Double Adjustable Shock Absorbers Utilising Electrorheological and Magnetorheological Fluids

Int. J. of Vehicle Design, Vol. 33, Nos. 1–3, 2003 189

Copyright © 2003 Inderscience Enterprises Ltd.

Double adjustable shock absorbers utilizing electrorheological and magnetorheological fluids

Jason E. Lindler*, Young-Tai Choi and Norman M. Wereley Smart Structures Laboratory, Department of Aerospace Engineering, University of Maryland, College Park, MD 20742, USA *Present address: CSA Engineering, 2565 Leghorn St, Mountain View CA 94043Fax: 301 314 9001 E-mail: [email protected] E-mail: [email protected]: Double adjustable shock absorbers allow for independent adjustment of the yield force and post-yield damping in the force versus velocity response. To emulate the performance of a conventional double adjustable shock absorber, an electrorheological (ER) and magnetorheological (MR) automotive shock absorber were designed and fabricated at the University of Maryland. For the ER shock absorber, an applied electric field between two tubular electrodes, located in the piston head, increases the force required for a given piston rod velocity. For the MR shock absorber, an applied magnetic field between the core and flux return increases the force required for a given piston rod velocity. For each shock absorber, two different shaped gaps meet the controllable performance requirements of a double adjustable shock absorber. A uniform gap allows for control of the yield force of the shock absorber, while a non-uniform gap allows for control of the post-yield damping. Force measurements from sinusoidal displacement cycles, recorded on a mechanical damper dynamometer, validate the performance of uniform and non-uniform gaps for adjustment of the yield force and post-yield damping, respectively.

Keywords: shock absorber; ER damper; MR damper; semi-active; double adjustable.

Reference to this paper should be made as follows: Lindler, J.E., Wereley, N.M. and Choi, Y.-T. (2003) ‘Double adjustable shock absorbers utilizing electrorheological and magnetorheological fluids’, Int. J. of Vehicle Design,Vol. 33, Nos. 1–3, pp.189–206.

Biographical notes: Jason E. Lindler earned his M.S. in mechanical engineering at the University of Maryland in June 2000. He is currently an Engineer at CSA Engineering Inc. in Mountain View CA.

Young-Tai Choi is a Research Assistant working at the University of Maryland at College Park. He hold B.S., M.S. and Ph.D. degrees in mechanical engineering from Inha University in Korea. He has joined Alfred Gessow Rotorcraft Center (AGRC) at the University of Maryland from 1999. He is interesting in the design and control of structures and systems using smart materials such as, particularly, electrorheological (ER) and magnetorheological (MR) fluids.

Norman M. Wereley received his doctorate in aeronautics and astronautics from the Massachusetts Institute of Technology in 1991. He joined the department of aerospace engineering at the University of Maryland in 1993,

190 J.E. Lindler et al.

where he is currently an Associate Professor. He is Member in AIAA, ASME, AHS, IOP. Dr. Wereley has published over 50 refereed international journal contributions and book chapters. In his writings, he has explored the analysis, modeling, and implementation of electrorheological and magnetorheological fluids and elastomeric materials to such applications as helicopter stability augmentation, aircraft landing gear, seismic control, and vibration/shock isolation. He is a fellow of the Institute of Physics and an Associate Fellow of the AIAA.

1 Introduction

In a conventional double adjustable shock absorber, its performance can be adjusted manually using mechanisms on the main piston head and in the pneumatic reservoir. Using these mechanisms, the yield force and damping can be independently controlled. However, manual adjustment of the shock absorber inevitably requires time consuming disassembly of the device.

In contrast, electrorheological (ER) and magnetorheological (MR) fluids, with field-dependent yield stress, can vary their damping levels without disassembly of the device. One approach might be to shape the force vs. velocity response using only the applied field obtained from a feedback control strategy [1]. A second approach, suggested here, is to exploit passive valve characteristics as well in shaping the force/velocity characteristics. Therefore, our goal in this study is to show the feasibility of double adjustable shock absorbers using both ER and MR fluids. To emulate the performance of a conventional double adjustable shock absorber, both ER and MR automotive shock absorbers were designed and fabricated at the University of Maryland. During piston rod motion, these field dependent fluids flow through an annular valve in the piston head. Electric (for ER fluids) or magnetic field (for MR fluids) is used to activate the controllable fluid, and increases its yield stress. Increasing the yield stress alters the velocity profile of the fluid via introduction of plug flow, which is a semi-solid plug of material in which the local shear stress is below the yield stress of the material. This raises the pressure required for a given flow rate.

In this paper, different gap configurations, uniform (concentric) and non-uniform (eccentric), are developed and modelled to control the shock absorber’s yield force and post-yield damping (that is double adjustable) in the force versus velocity response. Force measurements from sinusoidal displacement cycles validate the performance of the uniform and non-uniform gaps for yield force and post-yield damping adjustment.

2 Adjustable shock absorber

Due to its adjustable performance, the double adjustable shock absorber can easily meet the baseline design criterion for the performance requirement of automotive shock absorbers. The force versus velocity response of double adjustable shocks can be separated into four distinct regions: low-speed compression, high-speed compression, low-speed rebound and high-speed rebound [2]. A unique damping constant characterizes each region, and a distinct yield force divides the low and high-speed regions (Figure 1).

A conventional double adjustable shock absorber typically consists of a main hydraulic cylinder connected to a remote pneumatic reservoir via a hydraulic hose.

Double shock absorbers utilizing electro- and magnetorheological fluids 191

The main hydraulic cylinder contains a piston head assembly, piston rod and conventional hydraulic fluid. The remote pneumatic reservoir contains a floating piston that separates the compressed nitrogen reservoir from the hydraulic fluid reservoir [2]. Mechanisms on the main piston head and in the pneumatic reservoir allow for independent control of the shock absorber’s yield force and damping during the compression and rebound strokes (Figure 2).

Figure 1 Force versus velocity response of an adjustable shock absorber

Figure 2 Schematic of a double adjustable shock absorber

A typical cycle of a double adjustable damper begins with low-speed compression of the piston rod, during which fluid flows through small orifices in the piston head. In addition, the increasing rod volume within the damper body forces an equal volume of fluid through an orifice into the pneumatic reservoir. Changing the orifice size in the pneumatic


reservoir controls the compression damping (Figure 2a). As compression speed increases, fluid pressure on the compression valve stack increases. Each valve stack consists of a series of steel shims that collectively act as a preloaded spring (Figure 2b). As a result, high fluid pressure causes the valve stack to snap open, which allows fluid to flow directly through large ports in the piston head. This parallel flow greatly decreases the damping during high-speed compression. Changing the thickness of the shims alters the critical pressure required to open the valve stack, and therefore adjusts the yield force of the shock absorber.

During the rebound stroke, fluid bypasses the piston head through a needle and jet valve in the piston rod. The location of the jet determines the rebound damping. Similar to high compression speeds, at high rebound speeds, the fluid pressure yields the rebound valve stack that allows fluid to easily pass through the piston head.

3 Controllable fluid behaviour

ER and MR fluids are composed of two phases: dispersed particles and a carrier fluid. MR fluids are normally composed of ferromagnetic or paramagnetic particles, typically greater that 0.1 micrometers in diameter, dispersed in a carrier fluid. An applied magnetic field magnetizes the MR particles and results in particle chain formation. Similarly, ER fluids are polarizable particles dispersed in a non-conducting mineral or silicone oil. Application of an electric field polarizes the ER particles and also results in particle chain formation (Figure 3).

Figure 3 Behaviour of ER and MR fluids with and without field applied

The particle chains induce a yield stress in the fluid which results in a Bingham plastic behaviour during shear (Figure 4). A number of models at the micromechanical level predict shear stress by accounting for polarization of the dispersed particles and their interactive forces [3]. The chain formation is completely reversible and removing the


field reduces the yield stress of the fluid. Due to their field dependent properties and fast response times, ER and MR fluids are a possible replacement for mechanical valves in variable damping systems.

Figure 4 Bingham plastic shear mechanism for ER and MR fluids

For a Newtonian fluid, the shear stress is proportional to the shear rate.

dduy

(1)

Here u is the fluid velocity, y is the vertical coordinate, is the shear stress, and is the plastic viscosity.

For a Bingham plastic, a yield stress, y characterizes the material. In the pre-yield condition, no shearing occurs because the local shear stress, , is less than its yield stress,

y. When the shear stress exceeds the yield stress, the material flows like a Newtonian fluid with a plastic viscosity, . The plastic viscosity is relatively constant, with a value of about 40 mPa s for ER fluids and 400 mPa s for MR fluids. The Bingham-plastic model is usually expressed as follows:

d dsgnd dyu uy y

(2)

The yield stress, y, of ER and MR fluids typically exhibits quadratic behaviour as a function of the applied field. The maximum yield stress for ER fluids is on the order of 8 kPa at 4 kV/mm, while the yield stress for MR fluids reaches 80 kPa or higher at 1 Tesla. However, dielectric breakdown (ER) or magnetic saturation (MR) limits the application of higher field strengths to further increase the yield stress.


4 Steady laminar flow between in a rectangular duct

The governing equation for Poiseuille flow through a rectangular duct [4] is given by

dd

Py L

(3)

Here P is the pressure drop and L is the length of the rectangular duct. Note that the origin of y-axis is at the middle of the gap of the rectangular duct.

In a Bingham plastic material, no shearing occurs until the local shear stress, ,exceeds the fluid’s yield stress, y. Once the local shear stress exceeds the yield stress the material flows like a Newtonian fluid.

d dsgnd dyu uy y

(4)

Integrating the governing equation (equation 3) and applying the boundary condition, (0) = 0, solves for the shear stress profile in the rectangular duct:

Py yL

(5)

The shear stress profile (equation 5) demonstrates that the pressure gradient creates a region of low shear stress in the center of the gap and high shear stress along the rectangular duct walls. Assuming a Bingham plastic material, the fluid’s yield stress creates three distinct flow regions (Figure 5). Two post-yield regions occur along the rectangular duct walls, where the shear stress exceeds the yield stress of the material. A pre-yield region, of width , occurs in the center of the valve gap, where the shear stress is less than the yield stress of the Bingham plastic material.

Figure 5 Shear stress and velocity profiles of an ER or MR fluid in an applied field under Poiseuille flow

The shear stress profile (equation 5) at the plug boundaries, yp and –yp, must equal the yield stress, y. We can then solve for the plug region boundaries and determine the plug thickness, = 2yp. We use the non-dimensional plug thickness, , which is a normalization of the plug thickness or the pre-yield region width by the gap of the rectangular duct, d, or


2 2p yy Ld d d P

(6)

In the two post-yield regions, differentiating the Bingham plastic constitutive behaviour (equation 4) with respect to y, and substituting into the governing equation (equation 3), gives a second-order differential equation for the velocity down the valve, or

2

2

dd

u PLy

(7)

In region 1, integrating the differential equation (equation 7) twice with respect to y and applying the boundary conditions, 1 2( ) 0du and 1( ) 0pu y , solves for the velocity profile in the region. In region 3, integrating the differential equation (equation 7) twice with respect to y and applying the boundary conditions, 3 2( ) 0du and 3 ( ) 0pu y ,solves for the velocity profile in the region. In region 2, application of the continuity boundary condition, u1(yp) = u2(yp), solves for the plug region velocity.

22 2

121

8yPdu

L d (8)

2 2

2 18Pdu

L (9)

22 2

321

8yPdu

L d (10)

Integrating and simplifying the velocity profile for each region yield the flow rate per unit width in terms of the non-dimensional plug thickness as follows:

23 31

1 1d 124

d

py

Q d Pu y qb L (11)

3 222 2d 1

8p

p

y

y

Q d Pu y qb L (12)

2

3 333 3d 1

24p

d

yQ d Pu y qb L

(13)

Here Q1, Q2, Q3 are the flow rates for each region, respectively. b is the width of the rectangular duct.


Finally, summing the flow rates for each region gives the total flow rate per unit width for a Bingham plastic material in the rectangular duct.

3 2

1 2 3 1 112 2d Pq q q q

L (14)

5 ER and MR shock absorbers

Designed and fabricated at the University of Maryland, an ER automotive shock absorber emulates the performance of a conventional double adjustable shock absorber. The fabricated shock absorber is a monotube, single rod design, composed of hydraulic and pneumatic reservoirs separated by a floating piston (Figure 6). As the piston rod moves in and out of the hydraulic cylinder the floating piston head compresses the pneumatic reservoir to accommodate the changing rod volume within the hydraulic cylinder. In addition, the pneumatic reservoir allows for thermal expansion of the fluid during normal operation.

Figure 6 Cutaway drawing of the electrorheological and magnetorheological fluid automotive shock absorbers designed and fabricated at the University of Maryland. The shock absorbers, composed of hydraulic and pneumatic reservoirs separated by floating pistons, are a monotube, single rod design


Inside the hydraulic cylinder, the piston rod is attached to a piston head containing two tubular electrodes. Two piston end caps hold the tubular electrodes in place creating an annulus in the gap between the electrodes. Seals encircle the piston head and prevent fluid from flowing between the piston head and the walls of the hydraulic cylinder. During piston rod motion, ER fluid flows through holes in the piston end caps and into the gap between the tubular electrodes. To achieve semi-active properties, the hydraulic cylinder is filled with Bayer Rheobay 3565 electrorheological fluid. A plastic spacer electrically insulates the two electrodes from each other. As a result, an electrical voltage potential between the electrodes creates an electric field in the gap perpendicular to the ER fluid flow direction. The electric field increases the yield stress of the ER fluid between the electrodes. This increase in yield stress alters the velocity profile of the fluid in the gap and raises the pressure required for a given flow rate.

A magnetorheological (MR) automotive shock absorber was also fabricated. The MR shock absorber is a monotube, single rod design, composed of hydraulic and pneumatic reservoirs separated by a floating piston (Figure 6). The MR shock absorber operation is analogous to the ER shock absorber. However, in the case of the MR shock absorber, the piston head contains a magnetic core (bobbin) and flux return by which magnetic field is used to activate the MR fluid. The bobbin or core is wrapped with an insulated wire. A current sent through the wire coil creates a magnetic field in the gap between the core and the flux return. The magnetic field increases the yield stress of the MR fluid between the core and flux return. Lord Corporation VersaFlo MRF-132-LD was used to fill the shock absorber.

6 Adjustable yield force

This section derives equations that solve for the required pressure drop to achieve a given flow rate of a Bingham plastic material through a uniform gap. The derived analysis assumes that the radius of the annulus is much larger than that of the gap. As a result, the velocity profile in the rectangular duct depicts the velocity profile in the gap between the ER or MR valve walls (Figure 7).

Figure 7 Velocity profile of a Bingham plastic in a uniform (concentric) gap between two electrodes (ER) or two poles (MR)


The rectangular duct analysis gives the flow rate per unit width in terms of the pressure drop [5].

2 2 33

2

112 4 3

y yd Ldq PL P

(15)

Integrating the flow rate per unit width around the circumference, b, solves for the total flow rate.

2 2 33

2

112 4 3

y yc

bd bLbdQ PL P

(16)

Similar to a double adjustable shock absorber, a small valve allows a controlled amount of leakage through the piston, or piston bleed. Laminar fluid dynamic equations relate the leakage damping, Cl, to the geometry of the orifice [6],

2

4

8p ll

l

A LC

r (17)

Here Ap is the effective piston head area, and Ll and rl are the length and radius of the small valve, respectively. As a result, the leakage flow rate in terms of the pressure drop, damping coefficient and piston head area is given by

2p

ll

AQ P

C (18)

The continuity equation for steady incompressible flow requires that the flow rate through the piston head is equal to the sum of the flow rate through the electrodes and the leakage, Qt = Qc + Ql. Summing equations (16) and (18) gives the total flow rate as a function of the pressure drop across the piston head. Then multiplying by P2 and rearranging produces a polynomial function of the pressure drop in terms of the total flow rate.

2 2 2 333 2 0

12 4 3p y y

tl

A bd bLbd P Q PL C

(19)

The roots of equation (19) generate three values of required pressure. The correct pressure corresponds to a valid non-dimensional plug thickness, 0 1 , calculated using equation (6). Finally, the piston head area, Ap, relates the piston rod force to the pressure drop, F = PAp, and the piston velocity to the flow rate, Qt = Apv0. Here, v0 is the piston velocity.

Force measurements from sinusoidal displacement cycles, recorded on a 5HP mechanical dynamometer, validate the derived equations [7]. The dynamometer excites the piston rod while a load cell measures the force on the shock absorber and a


displacement transducer measures the piston rod displacement. For uniform gap, the force versus velocity cycles demonstrate that an increasing field increases the yield force of the device without greatly affecting the post-yield damping for both the ER shock absorber (Figure 8) and the MR shock absorber (Figure 9).

Figure 8 Typical force versus displacement and force versus velocity responses of the ER shock absorber with a uniform gap. Symbols are experimental measurements for a fixed stroke of 1 in. and frequency of 0.94 Hz. Solid lines are model predictions


Figure 9 Typical force versus displacement and force versus velocity response of the MR shock absorber with a uniform (concentric) gap. Symbols are experimental measurements for a fixed stroke of 1 in. and frequency of 0.94 Hz. Solid lines are model predictions

7 Adjustable post-yield damping

The combined flow rate equation and the experimental data, demonstrates that increasing the yield stress in the uniform gap controls the yield force of the device while incurring little change in the post-yield damping. However, double adjustable shock absorbers also allow for adjustment of the post-yield damping independent of the yield force. To emulate the performance of a double adjustable shock absorber, an eccentricity between the magnetic poles for the MR shock absorber and electrodes for the ER shock absorber creates field dependent post-yield damping (Figure 10).

The eccentricity creates a small gap region and a large gap region between the core and flux return for the MR shock absorber and the electrodes for the ER shock absorber. With the application of a field, the yield stress restricts flow in the small gap region, thereby increasing the pressure required for a given flow rate. At the same time, the large


gap region permits flow for any given pressure, reducing the field dependent yield force. The combination of the small gap region, to restrict the flow, and a large gap region, that allows flow for any given pressure, creates a field dependent post-yield damping.

Figure 10 Velocity profile of a Bingham plastic, due to a pressure gradient, in a non-uniform (eccentric) gap

Depending on the pressure drop, the addition of an applied field, which creates a yield stress, prevents flow in the small gap region of the eccentric cylinders. To determine the flow rate, the integration of the velocity profile around the remaining portion of the gap, requires the locations around the inner cylinder where local shear stress exceeds the yield stress, 1. Setting the non-dimensional plug thickness (equation 6) equal to one solves for the valid location of the yield point, by, and generates the limits of the integration. With the limits of the integration known, integrating the velocity profile, q, around the large gap region of the eccentric cylinders, –by < b < by, solves for the flow rate as a function of the non-dimensional plug thickness and the pressure drop.

3 2d 1 1 d

12 2y y

y y

b b

e b b

d PQ q b bL

(20)

We show experimental results here for the MR shock absorber. Force measurements from sinusoidal displacement cycles, recorded on a 5HP mechanical dynamometer, validate the derived equations. The dynamometer excites the piston rod while a load cell measures the force on the shock absorber and a LVDT measures the piston rod displacement. In the case of the MR shock absorber with non-uniform gap, the yield force of the shock absorber increases as a function of applied field (Figure 11). For a non-uniform gap, the force vs. velocity cycles demonstrates that an increasing field raises the post-yield damping of the device (Figure 12).


Figure 11 Typical force vs. displacement and force vs. velocity response of the MR shock absorber with a non-uniform gap. Shown are zero field and maximum field cases


Figure 12 The MR damper with a uniform gap has a relatively constant post-yield damping. Eccentricity between the core and the flux return allows for post-yield damping to be controlled via application of magnetic field

8 Double adjustable shock absorber

In double adjustable shock absorbers, mechanisms on the main piston head and in the pneumatic reservoir independently control the yield force and damping. To emulate the performance of a conventional double adjustable shock absorber, an ER automotive shock absorber was designed and fabricated at the University of Maryland (Figure 13). An ER shock absorber with two different gaps, uniform and non-uniform, allows for independent yield force and post-yield damping adjustment. Due to the fact that the non-uniform gap in the MR shock absorber raises both the yield force and the post-yield damping, the ER geometries were chosen to emulate the double adjustable performance.


Figure 13 Cross section of the piston head in the ER shock absorber that contains a uniform gap ER valve and non-uniform gap ER valve in series

The combination of uniform and non-uniform gaps in series creates an ER shock absorber with independently adjustable yield force and post-yield damping (Figure 14). A 0.7 in. uniform gap and a non-uniform gap electrode replaces the 1.7 in. inner electrode. A plastic spacer insulates the two electrodes from each other and separate wires allows for independent application of a voltage to each electrode. Applying no voltage to either electrode demonstrates the baseline Newtonian damping of the damper. Then applying a voltage to only the uniform gap increases the yield force of the device. Finally, application of a field only to the non-uniform gap increases the post-yield damping of the device without greatly increasing the yield force of the shock absorber.

Figure 14 Experimental force versus velocity response of the double adjustable ER damper. Increasing the field only in the uniform gap (concentric electrode) increases only the field. Applying field to the non-uniform gap (eccentric electrode) can then be used to adjust the post-yield damping


9 Conclusions

In this study, the feasibility of ER and MR double adjustable shock absorbers, which can easily meet the design criterion of conventional automotive shock absorber without disassembly, was presented. ER and MR shock absorbers with two different shaped gaps, uniform and non-uniform, were designed and fabricated at the University of Maryland, and their force measurements from sinusoidal displacement cycles were conducted by the 5HP mechanical dynamometer. From the results presented in this study, we reach the following conclusions.

For the uniform gap in both ER and MR shock absorbers, the force versus velocity response demonstrates that application of an electric or magnetic field increases the yield force of the device without greatly affecting the post-yield damping.

For the non-uniform gap in the ER shock absorber, the force versus velocity response shows that application of field raises the post-yield damping of the device. However, the non-uniform gap in the MR shock absorber simultaneously raises the post-yield damping and the yield force. A possible explanation for the difference is that the conductivity of the ER fluid is low in comparison to the permeability of the MR fluid. As a result, in the ER shock absorber, the electric field decreases as the gap increases for a constant voltage. However, in the MR shock absorber, the magnetic field is much less dependent of the gap distance. Therefore, an ER shock absorber was fabricated to emulate the double adjustable performance.

For the combination of uniform and non-uniform gaps in series, the force versus velocity response shows that the yield force and the post-yield damping can be independently controlled by independent application of field.

Acknowledgments

Research supported by the U.S. Army Research Office Young Investigator Program, contract no. 38856-EG-YIP (Dr. Gary Anderson, technical monitor). Additional support provided by the National Science Foundation under a NSF Career Award CMS-9734244 (Dr. Alison Flatau, technical monitor). Laboratory equipment supported under a grant by the FY96 Defense University Research Instrumentation Program (DURIP), contract no. DAAH-0496-10301 (Dr. Gary Anderson, technical monitor). We thank Lord Corporation (Ms. Monique Clarke and Dr. Mark Jolly) for providing the MR fluid used in this study. We also thank Bayer AFG (Dr. Eckhard Wendt) for providing the electrorheological fluid used in this study.

References

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Double Adjustable Shock Absorbers Utilising Electrorheological and Magnetorheological Fluids

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