1、13FTM08 AGMA Technical Paper Application and Improvement of Face Load Factor Determination Based on AGMA 927 By Dr. U. Kissling, KISSsoft AG2 13FTM08 Application and Improvement of Face Load Factor Determination Based on AGMA 927 (Accurate and Fast Algorithm for Load Distribution Calculation, for Ge
2、ar Pair and Planetary Systems, Including Duty Cycle Analysis) Dr. Ulrich Kissling, KISSsoft AG 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 The face load fact
3、or KH, which in rating equations represents the load distribution over the common face width in meshing gears, is one of the most important items for a gear strength calculation. In the international standard for cylindrical gear rating, the ISO 6336-1 1, using method C, some formulas are proposed t
4、o get a value for this factor. But as the formulas are simplified, the result is often not very realistic. Also AGMA 2001 (or AGMA 2101) 2 proposes a formula for KH, different from ISO 6336, but again not always appropriate. Therefore a note in AGMA stipulates, that “it may be desirable to use an an
5、alytical approach to determine the load distribution factor”. In the last edition of ISO 6336 (2006), a new annex E was added: “Analytical determination of load distribution”. This annex is entirely based on AGMA 927-A01 3. It is a well-documented procedure to get a direct and precise number for the
6、 face load factor. Today an increasing number of gear designers are using tooth contact analysis (TCA) methods 4 to get precise information over the load distribution on the full gear flank. Contact analysis is very time consuming and does not permit to get a value for KH, as defined by the ISO or A
7、GMA standard. A contact analysis result combines different factors of ISO 6336 as KH, KH, Z, Z, ZB, ZDand buttressing effects, etc., thus to extract KHfrom a TCA is not possible. The use of the algorithm, as proposed by AGMA 927, is a good solution to get proper values for KH; it is simpler and ther
8、efore much quicker than a contact analysis calculation. The paper explains how this algorithm can be applied for classic gear pair rating procedure, for ratings with complex duty cycles and even for planetary systems with interdependent meshings between sun, all planets and ring. Copyright 2013 Amer
9、ican Gear Manufacturers Association 1001 N. Fairfax Street, Suite 500 Alexandria, Virginia 22314 September 2013 ISBN: 978-1-61481-065-0 3 13FTM08 Application and Improvement of Face Load Factor Determination Based on AGMA 927 (Accurate and Fast Algorithm for Load Distribution Calculation, for Gear P
10、air and Planetary Systems, Including Duty Cycle Analysis) Dr. Ulrich Kissling, KISSsoft AG Introduction The face load factor KH, which in rating equations represents the load distribution over the common face width in meshing gears, is one of the most important items for a gear strength calculation.
11、 In the international standard for cylindrical gear rating, the ISO 6336-1 1, using method C, some formulas are proposed to get a value for this factor. But as the formulas are simplified, the result is often not very realistic. Also AGMA 2001 (or AGMA 2101) 2 proposes a formula for KH, different fr
12、om ISO 6336, but again not always appropriate. Therefore a note in AGMA stipulates, that “it may be desirable to use an analytical approach to determine the load distribution factor”. In the last edition of ISO 6336 (2006), a new annex E was added: “Analytical determination of load distribution”. Th
13、is annex is entirely based on AGMA 927-A01 3. It is a well-documented procedure to get a direct and precise number for the face load factor. Today an increasing number of gear designers are using tooth contact analysis (TCA) methods 4 to get precise information over the load distribution on the full
14、 gear flank. Contact analysis is very time consuming and does not permit to get a value for KH, as defined by the ISO or AGMA standard. A contact analysis result combines different factors of ISO 6336 as KH, KH, Z, Z, ZB, ZDand buttressing effects, etc., thus to extract KHfrom a TCA is not possible.
15、 The use of the algorithm, as proposed by AGMA 927, is a good solution to get proper values for KH; it is simpler and therefore much quicker than a contact analysis calculation. The paper explains how this algorithm can be applied for classic gear pair rating procedure, for ratings with complex duty
16、 cycles and even for planetary systems with interdependent meshings between sun, all planets and ring. How it started: A problem during the drilling of the world longest tunnel in the Swiss Alps Since 1999 the worlds longest tunnel (57 km or 36 miles) is under construction in the Swiss Alps. In 2002
17、 a problem was found in one of the tunnel boring machines during an inspection. The main drive of the machine consists of a large ring gear, driven by 8-12 pinions. The outer ring of some of the bearings on the pinion shaft did rotate in the housing and therefore the bearing seat was worn. Undergrou
18、nd in the tunnel the bores were repaired as well as possible, the final check showed that the coaxiality had a deviation up to 0.2 mm (0.008 in). We were requested to propose the best possible flank line modification to compensate the coaxiality error. For logistical reasons all the pinions had to b
19、e replaced; all pinions should get the same modification. Therefore our job was to propose a modification, which could compensate best possible a coaxiality error between -0.2 and +0.2 mm and to prove, that with these pinions, the remaining 1500 operation hours until the tunnel break-through could b
20、e performed without failure. This engineering problem contained some new, interesting aspects. In the shaft calculation of KISSsoft 5 we had since long-time a feature to calculate the gap between the face of the gear and a stiff wall. This was a helpful feature to find easily the optimum flank line
21、modification. But the given problem needed some improvement of the software, because for the life time calculation according ISO 6336 the determination of the face load factor KHwas needed; and therefore the load distribution over the face width had to be calculated considering the stiffness of the
22、mating gear. Determination of the load distribution over the face width The cause for the uneven load distribution over the face width are flank line deviations in the contact plane of two gears. Deviations are caused mainly by elastic deformations of the shaft, stiffness and clearance of bearings a
23、nd housing, manufacturing tolerances and thermal deformations. 4 13FTM08 The determination of the load distribution is as documented in the gear theory performed in two steps. At first the gap in the tooth contact is calculated. Then, using the tooth mesh stiffness (c1), the line load distribution i
24、s determined. This approach is well documented in ISO 6336-1. The standard simplifies the real situation through assumption of a linear load distribution (Figure 1). Determination of the gap in the tooth contact In the MAAG book 6, the deduction of the gap through superposition of bending and torsio
25、n deformation is explained (Figure 2). As additional simplification it is assumed, that the mating gear is infinite stiff. Without flank line modification, in the example shown in Figure 2, the load would be bigger on the torque input side. If a modification as shown in Figure 2 is applied on the pi
26、nion flank line, then a uniform load distribution would result. This is true, if the meshing gear is effectively very stiff or if also on the mating gear a flank line modification is applied. In the formulas for KHof ISO 6336-1 (chapter 7) it is assumed, that the pinion shaft is much slender than th
27、e gear shaft, thus the deformation of the gear shaft is much less and can be neglected. For gear pairs with a reduction i 2, in many cases this is a realistic assumption. In Figure 3 the wording “deviations in the contact plane” is explained. The deformation in every section of the shaft must be det
28、ermined in the operating pitch point (W). A displacement of the point W due to bending or torsion parallel to the tooth flank will change a little bit the sliding velocity between the flanks, but otherwise has no effect at all. To get the necessary data for the determination of the gap, the componen
29、t of deformation in point W (x, z coordinate) normal to the flank, fbnand fbt, are requested. With this data the gap between the meshing flanks is directly located. Manufacturing errors, housing deformations and bearing stiffness result normally as linear deviation over the face width. These values
30、can be considered through radial displacement of a bearing versus another and through considering the bearing stiffness when calculating the shaft deflection. This procedure was implemented in our shaft calculation software 5 in 1997. Figure 4 displays the user interface. The software recognises aut
31、omatically all the gears on the shaft, and deduces the meshing point W coordinates and the normal N to the flank. Figure 1. Display of the gap and the corresponding load distribution following ISO 6336-1 1 5 13FTM08 Figure 2. Display of the determination of gap through the deformation components, an
32、d deduction of the corresponding flank line modification 6 Figure 3. Determination of the gap in the gear mesh (in a shaft section) 6 13FTM08 Figure 4. Display of the gap and proposition for an optimum flank line modification in KISSsoft (Above: Shaft editor and parameters for the determination of t
33、he gap in the contact plain. Below: Bending, torsion and total deformation over the face width) Load distribution in the tooth contact and face load factor KHThe determination of the load distribution (in N/mm or lbf/in) according ISO 6336 1 is simple, because the tooth meshing stiffness cis conside
34、red as constant over the face width. The calculation is performed as displayed in Figure 1. The face width is subdivided in some (11100) sections. To start the iteration, an initial distance between the teeth is assumed. Then with cthe partial load Ftiper section is calculated. The sum of all Ftihas
35、 to be identical to the transmitted tangential load Ft: !ttiiF F(1) The distance is therefore (by iteration) changed until equation 1 is fulfilled. The result is the line load distribution as in Figure 5. The face load factor KHis then the quotient of the maximum line load divided by the mean line l
36、oad as defined in ISO 6336 1: maxmmaximum load per unit face width average load per unit face widthwKw (2)To compensate uneven load distribution (as in Figure 5), adapted flank line modifications should be used. As shown in the theory (MAAG book, figure 1), the optimum flank line modification is ide
37、ntical to the inverted gap curve. An example is shown in Figure 4. 7 13FTM08 Figure 5. Load distribution and numbers for the maximum and mean line load and KHOptimization of the load distribution with adapted flank line modifications In most cases, the optimum flank line modification can be composed
38、 of a helix angle modification plus a crowning (in some cases, an end relief is added). If these two basic modification types are correctly combined, the load distribution can become nearly uniform. We added therefore the input possibility for crowning (Cb) and helix angle modification (fHb) data in
39、 the user interface. When the calculation is executed with modifications, the gap is determined (as before), but compensated with the profile modification. Then the load distribution including profile modification is calculated and displayed. The KHis again defined according equation 2. In the examp
40、le of Figure 5, a crowning Cb = 1.8 m (0.07 mil) and a helix angle modification fHb= -7.6 m (-0.30 m) would give an uniform load distribution (Figure 6). With such a modification, the face load factor KHis theoretically KH = 1.0. However, for a real gear, not only the deformation should be compensat
41、ed. Due to manufacturing errors, the gear will have a flank line error, which is in a predefined tolerance band depending on the tolerance class. Manufacturing errors are stochastic; they may reduce or increase the gap. Good design practice is to get the maximum load in the center of the face width;
42、 thus the only way to compensate manufacturing errors is to increase the crowning (or to apply additional end relief). The proposition in ISO 6336-1 1, annex B, is to increase the crowning by 0.751.0 * fH(helix slope deviation). If this technique is used, which is recommended, then the face load fac
43、tor will theoretically be higher than 1.0; but will provide a better practical design. Flank line modification for the tunnel boring machine The approach to determine the load distribution described in this chapter is based on a single shaft and normally applied to the pinion shaft; thus supposing t
44、hat the meshing gear shaft is infinitely stiff. The approach is therefore comparable but less general then the method described in AGMA 927 3, which considers the deflection of both shafts. Still, for the problem encountered in the tunnel boring machine, where the huge ring gear is much stiffer than
45、 the driving pinion gear, this simpler procedure can very well be used. To compensate best the deviation up to 0.2 mm (0.008 in) of the pinion shafts, different modification variants (modifications with crowning and/or end relief) were calculated, always assuming the maximum deviation. As best solut
46、ion a long end relief (over 30% of the face width on both sides) with Cb40 m (1.57 mil) was found 9. 8 13FTM08 Figure 6. Same shaft as in Figure 5, but (above) with optimum profile modification and (below) with practical modification, including additional crowning to compensate manufacturing toleran
47、ces In the worst case (Table 1), the pinion without any modification would last only 500 hours. With flank line modification the prospected life is increased by 1350%, attaining 6750 hours. The requested life time to finish the task was 3000 hours, therefore we could attain the goal. The pinions wer
48、e produced as recommended, and the tunnel is in the meantime successfully finished. Load distribution and face load factor determination based on AGMA 927 The basic idea in AGMA 927 is exactly the same as described in the previous chapter, but applied on the gear pair, thus much more general. As thi
49、s standard was added in the newest edition of ISO 6336-1:2006 1, annex E, now this process is available in an international standard. It is, as will be shown with some examples in this paper, a very useful calculation method. It is therefore astonishing, that since 2006 to our knowledge in Europe (and even in the USA) nobody implemented this algorithm in an available software tool. We decided in 2008 to implement the complete algorithm in our software. Table 1. Life time preview Modifica
