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TECHNICAL PAPERS

# An Active Dynamic Vibration Absorber for a Hand-Held Vibro-Elastography Probe

[+] Author and Article Information
Hassan Rivaz

Department of Electrical and Computer Engineering, University of British Columbia, 2332 Main Mall, Vancouver, BC, Canada, V6T1Z4rivaz@jhu.edu

Robert Rohling1

Department of Electrical and Computer Engineering, University of British Columbia, 2332 Main Mall, Vancouver, BC, Canada, V6T1Z4rohling@ece.ubc.ca

This value is the mass of the magnet of the electromagnetic actuator.

Since the hand is a distributed mass system and vibrates around the arthroses at wrist, elbow and shoulder, the effective mass is only a percentage of the whole mass of the hand. As an example, for a rod with uniform mass distribution that rotates around a hinge at one of its ends, the effective mass is $1∕3$ of the total mass.

These values of the properties of the primary system will be allowed to vary over a certain range, since they vary for different persons holding the device.

It is not difficult to show that the characteristic equation of the absorber system, after inserting the numerical values for the absorber and primary systems and the electromagnetic actuator, has an extra root at $a=4.9×105×ωe−2$ where $ωe$ is in Hz and $a$ has the units $1∕s$. This root is associated with the dynamics of the electromagnetic actuator and is sufficiently far from the imaginary axis in the $5–25Hz$ frequency range to be neglected.

The characteristic equation of the absorber system of the DR, $P(s)$, has infinitely many roots. Therefore a DR absorber, unlike PI-DVA, is similar to a mass-spring system only after a settling time. This settling time is studied in Ref. 27 and should be distinguished from the settling time of the combined system, which can be observed in both PI and DR controllers.

1

Corresponding author.

J. Vib. Acoust 129(1), 101-112 (Sep 21, 2006) (12 pages) doi:10.1115/1.2424982 History: Received February 27, 2006; Revised September 21, 2006

## Abstract

Vibro-elastography is a new medical imaging method that identifies the mechanical properties of tissue by measuring tissue motion in response to a multi-frequency external vibration source. Previous research on vibro-elastography used ultrasound to measure the tissue motion and system identification techniques to identify the tissue properties. This paper describes a hand-held probe with a combined vibration source and ultrasound transducer to implement the new method as a practical device. The device uses a proportional integral active dynamic vibration absorber with an electromagnetic actuator to counterbalance the reaction forces from contact with the tissue. Experiments show an operational frequency range of $5–20Hz$, with at least $15dB$ vibration absorption in $0.4s$ for single frequency excitation. Experiments with variable frequency and amplitude excitation also show a high level of vibration absorption.

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## Figures

Figure 1

Hard and soft inclusions are subject to an external compression (F)

Figure 2

(a) A hand-held device for VE; and (b) mass-spring-damper model of the device held by hand. The term primary system refers to the combined effective mass, stiffness and damping of the hand held assembly, i.e., including the operator. fk and fb are the external forces from the hand.

Figure 3

(a) Vibration isolation; (b) semi-active vibration isolation; (c) passive dynamic vibration absorption (DVA); (d) semi-active DVA; and (e) active DVA

Figure 4

DVA with zero damping attached to the primary system

Figure 5

Active DVA attached to the primary system

Figure 6

Block diagram representation of the PI controller

Figure 7

Exploded view of the hand-held probe: (a) moving head; (b) ultrasound probe; (c) slide rod; (d) machined shell; (e) spacer; (f) linear potentiometer; (g) and (h) primary actuator’s coil and magnet; (i) accelerometer; (j) and (k) absorber actuator’s coil and magnet; and (l) absorber spring

Figure 8

Stability chart. Kp and frequency versus Ki. The dashed and solid curves correspond to the combined system and absorber system, respectively.

Figure 9

Minimum operational frequency versus k

Figure 10

Root locus plot of the poles of the transfer function of the PD with absolute absorber mass position and velocity, neglecting the dynamics of the actuator and filters

Figure 11

Root locus plot of the poles of the transfer function of the PD with relative absorber mass position and velocity, neglecting the dynamics of the actuator and filters

Figure 12

Root locus plot of PI transfer function’s poles, neglecting the dynamics of the actuator and filters

Figure 13

Root locus plot of DR transfer function’s poles and zeros, neglecting the dynamics of the actuator and filters

Figure 14

(a) Free vibration of the absorber mass; (b) vibration of the absorber mass with the PI controller tuned to 10Hz; (c) vibration of the absorber mass with the PI controller whose resonance frequency is changed from 15Hzto7.5Hz at t=2s

Figure 15

Combined system simulation results: (a) vibration of the hand-held device and the absorber mass at 10Hz excitation; and (b) vibration of the hand-held device at 10Hz. The amplitude of excitation is a constant 1N for t=0–5s and is increased linearly from 0.5N at t=5sto1.5N at t=10s; and (c) vibration of the hand-held device with a swept-sine excitation. Excitation frequency is a constant 8Hz for t=0–5s and is decreased linearly from 8Hz at t=4sto16Hz at t=10s.

Figure 16

(a) Free vibration experiment on the absorber system with no control force (b) vibration of the absorber mass controlled with PI tuned to 5Hz; and (c) vibration of the absorber mass controlled with PI tuned to 4.3Hz for t=0–2.6s and to 2.7Hz for t=2.6–5s

Figure 17

The hand-held device held by the mechanical arm

Figure 18

Vibration absorption experiments at three different frequencies: (a) 5Hz; (b) 10Hz; and (c) 15Hz

Figure 19

Vibration absorption experiments: (a) the amplitude of excitation is changed from 1.7mmto2mm at t=2s; (b) the excitation frequency is 8Hz for t=0–2s; and is increased linearly to 16Hz in 5s

Figure 20

Probe vibration for experiments with a human operator on real tissue. The vibration absorber is turned on at t=0.7

Figure 21

Ωi for i=3 and its corresponding ωe

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