INSTRUMENTATION • ELECTRONICS
GEARING UP S
Considering gear body stiffness for face load factor
wiss-based company Mesys develops software for technical calculations in mechanical engineering, with
a particular focus on the sizing of machine elements like gears, shafts, bolts and rolling bearings. Here, director Markus Raabe discusses gear body stiffness for face load factor. In gear ratings according to ISO 6336, the face load factor accounts for uneven load distribution along the face width of the gear. Mesh misalignments because of manufacturing deviations, bearing clearances and stiffnesses and shaft bending are considered in this face load factor.
ASSESSING THE CHALLENGES One difficulty lies in the consideration of the stiffening of the shaft by the gear body. ISO 6336-1 provides three values to be used for the calculation of shaft deflections under clause 7.4.3.4. First, it says to use a midway diameter between hub diameter and bore for shrink-fitted gears or other parts, and in this case the root diameter of the gear and its bore diameter might be used. This is reasonable to be used for the calculation of the shaft deflection, because the shaft can deform inside of the gear body and therefore using the outside diameter of the gear might be too stiff. Then, the standard says in the same clause to use the mean value of tip and root diameters for bending deflections of the gears and the root diameter plus 0.4 times module for torsional deformations. It is reasonable to use a mid-diameter of the tooth in the tooth area as the deformations of the teeth determines the mesh misalignment. On the other hand, the stiffening of the shaft will be too large. According to the standard, the first
midway diameter is generally used for gears or other parts shrink-fitted to the shaft, the other two diameters shall be used for the deformation in
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Figure 1: The line load distribution for the four cases
the tooth area. Some also use the first diameter for the tooth area, which will be too soft.
A COMBINED APPROACH The MESYS shaft calculation uses a 3D-FEA model for the gear body to combine these two approaches. Results of an example calculation for a gear pair with rigid supports and no manufacturing deviations are shown for four cases. The first case is using the root diameter plus 0.4 times module for stiffening of the shaft (a), the second case is using a midway diameter between root diameter and shaft diameter (b), the third example is using an 3D-FEA model reduced to central nodes on the outer diameter (c) and the fourth model is using a 3D-FEA model with local load introduction (d). Figure 1 shows the line load distribution for the four cases and table 1 some numeric results. Figure 2 shows the gear pair
Figure 2: The gear pair used for the calculation
used for the calculation. Cases ‘a’/’c’/’d’ show almost the
same line load for the gears while case ‘b’ leads to a larger line load. For case ‘a’ the shaft deflection is too small as expected and cases ‘b’/’c’/’d’ show almost the same shaft deflection. Case ‘b’ will suggest a flank line correction in a different direction than the other cases. Using a 3D-FEA model makes it
possible to combine the stiffness of the gear body for the flank line deformations with the lower stiffening effect for the shaft deflections. Moreover, different gear body geometries can be used easily as the 3D-FEA model allows variations of the gear body geometry, which is not possible with the beam model of the shaft.
Markus Raabe is the director of Mesys Ag.
www.mesys.ag
Case Shaft deflection Line load Face load factor a b c
d
13.6 µm 16.5 µm 17.0 µm 17.4 µm
408 N/mm 1.15 432 N/mm 1.22 411 N/mm 1.16 404 N/mm 1.14
Table 1: Results for the four calculation models
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