The vehicle-mounted equipment is easy to be disturbed by external vibration excitations during transportation, which is harmful to the measurement accuracy and performance of the equipment. Aiming at the vibration isolation of the vehicle-mounted equipment, a semiactively controlled quasi-zero stiffness (QZS) vibration isolator with positive and negative stiffness is proposed. The vertical spring is paralleled with a magnetorheological (MR) damper, and the semiactive on-off control scheme is adopted to control the vibration. The analytical expression of the isolator’s displacement transmissibility is derived via the averaging method. Then, the vibration isolation performance under different road excitations and different driving speeds is simulated and compared with the uncontrolled passive QZS vibration isolator. In addition, the mechanical structure of the semiactive QZS isolator is designed and manufactured, and the test system is built by LabVIEW software and PXI embedded system. The isolation effect of the semiactive QZS isolator is verified through test data. It is found that the proposed semiactive QZS isolator shows excellent vibration isolation performance under various road excitations, while the passive QZS isolator is effective only under harmonic excitations. The vertical acceleration of vehicle-mounted device can be decreased over 70% after isolation, and the vibration isolation effect is remarkable. The design idea and research results of the semiactive QZS isolator may provide theoretical guidance and engineering reference for vibration isolation.
Vibration isolation is a common method to eliminate or weaken vibration [
In recent years, QZS vibration isolation has become a research hotspot because of its large bearing capacity and extremely low natural frequency, which can effectively isolate low frequencies. It has various forms, such as cam roller [
Due to low energy consumption, magnetorheological (MR) damper has been widely used to implement the semiactive control [
In this work, a semiactive QZS vibration isolation system with positive and negative stiffness parallel mechanism is proposed. MR damper is installed in parallel to the vertical spring. Through the analysis of the characteristics of MR damper, an improved Bingham model based on excitation current and response speed is established. The semiactive on-off control scheme is developed, and the control effect is simulated under harmonic, stochastic, and semisinusoidal shock excitations at different vehicle speeds. Finally, the mechanical device of the semiactive QZS isolator is designed and manufactured, and the isolation effect of the system is tested based on LabVIEW software and PXI embedded system to verify the effectiveness of the semiactive control scheme and the good vibration isolation performance of the vibration isolation system.
The QZS vibration isolation system controlled by MR semiactive control is shown in Figure
QZS vibration isolation system with MR semiactive control.
According to D’Alembert’s principle, the dynamic equation of the MR semiactive vibration isolation system is obtained.
Compared with the semiactive control system shown in Figure
To the passive QZS vibration isolation system, it is assumed that the excitation displacement is given by
Let
The approximate analytical solution of equation (
According to the averaging method, the amplitude and phase of the first-order approximate solution can be obtained as follows:
In one period of [0, 2
Let
When the passive QZS vibration isolation system is excited by a harmonic force, the steady-state amplitude frequency response is as follows:
Then,
The damping force of MR damper is expressed by S-shape function as follows [
According to the parameters of RD-1097-01 MR damper manufactured by Lord company, the resistance of the excitation coil is 20 Ω at 25°C, the maximum damping force is 135 N, the maximum continuous working current is 0.5 A, and the current tends to be saturated when it is greater than 1 A. Then, the damping force of the MR damper can be expressed as follows:
The damping force curves under different currents in time domain are shown in Figure
Time domain response of damping force under different currents.
Relationship curve between damping force and velocity under different currents.
Since it is difficult to make the output damping force accurately match the desired control force in experiments and engineering applications, the on-off control scheme is used here due to its good real-time performance.
The control scheme is expressed as follows:
By judging the direction of relative velocity
Figure
TruckSim/Simulink on-off control cosimulation model.
The parameters of the semiactive QZS vibration isolation system are shown in Table
Parameters of the vibration isolation system.
Parameters | Values |
---|---|
9.2 kg | |
1 017 N/m | |
1 010 N/m | |
100 N·s/m | |
0.121 m | |
0.081 m | |
0.090 m |
A harmonic road excitation with an amplitude of 5 mm and length of 500 m is used, and the vehicle speed is 30 km/h, 40 km/h, and 50 km/h, respectively. The vibration isolation characteristics of the passive QZS and semiactive QZS isolators are obtained, as shown in Figures
Time domain response of displacement under harmonic excitation: (a) 30 km/h; (b) 40 km/h; (c) 50 km/h.
Time domain response of acceleration under harmonic excitation: (a) 30 km/h; (b) 40 km/h; (c) 50 km/h.
RMS and relative differences of displacement and acceleration under harmonic excitation.
Vehicle speed (km·h−1) | Body centre | Passive QZS system | Semiactive QZS system | |||||||
---|---|---|---|---|---|---|---|---|---|---|
Displacement (m) | Acceleration (m·s−2) | Displacement (m) | Displacement difference (%) | Acceleration (m·s−2) | Acceleration difference (%) | Displacement (m) | Displacement difference (%) | Acceleration (m·s−2) | Acceleration difference (%) | |
30 | 1.16 × 10−3 | 0.322 | 2.25 × 10−4 | −80.60 | 0.066 | −79.50 | 7.68 × 10−5 | −93.38 | 0.017 | −94.72 |
40 | 1.64 × 10−3 | 0.374 | 3.42 × 10−4 | −79.15 | 0.083 | −77.81 | 8.93 × 10−5 | −94.55 | 0.022 | −94.12 |
50 | 2.17 × 10−3 | 0.396 | 4.48 × 10−4 | −79.35 | 0.093 | −76.52 | 9.79 × 10−5 | −95.49 | 0.027 | −93.18 |
Relative difference between the vibration isolation system and vehicle body under harmonic excitation: (a) displacement; (b) acceleration.
It can be seen from Figures From the vertical displacement response, RMS of the passive QZS vibration isolation system is reduced by 80.6% and the maximum RMS of the semiactive QZS vibration isolation system is reduced by 95.49%, compared with that of the body centre. The maximum vertical displacement reduction of semiactive QZS isolator is 78.1% better than that of the passive QZS isolator. Compared with the passive vibration isolation system, the maximum vertical acceleration reduction of the semiactive QZS isolator is 74.2%. Under 5 mm harmonic excitation, the two vibration isolation systems show good vibration isolation performance at different vehicle speeds, but the semiactive QZS vibration isolation system has better vibration isolation performance. The change trend of body response of the passive and semiactive QZS is the same, but the maximum amplitude and RMS of the semiactive QZS are obviously decreased.
In practical engineering, the external excitation of a vehicle is mostly random or has strong randomness. The road is built adopting the three-dimensional stochastic road based on fractal theory [
The three-dimensional road spectrum can better reflect the three-dimensional texture characteristics, which not only reflect the longitudinal irregularity excitation of the road but also meet the requirements of the simulation test for the transverse elevation change, as shown in Figure
C-level stochastic road excitation: (a) cross section elevation setting; (b) road model.
Figures
Time domain response of displacement under stochastic road: (a) 30 km/h; (b) 40 km/h; (c) 50 km/h.
Time domain response of acceleration under stochastic road: (a) 30 km/h; (b) 40 km/h; (c) 50 km/h.
RMS and relative differences of displacement and acceleration response under stochastic road.
Vehicle speed (km·h−1) | Body centre | Passive QZS system | Semiactive QZS system | |||||||
---|---|---|---|---|---|---|---|---|---|---|
Displacement (m) | Acceleration (m·s−2) | Displacement (m) | Displacement difference (%) | Acceleration (m·s−2) | Acceleration difference (%) | Displacement (m) | Displacement difference (%) | Acceleration (m·s−2) | Acceleration difference (%) | |
30 | 0.011 | 0.742 | 2.37 × 10−3 | −78.45 | 0.242 | −67.39 | 1.67 × 10−3 | −84.82 | 0.074 | −90.03 |
40 | 0.013 | 1.163 | 3.54 × 10−3 | −72.77 | 0.441 | −62.08 | 2.04 × 10−3 | −84.31 | 0.126 | −89.17 |
50 | 0.021 | 1.654 | 5.89 × 10−3 | −71.95 | 0.647 | −60.88 | 3.35 × 10−3 | −84.05 | 0.187 | −88.69 |
Relative difference of RMS of (a) displacement and (b) acceleration under C-level random pavement
It can be seen from Figures
To verify the shock performance of the isolators, a semisinusoidal shock road with an amplitude of 0.1 m and frequency of 1.4 Hz is established in TruckSim, as shown in Figure
Semisinusoidal shock road: (a) cross section elevation setting; (b) road model.
The vertical displacement and acceleration response curves of the body centre and the two vibration isolators are shown in Figures
Time domain response curve of displacement under semisinusoidal shock road: (a) 30 km/h; (b) 40 km/h; (c) 50 km/h.
Time domain response curve of acceleration under semisinusoidal shock road: (a) 30 km/h; (b) 40 km/h; (c) 50 km/h.
RMS and relative differences of vertical displacement and acceleration under semisinusoidal shock road.
Vehicle speed (km·h−1) | Body centre | Passive QZS system | Semiactive QZS system | |||||||
---|---|---|---|---|---|---|---|---|---|---|
Displacement (m) | Acceleration (m·s-2) | Displacement (m) | Displacement difference (%) | Acceleration (m·s−2) | Acceleration difference (%) | Displacement (m) | Displacement difference (%) | Acceleration (m·s−2) | Acceleration difference (%) | |
30 | 0.032 | 4.278 | 0.012 | −62.50 | 1.267 | −70.38 | 2.59 × 10−3 | −91.91 | 0.38 | −91.12 |
40 | 0.057 | 6.096 | 0.023 | −59.65 | 2.118 | −65.26 | 5.65 × 10−3 | −90.09 | 0.579 | −90.50 |
50 | 0.064 | 7.257 | 0.029 | −54.69 | 2.626 | −63.81 | 9.37 × 10−3 | −85.36 | 0.735 | −89.87 |
Relative difference of RMS of (a) vertical displacement and (b) acceleration under semisinusoidal shock road.
As can be seen from Figures The isolation effect of the semiactive QZS isolator is clearly better than that of the passive one under semisinusoidal shock road excitation. With the increase in vehicle speed, the isolation efficiency of the passive QZS decreases, the response peak value increases, and the stability is poor. While the vibration isolation efficiency of the semiactive control system is about 90%, its stability is better than that of the passive QZS system.
To evaluate the shock resistance performance, the ratio of the peak acceleration response of the isolated object to that of the vehicle body centre is defined as the maximum acceleration ratio, as shown in Table
Maximum acceleration ratio at different vehicle speeds under semisinusoidal impact pavement.
Vehicle speed (km·h−1) | Body centre | Passive QZS system | Semiactive QZS system | ||
---|---|---|---|---|---|
Peak acceleration (m·s−2) | Peak acceleration (m·s−2) | Ratio | Peak acceleration (m·s−2) | Ratio | |
30 | 9.762 | 3.356 | 0.34 | 0.834 | 0.086 |
40 | 17.187 | 6.195 | 0.36 | 1.787 | 0.103 |
50 | 21.158 | 8.791 | 0.42 | 2.489 | 0.118 |
It can be seen from Table
The semiactive QZS vibration isolation system is composed of a mechanical structure and MR semiactive control system. The mechanical structure is shown in Figure
Mechanical structure of the semiactive QZS vibration isolation system: ① device base; ② MR damper; ③ limit adjusting structure; ④ negative stiffness mechanism; ⑤ vibration isolated mass.
The MR semiactive control system is mainly composed of a motion state sensor, controllable constant current power supply, signal conditioning converter, control arithmetic unit, input/output board, and shielded junction box, as shown in Figure
MR semiactive control system block diagram.
Using LabVIEW RT as the real-time control module can improve the reliability and time certainty of program operation. The program is written and debugged in the upper computer, and the running state of the system is monitored. The lower computer is connected to the upper computer through the network cable to ensure the real-time performance of the system and realizes the functions of data transmission and human-computer interaction.
The hardware of the semiactive control system is listed in Table
Hardware of the semiactive control system.
Type | Model | Number |
---|---|---|
Real-time controller | NI PXIe-8108 | 1 |
Data acquisition cabinet | NI PXIe-1082 | 1 |
Analog output module | NI 6363 | 1 |
Analog input module | NI 4496 | 1 |
Power amplifier | TPA10 | 1 |
68-pin shielded junction box | NI SCB-68A | 1 |
Acceleration sensor | BK 4528-B | 2 |
Laser displacement meter | LK-G500 | 1 |
Data acquisition instrument | INV306U | 1 |
Experiment site: ① control computer; ② control program interface; ③ PXI embedded system; ④ data acquisition computer; ⑤ acquisition instrument; ⑥ regulated power supply; ⑦ MR damper; ⑧ QZS vibration isolator; ⑨ laser displacement meter.
The excitation system is a six-degree-of-freedom vibration test bench jointly developed by the University of Wollongong and Hefei University of Technology, which is mainly composed of NI control system, PC computer controller, DMKE electric cylinder, and so on. The data acquisition system includes keyence LK-G500 laser displacement sensors and data collectors (model: INV306U), and the real-time waveforms are captured through DASP software on PC computed.
The design parameter of the spring is shown in Table
The parameter of the spring.
Medium diameter (mm) | Material diameter (mm) | Effective laps | Measured stiffness (N/m) | |
---|---|---|---|---|
Vertical spring | 65 | 4 | 8 | 1017 |
Oblique spring | 42 | 2.8 | 7.5 | 1085 |
When the QZS system is in a static balance, the following relationship should be satisfied:
The test conditions include harmonic excitation with different amplitudes and frequencies:
When the excitation frequency is 1.2 Hz and 2.5 Hz, the test and simulation results of the displacement response of the isolated object are shown in Figures
Time domain response of displacement under 1.2 Hz harmonic excitation with different amplitudes: (a) 3 mm; (b) 5 mm; (c) 7 mm.
Time domain response of displacement under 2.5 Hz harmonic excitation with different amplitudes: (a) 3 mm; (b) 5 mm; (c) 7 mm.
Relative differences of displacement peak between experiment results and simulation results.
Excitation amplitude (mm) | Excitation frequency 1.2 Hz | Excitation frequency 2.5 Hz | ||||
---|---|---|---|---|---|---|
Simulation (mm) | Experiment (mm) | Difference (%) | Simulation (mm) | Experiment (mm) | Difference (%) | |
3 | 3.32 | 3.451 | 5.12 | 0.96 | 1.047 | 9.03 |
5 | 6.05 | 6.456 | 6.71 | 1.05 | 1.261 | 10.54 |
7 | 9.17 | 9.718 | 5.97 | 1.47 | 1.613 | 9.76 |
From Figures
The vibration experiment of the semiactive QZS system with different harmonic excitation frequencies is carried out. The amplitude is 5 mm, and the frequencies are 1.0 Hz, 1.2 Hz, 1.4 Hz, 1.6 Hz, and 1.8 Hz, respectively. The tested and simulated displacement responses of the mass block under different excitation frequencies are shown in Figure
Time domain response of displacement under different excitation frequencies: (a) 1 Hz, (b) 1.2 Hz. (c) 1.4 Hz, (d) 1.6 Hz, and (e) 1.8 Hz.
Displacement peaks from experiment results and simulation results under different excitation frequencies.
Excitation frequency (Hz) | Simulation (mm) | Experiment (mm) | Difference (%) |
---|---|---|---|
1.0 | 6.01 | 6.377 | 5.93 |
1.2 | 6.05 | 6.456 | 6.71 |
1.4 | 4.04 | 4.369 | 8.14 |
1.6 | 2.76 | 3.071 | 11.27 |
1.8 | 2.02 | 2.234 | 10.56 |
From Figure
Let
The tested and simulated displacement transmissibility of the passive and semiactive QZS isolators under different excitation amplitudes is shown in Figure
Displacement transmissibility under different harmonic excitation: (a) amplitude is 3 mm; (b) amplitude is 5 mm; (c) amplitude is 7 mm.
As can be seen from Figure The resonance peak of the system increases with the rise of the excitation amplitude. The initial vibration isolation frequencies of the two kinds of isolators are the same and lower than those of the corresponding linear system, which indicates that the semiactive QZS vibration isolation system also has the characteristics of low-frequency vibration isolation. The semiactive QZS vibration isolator can suppress the resonance much better than the passive one. After reaching the initial isolation frequency, the vibration isolation performance of the semiactive QZS isolator is also superior to the passive QZS.
The RMS of the displacement transmissibility of passive and semiactive QZS isolators under different excitation amplitudes is also computed, as shown in Table
RMS and differences of displacement transmissibility under different harmonic excitations.
Excitation amplitudes (mm) | RMS of passive QZS (mm) | RMS of semiactive QZS (mm) | Differences (%) |
---|---|---|---|
3 | 0.907 | 0.672 | −25.9 |
5 | 1.166 | 0.684 | −41.3 |
7 | 1.474 | 0.698 | −52.6 |
It can be seen that the RMS of displacement transmissibility of semiactive QZS isolator is smaller significantly than that of the passive one, and the larger the excitation amplitude is, the more obvious the difference is.
A semiactive QZS vibration isolator is proposed and designed based on MR damper. The simulation analysis is carried out under different road conditions and different vehicle speeds. The test device and semiactive on-off control system are developed and manufactured, and the correctness of the theoretical derivation and simulation method is verified by experimental results. It can be concluded that For the condition of harmonic, stochastic, and shock road excitations, the semiactive QZS isolator is always superior to the passive QZS in different working conditions, with more obvious control effects The proposed semiactive QZS isolator shows better universality at different frequencies and amplitudes of excitations in the test, and the control algorithms are feasible for the mechanical devices of the isolator and the hardware system
The data used to support the findings of this study are included within the article.
The authors declare that they have no conflicts of interest regarding the publication of this paper.
The work described in this paper was supported by the National Science Foundation of China under grant nos. 11972238 and 11902206.