The number of factors in the new gear teeth is restricted by the operation
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According to the number of teeth engaged at the same time, the values ​​are as follows: kmr, ms=Erp, spkr, s-0.5kr, s single tooth meshing area Erp, spkr, s 0.5kr, s double tooth meshing zone, Erp, sp is inner ring gear - The coincidence of the planet wheel and the sun gear-planet wheel; F is the invariant of the external load; Fsin(Xt) is the variation of the external load; Fl=[0,0,0,0,0,0,0,0, 0, mpX2Rc, 0, 0, mpX2Rc, 0, 0, mpX2Rc, 0, 0] T is the centrifugal force; analysis and calculation 1 analysis process and calculation method In the gear transmission system, the time-varying meshing stiffness of the gear will affect the vibration of the whole system . This effect occurs in two ways: (1) the number of gear teeth, which affects the vibration of the system by changing the phase of the single-tooth-tooth meshing zone between the planet wheels; (2) the degree of coincidence between the gear teeth, which changes the single-pair meshing The proportional relationship between the size of the single and double tooth meshing zone between the gears affects system vibration. In this paper, the influence of the number of teeth on the gear load is studied. Therefore, the influence of the coincidence degree is not considered. In the calculation, the variable external load is omitted, and the free vibration generated by the excitation of the time-varying meshing stiffness under constant external load is studied.
The weak damping of the system does not affect the steady state unless it is overdamped or the system resonates. The example analysis article analyzes two examples, parameters such as (some data are taken from the literature [1]). The sun gear and the ring gear of the first example are both integer multiples of the number of planet wheels, and the number of teeth of the planet gears is even. Therefore, the three planet wheels and the sun gear or the ring gear are both in the single tooth meshing zone or the double tooth meshing zone. In the second example, the sun gear and the inner ring gear are not integer multiples of the number of planet wheels, so the planet gear and the sun gear, the planet gear and the inner ring gear are different in the single tooth meshing zone or the double tooth meshing zone. The external excitation of the system is: 10kw, 1500radPs input from the sun gear; the article uses proportional damping C=0.07M 0.07K for system damping [1] to facilitate calculation.
(a) (b) For example 1, 2, with the planet carrier as the reference coordinate, the planetary gear rotates through one tooth for one cycle (referred to as the rotation period T, with the sun gear-planetary wheel 1 at the midpoint of the double-tooth meshing zone) The starting point of the cycle, the initial value of the system stiffness referred to below is discussed in the position of the T. The three planetary gears and the sun gear and the inner ring gear mesh the tooth map. In the first example, the stiffness of the example 1 changes 4 times in one cycle, and the variation of the example 2 occurs 12 times.
It is found through calculation that the steady state of the system is related to the initial state of vibration, that is, the combination of the meshing stiffness when the system has not vibrated (referred to as the initial value of stiffness).
For a single planetary gear, there are two kinds of initial state of meshing with the sun gear or the inner ring gear: single or double tooth meshing state (referred to as the initial value of single or double tooth stiffness, if the coincidence is greater than 2, it is double tooth) Or the initial value of the three-tooth stiffness); there are two kinds of steady-state vibration meshing forces corresponding to each. The steady state meshing force of the entire system is a combination of the above two cases.
Conclusion The stiffness combination of the system makes the load between the planetary wheels uneven. When the sun gear and the inner ring gear are integer multiples of the number of planetary wheels, the system has good load sharing performance; the sun gear-planetary gear and the inner ring gear-planetary wheel There are two kinds of steady-state meshing forces, and the waveform is related to the number of teeth, which is independent of the initial value of stiffness; the system has several stable points related to the initial value of stiffness. Through the parameter optimization, the amplitude of the steady mesh meshing force of the gear teeth can be reduced.