A MAGNETORHEOLOGIC SEMI-ACTIVE ISOLATOR TO REDUCE NOISE AND VIBRATION TRANSMISSIBILITY IN AUTOMOBILES

Transcription

1 A MAGNETORHEOLOGIC SEMI-ACTIVE ISOLATOR TO REDUCE NOISE AND VIBRATION TRANSMISSIBILITY IN AUTOMOBILES Gregory J. Stelzer Delphi Automotive Systems Chassis Systems Test Center, Dayton, OH Mark J. Schulz, Jay Kim, Randall J. Allemang Department of Mechanical Engineering University of Cincinnati, Cincinnati, OH

2 1. INTRODUCTION OUTLINE 2. BACKGROUND 3. MODELING OF RHEOLOGIC FLUIDS 4. MODELING OF ISOLATION SYSTEMS 5. RESULTS 6. MR ISOLATOR COIL DESIGN 7. CONCLUSIONS 8. RECOMMENDATIONS OF FUTURE WORK

3 INTRODUCTION Passive vibration isolators are inexpensive and simple. For these reasons, most isolation systems in automobiles use passive isolators. When using a passive vibration isolator, there is a tradeoff between Noise, Vibration, and Harshness (NVH) performance and durability characteristics. Passive isolators cannot provide both optimal isolation and optimal durability. The object of this thesis is to develop an advanced vibration isolator design for automotive components that can provide substantial and d cost- effective improvements in NVH performance. The new work in this thesis will provide: 1. Information on the advantages and limitations of semi-active isolation. 2. A detailed nonlinear model of the isolator. 3. The results of extensive simulation studies of a practical design.

4 1-2. INTRODUCTION In the automotive industry, noise control expectations from the end user are becoming more strict, and consequently the Original Equipment Manufacturer (OEM) has responded by placing higher expectations on the suppliers. Noise control specifications have now become standard on many of the smallest components in the vehicle. A customer will now use component performance to develop a list of acceptable candidates, and then use NVH to determine where the business b is awarded. This increased emphasis on noise reduction and operator comfort is requiring that more attention be paid to the use of vibration and d noise isolation and attenuation systems in automobiles.

5 1-3. INTRODUCTION A compressor, used in an automobile s leveling systems, will be used as an example in this research. A leveling system is used to keep a vehicle level with respect to road surface, ie,, when a load is placed in the back of the truck, the rear suspension is compressed more than the front. A leveling system will raise the back end of the vehicle so that it is once again level with the front. The compressor pumps air into the vehicle shocks, and this is what raises the back end of the vehicle. When the compressor runs, it generates high frequency vibration that is transmitted to the vehicle structure.

6 1-4. INTRODUCTION In this research, the compressor will be modeled as a mass with a force that produces high frequency excitation. The isolator design will minimize the transmitted force from the compressor to its structural base, a vehicle body. From this point, the component generating the high frequency excitation will be referred to as a compressor.

7 FIGURE 1.1. A compressor assembly with passive isolators.

8 2-1. VIBRATION ISOLATORS A vibration isolator is a flexible device that is used to attach the compressor to a mounting base. The purpose of the isolator is to reduce the vibration or force transmitted between the compressor and the base. Different possible approaches for vibration isolation of automobile components are described and compared. The following systems are discussed: 1. Passive isolation systems. 2. Semi-active isolation systems. 3. Active isolation systems. 4. Smart materials for actuators.

9 Passive Isolation Systems In a passive isolation systems, no controls are needed for the isolator. i The design consists of a simple natural rubber material, or a comparable synthetic material. This is the cheapest option because it is the simplest design and d the easiest to manufacture. The durability of the isolator can be improved by stiffening the isolator. This can be done simply by increasing the durometer hardness of the material or by changing material. However, as the stiffness of the isolators is increased, the noise performance of the compressor will be compromised, because a stiffer isolator will generally transmit higher frequency vibration.

10 2-3. Passive Isolation Systems FIGURE 2.1. Design of a passive isolator.

11 2-4. Passive Isolation Systems A hydromount is a more complex passive isolator. A fluid is incorporated into the design to provide extra damping. Fluid is forced through an orifice within the isolator. The resistance provided by the orifice provides damping for the isolated compressor. The increased damping allows the isolator to be designed of a less stiff material. The combination of reduced stiffness and increased damping allows the hydromount to provide better isolation without compromising durability. However, the added damping increases the transmitted force, and therefore, the system is not an optimal solution.

12 2-5. Passive Isolation Systems MOUNTING LOCATION ORIFICE ORIFICE FLUID FLUID MOUNTING LOCATION ELASTOMER SURROUNDING FLUID FIGURE 2.2. Design of a passive hydromount.

13 2-6. Passive Isolation Systems A transmissibility model was developed to show some of these concepts. It shows the compressor mounted to its structural base through an isolator that has only passive stiffness and passive damping components (k and c, respectively). k Compressor Base c x y FIGURE 2.3. Transmissibility model.

14 2-7. Passive Isolation Systems The transmissibility model is used to create a ratio between force seen in the compressor due to rotation unbalance and force transmitted through the isolator into the base. The ratio is developed by summing the forces in the model. F + = mx & = k( y x) + c y x (2.1) Assuming x and y are sinusoidal displacements for the compressor and base, respectively, velocity and acceleration can be calculated by taking the derivative of the displacement. The result is: 2 mω X = ky kx + jωcy jωcx (2.2) where X and Y are amplitudes of vibration and ω is the rotational speed of the compressor.

15 2-8. Passive Isolation Systems The equation is rewritten as: k mω 2 + jωc X = k + jωc Y (2.3) Solving, the amplitude of the mass, X, divided by the amplitude of the base, Y, gives the transmissibility. Y X k + jωc k mω + jωc = 2 (2.4)

16 2-9. Passive Isolation Systems X Y FIGURE 2.4. Transmissibility as a function of the stiffness of the isolator.

17 2-10. Passive Isolation Systems X Y FIGURE 2.5. Transmissibility as a function of the damping of the e isolator.

18 2-11. Semi-Active Isolation Systems A semi-active isolator can only remove energy from the system. However, a semi-active isolator is capable of changing one or more properties in response to a command signal. The ability to change system properties gives the system designer r more control while using very little input power. An example of a semi-active system is a shock absorber with a variable orifice that allows the damping coefficient to be changed as needed.

19 2-12. Active Isolation Systems Active isolation systems can be controlled by computers through input signals from sensors. Unlike passive and semi-active systems, active systems are able to add energy to the system. The goal of active isolation is to provide energy equal in magnitude and opposite in phase of the vibration input. In doing so, an active e isolation system can improve noise performance and durability performance. An example of an active system is an electromechanical actuator arranged to generate force by responding to a velocity or displacement feedback signal.

20 2-13. Active Isolation Systems However, active systems are very design intensive and require sensors and processors to provide real time data to the isolator. Large amounts of power are also required to operate an active isolator. These necessary features of the active isolation system make it the most expensive isolation design. Because of the expense, active isolation systems are very uncommon. on.

21 2-14. Smart Materials As Actuators Several different materials have been developed to allow designers to use them as actuators in a system. Piezoelectric materials experience a dimensional change when an electrical voltage is applied to them. Conversely, these materials produce an electrical charge when a pressure is applied to them. This rare property allows the piezoelectric material to be used as a sensor or an actuator. The best known such material is lead-zirconate zirconate-titanatetitanate (PZT). However, the use of PZT for vibration isolation is limited due to the small strain capability of the material.

22 2-15. Smart Materials As Actuators Shape memory alloy (SMA) material possesses the interesting property in that a metal remembers its original shape and size and changes back to that shape and size at a characteristic transformation temperature. Materials that exhibit these characteristics include: gold-cadmium, brass, and nickel-titanium. The alloys inherent properties have become very useful to the medical field. The SMA s ability to generate high forces at low frequency allows the material to be used as an actuator. However, the use of SMA in engineering applications has been limited ited because of slow response time and due to the limited temperature range in which it can be effective.

23 3-1. MODELING OF RHEOLOGIC FLUIDS A rheologic fluid changes properties as an external field is applied. These fluids can be used as controllable energy dissipaters. The control used is semi-active, and with this approach small control energy can produce large actuation forces. The following characteristics of a rheologic fluid will be discussed: 1. ER/MR fluid isolator systems. 2. Bingham plastic model of MR fluids. 3. MR fluid isolator systems.

24 3-2. ER/MR Fluid Isolator Systems A great deal of research has been conducted on semi-active control to look for a compromise between passive and active isolation systems. These systems can be used for vibration suppression or isolation and require minimal power as compared to an active system. With a semi active system, noise performance can be improved without dramatically hindering durability capabilities.

25 ER/MR Fluid Isolator Systems Extensive studies have been conducted on Electro-Rheologic (ER) and Magneto-Rheologic (MR) fluids for use in semi-active systems that are used for vibration suppression. The two materials were discovered in the late 1940 s. Jack Rabinow reported on a MR fluid experimental program at the U.S. National Bureau of Standards for the Army s Chief of Ordinance in Winslow published his account of a lengthy research program investigating the properties and applications of ER fluid in

26 3-4. ER/MR Fluid Isolator Systems Initial testing with ER fluids showed problems with the fluid, namely n operating temperature limitations and storage stability problems. Over time improvements have been made, but new problems have arisen. Today, ER fluids are considered to have low shear strengths. The fluid provides shear strengths that are two to ten times lower than t needed for many practical applications. High voltages are required to operate ER fluids. There is a lack of universal fluid for ER technology. Because of these limitations, commercial success of ER fluids has been elusive.

27 3-5. ER/MR Fluid Isolator Systems MR fluids are more practical. When compared to ER fluids, MR fluids offer higher order yield stresses and provide a better operating temperature range. At the same time, companies such as Lord Corporation have commercial MR products. Because of the advantages of MR fluid over ER fluid, MR fluid will be considered from this point.

28 3-6. Bingham Plastic Model Of MR Fluids MR fluids are traditionally modeled as a Bingham plastic, where there is a passive and active component to the fluid. Where F MR = + f yield c MR x y τ = τ y + η MR γ (3.1) is the equation used to model the fluid. The passive component c MR is a function of the fluid resistance r from the viscosity, which is a property of the fluid and cannot be controlled. f The active component yield is derived from the yield stress, which changes proportionally with the applied magnetic field.

29 3-7. Bingham Plastic Model Of MR Fluids Initial research showed the passive resistance could be modeled as a constant. τ τ y (F 3 ) τ y (F 2 ) τ y (F 1 ) 0 F 3 F 2 F 1 η η 0 γ F o =0 INCREASING FIELD STRENGTH Figure 3.1. Shear stress versus shear strain rate for a Bingham plastic material.

30 3-8. Bingham Plastic Model Of MR Fluids However, further investigation showed that viscosity is a function of shear rate, with the viscosity increasing dramatically at lower shear rates. 5 MR Fluid Characteristics - MRF 132LD - Lord Corporation 4 3 Viscosity (Pas) Shear Rate (1/s) Figure 3.2. Viscosity of a MR fluid is a function of shear rate.

31 3-9. Bingham Plastic Model Of MR Fluids The active component is derived from resistance due to yield stress, which is a function of the magnetic field created by a coil c that is incorporated into the isolator. 5 x 104 MR Fluid Characteristics -- MRF 132 LD - Lord Corporation Y ield S tre s s (P a) H (Amp/m) x10 5 Figure 3.3. Yield stress as a function of magnetic field.

32 3-10. MR Fluid Working Modes MR fluid has three different types of working modes, depending on o how the fluid is loaded. The modes include: 1. Shear mode. 2. Flow mode. 3. Squeeze mode. Different equations are used to calculate resistive force for each of the different modes.

33 3-11. MR Fluid Working Modes COIL COIL v COIL Compression Tension F Moving Surface Moving Surface B p 1 p 2 B B Flux Guide Flux Guide Flux Guide (a) (b) (c) Figure 3.4. Three working modes of a MR fluid (a) shear, (b) flow, and (c) squeeze. B is the magnetic flux direction.

34 3-12. MR Fluid Working Modes The shear mode works when one surface moves through the fluid with respect to another surface. The magnetic field is perpendicular to the direction of motion. A MR based clutch is a good example of working the fluid in the shear mode. The equation corresponding to the shear mode is: f = SLbη + Lbτ h y (3.2) where f is the resultant force based on the plate area, and S, L, b, and h are the surface area, length, width, and height, respectively. η Is the viscosity of the fluid and is the yield strength of the e fluid. τ y

35 3-13. MR Fluid Working Modes The flow mode is characterized by two static flux guides with the magnetic field normal to the flow. The magnetic field can be used to control flow resistance and pressure drop across the valve. Automotive shock absorbers work in the flow mode. The equation corresponding to the flow mode is: P = P + P ER HF 0, HF, where Q is the flow rate of the fluid. = 12η QL + 3Lτ h y bh3 (3.3)

36 3-14. MR Fluid Working Modes The squeeze mode works when two parallel surfaces are used to compress the fluid. The magnetic field is parallel to the motion of the surfaces. The magnetic flux density can be used to adjust the normal force to resist the motion. The squeeze mode has been shown to damp vibrations with high forces and low amplitudes. The equation corresponding to the squeeze mode is: 2 a3 F = πτ 0 Φ( x) h h( t) 0 (3.4)

37 4-1. MODELING THE ISOLATION SYSTEM A single degree of freedom model is used to model the compressor system. The model simulates a compressor mounted to a vehicle body. To simplify the model, the motion of the vehicle body is modeled as a 1 Hz sine wave. This simulates the vehicle body bouncing at the natural n frequency of the suspension system. Two seconds of data are simulated. Halfway through the model, a speed bump is introduced. The speed bump is a severe test of the isolator s durability.

38 4-2. MODELING THE ISOLATION SYSTEM Two models are created. One for the passive system and the other r for the semi-active system. The following discussion is included: 1. Simulation of the passive isolator. 2. Simulation of the semi-active isolator. 3. Newmark-Beta explicit time integration. 4. Filter design. 5. Control law design. 6. System inputs. 7. System outputs. 8. Detailed design of the MR isolator.

39 4-3. Simulation Of The Passive Isolator The passive model was used to create baseline performance standards for the existing isolator, and to show trend lines when stiffness s and damping parameters are changed. The passive model can be seen in Figure 4.1. The model shows the compressor mounted to the vehicle body through an isolator that has only passive stiffness and passive damping components (k( passive and passive, respectively). c passive 1. The free body diagram for the passive system can be seen in Figure 4.2. This diagram helps show how the equation of motion and the equation for transmitted force are developed.

40 Simulation Of The Passive Isolator x(t) F COMPRESSOR F COMPRESSOR ASSUME x>y COMPRESSOR COMPRESSOR k PASSIVE y(t) c PASSIVE k PASSIVE ( x y) cpassive ( x y ) VEHICLE BODY VEHICLE BODY Figure 4.1. Passive model. Figure 4.2. Passive free body diagram.

41 4-5. Simulation Of The Passive Isolator The equation of motion is created by summing the forces seen in the free body diagram, given by: + F = mx (4.1) This summation of forces is: = m x k ( x y) c x y + F PASSIVE PASSIVE COMPRESSOR (4.2) Rearranging gives: m x = k y k x + c y c x+ PASSIVE PASSIVE PASSIVE PASSIVE F COMPRESSOR (4.3) The acceleration of the compressor, x, is then calculated as: 1 x = m k ( y x) + c y x + F PASSIVE PASSIVE COMPRESSOR (4.4)

42 4-6. Simulation Of The Passive Isolator The force transmitted into the vehicle body is also seen in the free body diagram. A transmitted force is considered any force created from the relative motion between the vehicle body and the compressor that acts upon the vehicle body. The transmitted force is computed using: + F = F TRANS (4.5) Including the spring and damper force in (4.5) gives: + F = F = k ( x y) + c x y TRANS PASSIVE PASSIVE (4.6)

43 4-7. Simulation Of The Passive Isolator The compressor assembly consists of three baseline isolators and the compressor. Each isolator is a simple passive isolator with the following properties: Synthetic rubber material of 60 durometer. Rated to withstand temperatures up to 110 C. Measured stiffness of k=50,000 N/m and damping ratio of zeta=0.1. Height of 20 mm, outer diameter of 14 mm, and mass of 6.8 grams. The compressor has the following properties: 230 mm long, 180 mm wide, and 110 mm tall. Mass of 3 kg (6.6 lbs.) For the model, it was assumed that one-third of the mass (1 kg) was on each isolator.

44 4-8. Simulation Of The Semi-Active Isolator The semi-active isolator was modeled to replace the passive isolator. The fluid was modeled as a Bingham plastic, where there is a passive sive and active component to the fluid. The equations used to model the fluid are as follows: F MR x = f + c y yield MR (4.7) τ MR = τ + ηγ y (4.8)

45 4-9. Simulation Of The Semi-Active Isolator The c MR component of the fluid is the passive part of the fluid. It is a function of the viscosity of the fluid, η, the shear rate of the fluid, γ, and the geometry of the flow path. The shear rate of the fluid is a function of the relative velocity and the fluid gap width. The viscosity of the fluid is a function of the e shear rate. The f yield is the active isolation component of the MR fluid. It is a function of the yield strength of the fluid,. The yield strength of the MR fluid is related to the resistance force through the gap area of the isolator s flow channels and the strength of the magnetic field surrounding it. τ y

46 4-10. Simulation Of The Semi-Active Isolator F component x(t) Compressor Amplifier For MR Coil y(t) k passive MR Vehicle Body c passive Control Filter Integrator Processor With Control Law Figure 4.3. Semi-active model of the MR isolator.

47 4-11. Simulation Of The Semi-Active Isolator F COMPRESSOR ASSUME x>y COMPRESSOR k ( x y) F PASSIVE MR cpassive ( x y ) VEHICLE BODY Figure 4.4. Semi-active free body diagram.

48 4-12. Simulation Of The Semi-Active Isolator The equation of motion is created by summing the forces seen in the free body diagram, given by: + F = mx (4.9) However, in the semi-active system, forces created by the MR fluid are included in the equation of motion. + F = m x = k ( x y) c x y F + F PASSIVE PASSIVE MR COMPRESSOR (4.10) Rearranging gives: m x = k y k x + c y c x F + PASSIVE PASSIVE PASSIVE PASSIVE MR F COMPRESSOR The acceleration of the compressor,, is then calculated as: 1 x = m k ( y x) + c y x F + F PASSIVE PASSIVE MR COMPRESSOR x (4.11) (4.12)

49 4-13. Simulation Of The Semi-Active Isolator The transmitted force equation for the semi-active system is very similar to the passive equation. The transmitted force is computed using: + F = F TRANS (4.13) But once again, the forces generated by the MR fluid need to be considered. + F = F = k ( x y) + c x y + F TRANS PASSIVE PASSIVE MR (4.14) It is important to note that the MR force is transmitted into the e vehicle body. For this reason, the control of the MR fluid is very important.

50 4-14. Simulation Of The Semi-Active Isolator To generate the passive and active force components from the MR fluid, the pressure drop through the isolator must be analyzed. L ηql P = 3 τ y + 12 h bh3 (4.15) From (4.15), the force components can be derived using the area of the flow channel, A gap, and the area of the isolator plunger, A i. The derivation of the active component follows: f yield L = A gap 3 τ y = 3π r2 o r2 h i L τ h y (4.16) It is important to note that the active component of the MR fluid d is directly proportional to the yield stress of the fluid.

51 4-15. Simulation Of The Semi-Active Isolator The derivation of the passive component is a little more complicated. The passive force is related to the viscosity and flow rate. c MR ηql x y = 12 bh 3 (4.17) However, the flow rate is a function of relative velocity. c MR x y 2 L ηπr x y i = π r o r i bh3 ηa i x y ηql 12A gap 12A = = 3 gap bh bh3 (4.18) When the velocity is factored out, the passive component is seen as being proportional to the viscosity of the fluid and the geometry y of the isolator ηπr L c = 12π r r i 12 r2 r2 r2 MR o i π 3 i π = o bh i ηl bh3 L (4.19)

52 4-16. Simulation Of The Semi-Active Isolator Simplifying, the equation for the passive component of the MR fluid is found. c MR ηl = 12 A i A gap bh3 (4.20) Combining the passive rubber components and the MR components of the isolator, the MR based isolator is modeled as follows: = ( x y) + ( c + c ) x y f MR yield F k + Isolator (4.21)

53 4-17. Simulation Of The Semi-Active Isolator The control of the f yield component is very important. The goal of the f yield term is to control road input frequencies without transmitting higher frequencies created by the compressor. This done by controlling the active MR component to model the passive damping provided by the isolator, but using a low pass filter to eliminate the higher frequencies created by the compressor.

54 4-18. Newmark-Beta Explicit Time Integration Method This is an integration method with force balance iteration used to move from one time point to the next because the equations of the isolator system are nonlinear and cannot be solved in closed form. The integration method requires initial displacement, velocity, and acceleration components. It then calculates displacement and velocity for the next time point, and inputs them into the equation of motion. Ten iterations are run for each point, allowing the calculations to converge. This is an accurate, flexible, and simple method for solving nonlinear equations. However, a small time step is required.

55 4-19. Filter Design The low-pass filter was designed as a second order Butterworth filter. The filter was designed with a cutoff frequency of 30 Hz in order r to turn off the actuator at 50 Hz so the compressor vibration is not transmitted to the automobile frame. Figure 4.5 shows how the filter introduces amplitude distortion based on frequency. It also shows how the filter introduces phase lag into the response of the active MR component.

56 4-20. Filter Design 1 Second Order Butterworth Low Pass Filter Properties Hz 0.8 Magnitude Frequency (Hz) Phase (deg) Frequency (Hz) Figure 4.5. Characteristics of a second order Butterworth filter.

57 4-21. Filter Design The following shows how the low-pass filter works: v = relative velocity v Filter z yield stress=z*scale The active variable v is set equal to the relative velocity between een the compressor and the structural base. It is then filtered, producing a variable z with the compressor excitation content removed. The variable z is then scaled to produce the yield stress of the fluid.

58 4-22. Filter Design The variable v is exactly in phase with the passive isolation force. If the filter was a perfect filter, there would be no phase lag in variable z, and it too would be exactly in phase with the passive isolation force. However, as seen in Figure 4.6, when the vehicle hits the bump, the response of the active component lags behind the passive component nt by roughly ninety degrees. Because the active component lags, it cannot be as effective as possible. If the amplitude of the active MR component is scaled too high, this phase lag can cause a phase lag induced instability in the model.

59 4-23. Filter Design 15 Active component lags behind the passive component. passive active 10 Damping Force (N) Time (s) Figure 4.6. Showing the phase lag with a Butterworth low pass filter. f

60 4-24. Filter Design Several ideas were explored to resolve this phase lag issue and improve results. A phase lag compensator can be used to correct the phase lag. Displacement and velocity feedback control with phase lag can be resolved into corrected displacement and velocity components. This feedback can be used in a linear control law. The limitation of this technique is that both position and velocity feedback are needed. Another idea is the concept of an ideal filter, as seen in Figure e 4.7. This filter would have no phase lag at any frequency. The amplitude cut-off is perfect at the cutoff frequency.

61 4-25. Filter Design 180 Ideal Low Pass Filter Phase Frequency (Hz) 0 1 Magnitude Frequency (Hz) Figure 4.7. Characteristics of an ideal low-pass filter.

62 4-26. Filter Design To get the desired results for this type of control system, research showed that the design of the low pass filter is a very important t factor. Research also showed that compensating for phase lag is very complicated. While this subject needs further research, a simpler approach was s taken for this model. To illustrate the adverse affects of the low pass filter, the filter was simply turned off when the compressor was off. The filter was there for the sole purpose of taking out the component onent in the relative velocity response due to the compressor. If the compressor is not running, there is no reason to have the filter on.

63 4-27. Control Law Design A skyhook control algorithm was considered for the control of the isolator. It was based on the following logic: Positive absolute velocity (+) Positive relative velocity (+) Controller ON Negative relative velocity (-) Negative absolute velocity (-) Positive relative velocity (+) Controller OFF Negative relative velocity (-) Controller ON Figure 4.9. Diagram of skyhook control law.

64 4-28. Control Law Design A careful evaluation of the results showed that the active MR component would not react immediately to the bump in the model. 15 Skyhook control does not allow the active component to react properly. passive active 10 Damping Force (N) Time (s) Figure Skyhook control law does not allow the isolator to react properly to a bump.

65 4-29. Control Law Design A relative skyhook control algorithm was investigated. It was based b on the logic below. It was quickly noted that this control was the same as always having the control on. Positive relative velocity (+) Positive relative velocity (+) Controller ON Negative relative velocity (-) Negative relative velocity (-) Controller ON Figure Diagram of relative skyhook control law.

66 4-30. Control Law Design With no skyhook control, the isolator is able to react properly. 15 No skyhook control allows the active component to react properly. passive active 10 Damping Force (N) Time (s) Figure No skyhook control allows the isolator to react properly.

67 4-31. Control Law Design In the control system shown in Figure 4.3, an accelerometer is located l on the compressor and another accelerometer is located on the vehicle body. The acceleration signals can be integrated and then subtracted to give the velocity of the compressor relative to the vehicle body. This relative velocity is used as a feedback signal in the control ol algorithm. While this approach is feasible, the two channels of data acquisition ition and the signal processing would add complication and cost to the isolator system.

68 4-32. Control Law Design Another approach is to design a direct relative velocity sensor that is built into the isolator. The velocity of the piston in the isolator with respect to the base b is the relative velocity that must be measured. It may be possible to have a magnet built into the piston rod and d a small coil of wire attached to the isolator housing which is attached to the base. The magnet moving through the coil of wire around the piston rod will produce a voltage in the coil that will be proportional to the velocity v of the magnet relative to the coil.

69 4-33. Control Law Design Another possible approach is to use a Linear Variable Differential Transformer. These devices are used to measure relative displacement and may be adapted to measure velocity, or the derivative of the relative displacement may be taken to obtain relative velocity. A design with a sensor in each isolator would have the added possibility sibility and advantage of individually controlling each isolator. This would w provide rotational isolation for the component and is a potentially simple approach to achieve multi-degree degree-of-freedom freedom control. The development of such a sensor should be investigated in future work.

70 4-34. System Inputs The unbalance force due to the compressor rotation is simulated as a sinusoidal force input to the compressor mass. As discussed earlier, the compressor is turned on and off during the simulation. The vehicle body motion is modeled as a body heave mode, with a speed bump input midway through the simulation. Both inputs can be seen in Figure 4.13.

71 4-35. System Inputs 20 Model Inputs Noise Source Input (N) Vehicle Body Motion (m) Time (s) Figure Model inputs for the compressor and vehicle body.

72 4-36. System Outputs The main outputs from the simulation are: Power spectral density of the transmitted force at 50 Hz, the frequency of the compressor. The PSD is calculated during the time period that the compressor is on. An example of the PSD is seen in Figure Maximum relative displacement between the compressor and the vehicle body. This occurs shortly after the bump. This is considered a measure of durability of the isolator.

73 4-37. System Outputs 10 2 Power spectral density of the transmitted force Power Spectral Density (N 2 /Hz) Frequency (Hz) Figure Example of a power spectral density plot.

74 4-38. Detailed Design Of The MR Isolator Once the control and filter issues were resolved, a fluid was chosen. Lord Corporation s web site was used to get fluid properties on their product MRF 132LD. This fluid was chosen because it had low viscosity properties. The properties of MRF 132LD can be seen in Figure 4.15.

75 4-39. Detailed Design Of The MR Isolator MR Fluid Characteristics - MRF 132LD - Lord Corporation Viscosity (Pas) Shear Rate (1/s) 5 x 104 Yield Stress (Pa) H (Amp/m) x B (Tesla) H (Amp/m) x 10 5 Figure Properties of MRF 132LD.

76 Detailed Design Of The MR Isolator Using the fluid properties, the size of the isolator needed to obtain o the performance necessary was determined. The power capability and coil design needed to generate the power r was also determined. Final design parameters, such as weight, size, fluid volume, coil length,etc., were determined. Results are compared. The goal is to show that the semi-active design can give the same maximum relative displacement as the passive baseline, but, in addition, a provide a significant reduction in noise transmission.

77 5-1. RESULTS The results of the passive and semi-active models are plotted. The maximum relative displacement and transmitted force seen with the passive system are plotted. These results are used to develop the t baseline performance of the passive isolator. The following four designs are discussed: Design Case 1 Design Case 2 Design Case 3 Design Case 4 Passive rubber isolator. Passive rubber isolator with passive MR fluid. Passive rubber isolator with active MR fluid with Butterworth filter. Passive rubber isolator with active MR fluid with filter off. The forces seen in the different isolator components are evaluated. ed. The change in viscosity of the fluid is analyzed.

78 5-2. Results For The Passive Isolator Design The power spectrum of the transmitted noise at 50 Hz is seen to increase as the stiffness of the isolator increases. Power Spectrum Of Transmitted 50 Hz PS Of Transmitted Noise (N^2/Hz) PASSIVE RESULTS Baseline Transmission Stiffness (N/m) Figure 5.1. The effect of passive stiffness seen on transmitted force.

79 5-3. Results For The Passive Isolator Design The maximum relative displacement is seen to decrease as the stiffness of the isolator increases. Maximum Relative Displacement PASSIVE RESULTS 20.0 Baseline Displacement Max Rel Disp (mm) Stiffness (N/m) Figure 5.2. The effect of passive stiffness seen on maximum relative displacement.

80 5-4. Results For The Passive Isolator Design From the previous two figures, the baseline performance of the isolator i is determined. This is seen below. (i) (ii) Maximum relative displacement of 2.3 mm. Maximum transmitted force from the compressor of 6.3 N 2 /Hz.

81 Results For The Semi-Active Isolator Design The power spectrum of the transmitted noise at 50 Hz is seen to increase as the stiffness of the isolator increases. Power Spectrum Of Transmitted 50 Hz PS Of Transmitted Noise (N^2/Hz) PASSIVE RESULTS MR INACTIVE RESULTS MR ACTIVE RESULTS -- Butterworth Lowpass Filter MR ACTIVE RESULTS -- Ideal Low Pass Filter Baseline Transmission Stiffness (N/m) Figure 5.3. The effect of passive stiffness seen on transmitted force.

82 5-6. Results For The Semi-Active Isolator Design The maximum relative displacement is seen to decrease as the stiffness of the isolator increases. Maximum Relative Displacement 30.0 PASSIVE RESULTS 25.0 MR INACTIVE RESULTS MR ACTIVE RESULTS -- Butterworth Lowpass Filter MR ACTIVE RESULTS -- Ideal Low Pass Filter 20.0 Baseline Displacement Max Rel Disp (mm) Stiffness (N/m) Figure 5.4. The effect of passive stiffness seen on maximum relative displacement.

83 5-7. Results For The Semi-Active Isolator Design The results show the passive component of the MR fluid has a significant affect on results. As expected, the maximum relative displacement is reduced, and the t transmitted force increases. The following effects were seen when the active component of the MR fluid is introduced with the Butterworth filter. The maximum relative displacement at low stiffness is reduced. However, there is little effect at higher stiffness. The transmitted noise is not affected much by the active component. nt.

84 5-8. Results For The Semi-Active Isolator Design When the filter is turned off, the active fluid is in phase and the results improve significantly. With the filter turned off, the following effects are seen in the e results: The transmitted force is not affected. The maximum relative displacement is reduced at each stiffness.

85 5-9. Results For The Semi-Active Isolator Design 8 x Passive Passive MR Active MR 4 Relative Displacement (m) Time (s) Figure 5.5. Improvement to relative displacement with MR fluid.

86 5-10. Results For The Semi-Active Isolator Design The results can be seen in Table 5.1. Shown in the table are the following properties: (i) Isolator stiffness. (ii) Isolator passive damping ratio. (iii) Compressor mass per isolator. (iv) Natural frequency of the isolator. (v) Maximum relative displacement. (vi) Compressor transmitted force. (vii) Maximum forces seen by the isolator components.

87 5-11. Results For The Semi-Active Isolator Design PASSIVE RESULTS POWER SPECTRUM MAXIMUM FORCES stiffness mass zeta nat. freq. scale max. rel. displacement comp. transmitted spring damper passive fluid active fluid total (N/m) (kg) (Hz) (mm) (N^2/Hz) (N) (N) (N) (N) (N) MR INACTIVE RESULTS POWER SPECTRUM MAXIMUM FORCES stiffness mass zeta nat. freq. scale max. rel. displacement comp. transmitted spring damper passive fluid active fluid total (N/m) (kg) (Hz) (mm) (N^2/Hz) (N) (N) (N) (N) (N) MR ACTIVE RESULTS -- Butterworth Lowpass Filter POWER SPECTRUM MAXIMUM FORCES stiffness mass zeta nat. freq. scale max. rel. displacement comp. transmitted spring damper passive fluid active fluid total (N/m) (kg) (Hz) (mm) (N^2/Hz) (N) (N) (N) (N) (N) MR ACTIVE RESULTS -- Ideal Low Pass Filter POWER SPECTRUM MAXIMUM FORCES stiffness mass zeta nat. freq. scale max. rel. displacement comp. transmitted spring damper passive fluid active fluid total (N/m) (kg) (Hz) (mm) (N^2/Hz) (N) (N) (N) (N) (N) Table 5.1. Summary of simulation results.

88 5-12. Results For The Semi-Active Isolator Design The maximum forces are shown in the right columns of Table 5.1. They give an indication of how the forces seen by the different components of the isolator compare to each other. The columns are linked to the following forces: (i) Spring force resulting from the passive stiffness component k. (ii) Damper force resulting from the passive damping component c. (iii) Fluid force resulting from the passive component of the MR fluid. (iv) Fluid force resulting from the active component of the MR fluid. (v) Total force resulting from the sum of all the isolator forces.

89 5-13. Results For The Semi-Active Isolator Design The results show the force resulting from the passive stiffness and damping components decreases as the passive stiffness of the isolator decreases. This explains why transmitted noise decreases when stiffness and damping decrease. Also, the results show the negative affect on relative displacement, ent, and thus durability, when the stiffness decreases.

90 5-14. Results For The Semi-Active Isolator Design The active results show why turning the filter off is necessary. When the Butterworth low pass filter is used, the active component nt of the MR fluid is roughly the same size as the passive component of the MR fluid. If the active force is scaled higher than this, the isolator i becomes inefficient. When the filter is turned off, the semi-active force of the MR fluid is nearly eight times the force from the passive component. Because there is no phase lag, the active component can efficiently be scaled s very high. The percentage of noise reduction for each case is seen below: Inactive control with MR fluid. 50% Semi-Active control with Butterworth low pass filter 55% Semi-Active control with filter off 83%

91 5-15. Results For The Semi-Active Isolator Design Figure 5.6 shows all four isolator components with the filter turned off, along with the relative displacement of the compressor. Relative Displacement (mm) Four Isolator Components -- Filter Off Resistance Force (N) Time (s) Passive Damping Passive Stiffness Passive MR Fluid Active MR Fluid Figure 5.6. Relative displacement and isolator components with the filter off.

92 5-16. Results For The Semi-Active Isolator Design A look at the MR fluid viscosity yields another interesting result. A plot of the viscosity shows that it varies significantly during the model. m This contradicts the assumption of a constant passive MR component, nt, as seen in a Bingham plastic model. The plot showing the viscosity is dependent on relative velocity is seen in Figure 5.7.

93 5-17. Results For The Semi-Active Isolator Design 0.5 Viscosity is dependant on relative velocity. Relative Velocity (m/s) Viscosity (Pa s) Time (s) Figure 5.7. Viscosity is dependent on relative velocity.

94 6-1. MR ISOLATOR COIL DESIGN A detailed design of an isolator that can be used for the compressor application will be presented. The isolator could not be built within the scope of this thesis, but all the design information is presented to allow construction of the isolator. The following requirements of the design will be investigated: 1. Determining the necessary yield stress. 2. An electromagnetic model of the isolator. 3. Isolator coil properties. 4. Final design of the optimal isolator based on research.

95 6-2. Determining The Necessary Yield Stress Once the necessary yield stress needed for results was determined, d, the strength of the magnetic field needed to generate that yield stress is determined Yield Stress And Magnetic Flux Yield Stress (Pa) Magnetic Flux (Tesla) Time (s) Figure 6.1. Yield stress and magnetic flux in the model.

96 6-3. Electromagnetic Model Of The Isolator A electromagnetic model was created to develop a coil design that t will produce the necessary magnetic flux. In discussions, MR engine mount designers stated that a well designed coil will produce five hundred amp-turns. However, the efficiency of the coil begins to decrease when the coil is designed to produce more e than this. Figure 6.2 shows the coil design that provided the flux necessary. The arrows indicate the intended flux pattern. The results of the electromagnetic model are seen in Figure 6.3.

97 6-4. Electromagnetic Model Of The Isolator + + PISTON STEEL CASTING - - COILS STEEL 1020A + + MR FLUID (20%) Figure 6.2. Coil design with the intended flux pattern.

98 6-5. Electromagnetic Model Of The Isolator Flux Density B (T) Figure 6.3. Finite element results showing flux in the isolator.

99 Coil Properties The electromagnetic model defined the following parameters: The number of amp-turns in the coil The area of the coils Design of flux guides Once the model was completed, the specifics of the coil could be calculated. This included: Coil gage Coil length Coil mass Voltage applied to the wire Current through the wire Resistance from the wire

100 6-7. Coil Properties The following parameters were used to determine coil volume: Coil inner diameter Coil maximum outer diameter Coil width The following parameters were determined by wire gage: Copper diameter Insulation thickness Insulated diameter (which is equivalent to the copper diameter plus twice the insulation thickness)

101 6-8. Coil Properties The following equations were used to calculate the coil properties: es: Determining the number of turns. Coil physical properties Coil electrical properties #turns = layer # layers = CoilWidth InsulatedDiameter ( CoilID CoilOD) 2( InsulatedDiameter)( PackingHeight # turns # turns INT INT (# layers) layer = CoilActual OD = CoilID + ( InsulatedDiameter)( PackingHeight)( INT (# layers)) CoilID + CoilActualOD CoilAverageDiameter = 2 CoilLength = π ( CoilAverageDiameter)(# turns) CoilMass CoilMass = CoilLength CoilLength Coil Re sis tan ce(@ C) = Voltage Current = Re sis tan ce AmpTurns = (# turns)( Current) Coil CoilLength ) Re sis tan ce(@ C) CoilLength

102 6-9. Coil Properties The following dimensions were used for the modeling of the coils.. This geometry limited the area in which the coil could be wound. Coil inner diameter Coil maximum outer diameter Coil width 17 mm 19 mm 13 mm The number of turns that could fit into this area jumped significantly when the wire gage was increased from 24 to 25. With 24 gage wire, the wire is too thick to allow for a second layer l of coils. This can be seen in Figure 6.4

103 6-10. Coil Properties Number Of Turns Coil Mass (g) Coil Properties Of Different Wire Gages Wire Gage Number Figure 6.4. Number of coil turns and coil mass as a function of wire gage.

104 6-11. Coil Properties 7 6 Coil Properties Of Different Wire Gages Coil Length (m) Coil Resistance (Ohms) Wire Gage Number Figure 6.5. Coil length and resistance as a function of wire gage. ge.

105 6-12. Coil Properties Electrical Properties To Achieve 500 Amp Turns Voltage (V) Current (Amps) Wire Gage Number Figure 6.6. Voltage and current needed to achieve 500 amp turns.

106 6-13. Final Design The final design of the optimal isolator is seen below. PISTON STEEL CASTING COILS STEEL 1020A MR FLUID PASSIVE RUBBER Measurements in millimeters. Figure 6.7. Proposed design of a MR based semi-active isolator.

107 6-14. Final Design The final design parameters are seen below. Coil ID 17 mm Plunger Diameter 13 mm Coil OD 19 mm Gap Width 1 mm Coil Length 3.2 m Channel Length 20 mm Wire Gage 25 Fluid Volume 13 cc Voltage 10 V Table 6.1. Final design parameters.

108 6-15. Final Design The power requirements of the semi-active isolator increase as the relative velocity between the vehicle and the compressor increase. e. The maximum power requirement for each isolator is 0.04 W. This occurs when the vehicle hits the bump. Therefore, the maximum power needed for the entire isolation system (assuming 3 isolators) is 0.12 W. A plot showing the power requirements throughout the model are seen s in Figure 6.8.

109 6-16. Final Design Power requirements of the isolator Power (W ) Time (s) Figure 6.8. Power requirements of the semi-active isolator.

110 6-17. Final Design The overall mass of each isolator comes to grams, or 8.4 oz. o This is significantly larger than the baseline isolator, which has a mass of 7.0 grams, or 0.25 oz. Component Density Volume Mass (g) Rubber and Piston 7.3 (1) MR Fluid g/cc 13 cc 39.1 Coils 4 (2) Steel Casting 7900 kg/m E-5 m Flux Guide (Steel) 7900 kg/m E-6 m Total Table 6.2. Mass of semi-active isolator.

111 6-18. Final Design Studies can be done to reduce mass. A simple analysis of the mass breakdown shows that the steel parts of the isolator contribute most of the mass. The steel could possibly be replaced with aluminum or graphite to reduce mass. Also, a less dense fluid will lower the mass of the isolator.

112 7-1. Conclusions The MR fluid based semi-active isolator should have the following characteristics: Very soft rubber component. Fluid should work in flow mode. MR fluid should have low viscosity and high yield stress. The control algorithm should scale the active component of the MR M fluid proportional to the relative velocity. The control algorithm should include an improved low pass filter. The coil design needs to be sufficient to generate the necessary magnetic field. Use a small enough diameter wire that multiple layers of coils can c be wound, in this case, wire gage of 25. The semi-active isolator has significantly more mass than the baseline isolator.

113 7-2. Conclusions The MR fluid based semi-active isolator can give the same durability performance of a stiff passive isolator. The MR fluid based semi-active isolator can reduce transmitted noise by as much as 83%. Without mass reduction measures, the MR fluid based semi-active isolator will have 34 times more mass than the stiff passive isolator. The vibration isolator designed here can be used for other applications. Independent control of the each isolator also allows for use in multiple degree of freedom systems.

114 8-1. Recommendations For Future Work An algorithm could be developed to more effectively control to a relative plane. This would allow more efficient use of energy, by reducing the amount of power required for the isolator. The filter used with the control algorithm needs to be improved. A fluid that has low viscosity and a high shear stress can be developed. Optimization of the coil design would allow the isolator to more effectively use the unique characteristics of the MR fluid, while e requiring less input power. Building and testing of a prototype isolator is needed to validate performance.