VOICE COIL FLUID-TUNED ACTUATOR

Transcription

1 VOCE COL FLUD-TUNED ACTUATOR Nader Vahdati etroleum nstitute, O Box 25, Mechanical Engineering, Abu Dhabi, UAE nvahdati@pi.ac.ae A new actuator concept is presented here in this paper. This unique actuator concept combines the features of voice coil actuation and fluid tuned vibration isolation technologies to provide an actuator that is very efficient in power consumption for tonal dominant noise and vibration problems. An analytical model, using bond graph modeling technique, is presented that can be used to optimize the actuator for specific applications. Experimental results are also presented demonstrating the unique features of the actuator and the validity of the analytical model. 1. ntroduction Conventional passive elastomeric mounts have been used as noise and vibration isolators in the aircraft industry since 1970s. For better cabin noise and vibration isolation, passive fluid mounts [1, 2] have been replacing elastomeric mounts in the aerospace industry during the past ten years. However, with ever increasing noise and vibration reduction requirements, the aircraft industry is looking forward to active systems as a means for even better cabin noise and vibration isolation. Active vibration isolation systems require actuators to provide the active force inputs. Here in this paper, a new actuation design is presented to provide this active force. This unique actuator concept combines the features of voice coil actuation and fluid tuned vibration isolation technology to provide an actuator that is very efficient in power consumption for tonal dominant noise and vibration problems. An analytical model is presented that can be used to optimize the actuator design for specific applications. Experimental results are presented and compared with analytical results to validate the analytical model. 2. Hardware Description Figure 1 shows the internal mechanism of the actuator. Actuation authority is provided by a voice coil located in the lower chamber. Both the lower and upper chambers are filled with a nearly incompressible fluid. The lower chamber s low volume stiffness is provided by a metal bellows. The voice coil has six layers of 30 gauge wire with 22 wraps per layer. Current is run in and out of the voice coil by the inner and outer conductive springs located in the lower chamber (not shown). A spring is also used inside the bobbin (Spool) assembly to keep the bobbin centered. The magnets used are neodymium-iron-boron with a measured magnetic flux in the gap of approximately 0.45 tesla. n the upper chamber, the volume stiffness is provided by the rubber tube-form and fluid compressibility. 1

2 The 23 rd nternational Congress on Sound and Vibration Current, provided to the voice coil, creates a force which is applied to the upper chamber on a small area giving an approximate 20.5 mechanical advantage. The actuator is placed parallel to a rubber isolator. current is applied to the actuator, an active force is generated across the passive rubber mount. See Figure Mathematical Model Since the actuator/rubber isolator system involves several different energy domains such as hydraulic, mechanical, and electrical, the bond graph modeling technique [3] is used for modeling purposes. Figure 2 shows the schematic of the active isolator. n Figure 2, the voice-coil fluid actuator is placed in parallel with a passive rubber mount. n series with the actuator, another rubber mount called the decoupler is placed. The function of the decoupler is to decouple the vertical motion from the horizontal motion in the actual application. The bond graph model of Figure 3 was developed from the schematic diagram of Figure 2. Here in this paper, the equations of the motion (state space equations) are derived from the bond graph model of Figure 3. The model of Figure 3 includes all the electrical components (shown as bonds 1 through 5). The inputs to the bond graph model are the current, (Bond 1), and the velocity Vg (t) representing the input velocity. The bond graph model was developed such that it would reflect the way the active isolator is to be tested. 4. Bond Graph Equations The state space equations, derived from the bond graph model of Figure 3, are shown below. q35 q18 q 1 i( t) R31( ) R53( C C C ( 1 ) q ( t) ( 2 ) 1 q q R15 R53( C C ( 3 ) q 18 ) ( 4 ) 1 q R28( ) ( 5 ) C q 29 ( ) 27 q49 q18 q29 27 q38 q35 q 1 R50( ) ) R28( ) R31( ) ) ) R53( C C C C C C ( 7 ) q 35 ( 8 ) q 38 Vg ( t) ( 9 ) q49 q4 q51 R50( ) R47( Vg C C C ( ) CSV23, Athens (Greece), -14 July 201

3 The 23 rd nternational Congress on Sound and Vibration q 4 Vg ( t) ( 11 ) q 49 ( 12 ) q 51 ( 13 ) Notice that the state space A ~ matrix will be a 13 by 13 matrix. n the state space equations, the states are: Spool/Bobbin linear momentum q Change in volume of the upper chamber 1 The momentum of the mass of the fluid in the inertia track q18 Change in volume of the lower chamber 27 The momentum of the mass of the bellows q29 Relative motion across the bellows The momentum of the mass of the actuator body q35 Relative motion across the centering springs q38 Relative motion across the rubber tube-form The momentum of the mass of the fluid in the inertia track q4 Relative motion across the spring Km (see Fig. 2) q49 Relative motion across the decoupler q51 Relative motion across the test fixture stiffness Kfix (see Fig. 2) The output equations are: u q 1 R53( ( 14 ) C 1 V s ( 15 ) F in q4 q38 q 1 R47( Vg Ap ApR53( ( 1 ) C C C 4 38 q4 q 4 ( 17 ) The output equations are defined as: u ressure in the upper chamber Vs Spool/Bobbin velocity Fin nput force to the entire active mount, effort on bond 13 q4 Relative motion across the spring Km (see Fig. 2) The inputs to the state space equations are the current i(t) given to the coil and the velocity Vg(t), see Figure MATLAB Simulations An M-file was written using MATLAB software to simulate the behavior of the active isolator (Figure 2). Two sets of simulations were conducted. n the first simulation, the MATLAB program was used with the baseline parameters given in Table 1. The baseline simulation results were compared to experimental results. Several parameters were then varied till the simulation results 1 CSV23, Athens (Greece), -14 July 201 3

4 The 23 rd nternational Congress on Sound and Vibration matched the experimental results. These new parameters are shown in Table 2 and used to for future improved design of the actuator. Active Mount Baseline arameters Table 1 shows the baseline parameters used for the baseline simulation. Table 1: Active Mount Baseline arameters. Definition Symbols in MATLAB English Units Value S Units Value Force to current ratio of the coil ALHA lbf/a 3.22 N/A Spool Mass Ms.8e-5 lbf-s^2/in grams Fluid inertia in the gap SB lbf-s^2/in^5 8e N-s^2/m^5 Flow resistance in the gap RSB lbf-s/in^5 9.35e N-s/m^5 Viscous damping coeff. RSC 8.e-5 lbf-s/in N-s/m Stiffness of the conductive & Centering springs KCS.0 lbf/in 7530 N/m Effective piston area Ap 1.22 in^ mm^2 Area of Spool in^ mm^2 Mass of the bellow MBEL lbf-s^2/in 95.4 grams Stiffness of the bellow KBEL 5.0 lbf/in 11,382 N/m Damping coeff. of the bellow CBEL Upper Chamber Volume stiffness KVUC 50,000 lbf/in^5 2.7 e14 N/m^5 Lower Chamber Volume stiffness KVLC 9205 lbf/in^ e12 N/m^5 Tan of the rubber TAND Decoupler stiffness KLD 300,000 lbf/in 52,535,328 N/m Core mass, mass of the mount inner member MCORE 2.59e-3 lbf-s^2/in grams Flame body mass MBODY 3.88e-3 lbf-s^2/in 80.3 grams Shear stiffness of the tube-form KSH lbf/in 923,220 N/m Mount stiffness KR 8,251 lbf/in 15,4,082 N/m Simulation Results of the Baseline arameters The baseline parameters tabulated in table 1, were used to perform the baseline MATLAB study. The M-file program written in MATLAB was used for the simulation. Many nonlinearities such as friction, or material nonlinearities of the rubber were ignored. t is expected that the actuator will provide upper chamber pressure in the order of 12.5 psi/amp for most frequencies and at the fluid resonance (250 Hz) provide larger pressures. t is also expected that the free displacement across the mount to be 1.75e-4 inches/amp for most frequencies and have larger free displacement at 250 Hz. Figures 4 through 7 were obtained from MTALAB. Figure 4 shows the Bode magnitude and phase plots of the spool displacement divide by the input current. Figure 4 indicates that the maximum spool displacement indeed occurs at around 250 Hz, if the actuator operates at the baseline parameters. f the current is turned off and the isolator plus the actuator is driven with an input displacement, the passive dynamic stiffness of the isolator/actuator system will be as of Figure. The notch frequency of the dynamic stiffness is a bit above 250 Hz. Figure 8 shows the free-displacement experimental test data that was achieved with the active mount. Sweeps were conducted at 0.5, 1.0, 2.0, and 4.0 amps from to 500 Hz. Figure 9 shows the experimental passive dynamic stiffness of the isolator which includes the active actuator. t should be noted that the notch frequency is about Hz and that the notch depth is almost nonexistent. This indicates that considerable damping exists within the actuator. Experimental results of Figures 8 and 9 indicate that the resonance frequency has shifted to 175 Hz from the calculated 250 Hz. The experimental results suggest that these results are probably due to too much damping and inertia. The experimental results reveal that the actual pressure in the upper chamber is less than CSV23, Athens (Greece), -14 July 201

5 The 23 rd nternational Congress on Sound and Vibration psi/amp for most frequencies and about 12.5 psi/amp at 175 Hz (data not shown). The free displacement of the active mount is less than inches/amp at most frequencies and about inches/amp at 175 Hz. The experimental results also reveal that the actuator is not linear meaning the pressure-current ratio or free displacement-current ratio does not stay the same as current is increased, see Figure 8. Active Mount New arameters When the actuator plus the isolator mathematical model was being developed and the active mount parameters were being estimated, some assumptions were made. For example, the spool's movement was assumed to have no impact on the value of fluid inertia and viscous damping. Friction was assumed negligible. The high hydrodynamic pressure build up in the lower chamber due to spool movement causing fluid to be wedged into the decreasing space was ignored. The dependency of the elastomer material properties to frequency was ignored. t is obvious that the actual active mount damping is much higher than what we have estimated in Table 1, and fluid inertia (or effective moving mass) is higher than what was estimated. To emulate the effect of fluid inertia, the spool mass, Ms, was increased by a factor of two. To add more damping due to friction, spool motion and its effect on fluid viscous damping, hydrodynamic pressure build up in the lower chamber, and so on, the viscous damping parameter, RSC, was increased. Table 2 shows the new parameters that best matched the experimental results. it can be seen from Table 2, only two parameters were changed, namely the spool mass, Ms, and viscous damping, RSC. Sensitivity analysis was performed with MATLAB till the simulation results were matched with the experimental results. The only parameter that was varied here was RSC, and the spool mass, Ms, set to 22.7 grams. Table 2 shows the final parameters. RSC was increased by a factor of 988 times. Table 2: Active Mount arameters Best Matched the Experimental Results. Symbols in English Units Value S Units Value Definition MATLB program Force current ratio of the coil ALHA lbf/a 3.22 N/A Spool Mass Ms 1.295e-4 lbf-s^2/in 22.7 grams Fluid inertia in the gap SB lbf-s^2/in^5 8. e N-s^2/m^5 Flow resistance in the gap RSB lbf-s/in^5 9.35e N-s/m^5 Viscous damping coeff. RSC lbf-s/in 14.8 N-s/m Stiffness of the conductive and Centering springs KCS.0 lbf/in 7530 N/m Effective piston area Ap 1.22 in^ mm^2 Area of Spool in^ mm^2 Mass of the bellow MBEL lbf-s^2/in 95.4 grams Stiffness of the bellow KBEL 5.0 lbf/in 11,382 N/m Damping coeff. of the bellow CBEL Upper Chamber Volume stiffness KVUC 50,000 lbf/in^5 2.7 e14 N/m^5 Lower Chamber Volume stiffness KVLC 9205 lbf/in^ e12 N/m^5 Tan of the rubber TAND Decoupler stiffness KLD 300,000 lbf/in 52,535,328 N/m Core mass, mass of the mount inner member MCORE 2.59e-3 lbf-s^2/in grams Flame body mass MBODY 3.88e-3 lbf-s^2/in 80.3 grams Shear stiffness of the tube-form KSH lbf/in 923,220 N/m Mount stiffness KR 8,251 lbf/in 15,4,082 N/m Simulation Results With the New arameters MATLAB simulation results of Figures and 11 indicate that with the increase in inertia and damping, the resonance frequency indeed shifted from 250 to 175 Hz. From these results one can conclude that the actual fluid inertia (accounted for in the mass of the CSV23, Athens (Greece), -14 July 201 5

6 The 23 rd nternational Congress on Sound and Vibration spool) and the viscous damping are much higher than the estimated baseline parameters.. Conclusions The mathematical model of the active mount (rubber mount plus the actuator) was quite accurate in predicting the active mount behavior. When the inertia and fluid damping was increased, the simulation results very well matched the experimental results. This indicates that the bond graph model is good and the only issues are the baseline parameters. f careful attention is given to active mount parameters, the bond graph model is good enough to predict active mount performance. Experimentally, mechanical aspects of the active mount worked quite well. erformance was limited by fluid damping and inertia effects in the lower chamber. Figure 8 indicated that the active mount behavior is somewhat nonlinear. At frequency near 200 Hz, the free displacement current ratio is 380/4=95 in/amp (for 4 amps), 200/2=0 in/amp (for 2 amps), and 80/1=80 in/amp (for 1 amp). To account for such nonlinearities, a nonlinear model will be needed. Figure 1: nternal Mechanism of the Actuator. Figure 2: Single Axis Schematic Diagram of the actuator parallel to a rubber mount. Figure 3: Bond Graph Model of the Figure 2. CSV23, Athens (Greece), -14 July 201

7 The 23 rd nternational Congress on Sound and Vibration Simulation Results with Baseline arameters Figure 4: Spool Displacement. Figure 5: Upper Chamber ressure & Mount Free Displacement lots. Figure : Baseline arameters - assive Dynamic Stiffness of the Active Mount. Figure 7: Baseline arameters - Spool Displacement (Magnitude and hase). CSV23, Athens (Greece), -14 July 201 7

8 The 23 rd nternational Congress on Sound and Vibration Figure 8 Figure 9 Figure 8: Experimental free displacement results versus frequency at different currents. Figure 9: assive Dynamic Stiffness of the solator. Figure Figure 11 Figure : New parameters - Upper Chamber ressure and Mount Free Displacement lots. Figure 11: New arameters - assive Dynamic Stiffness of the solator. REFERENCES 1 Vahdati, N. A Detailed Mechanical Model of a Double umper Fluid Mount, ASME Journal of Vibration and Acoustics, 120 (2), , (1998). 2 Vahdati, N. Double Notch Single umper Fluid Mounts, Journal of Sound and Vibration, 285 (3), 97-7, (2005). 3 Rosenberg, R. C. and Karnopp, D. C., ntroduction to hysical System Dynamics, McGraw- Hill Book Company, New York, (1983). 4 Streeter, V. L. and Wylie, E. B. Fluid Mechanics, McGraw-Hill Book Company, New York, (1979). 5 Freakley. K. and ayne, A. R. Theory and ractice of Engineering with Rubber, Applied Science ublishers LTD, London, (1978). 8 CSV23, Athens (Greece), -14 July 201