In a common simple gear dynamic model, to represent a mesh there will be stiffness (k(t)), damping (c(t)), and meshing error (e(t)). What causes e(t)? If it is defects in the gears, why is it not captured in k(t)?
e(t) is actually profile error which is also known as geometric transmission error (GTE). e(t) is how the shape of the gear changed compared with the identical gear (involute gear, for example). A defect, tooth spall/wear can change tooth profile and then introduce e(t) into dynamics. k(t) can be affected by the shape of the gear as well and it is related to the static transmission error (STE). If anther kind of defect, tooth crack occurred, it can change the stiffness rather than the geometric. So for that case, k(t) will be changed rather than e(t). When a gear is loaded, the gear in mesh is not held in its theoretical position, which is called transmission error (TE), which is the summation of STE and GTE.
Hope it helps.
I also add some description to the answer of dear Dikang Peng :
When the gear pair are rotated by a low load, the elastic deflection in gears materials are actually zero (it is related to k(t) ), but there is also an error in output shaft angular position related to its theoretical position. It is duo to errors in teeth profiles and their mating caused by gear production, assembly or some defects happens during long life operation such as wear (as mentioned). This error is known as geometric transmission error and added in dynamic equation by symbol e(t).
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