Research on vibration isolation of single-axis spring
The control strategy assumes that all degrees of freedom are used as feedback, ie: u = EiGixi (7) from equation (5), where the above formula is: u = (G1 + Eni = 2Ti1Gi) x1 (8) so theoretically All degrees of freedom feedback control is equivalent to interface unit feedback control. It is assumed that the transfer rate of the interface unit after the control is Tc1b. Since the control action only acts directly on the interface unit, the transfer rate of the other units of the flexible body to the interface unit does not change. Therefore, there is: Tcib=Ti1Tc1b(10), which means that as long as Tc1b is controlled, the transfer rate of all units can be controlled. . Previously, Ti1 was the transmission rate of the vibration of each unit of the flexible body without the vibration isolation system, so Tc1b is also the improvement of the transmission rate of each unit of the flexible body by the active vibration isolation system. Let the expected transfer rate of each unit be Tcib, then the desired transfer rate of the interface unit should satisfy the following conditions: According to the requirements of Tc1b, controllers G1 and G2 can be designed.
The design example demonstrates the above design idea with an example. Let the four degree of freedom flexible body be as shown. The connection spring and damping of the interface unit and the base are denoted as k1 and c1, and the parameters are as shown. Four-degree-of-freedom flexible body gas spring equivalent section diameter 40mm, length 100mm, control valve bandwidth is 100Hz. Four degrees of freedom flexible body parameter table item number 1234m (kg) 141k (N / m) 4@108@103.6@10c ( Ns/m) 1203010 design controllers G1 and G2, the transmission rate change of the interface unit m1 is shown in a. The curve 1 is the transmission rate T1b of the passive vibration isolation, and the curve 2 is the closed-loop transmission rate Tc1b controlled only by the feedback, the curve 3 It is a closed-loop transmission rate Tc1b that uses both feedback and feedforward control. It can be seen that after the active control, the transmission rate of the interface unit is greatly attenuated, which means that the transmission rate of all the units of the flexible body is greatly attenuated.
The interface unit primary/passive transfer rate is the transfer rate comparison of the other three units m2, m3 and m4 of the flexible body. In the figure, curve 1 is the vibration-free transmission rate, curve 2 is the passive vibration isolation transmission rate, and curve 3 is the active vibration isolation transmission rate. It can be seen that passive vibration isolation dampens vibration at high frequencies, but introduces additional resonance at low frequencies. Active vibration isolation eliminates this resonance and further reduces transmission.
Although there is a point close to 1 or slightly higher than 1 in the active vibration isolation transmission rate of m4, it does not affect the evaluation of the vibration isolation system. After using the vibration isolation system, the transmission rate of each unit of the flexible body is reduced a lot. . Conclusion This paper studies the active vibration isolation of uniaxial flexible bodies. Theoretical analysis and numerical examples show that the transmission rate of the interface unit can be used as an indicator for designing and evaluating the uniaxial flexible body vibration isolation system.
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