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The mathematical model now establishes a mathematical model for the analysis object at a high speed level. Determine the design variable x=[x0x1x2x3]T=[z1m1x1x2]T where: z1 is the number of teeth of the high-speed gear shaft; m1 is the modulus of the high-speed gear shaft, the unit is mm; x1 is the displacement coefficient of the gear shaft; x2 Is the displacement coefficient of the gear. Determining the central moment of the objective function displacement gear is y=cos5cos5'm1(1 ihigh)z1=5.61cos5'm1z1 where: “5 is the pressure angle of the gear, generally 5=20°; 5′ is the meshing angle. Determine the constraint function and perform scale transformation transformation to obtain g0(x)=1.0-x017≤0; g1(x)=2.0-x1≤0; g2(x)=-∑2i=1Xi≤0; g3(x)= 1.2-x02P[tan5a1-tan5' 5(tan5a2-tan5')]≤0; g4(x)=0.5x1-da1 where: da is the diameter of the top circle of the gear shaft, the unit is mm; 5a1 is the tip circle The pressure angle is 5a1=arccosdb1da1; db1 is the base circle diameter of the gear shaft; ∑2i=1Xi=6x02tan20° (inv5'-inv5).
The algorithm design and program optimization program are divided into three parts: using the golden section method to find the optimal step size, the one-dimensional optimal solution using the conjugated Powell method [1], and the center distance calculation using the external penalty function method. The penalty function of the program is penalty(x,m)=5.61cos5'x0x1 m∑10i=1{min[0,g(i)]}2 where m is the penalty factor variable; g[i] is the i Constraint functions; m∑10i=1{min[0,g(i)]}2 is a penalty function term. The program structure is as shown.
The external gear penalty function algorithm algorithm frame gear parameterization automatic modeling platform establishment The traditional gear transmission design method is quite complicated, the design cycle is long, the workload is large, the design process is repeated, and the efficiency is low. Therefore, the secondary development of Pro/E to achieve gear parameterization, intelligent design and virtual assembly [2] is very necessary.
Acquisition and assembly of the gear model The main parameters of the cylindrical spur gear reducer used in this example are as follows: input power: P = 7.5 kW / h; input speed n = 1500 r / min; transmission ratio i = 20, where ihigh = 5, ilow = 4, the load is stable, no big impact, the steering is unchanged.
Gear parametric automatic modeling Parametric automatic modeling means: using the secondary development module platform for Pro/E in Section 2 of this paper, it is convenient to use the dialog menu ((a)) to input the proposed section 1. The optimized value (see), you can quickly get the four gears that the agency wants. The gear model created by this method is a true involute accurate model, which not only meets the needs of CNC machining, but also meets the needs of finite element and simulation analysis. The creation of the previous objective function and the processing method of the constraint can be applied not only to involute spur gears, helical gears, but also to other linear gears such as cycloids.
Conclusion This paper mainly introduces a CAE method. Through the example analysis, the following conclusions are drawn: (1) The automatic gear modeling method based on optimization design is universal and original, and can be integrated with CAM/CAPP module; (2) Optimization The design mathematical model is universal, suitable for all kinds of linear gears, and because the number of model constraint equations is reasonable, the quality of the model is good; (3) the simulation result of the prototype and the actual measurement data are 98, which proves The correctness of the designed virtual prototype.