Small-scale magnetorheological dampers for vibration mitigation ...

Outline
Introduction
Hysteretic models
Identification methodology
Future work
New MR Dahl friction model
1 Introduction
Motivation
2 Hysteretic models
MR damper dynamic models
Normalized Bouc-Wen model
New MR Dahl friction model
3 Identification methodology
New MR Dahl friction model
4 Future work
Experimental identification
Summary
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Introduction
Hysteretic models
Identification methodology
Future work
New MR Dahl friction model
New MR Dahl friction model identification methodology steps
Identification methodology steps
Ikhouane et. al. Previous considerations
Step 1 Excite the system with a T-periodic input signal convex in its loading part
Step 2 Compute k x
Proof
¯F(T + ) + ¯F(0)
k x =
ẋ(0) + ẋ(T + )
Step 3 Compute θ(x)
Proof
θ(τ) with τ ∈ [0, T + ] is now known, then
k w¯w(τ) = ¯F(τ) − k xẋ(τ) θ(τ)
k w¯w(x) = θ(x)
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Introduction
Hysteretic models
Identification methodology
Future work
New MR Dahl friction model
New MR Dahl friction model identification methodology steps
Identification methodology steps
Ikhouane et. al. Previous considerations
Step 1 Excite the system with a T-periodic input signal convex in its loading part
Step 2 Compute k x
Proof
¯F(T + ) + ¯F(0)
k x =
ẋ(0) + ẋ(T + )
Step 3 Compute θ(x)
Proof
θ(τ) with τ ∈ [0, T + ] is now known, then
k w¯w(τ) = ¯F(τ) − k xẋ(τ) θ(τ)
k w¯w(x) = θ(x)
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Introduction
Hysteretic models
Identification methodology
Future work
New MR Dahl friction model
New MR Dahl friction model identification methodology steps
Identification methodology steps
Ikhouane et. al. Previous considerations
Step 1 Excite the system with a T-periodic input signal convex in its loading part
Step 2 Compute k x
Proof
¯F(T + ) + ¯F(0)
k x =
ẋ(0) + ẋ(T + )
Step 3 Compute θ(x)
Proof
θ(τ) with τ ∈ [0, T + ] is now known, then
k w¯w(τ) = ¯F(τ) − k xẋ(τ) θ(τ)
k w¯w(x) = θ(x)
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Introduction
Hysteretic models
Identification methodology
Future work
New MR Dahl friction model
New MR Dahl friction model identification methodology steps
Identification methodology steps (Cont’d)
Ikhouane et. al.
Step 4 Determine the zero of the function θ(x), which is the quantity x ∗ such that θ(x ∗) = 0
Step 5 Compute a by using
( ) dθ(x)
a =
dx x=x∗
Step 6 Choose 1 design parameter, which is x ∗1 ≥ x ∗
Step 7 Compute k w and ρ
( ) dθ(x)
a −
dx x=x
ρ =
∗1
θ(x ∗1 )
k w = a ρ
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Introduction
Hysteretic models
Identification methodology
Future work
New MR Dahl friction model
New MR Dahl friction model identification methodology steps
Identification methodology steps (Cont’d)
Ikhouane et. al.
Step 4 Determine the zero of the function θ(x), which is the quantity x ∗ such that θ(x ∗) = 0
Step 5 Compute a by using
( ) dθ(x)
a =
dx x=x∗
Step 6 Choose 1 design parameter, which is x ∗1 ≥ x ∗
Step 7 Compute k w and ρ
( ) dθ(x)
a −
dx x=x
ρ =
∗1
θ(x ∗1 )
k w = a ρ
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Introduction
Hysteretic models
Identification methodology
Future work
New MR Dahl friction model
New MR Dahl friction model identification methodology steps
Identification methodology steps (Cont’d)
Ikhouane et. al.
Step 4 Determine the zero of the function θ(x), which is the quantity x ∗ such that θ(x ∗) = 0
Step 5 Compute a by using
( ) dθ(x)
a =
dx x=x∗
Step 6 Choose 1 design parameter, which is x ∗1 ≥ x ∗
Step 7 Compute k w and ρ
( ) dθ(x)
a −
dx x=x
ρ =
∗1
θ(x ∗1 )
k w = a ρ
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Introduction
Hysteretic models
Identification methodology
Future work
New MR Dahl friction model
New MR Dahl friction model identification methodology steps
Identification methodology steps (Cont’d)
Ikhouane et. al.
Step 4 Determine the zero of the function θ(x), which is the quantity x ∗ such that θ(x ∗) = 0
Step 5 Compute a by using
( ) dθ(x)
a =
dx x=x∗
Step 6 Choose 1 design parameter, which is x ∗1 ≥ x ∗
Step 7 Compute k w and ρ
( ) dθ(x)
a −
dx x=x
ρ =
∗1
θ(x ∗1 )
k w = a ρ
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Introduction
Hysteretic models
Identification methodology
Future work
New MR Dahl friction model simulation
New MR Dahl friction model
Results
New MR Dahl friction model simulation under a convex input signal in its loading part
Parameters Real Identified Relative error %
k x 0.0320 0.0322 0.7722
k w 5.4600 5.4591 0.0170
ρ 600.0000 601.4496 0.2416
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Introduction
Hysteretic models
Identification methodology
Future work
New MR Dahl friction model simulation
New MR Dahl friction model
Results
New MR Dahl friction model simulation under a convex input signal in its loading part
Parameters Real Identified Relative error %
k x 0.0320 0.0322 0.7722
k w 5.4600 5.4591 0.0170
ρ 600.0000 601.4496 0.2416
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Outline
Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
1 Introduction
Motivation
2 Hysteretic models
MR damper dynamic models
Normalized Bouc-Wen model
New MR Dahl friction model
3 Identification methodology
New MR Dahl friction model
4 Future work
Experimental identification
Summary
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Identification of a small-scale MR controllable-friction damper
Main characteristics
Chrzan and Carlson, 2001
Enable low cost appropriate for less
demanding, low-force applications with a high
degree of control
Consists in an absorbent foam saturated with
MR fluid (aprox. 3 ml).
Doesn’t have an accumulator and a bypass of
the fluid.
Operates in a direct shear mode without seals,
bearings or precision mechanical tolerance.
Technical data
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Identification of a small-scale MR controllable-friction damper
Main characteristics
Chrzan and Carlson, 2001
Enable low cost appropriate for less
demanding, low-force applications with a high
degree of control
Consists in an absorbent foam saturated with
MR fluid (aprox. 3 ml).
Doesn’t have an accumulator and a bypass of
the fluid.
Operates in a direct shear mode without seals,
bearings or precision mechanical tolerance.
Technical data
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Identification of a small-scale MR controllable-friction damper
Main characteristics
Chrzan and Carlson, 2001
Enable low cost appropriate for less
demanding, low-force applications with a high
degree of control
Consists in an absorbent foam saturated with
MR fluid (aprox. 3 ml).
Doesn’t have an accumulator and a bypass of
the fluid.
Operates in a direct shear mode without seals,
bearings or precision mechanical tolerance.
Technical data
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Identification of a small-scale MR controllable-friction damper
Main characteristics
Chrzan and Carlson, 2001
Enable low cost appropriate for less
demanding, low-force applications with a high
degree of control
Consists in an absorbent foam saturated with
MR fluid (aprox. 3 ml).
Doesn’t have an accumulator and a bypass of
the fluid.
Operates in a direct shear mode without seals,
bearings or precision mechanical tolerance.
Technical data
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Diagram of the identification experiment layout
MR damper fixed on top of the Shake Table. The sensors used are: (i) a load cell, (ii) laser
displacement, and (iii) accelerometer.
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Identification of a small-scale MR controllable-friction damper tests
Experimental input current
From the shear-mode MR damper model, the modified Dahl model has to include the voltage as
k x(v) = k xa + k xb v
k w(v) = k wa + k wb v
˙v = −η(v − u)
η = positive constant, u = command voltage applied to the Wonder Box, and v = is a varying
voltage. η can be determined if u is available as the system is linear.
Loading experiments using constant and variable input current using a convex input signal in its
loading part.
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Identification of a small-scale MR controllable-friction damper tests
Experimental input current
From the shear-mode MR damper model, the modified Dahl model has to include the voltage as
k x(v) = k xa + k xb v
k w(v) = k wa + k wb v
˙v = −η(v − u)
η = positive constant, u = command voltage applied to the Wonder Box, and v = is a varying
voltage. η can be determined if u is available as the system is linear.
Loading experiments using constant and variable input current using a convex input signal in its
loading part.
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Identification of a small-scale MR controllable-friction damper tests
Experimental input current
From the shear-mode MR damper model, the modified Dahl model has to include the voltage as
k x(v) = k xa + k xb v
k w(v) = k wa + k wb v
˙v = −η(v − u)
η = positive constant, u = command voltage applied to the Wonder Box, and v = is a varying
voltage. η can be determined if u is available as the system is linear.
Loading experiments using constant and variable input current using a convex input signal in its
loading part.
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Identification of a large-scale MR controllable-fluid damper
Main characteristics
Yang et. al., 2004
Real-time damping is controlled by the
increase in yield stress of the MR fluid in
response to magnetic field strength
High dissipative force at low velocity
Continual optimization
High dynamic range
Inherent stability and failure-safety
Mechanical simplicity
Fast response-time
Small device size
Large temperature range
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Identification of a large-scale MR controllable-fluid damper
Main characteristics
Yang et. al., 2004
Real-time damping is controlled by the
increase in yield stress of the MR fluid in
response to magnetic field strength
High dissipative force at low velocity
Continual optimization
High dynamic range
Inherent stability and failure-safety
Mechanical simplicity
Fast response-time
Small device size
Large temperature range
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Identification of a large-scale MR controllable-fluid damper
Main characteristics
Yang et. al., 2004
Real-time damping is controlled by the
increase in yield stress of the MR fluid in
response to magnetic field strength
High dissipative force at low velocity
Continual optimization
High dynamic range
Inherent stability and failure-safety
Mechanical simplicity
Fast response-time
Small device size
Large temperature range
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Identification of a large-scale MR controllable-fluid damper
Main characteristics
Yang et. al., 2004
Real-time damping is controlled by the
increase in yield stress of the MR fluid in
response to magnetic field strength
High dissipative force at low velocity
Continual optimization
High dynamic range
Inherent stability and failure-safety
Mechanical simplicity
Fast response-time
Small device size
Large temperature range
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Identification of a large-scale MR controllable-fluid damper
Main characteristics
Yang et. al., 2004
Real-time damping is controlled by the
increase in yield stress of the MR fluid in
response to magnetic field strength
High dissipative force at low velocity
Continual optimization
High dynamic range
Inherent stability and failure-safety
Mechanical simplicity
Fast response-time
Small device size
Large temperature range
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Identification of a large-scale MR controllable-fluid damper
Main characteristics
Yang et. al., 2004
Real-time damping is controlled by the
increase in yield stress of the MR fluid in
response to magnetic field strength
High dissipative force at low velocity
Continual optimization
High dynamic range
Inherent stability and failure-safety
Mechanical simplicity
Fast response-time
Small device size
Large temperature range
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Identification of a large-scale MR controllable-fluid damper
Main characteristics
Yang et. al., 2004
Real-time damping is controlled by the
increase in yield stress of the MR fluid in
response to magnetic field strength
High dissipative force at low velocity
Continual optimization
High dynamic range
Inherent stability and failure-safety
Mechanical simplicity
Fast response-time
Small device size
Large temperature range
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Identification of a large-scale MR controllable-fluid damper
Main characteristics
Yang et. al., 2004
Real-time damping is controlled by the
increase in yield stress of the MR fluid in
response to magnetic field strength
High dissipative force at low velocity
Continual optimization
High dynamic range
Inherent stability and failure-safety
Mechanical simplicity
Fast response-time
Small device size
Large temperature range
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Identification of a large-scale MR controllable-fluid damper
Main characteristics
Yang et. al., 2004
Real-time damping is controlled by the
increase in yield stress of the MR fluid in
response to magnetic field strength
High dissipative force at low velocity
Continual optimization
High dynamic range
Inherent stability and failure-safety
Mechanical simplicity
Fast response-time
Small device size
Large temperature range
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Outline
Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
1 Introduction
Motivation
2 Hysteretic models
MR damper dynamic models
Normalized Bouc-Wen model
New MR Dahl friction model
3 Identification methodology
New MR Dahl friction model
4 Future work
Experimental identification
Summary
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Summary
Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Presentation summary
Understand the dynamic behavior of the MR dampers with a feasible
hysteretic model.
Apply an identification methodology to the chosen hysteretic model.
Outlook for future work
To do the experimental identification of the small-scale controllable
friction MR damper.
To do the experimental identification of the large-scale controllable
friction MR damper.
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Muchas gracias
Figure: Stenocutter - longest cable stayed bridge using MR dampers for cable
vibration mitigation. Hong Kong, China
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Bibliography
Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Tsu T. Soong and B.F. Spencer.
Supplemental energy dissipation: State-of-the-art and state-of-the-practice.
Engineering Structures 24(1):243–259, 2002.
Michael D. Symans and Michael C. Constantinou
Return
Development and experimental study of semi-active fluid damping devices for seismic protection of
structures.
National Center for Earthquake Engineering Research. Report No. NCEER 95-0011. Buffalo, NY. 1995
Return
G.W. Housner, L.A. Bergman, T.K. Caughey, A.G. Chassiakos, R.O. Claus, S.F. Masri, R.E. Skelton, T.T.
Soong, B.F. Spencer, and J.T.P. Yao
Structural control: Past, present, and future.
Journal of Engineering Mechanics 123(9):897–971, 1997.
S. Nagarajaiah and S. Sahasrabudhe
Return
Seismic response control of smart sliding isolated buildings using variable stiffness systems: An
experimental and numerical study.
Earthquake Engineering and Structural Dynamics 35(2):177–197, 2005.
Return
N. Makris and S. McMahon
Structural control with controllable fluid dampers: Design and implementation issues.
Proceedings of Second International Workshop on Structural Control. Hong Kong. 1996:311Ű-322
Return
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Bibliography (Cont’d)
Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Dorka, U.E.
Testing algorithms for semiactive control of bridges.
Kassel, Germany. 2000 Return
Villamizar Mejia, Rodolfo
Robust control of systems subjected to uncertain disturbances and actuator dynamics.
PhD Universitat de Girona. 2005 Return
H. Fujitani, H. Sodeyama, T. Tomura, T. Hiwatashi, Y. Shiozaki, K.Hata, K.Sunakoda, S.Morishita, and S.Soda
Development of 400kN magnetorheological damper for a real base-isolated building.
SPIE - Conference on Smart Structures and Materials. Bellingham, Washington. 5027:265–276
Return
Stanway, R., Sproston, J.L., and Stevens, N.G.
Non-linear Modelling of an Electrorheological Vibration Damper.
Journal of Electrostatics. 1987(20):167Ű-184 Return
D. R. Gamato and F. E. Filisko
Dynamic mechanical studies of electrorheological materials: Moderate frequencies.
Journal of Rheology. 1991(35):399–425 Return
B.F. Spencer, S.J. Dyke, M.K. Sain, and J.D. Carlson
Phenomenological model of a magnetorheological damper.
ASCE Journal of Engineering Mechanics. 1997(123):230-238
Return
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Bibliography (Cont’d)
Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Y.K. Wen
Method of random vibration fo hysteretic systems.
Journal of Engineering Mechanics. 1976(102):246–263
Return
Fayçal Ikhouane and José Rodellar
On the hysteretic Bouc-Wen model. Part I: Forced limit cycle characterization.
Nonlinear Dynamics. 2005(42):63–78 Return
Fayçal Ikhouane and José Rodellar
On the hysteretic Bouc-Wen model. Part II: Robust parametric identification.
Nonlinear Dynamics. 2005(42):79–95 Return
Fayçal Ikhouane, Victor Mañosa, and José Rodellar
Dynamic properties of the hysteretic Bouc-Wen model.
Sytems and Control Letters. 2006. in press Return
Fayçal Ikhouane, Oriol Gomis-Bellmunt, and Pere Castell-Vilanova
A limit cycle approach for the parametric identification of hysteretic systems.
Submitted to IEEE - Control Systems Technology Return
Fayçal Ikhouane and Shirley J. Dyke
Modeling and identification of a shear mode magnetorheological damper.
Submitted to Smart Materials and Structures Return
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Bibliography (Cont’d)
Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Silvano Erlicher and Nelly Point
Thermodynamic admissibility of BoucŰWen type hysteresis models.
Comptes Rendus Mecanique. 2004(332):51–57 Return
Fayçal Ikhouane, José Rodellar, and José E. Hurtado
Analytical characterization of hysteresis loops described by the Bouc-Wen model.
Mechanics of Advanced Materials and Structures. 2006(13):463-472 Return
P. R. Dahl
A solid friction model.
The Aerospace Corporation, El-Segundo, TOR-158(3107-18), California. 1968
Return
F. Yi, S. J. Dyke, J. M. Caicedo, and J. D. Carlson.
Experimental verification of multiinput seismic control strategies for smart dampers.
ASCE Journal of Engineering Mechanics. 2001(127):1152–1164 Return
LORD Corp.
Rheonetic Magnetorheological (MR) Fluid Technology MR damper.
Cary, NC Return
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Bibliography (Cont’d)
Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Michael J. Chrzan and J. David Carlson
MR fluid sponge devices and their use in vibration control of washing machines.
SPIE - 8th Annual Symposium on Smart Structures and Materials. Newport Beach, CA. 2001
Return
G. Yang, B.F. Spencer, J.D. Carlson, and M.K. Sain
Large-scale MR fluid dampers: Modeling and dynamic performance considerations.
Engineering Structures. 2002(24):309–323 Return
G. Yang, B.F. Spencer, H.J. Jung, and J.D. Carlson
Dynamic modeling of large-scale magnetorheological damper systems for civil engineering applications.
Journal of Engineering Mechanics. 2004(130):1107–1114 Return
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Proofs
Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Proof.
Demonstration of alternative to shear-mode MR damper
Previous considerations
Overparametrized → perform normalization
Ikhouane and Dyke
The fact that lim ρ−→∞ ψ σ,n(¯x tp) = −1 is independent from σ and n for large values of ρX max
Proof
Conclusion → for large values of ρX max, the values of the parameters σ and n are irrelevant.
After considering the previous alternatives a new model is suggested
F(T) = k vẋ(t) + k vF c(ẋ)
k x and k w are voltage dependent, and F c is the Coulomb dry friction force representation
F c(ẋ) = 1 for ẋ > 0
F c(ẋ) = −1 for ẋ < 0
Disadvantage → discontinuity at zero velocity or numerical instability when the ẋ of the damper is
close to 0
Return
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Proofs
Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Proof.
Demonstration of alternative to shear-mode MR damper
Previous considerations
Overparametrized → perform normalization
Ikhouane and Dyke
The fact that lim ρ−→∞ ψ σ,n(¯x tp) = −1 is independent from σ and n for large values of ρX max
Proof
Conclusion → for large values of ρX max, the values of the parameters σ and n are irrelevant.
After considering the previous alternatives a new model is suggested
F(T) = k vẋ(t) + k vF c(ẋ)
k x and k w are voltage dependent, and F c is the Coulomb dry friction force representation
F c(ẋ) = 1 for ẋ > 0
F c(ẋ) = −1 for ẋ < 0
Disadvantage → discontinuity at zero velocity or numerical instability when the ẋ of the damper is
close to 0
Return
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Proofs
Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Proof.
Demonstration of alternative to shear-mode MR damper
Previous considerations
Overparametrized → perform normalization
Ikhouane and Dyke
The fact that lim ρ−→∞ ψ σ,n(¯x tp) = −1 is independent from σ and n for large values of ρX max
Proof
Conclusion → for large values of ρX max, the values of the parameters σ and n are irrelevant.
After considering the previous alternatives a new model is suggested
F(T) = k vẋ(t) + k vF c(ẋ)
k x and k w are voltage dependent, and F c is the Coulomb dry friction force representation
F c(ẋ) = 1 for ẋ > 0
F c(ẋ) = −1 for ẋ < 0
Disadvantage → discontinuity at zero velocity or numerical instability when the ẋ of the damper is
close to 0
Return
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Proofs
Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Proof.
Demonstration of alternative to shear-mode MR damper
Previous considerations
Overparametrized → perform normalization
Ikhouane and Dyke
The fact that lim ρ−→∞ ψ σ,n(¯x tp) = −1 is independent from σ and n for large values of ρX max
Proof
Conclusion → for large values of ρX max, the values of the parameters σ and n are irrelevant.
After considering the previous alternatives a new model is suggested
F(T) = k vẋ(t) + k vF c(ẋ)
k x and k w are voltage dependent, and F c is the Coulomb dry friction force representation
F c(ẋ) = 1 for ẋ > 0
F c(ẋ) = −1 for ẋ < 0
Disadvantage → discontinuity at zero velocity or numerical instability when the ẋ of the damper is
close to 0
Return
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Proofs
Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Proof.
Demonstration of alternative to shear-mode MR damper
Previous considerations
Overparametrized → perform normalization
Ikhouane and Dyke
The fact that lim ρ−→∞ ψ σ,n(¯x tp) = −1 is independent from σ and n for large values of ρX max
Proof
Conclusion → for large values of ρX max, the values of the parameters σ and n are irrelevant.
After considering the previous alternatives a new model is suggested
F(T) = k vẋ(t) + k vF c(ẋ)
k x and k w are voltage dependent, and F c is the Coulomb dry friction force representation
F c(ẋ) = 1 for ẋ > 0
F c(ẋ) = −1 for ẋ < 0
Disadvantage → discontinuity at zero velocity or numerical instability when the ẋ of the damper is
close to 0
Return
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Proofs
Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Proof.
Demonstration of alternative to shear-mode MR damper
Previous considerations
Overparametrized → perform normalization
Ikhouane and Dyke
The fact that lim ρ−→∞ ψ σ,n(¯x tp) = −1 is independent from σ and n for large values of ρX max
Proof
Conclusion → for large values of ρX max, the values of the parameters σ and n are irrelevant.
After considering the previous alternatives a new model is suggested
F(T) = k vẋ(t) + k vF c(ẋ)
k x and k w are voltage dependent, and F c is the Coulomb dry friction force representation
F c(ẋ) = 1 for ẋ > 0
F c(ẋ) = −1 for ẋ < 0
Disadvantage → discontinuity at zero velocity or numerical instability when the ẋ of the damper is
close to 0
Return
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Proofs (Cont’d)
Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Proof.
Regions of the hysteresis BW loops Ikhouane et. al., 2006
The main slope of the linear region is ρX max. This slope comes from d¯w(¯x) at the point of the loading
d¯x
part of the limit cycle where ¯w(¯x) = 0
The abscissa of the point P tp where the plastic region starts is ¯x tp
We have
lim
u−→∞ ψσ,n(u) = 1
Return
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Proofs (Cont’d)
Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Proof.
Regions of the hysteresis BW loops Ikhouane et. al., 2006
The main slope of the linear region is ρX max. This slope comes from d¯w(¯x) at the point of the loading
d¯x
part of the limit cycle where ¯w(¯x) = 0
The abscissa of the point P tp where the plastic region starts is ¯x tp
We have
lim
u−→∞ ψσ,n(u) = 1
Return
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Proofs (Cont’d)
Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Proof.
Regions of the hysteresis BW loops Ikhouane et. al., 2006
The main slope of the linear region is ρX max. This slope comes from d¯w(¯x) at the point of the loading
d¯x
part of the limit cycle where ¯w(¯x) = 0
The abscissa of the point P tp where the plastic region starts is ¯x tp
We have
lim
u−→∞ ψσ,n(u) = 1
Return
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Proofs (Cont’d)
Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Proof.
Proof shear mode
The fact that lim ρ−→∞ ψ σ,n(¯x tp) = −1 is independent from σ and n for large values of ρX max
1
¯x tp ≈ −1 [ϕ + σ,n
ρX ( n√ 1 − r 2 ) − ϕ + σ,n (−1)]
max
Return
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Proofs (Cont’d)
Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Proof.
Previous considerations in the Identification Methodology
Ikhouane and Rodellar, 2005b
Assumes knowledge of the limit cycle → (x(τ), ¯F(τ)) by a variable τ ∈ [0, T]
Only the loading part of the input signal is considered τ ∈ [0, T + ]
The equation of the loading part is
¯w(x) = ψ + σ,n (ϕ+ σ,n [−ψσ,n(ρ(Xmax − X min))] + ρ(x − X min ))
Its derivative is
Proof
Theorem 1 shows that
d¯w(x)
= ρ(1 − ¯w(x))
dx
x = X min → τ = 0 → −ψ 1,1 (ρ(X max − X min ))
x = X max → τ = T + → ψ 1,1 (ρ(X max − X min ))
Return
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Proofs (Cont’d)
Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Proof.
Previous considerations in the Identification Methodology
Ikhouane and Rodellar, 2005b
Assumes knowledge of the limit cycle → (x(τ), ¯F(τ)) by a variable τ ∈ [0, T]
Only the loading part of the input signal is considered τ ∈ [0, T + ]
The equation of the loading part is
¯w(x) = ψ + σ,n (ϕ+ σ,n [−ψσ,n(ρ(Xmax − X min))] + ρ(x − X min ))
Its derivative is
Proof
Theorem 1 shows that
d¯w(x)
= ρ(1 − ¯w(x))
dx
x = X min → τ = 0 → −ψ 1,1 (ρ(X max − X min ))
x = X max → τ = T + → ψ 1,1 (ρ(X max − X min ))
Return
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Proofs (Cont’d)
Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Proof.
Previous considerations in the Identification Methodology
Ikhouane and Rodellar, 2005b
Assumes knowledge of the limit cycle → (x(τ), ¯F(τ)) by a variable τ ∈ [0, T]
Only the loading part of the input signal is considered τ ∈ [0, T + ]
The equation of the loading part is
¯w(x) = ψ + σ,n (ϕ+ σ,n [−ψσ,n(ρ(Xmax − X min))] + ρ(x − X min ))
Its derivative is
Proof
Theorem 1 shows that
d¯w(x)
= ρ(1 − ¯w(x))
dx
x = X min → τ = 0 → −ψ 1,1 (ρ(X max − X min ))
x = X max → τ = T + → ψ 1,1 (ρ(X max − X min ))
Return
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Proofs (Cont’d)
Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Proof.
Previous considerations in the Identification Methodology
Ikhouane and Rodellar, 2005b
Assumes knowledge of the limit cycle → (x(τ), ¯F(τ)) by a variable τ ∈ [0, T]
Only the loading part of the input signal is considered τ ∈ [0, T + ]
The equation of the loading part is
¯w(x) = ψ + σ,n (ϕ+ σ,n [−ψσ,n(ρ(Xmax − X min))] + ρ(x − X min ))
Its derivative is
Proof
Theorem 1 shows that
d¯w(x)
= ρ(1 − ¯w(x))
dx
x = X min → τ = 0 → −ψ 1,1 (ρ(X max − X min ))
x = X max → τ = T + → ψ 1,1 (ρ(X max − X min ))
Return
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Proofs (Cont’d)
Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Proof.
Previous considerations in the Identification Methodology
Ikhouane and Rodellar, 2005b
Assumes knowledge of the limit cycle → (x(τ), ¯F(τ)) by a variable τ ∈ [0, T]
Only the loading part of the input signal is considered τ ∈ [0, T + ]
The equation of the loading part is
¯w(x) = ψ + σ,n (ϕ+ σ,n [−ψσ,n(ρ(Xmax − X min))] + ρ(x − X min ))
Its derivative is
Proof
Theorem 1 shows that
d¯w(x)
= ρ(1 − ¯w(x))
dx
x = X min → τ = 0 → −ψ 1,1 (ρ(X max − X min ))
x = X max → τ = T + → ψ 1,1 (ρ(X max − X min ))
Return
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Proofs (Cont’d)
Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Proof.
Derivative of the loading part of the limit cycle of the new MR Dahl friction model
¯w(x) = ψ + σ,n (ϕ+ σ,n [−ψσ,n(ρ(Xmax − X min))] + ρ(x − X min ))
} {{ }
f (x)
, where
∂f (x)
= ρ
∂x
Then by using the fact that the function ψ σ,n + is the inverse of the function ϕ+ σ,n the following relationship is true
∂ψ σ,n + (f (x))
∂x
(
∂f (x) ∂ψ
+ )
σ,n (u)
= = ρ ∗
(
∂x ∂u
⎜
u=f (x) ⎝
⎛
∂ϕ + σ,n (v)
∂v
⎞
1
)
⎟
⎠
v=ψ σ,n + (f (x))
The fact that ψ σ,n + (f (x)) = ¯w(x) so the previous equation becomes
⎛
∂¯w(x)
= ρ ∗
(
∂x ⎜
⎝
∂ϕ + σ,n (v)
∂v
1
)
v=¯w(x)
⎞
⎟
⎠
Return
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Proofs (Cont’d)
Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Proof.
Step 2 k x demonstration
x = X min
¯F(0) = k xẋ(0) + k w¯w(x)
x = X max
¯F(T + ) = k xẋ(T + ) + k w¯w(x)
¯F(0) = k xẋ(0) + k w(−ψ 1,1 (ρ(X max − X min ))) ¯F(T + ) = k xẋ(0) + k w(ψ 1,1 (ρ(X max − X min )))
Then if we combine the previous equations we arrive at the parameter k x the following way
−¯F(0) + k xẋ(0) = ¯F(T + ) − k xẋ(T + )
¯F(T + ) + ¯F(0)
k x =
ẋ(0) + ẋ(T + )
Return
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Proofs (Cont’d)
Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Proof.
Step 3 θ(x) demonstration
Then its derivative
dθ(x)
= k wρ(1 − w(x))
dx
Defining a = k wρ and b = ρ, the derivative can be rewritten as
dθ(x)
= a − ρθ(x)
dx
Return
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Small-scale technical data
Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Technical data of the small-scale MR friction
controllable damper
LORD Corp.
Stroke = 58 mm, Weight = 0.48 Kg, Input
current = 0.5 A (continuous) and = 1 A
(intermittent), Resistance (ambient temp.)
= 20Ω
Operating temperature = 70 C
Damper forces (peak-to-peak) = 100 N (5
cm/sec @ 1 A) and = 2 N (20 cm/sec @ 0 A)
Disadvantage → do not apply more than 0.5 A
for longer than 30 sec at a time, or heat buildup
may melt the plastic shaft.
Wonder Box → device to control the MR
damper. Power supply = 12 V DC and 2 A DC,
the PC voltage signal is from 0 to 5 V DC, and
the output current is from 0 to 2 A DC.
Return
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Small-scale technical data
Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Technical data of the small-scale MR friction
controllable damper
LORD Corp.
Stroke = 58 mm, Weight = 0.48 Kg, Input
current = 0.5 A (continuous) and = 1 A
(intermittent), Resistance (ambient temp.)
= 20Ω
Operating temperature = 70 C
Damper forces (peak-to-peak) = 100 N (5
cm/sec @ 1 A) and = 2 N (20 cm/sec @ 0 A)
Disadvantage → do not apply more than 0.5 A
for longer than 30 sec at a time, or heat buildup
may melt the plastic shaft.
Wonder Box → device to control the MR
damper. Power supply = 12 V DC and 2 A DC,
the PC voltage signal is from 0 to 5 V DC, and
the output current is from 0 to 2 A DC.
Return
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Small-scale technical data
Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Technical data of the small-scale MR friction
controllable damper
LORD Corp.
Stroke = 58 mm, Weight = 0.48 Kg, Input
current = 0.5 A (continuous) and = 1 A
(intermittent), Resistance (ambient temp.)
= 20Ω
Operating temperature = 70 C
Damper forces (peak-to-peak) = 100 N (5
cm/sec @ 1 A) and = 2 N (20 cm/sec @ 0 A)
Disadvantage → do not apply more than 0.5 A
for longer than 30 sec at a time, or heat buildup
may melt the plastic shaft.
Wonder Box → device to control the MR
damper. Power supply = 12 V DC and 2 A DC,
the PC voltage signal is from 0 to 5 V DC, and
the output current is from 0 to 2 A DC.
Return
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Small-scale technical data
Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Technical data of the small-scale MR friction
controllable damper
LORD Corp.
Stroke = 58 mm, Weight = 0.48 Kg, Input
current = 0.5 A (continuous) and = 1 A
(intermittent), Resistance (ambient temp.)
= 20Ω
Operating temperature = 70 C
Damper forces (peak-to-peak) = 100 N (5
cm/sec @ 1 A) and = 2 N (20 cm/sec @ 0 A)
Disadvantage → do not apply more than 0.5 A
for longer than 30 sec at a time, or heat buildup
may melt the plastic shaft.
Wonder Box → device to control the MR
damper. Power supply = 12 V DC and 2 A DC,
the PC voltage signal is from 0 to 5 V DC, and
the output current is from 0 to 2 A DC.
Return
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation

Small-scale technical data
Introduction
Hysteretic models
Identification methodology
Future work
Experimental identification
Summary
Technical data of the small-scale MR friction
controllable damper
LORD Corp.
Stroke = 58 mm, Weight = 0.48 Kg, Input
current = 0.5 A (continuous) and = 1 A
(intermittent), Resistance (ambient temp.)
= 20Ω
Operating temperature = 70 C
Damper forces (peak-to-peak) = 100 N (5
cm/sec @ 1 A) and = 2 N (20 cm/sec @ 0 A)
Disadvantage → do not apply more than 0.5 A
for longer than 30 sec at a time, or heat buildup
may melt the plastic shaft.
Wonder Box → device to control the MR
damper. Power supply = 12 V DC and 2 A DC,
the PC voltage signal is from 0 to 5 V DC, and
the output current is from 0 to 2 A DC.
Return
Arturo Rodríguez Tsouroukdissian
Small-scale MR dampers for vibration mitigation