The main excitation in a spur gear pair system comes from gear tooth meshing. When the meshing frequency of the spur gear pair approaches the natural frequency of the system, resonance will occur. Combining the formula and the above stiffness analysis, it can be seen that the natural frequency of the spur gear pair system is closely related to the meshing stiffness, and the meshing stiffness of the spur gear pair changes periodically over time, so its natural frequency must also fluctuate within a certain range. When the meshing frequency of a spur gear pair is within the range of natural frequency fluctuations, the corresponding spur gear speed is the resonant speed. Combining the formula, the resonance speed N1 can be expressed as:
The rotational inertia I1 of the driving wheel is 0.905103 and the rotational inertia I2 of the driven wheel is 0.488188 extracted from the ANSA finite element preprocessing software. According to the figure, when the center distance deviation is 0.06 mm, the meshing stiffness of the spur gear pair is between 19075789 N/m and 11747290 N/m. By introducing the meshing stiffness and rotational inertia into the formula, it can be obtained that the resonance speed range of the spur gear is 2764 r/min to 3523 r/min. Through calculation, it is known that 0.56n is the resonant rotational speed, so subsequent analysis needs to focus on it.
