| Quasi-zero-stiffness isolator has been paid much more attention in recent years due to its high-static-low-dynamic stiffness characteristic.It is usually obtained by combining the positive stiffness and the negative stiffness in parallel.The positive stiffness is generally achieved by using mechanical springs or rubber material,whose force characteristic has been well studied.However,the negative stiffness is not.The negative stiffness mechanism usually has a more complex structure.The nonlinear term in the negative stiffness makes the dynamic characteristic of the isolation system much more complex than the equivalent linear system.So far there has been a lot of things can be used to realize the negative stiffness,such as pre-stressed mechanical springs,magnets,pre-stressed plate,cam roller.However,most of them are passive mechanisms whose stiffness characteristic can’t been tuned online,and they are unsuitable for solving vibration problems with variable working conditions.Thus it becomes more and more necessary to propose some new ways to obtain tunable negative stiffness.This thesis proposes a new way to get tunable negative stiffness by using an electromagnetic tooth structure(ETS).An electromagnetic vibration isolator is presented.The dynamic characteristics of the isolator are well studied.The negative stiffness controller of the isolator is designed.A series of experimental studies have been conducted to verify the excellent vibration isolation performance.The following work has been conducted in this thesis.An asymmetric electromagnetic tooth structure which can provide tunable negative stiffness is proposed.A tooth electromagnetic vibration isolator is designed by using the coil spring as the positive stiffness mechanism.Equivalent magnetic circuit of the ETS is built and theoretical electromagnetic force of the ETS is derived by using the dividing magnetic circuit method.Simulations of the magnetic circuit are conducted to validate the negative stiffness.Effects of the system parameters on the magnitude of the electromagnetic negative stiffness are investigated.The results show that the magnitude of the negative stiffness depends on the tooth gap and the range of the negative stiffness depends on the tooth width.Effects of the current on the magnitude of the electromagnetic stiffness are studied.The results show that the magnitude of the negative stiffness near the equilibrium position is proportional to the square of the current,which verify that the negative stiffness can be tuned online by changing the current.Experimental measurements of the electromagnetic force have been carried out to verify the negative stiffness.According to the theoretical model of the electromagnetic force,dynamical equation of the electromagnetic vibration isolation system is derived.Effects of the system parameters on the dynamic characteristic of the isolation system are studied,which can provide a theoretical support for the illustration of the further experimental results.A single-degree-of-freedom experimental test rig is established and a series of frequency sweep experiments and single frequency experiments are carried out to verify the theoretical investigation and the negative stiffness characteristic of the ETS.The correctness of the theoretical electromagnetic force is verified by comparing the measured resonance frequency and the theoretical natural frequency.Taking aim at the isolation performance of the electromagnetic isolation system in large displacement,the nonlinear piece-wise model of the TES are built by using finite simulation method and numerical data fitting method.Theoretical solution of the piece-wise nonlinear dynamic equation is obtained by using the averaging method.Effects of the magnitudes of the base excitation and the damping ratio on the dynamic characteristic,especially vibration isolation performance,are studied in depth.The results show that the electromagnetic vibration isolator outperforms the equivalent linear vibration isolation system and the equivalent nonlinear vibration isolator.The natural piece-wise characteristic of the electromagnetic tooth structure makes the isolation performance of the electromagnetic isolator much better.A control strategy is proposed by tuning the control current online according to the base excitation frequency.The controller of the electromagnetic vibration isolator is designed and its regulating capability of the current is tested by experimental measurements.The electromagnetic isolator with controller is assembled and the test rig is built.Currents provided by the semi-active control system are measured and the results show that the designed semiactive controller can output the right current according to the excitation frequency.A series of the dynamic experiments of the tooth electromagnetic vibration isolator with semi-active controller are carried out.The results show that the natural frequency of the electromagnetic vibration isolator can be tuned online according to the base excitation frequency and the vibration is obviously attenuated.In the condition of the current of 0.6A,the resonance frequency of the tooth electromagnetic vibration isolator with controller reduces from 23.25 Hz to 19 Hz.The initial isolation performance reduces from 33 Hz to 20.5Hz.The maximum acceleration reduces by 13.8dB.The acceleration of the isolated mass at the original resonance frequency reduces from 153.4dB to 126.1dB,and reduces by 27.3dB.The experimental measurements of the accelerations of the designed isolator in random base excitation is performed.Root mean square acceleration,transmissibility of the root mean square acceleration and the natural frequency of the electromagnetic isolator before and after applying the current are mainly discussed.Compared with the equivalent linear isolator,the electromagnetic negative stiffness can reduce the whole dynamic stiffness while keeping the static stiffness invariable.Furthermore,the natural frequency of the isolation system with electromagnetic negative stiffness decreases and the isolation performance becomes much better than before. |
PDF Full Text Request