The establishment of the constraint condition is known from the mechanical principle. The number of teeth of the gear must be a positive integer, and the product of the number of teeth of the number of teeth must also be a positive number, that is, Z1, Z2Zn 1, X, Y must be positive integers. However, in most cases, it is not possible to obtain integer teeth in order to satisfy the gear ratio I. The processing method is: artificially, the number of teeth is rounded up under the premise of satisfying the processing precision.
Rounding error constraints: X-Int(X)1, Z1-Int(Z1)2, Z2-Int(Z2)3, Zn-Int(Zn)2, Zn 1-Int(Zn 1)2. Where Int(X)=[X 05], that is, take the nearest integer of X. 1, 2 is the rounding error determined according to the machining accuracy. In general, when X100, 10001; when X>100, 1002; take 20001.
Center distance limitation condition: [mZ1 Z2/2]-a(1) maxm(2) where m gear modulus, gear maximum displacement, max gear maximum displacement coefficient, and center distance between gears Z1 and Z2. Finishing (1), (2) is: (Z1 Z2) - 2m2max. The number of teeth that the gear does not produce undercut is Zmin17.
According to the established mathematical model and the constraint function, Y can be made into a positive integer, and starting from a certain value, the step size is incremented by 1, and the X value is calculated sequentially, and the search satisfying the constraint condition is obtained, and the satisfaction is determined sequentially. The Z1 and Z2 values ​​of the constraint. By analogy, the values ​​of Z3, Z4Zn, and Zn 1 are obtained, and the calculation box is as shown.
For example, a machine tool should use the matching of the hanging wheel to get a special gear ratio / 4.
Establish a mathematical model: Z1Z3Z2Z4=4, let: X=Z1Z3, Y=Z2Z4, then XY=4, Z1=XZ3, Z2=YZ4. Then the constraint is established (the center distance is adjustable, and the modulus is small): 70Z1120, 70Z2120, 70Z3120, 70Z4120X-Int(X)002, Z1-Int(Z1)0001, Z2-Int(Z2)0001.
Conclusion Computer-aided design provides designers with a simple and reliable calculation method. This paper is the specific application of this method to the problem of the number of teeth.
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