For the transmission error on the Z2k axis of multiple pairs (k pairs) of fixed axis gear trains (Z1j, Z2j) (j=1~k) (see Figure 5), the above method can be used for analogy, and the speed ratio ujk on the output shaft Z2j to Z2k axis (reference shaft) of each level of transmission (speed ratio u12j) can be considered= Π U12j, (j+1 → k), so that the transmission error amplitude of each spur gear relative to the Z2k axis is 1/ujk, but the speed and frequency remain unchanged:
The above formula indicates that for a fixed shaft transmission with multiple pairs of spur gears, all shaft frequencies and tooth frequencies of each pair of spur gears and their higher-order frequencies will occur.