The dynamic factor used in gear design has been the
subject of many studies, most of them being analytical in
format. Buckingham’s first formulation [1] of a dynamic
factor was based on entering contact impacts due to
spacing errors and subsequent work by Tuplin [2], and
Houser and Seireg [3, 4] continued applying this
approach. However, in modern gear design, these
impacts are eliminated through the use of tip relief and
lead crowning so that the later formulations of Harianto
and Houser [5, 6] and Lin [7] have been based on errors
in the tooth form that result in a transmission error
excitation.
Three types of dynamic factors defined by Harianto
and Houser [5] are the “dynamic load factor” which is
the same as the factor used by AGMA [8], the “dynamic
root stress factor” and the “dynamic contact stress
factor”. In this paper, spacing errors and runout will be
introduced and further analyzed using these three
dynamic factor definitions. The “static value” depends on the type of analysis,
namely load, pinion root stress, gear root stress or contact
stress, and these two factors give the net static and
dynamic effect of the respective spacing errors and
runout.
The procedure for determining these factors is first
to use the Load Distribution Program (LDP) [9] to obtain
the static transmission error and mesh stiffness as
functions of gear rotation. These parameters are then
used as excitations to the Dynamic Transmission Error
Program (DYTEM) that uses a six degree-of-freedom non-linear time domain model to simulate gear dynamics
[10]. Dynamic loads are predicted from the DYTEM
program and then fed back to LDP to calculate the values
of both root and contact stresses at each contact position.
The procedures used in this paper for predicting dynamic
load, root stress and contact stress are similar to those
presented by Harianto and Houser [5, 6]. A description
of each of these programs is provided in the APPENDIX.