# Comparison and analysis of acceleration of involute spur gear drive system

Torsional angular acceleration of gears 1 and 4 can be obtained by substituting acceleration test results of each gear into formulas, and its root mean square value is calculated and compared with simulation results.Test results and simulation results of root mean square values of angular torsional acceleration of gears 1 and 4 under various operating conditions and errors between the two are presented.With the increase of rotational speed, the mean square root of torsional angular acceleration of gears 1 and 4 increases gradually, and the simulation results are basically in agreement with the test results.The maximum relative error between simulation results and test results under each operating condition is 23.51%.

When the input speed of two-stage fixed-shaft gear drive system is 850r/min, the frequency spectrum of test results and simulation results of angular acceleration of gear torsion is shown in the figure.It can be seen from the diagram that the angular torsional acceleration of the simulation results is mainly in the three axes rotation frequency in the low frequency region [0,500 Hz], and the amplitude of other frequency components is very small.

In contrast, the test results in the low frequency region not only include the frequency conversion of each shaft, but also include some frequency components which can not be analyzed to determine the cause.Simultaneously, simulation results and test results are slightly different in amplitude corresponding to each frequency.

In the high frequency region [500Hz, 1000Hz], the simulation results of angular torsional acceleration of gear 1 are mainly based on the rodent frequency and its 2nd frequency multiplication, at the same time, the engagement frequency of the second stage gear drive appears.In contrast, the test results show that not only the rodent frequency and its frequency multiplication exist in the high frequency region, but also the rodent frequency and its frequency multiplication of the second stage gear drive. At the same time, there are some combined frequencies near the meshing frequency and its frequency multiplication.

The simulation results and test results are slightly different in magnitude of each rodent frequency and its frequency multiplication.When the input speed is 850r/min, the spectrum of angular torsional acceleration of gear 4 is compared with that of simulation results as shown in the figure.It can be seen from the diagram that the test results and simulation results of angular torsional acceleration of gear 4 are mainly based on rotation frequency, rodent frequency and frequency multiplication of each shaft.Similarly, the test results contain richer frequency components.The simulation results and test results are slightly different in amplitudes corresponding to each rotation frequency, rodent frequency and its frequency multiplication. 