The time-varying meshing stiffness, stiffness phase difference, time-varying backlash, comprehensive transmission error, meshing damping and various meshing states of helical gears are considered comprehensively. They are dynamic equations with strong nonlinearity. Therefore, it is difficult to obtain the evolution law of their dynamic characteristics through analytical methods.
The dynamic equation of the system is solved by the variable step-size fourth to fifth order Runge-Kutta numerical method, and the calculation results of the first 2000 time series are discarded to eliminate the influence of transient response.
| Structural parameters | Driving wheel/driven wheel |
| Number of teeth | 50/100 |
| Modulus/mm | 4 |
| Pressure angle/(°) | 20 |
| Helix angle/(°) | 10 |
| Tooth width/mm | 50 |
| Poisson’s ratio | 0.3 |
| Modulus of elasticity/Pa | 2.06X^11 |
| The overlap ratio | 0.69 |
| Transverse contact ratio | 1.76 |
| Total coincidence | 2.45 |
The structural parameters of the helical gear system are shown in the table. The rotational inertia of the power output gear and the flywheel meets Jg2/Jg1=10, and the damping ratio ξ= 0.03， ωˉ = 0.5, load ratio of asymmetrical parallel input λ=| f2 / f1 |。