During the dynamic condition shifting process, the collision analysis of the inner and outer gears is as follows: When the gear is dynamically meshed, the moment of inertia converted to the inner and outer gears is large. If there is a difference in rotational speed between the inner and outer gears to be engaged, collision, impact, and even the contact teeth may be broken during the engagement. Based on the allowable breaking strength of the gear teeth, we solve the dynamic conditions of the safe meshing of the inner and outer gears.
At the moment of meshing, the impact force of the gear is much greater than the other forces received, and the gear is considered to be only subjected to the impact force. During the collision, the external gear is rigidly connected with the wheel reducer, the wheel, etc., and the inertia is large, and the movement state is difficult to change. In the short time of the collision, the portion maintains the uniform X0 motion. The external gear with angular velocity X0 meshes with the internal gear with angular velocity Xn and collides. After the collision, the inner and outer gears rotate together, and the angular velocity is X0. According to the momentum moment theorem, the internal gear is analyzed: M=I fold óXn-X0t1 (3) where M is the collision torque (Nm); I fold is converted to the internal gear by the rotating parts involved in the transmission process The moment of inertia (kgm2); Xn is the angular velocity (radPs) before the internal gear collision; X0 is the angular velocity (radPs) before the external gear collision, and is also the angular velocity of the internal and external gears after the collision; t1 is the collision time ( s), estimate t1 is 0.005s.
According to the calculation formula of 5 mechanical parts 6 (Editor Liang Lianggui, 5th edition, 1989), the calculation formula of tooth root bending fatigue strength 2F=2KFTFYFaYSaUdm3z2F[RF](4) Tooth surface contact fatigue strength calculation formula 2H=2KHTHUd3u 1uZHZEF[RH (5), T gear transmission torque (Nmm); k load factor; YFa tooth profile; YSa stress correction coefficient; Ud tooth width coefficient; m gear modulus (mm); Z gear teeth; d gear Pitch diameter (mm); u transmission ratio; ZH area coefficient; ZE elastic influence coefficient; 2F gear bending fatigue strength (MPa); 2H gear contact fatigue strength (MPa); [2F] gear allowable bending fatigue strength (MPa) ; [2H] gear allowable contact fatigue strength (MPa). The shifting conditions required by the kinetics are calculated according to the above formula.
Kinematic conditions When the internal and external gears meet the geometric and dynamic conditions, the teeth can be inserted smoothly and safely, but the detection of the motion parameters and the shifting action are not performed at the same time, and the gearing reaction time t2 is required to insert the teeth. The shift reaction time t2 refers to the time elapsed from the time when the internal and external gears reach the shifting condition, after the reaction time of the sensor and the controller, and when the driving device makes the inner and outer gears just touch, the empirical estimate t2 is 1.5s. Therefore, we must ensure that the shift geometry and dynamics are met after t2 time.
The phase difference between the inner and outer gears at the start of the shift is $<. Because of the existence of $X and $E, the phase difference between the inner and outer gears becomes $<0 after t2, and $<0 must be at $
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