The condition of noncircular gear design

The diagram of stepless transmission mechanism is shown in Figure 1. The driving noncircular gears 1 and 3 are the same, only the initial phase is different; Driven noncircular gears 2 and 4 have only the difference of initial phase. The power is transmitted from the driving non-circular gears 1 and 3 at the right end to the differential 5, and the differential cross shaft drives the cylindrical gears 6 and 7 to realize the power output. The working principle of this kind of stepless transmission mechanism is described in detail, which will not be repeated here. The difficulty in the design and manufacture of the whole mechanism is the non-circular gear

(1) The maximum input torque is 200 N · m and the maximum input speed is 2 500 R / min;

(2) The whole mechanism is driven by electric motor and its expected working life is 3 years. It works 240 days a year and 6 hours a day;

(3) The transmission ratio of non-circular gear is 1 / i12 and the rotation angle of driving non-circular gear φ 1 satisfies the curve shown in Fig. 2, where ABC is a straight line and CDE is a sine curve, and the derivatives of C and E are equal to the derivatives of ABC.

Before the next step, the expressions of ABC and CDE are needed.

Finally, i12 and I2 can be obtained φ 1 and the curve shown in Figure 3.

Considering the manufacturing cost of the product and the advantages of WEDM, the non-circular gear material is 40Cr, modulation treatment, no surface quenching, and the tooth surface hardness is less than or equal to 286 HBS, which belongs to the soft tooth surface closed transmission. The manufacturing accuracy of the primary gear is grade 6. When the input torque, speed and i12 take the maximum value (calculated from Figure 3, the maximum value of i12 u = 2.116, at this time φ 074 RAD), the contact stress of tooth surface is the maximum, which is the limit condition. According to the known conditions of limit working condition and the design method of contact fatigue strength of spur gear tooth surface, the center distance a of non-circular gear can be determined. Assuming that the pitch curve diameter of the driving non-circular gear is D1, the pitch curve diameter of the driven non-circular gear is D2 = D1 × u。 The primary diameter d1t meets the following requirements: