The modeling of Pro / E software is based on the characteristics of 3D model, and it can also carry out parametric modeling. It is a new industry standard in the field of mechanical CAD. Pro / E provides a large number of compatible interfaces, including various CAD and CAE software, and supports input and output model files in various formats, including IGES, step, para solid, etc. Adams is a powerful simulation analysis software with various constraint libraries and dynamic model libraries. It can solve Lagrange equation or discrete element equation by using rigid body dynamics theory, and obtain displacement, velocity, acceleration and reaction curve of virtual model by solving. It is widely used to verify various performance of mechanical virtual prototype The solution of limit value such as displacement can realize the optimization of mechanical device.
The discrete element method can solve the force between rigid bodies by using the contact method, which can be linear or nonlinear. The solution of the mechanical dynamic model, using a simple combination of linear model and nonlinear model. Among them, the force model is mainly divided into two parts: one is normal force, the other is tangential force. The calculation formula is as follows:
Where FN is the normal force; Kn is the normal stiffness coefficient; δ N is the normal superposition; Cn is the damping coefficient; VN is the normal repulsive force.
For the tangential contact force model, the magnitude of the force is related to the force acting time
Where FS is the tangential force at time t; Δ T is the time step of load; KS is the tangential stiffness coefficient; CS is the tangential damping coefficient; Vs is the tangential repulsion.
When solving the nonlinear force model, the nonlinear elastic model can be used
R1 and R2 are the radius of curvature; E1 and E2 are elastic modulus; V1 and V2 are Poisson’s ratio.
If the device has plastic deformation, the plastic force should also be considered
Where K1 and K2 are the normal stiffness coefficients under loading and unloading; δ、δ 0 is the normal superposition amount and residual normal superposition amount of two contacting bodies respectively.
When the distance D ≤ R1 + R2, the normal contact force model is as follows:
When the distance between the two contact elements R1 + R2 ≤ D ≤ (1 + CAD) R1 + R2, the normal contact force is:
Where, CAD is the critical contact distance when the contact force is tensile force; Kad is the critical stiffness coefficient when the contact force is tensile force.
According to the formula and principle of discrete element algorithm, it can be divided into five steps:
1) Set simulation parameters. It mainly includes all kinds of mechanical loads and degree of freedom constraints, as well as some parameters and properties of materials. In the specific setting, the parameters can be set in ADMAS software with reference to the model material and load of the gear system.
2) Select the dynamic model. This paper mainly refers to the approximate dynamic model of the gear system, and selects the appropriate dynamic parameters, including speed model, acceleration, displacement and so on.
3) The calculation model is established. Because the gear system is a multi rigid body system, the discrete element model principle can be used to create a suitable calculation model.
4) Determine the parameters. To ensure the accuracy and efficiency of simulation, the parameters of all aspects are checked and further determined.
5) Simulation analysis. The ADMAS software is used to analyze and solve the model.