0 Introduction The development of modern mechanical technology puts forward higher requirements for the vibration reduction of mechanical transmission systems. Therefore, the research on the theory and method of vibration reduction design of mechanical transmission systems is increasingly concerned by engineering designers. However, due to various reasons, the research progress of the vibration reduction design theory of mechanical transmission systems is relatively slow. As the most commonly used gear system in the transmission system, research data in this area is even more scarce. Therefore, it is necessary to conduct in-depth research on the design method of gear system vibration reduction. Only the torsional motion of the system is considered, the coupling with other directions is neglected, the torsional vibration mechanics model of the gear system is established, and the sensitivity of the system is analyzed. The gear load is in the transverse direction, the torsion direction, the axial direction and the rotation. (Swing) Coupling between directions, so this model should be a complex coupling model. In this paper, based on the dynamic coupling effect between the one-axis and one-axis motion, the dynamic model of the gear system is established, and the sensitivity calculation formula of the system eigenvalue is derived. The dynamic parameters of the system support structure are found. The most sensitive value of the order frequency provides a basis for the system's vibration reduction design.
1 Gear system dynamics model is convenient for research. The dynamic analysis of single-stage gear system is now discussed. On this basis, it is not difficult to promote to multi-stage gear systems. To the movement. However, it is generally assumed that the rotation in the 9z2 direction is negligible unless the teeth are wide or the load is unevenly distributed along the tooth width p4. The rotating component shaft and the bearing are simplified into elastic members having equivalent stiffness and equivalent damping. The torsional mass inertia of the input and output components is not included in the analysis because they are only important at relatively low frequencies. It is assumed that the input and output torques are constant. Gear tooth profile error, commonly known as static gear error, is considered to be the only source of excitation. The friction generated when the tooth surfaces are engaged is also negligible, and thus the lateral movement on the meshing plane is uncoupled from the inertia in the Z-axis direction (the normal direction of the meshing plane). For medium and heavy-duty gear systems, the nonlinear effects of the flank clearance are assumed to be negligible, and the meshing stiffness of the helical gear pair is assumed to be constant.
The vibration equations of the system shown are represented in the form of a matrix as a dynamic response vector, the mass matrix, and the equivalent damping and equivalent stiffness matrix of the shafting are shown as a dynamic model of a pair of gear systems. Under the action of transmission load = diag (ca1, Gz2, Cr1, Cr2, Fn, each gear will be along X, Y, 0x, 0> and (supposed: 2000-19 Wei-2 Bing i female master lecturer lie gear Meshing damping and stiffness matrix; F(t) load vector; moment of inertia of two gears relative to the X axis: /) 1,12 are the moment of inertia of the two gears relative to the Y axis; U is the base circle helix angle; ri R2 is the base circle radius of the driven wheel; kc is the gear meshing stiffness; cc is the gear meshing damping; kai, ka2 is the main bearing and the radial bearing stiffness of the driven wheel; kri, kr2 ​​are the radial bearing stiffness of the two gears respectively ;kh, kh2 are the slewing bearing stiffness of the two gears respectively.
The corresponding system characteristic equation is the quantity.
The equation (i2) is multiplied by the urT equation (i3) to derive the support stiffness ki: from this it can be concluded that the equation (6 is substituted into equation (i5), whereby the sensitivity of the natural frequency k relative to the support stiffness ki can be derived. Calculation formula: According to the calculation result of formula (i6), the engineering designer can effectively change the support structure parameters to adjust the natural frequency of the system to achieve the purpose of vibration reduction.
2 Sensitivity analysis of the characteristic value of the gear system The undamped free vibration equation of the system shown in Figure 11 is: when calculating, the parameters of the gear system taken are shown in Table i. Substituting the data in Table i into the equation (i2), solving the equation Obtain the natural frequency and mode shape vector of the system, as shown in Table 2.
Substituting the relevant data in Table 2 of Table i into equation (i6), the sensitivity of the natural frequency with respect to the support stiffness can be obtained, as shown in Table 3.
It can be seen from Table 3 that the most sensitive parameters corresponding to the frequency of each order are: the natural frequency of the second order is kh:; the parameter of the gear system of the third order natural frequency table 1 is inherent in the natural frequency and the mode vector table 3 The sensitivity of the frequency is fci and kh; the natural frequency for the fourth order is kri and kr2; the natural frequency for the fifth order is kh; the natural frequency for the sixth order is kh; the natural frequency for the seventh order is fcl; for the eighth The natural frequencies of the order are krl and kh. Therefore, as long as the corresponding sensitive support stiffness changes, the natural frequency will also change accordingly.
There are multi-stage coupled vibration modes in the 4-junction gear system. Each natural frequency of the system has corresponding sensitive support structure parameters. Therefore, the natural frequency can be changed by adjusting the support structure parameters to avoid the natural frequency approaching the gear meshing frequency.
In this paper, the sensitivity analysis of the support structure of the gear system is studied by the derivative method. The modified part and content of the system are determined by sensitivity analysis, which provides an effective tool for the dynamic modification of the system and the dynamic design with the target of vibration reduction.
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