Modeling of low-frequency vibration model The main frequency of low-frequency braking vibration is below 100Hz, while the modal frequency of brake main components is the lowest with the bottom plate and brake drum, but it is also above 200Hz, so in addition to the friction lining during the modeling process The remaining parts of the chip are all treated as a rigid body, irrespective of their elastic modality, so a five-degree-of-freedom drum brake structural model model can be established as shown. In the figure, the brake drum rotates counterclockwise, and the leading shoe S1 and the trailing shoe S2 rotate on the one hand around the respective shoe axles O1 and O2 under the action of the braking force, and rotate together with the bottom plate about the center O of the bottom plate. The rotations of S1, S2 around O1, O2 are denoted by 1, 2 respectively, and the rotation of the base plate is denoted by b, the directions of which are respectively shown.
According to the value of each parameter, the friction coefficient can be changed to calculate the change of the root of equation (5) with the friction coefficient. By calculation, the bifurcation point is near f0=0.27. The variation of the modal frequency with the friction coefficient is given. (a) gives the process of the change of the corresponding eigen-root real part, and (b) is the enlargement near the bifurcation point in (a). It can be seen from the figure that when ff0, the two modalities are coupled, and the real part of a pair of eigenvalues ​​is positive and the system is unstable.
The coupling of the modal frequency with the friction coefficient changes the process of the root of the process with the change of the friction coefficient. The stability of the system and the characteristic root with Kb1 and the included angle change graph (coupling frequency is 5265 Hz). These phenomenons indicate that the system instability phenomenon is even if The friction coefficient also occurs. It can also be seen from the figure that the coupling frequency of the system is about 55 Hz, which is also exactly the same as the frequency range of the drum brake low frequency vibration observed in practice is 4070 Hz.
The basic parameter values ​​used in the calculation are the same as before. (a) and (a) give the system stable and unstable regions in the parameter plane; (b) and (b) give the distribution of characteristic roots in the complex plane, where the vertical axis represents the frequency and the horizontal axis represents the characteristic root. unit. It can be seen that on the left side of the complex plane of (b) and (b) is a stable region, while on the right is an unstable region, and the two modalities are coupled.
It can be seen from the above that since Kb1 cannot be less than 2106 in practice, the stability area of ​​the system is larger when Kb1 is larger, and the system is unstable when Kb1 is small. This explains the fact that brake pads that are less rigid in practice and that the stiffness of the base plate becomes less due to long use time are prone to brake vibration. It can be seen that when the base plate stiffness Kb1 is small, the system stability area is increased, but the change is small. However, when the base plate stiffness Kb1 is large, the influence on the stability is obvious. It can be seen that as the friction coefficient decreases, the unstable area gradually decreases. Therefore, reducing the friction coefficient is one of the methods to stabilize the system.
By analyzing the stability of the five-degree-of-freedom model, the low-frequency vibration of the drum brake is considered even if the changing friction coefficient is not considered. This self-excited vibration due to friction can only explain the structure and nonlinear factors. s reason. The analysis of the influence of stability by the change of parameters shows that certain structural parameters have a great influence on the stability of the system. This shows that the low-frequency vibration of the drum brake is closely related to the structure itself, which is of guiding significance for improving the design of the drum brake and suppressing the low-frequency brake vibration of the drum brake.
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