1. Establishment of objective function and optimization model The known gear ratio is u, the input power is p, the driving gear speed is n1, and the design parameters that minimize the volume of the reducer under the condition of satisfying the strength and stiffness of the part are obtained.
Since the size of the gears and shafts is the basis for determining the volume of the reducer, we can establish the objective function based on the principle that the sum of their volumes is the smallest. According to the calculation formula of the gear geometry and the gear structure size, the volume of the gear and the shaft in the housing can approximately represent the following nine items of the constraint function: (1) The number of teeth Z1 should be greater than the minimum number Z of teeth without rooting. Get: () 01min1 ≤
=zxg(2) The tooth width satisfies maxmin≤db, generally taking 4.1,9.
0 The objective function is an optimization design problem with 6 design variables and 12 constraints, which can be solved by penalty function method or other methods.
2. Using the optimization method to analyze the example, design a single-stage helical-toothed cylindrical gear reducer with a belt conveyor as the target. It is known that the working tension of the conveyor belt is F=5.5kN, v=1.4m/s, D=450mm, and the drum efficiency is 0.96. The allowable contact stress of the gear is the optimization design problem with 6 variables and 12 constraints. Can be solved by the internal point penalty function method. Now take the parameters of the traditional design as the initial point, the initial point is 75,50,168,4,25,1050=X,=XF3.263106. After 23 iterations, the optimal solution is obtained: X=[30.6,17 , 2,55.6,100,130], rounding the optimal result according to national standards, can obtain X=[31,17,2,56,100,130], F(X)=2.305106, and satisfy all items Constraint condition, the value of the objective function, that is, the volume of the reducer is reduced. 3. Conclusion The design method of the single-stage cylindrical gear reducer is optimized with the minimum volume of the reducer, and the internal geometric parameters are optimized by the internal point penalty function method.
With this method, we can quickly obtain different design requirements, which greatly improves the design efficiency. At the same time, the volume value has dropped by about 30, and the economic benefits of the production of the reducer have also been significantly improved.
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