and bearings and the deformation, that has to be considered in the mesh, but also th
45、e robustness of the design. To have a good basis for microgeometry design, the contact condition should be stable over a wide load range. This is strongly influenced by the design of the shaft and bearing system, even the housing may have to be considered as mentioned above. A design value for the o
46、verlap ratio is only valid if the tooth flank is engaged over the whole width and the overlap is in working contact. For the example gearbox shown in Figure 2, the design becomes more robust if the shaft geometry and the bearing location are changed, see Figure 6. In the design with the longer shaft
47、, the intermediate stage and the final stage have swapped positions. The pinion is moved closer to the supporting bearing on the right. Shaft deformation then leads to an inclination of the gear and to deviations in the mesh. However, the bending deformation now compensates the torsional deformation
48、 of the pinion that is also acting in the mesh. Since both effects are proportional to the applied load, contact conditions in the mesh are much more stable with the changed design over a wide load range. 8 13FTM11 Figure 6. Alternative shaft designs and resulting load distribution at 100% load with
49、out flank modifications Tooth contact analysis Contact pattern, load and pressure distribution and further values can be derived from the tooth contact analysis. The displacement and the elasticity resulting from the shaft-bearing-system and the housing are transformed into the plane of action and included in a system of equations. Important input data are the elasticity matrices of the teeth and the flank microgeometry. These data allow an analysis of the load distribution along the contact lines. To evaluate the loads acting on
