Vibration Response Study to
Understand Hand-Arm Injury
Shrikant Pattnaik, Robin DeJager-Kennedy
Jay Kim
Department of Mechanical Engineering,
University of Cincinnati, Cincinnati, OHIO
1
Research focus: how vibration affects hand
and arm injuries
• Develop hypotheses that can explain the
mechanism with scientific rationale
– Musculoskeletal disorder
– Vascular disorder
• Develop scientific approaches
– Engineering models
– Develop numerical analysis methods
– Direct or indirect Experimental validation
2
Presentation summary
• Vibration analysis models
• A hypothetical model proposed to explain a
cause of vascular system disorder
• Plan to work on discrete system models
3
Initial FEA Vibration Model
Displacement
Goals: Obtain basic data for further analysis of
Musculoskeletal and vascular systems
•Step 1 : Pre compression, non linear contact analysis
•Step 2 : Extraction of natural modes
•Step 3 : Steady state dynamic analysis
4
Strain
Issues
• Overly simplified boundary conditions and
models
– Un-modeled parts, initial configuration/posture, grip,
significantly influences natural modes and dynamic
responses significantly
– Effects of grip force and length of handling are not
difficult to be considered
• Overly simplified muscle forces
– Active tendon forces are not included
– Most finger musculo-tendon structure extends to
elbow
5
LifeMOD
•
•
•
The LifeMOD Biomechanics Modeler is a
plug-in module to the ADAMS physics
engine.
LifeMOD allows full functionality of
ADAMS/View.
Human models can be combined with
any ADAMS model for full dynamic
interaction.
Building a Model
Segments
Joints
Soft Tissues
Passive Modeling
Contact
Hybrid III Parameters
Active Modeling
Motion Capture integration
LifeMOD Inverse and Forward dynamics
Post Processing and Export
Multi-level Approach based in
Adams/LifeMod
7
The LifeMOD Suite
HandSIM – shrikant
LumbarSIM
CervicalSIM
LifeMOD
HipSIM
KneeSIM
Development of Hand Model
9
Tissue-wrapping
Forearm model with the flexor
digitorum profundus set up to slide
with respect to the third metacarpal
bone.
The flexor digitorum profundus
muscle group before slide points are
introduced (left) and after (right).
10
Muscle Model (Nonlinearity)
A – they are tension only elements
B – there is redundancy
Muscle Matrix for the active muscle groups
11
Active + Passive contribution
12
Muscle Fatigue
• Tetanic Frequency full motor unit
recruitment
• maintained for a short period of
time, 6 s
• 70% max the blood flow is
completely occluded and fatigue
• hyperbolic relationship with an
asymptote at roughly 15% of
maximum strength
13
Frequency Analysis
•
•
•
•
In terms of passive muscle, this means that at very low or high frequencies the
forcing function and muscle response are practically in phase
elastically dominated by either the series elastic element (KSE) for very high
frequencies (i.e., the dashpot cannot respond sufficiently quickly, eliminating
the parallel elastic element from the model) or
by a combination of both elastic elements KSE/(KSE + KPE) for very low
frequencies (i.e., the dashpot responds, stretching the parallel elastic element
with it).
Around the critical break frequency the muscle is fully viscoelastic with the
dashpot involved.
14
FRF Analysis: Input point impedance
15
Strategy of complete Frequency Analysis
o
o
o
o
o
Grip the required hand tool
Find the equilibrium
Train the muscle and joints
Find natural Frequencies and modes
Identify critical elements from the natural modes
•Forced response for particular configuration
•Introduce fatigue model – endurance analysis
•connect with individual flexible part in
Adams/Flex
16
Integration of Rigid + Flexible body
• Originally ADAMS – rigid body with 3 translation and 3
rotational DOF.
• Adams/Flex, flexible body
• Deformation = linear combination of linear mode shapes from
FEA or Experimental modal analysis
• Component Mode Synthesis – selected modes transferred
using MNF (mode neutral files) from say Abaqus.
• Generalized stiffness is diagonalized, Mass matrix formulated
using inertia invariants, Damping specified as fraction of
critical damping.
• Subset of mode shapes goes to solver
17
Test/Demo Case I
• Initial Equilibrium Analysis using the full hand-arm model; for
the given contact force;
– Find how muscles/tendons are loaded
– Find how joint forces are loaded
• Detail analysis of the fingertip
by a ABACUS model
– Contact analysis
– Vibration analysis
– Review the time histories
of the forces in the bone joint
and tendon
18
Test/Demo Case I – continue
1st Phalange
2nd Phalange
3rd Phalange
Hand
Muscle and Joints
Shown is the example of 1st phalange
19
Test/Demo Case II
• LifeMod model of Hand-Arm
• Find Gripping force to hold two different type of tools
• Ensuing vibration analysis
– Response characteristics; comparison to discrete models; possible
experiments
Tools lifted
Tools pushed
20
Integration
Ergonomic
Standards
Chosen Hand configurations
Pressure Data
Motion
Capture
Hand Model
5%ile
Hand Model
50%ile
Hand Model
95%ile
Validation
Consumer
Research
Database
Pain Locations
Muscle/Tendon
Forces
Joint
Forces
Risk+Pain+Discomfort
Assessment
Test New
Designs
Guidelines for
new packages
Data Collection
Pressure Mat
Vicon Motion Capture
Cyber Glove
Pressure Map
Example Animation with plot
Vascular system disorder: A view from wave
propagation / fluid-structure dynamics
• Desire to understand why vibration is
detrimental to vascular disorder
• Blood in an artery comprise a fluid-structure
system
• Optimal wave propagation condition may be
responsible
24
Wave propagation in Artery wall
Surrounding tissue
Artery wall,
radius R
p
Fluid flow in artery
W
u
2 R
dx   A
dx
t
x
P
u

x
t
Artery cross-section
Continuity
P  K W R  t  t E   t E WR 
Fluid eq.

2P
 2W
A 2  2R 2
x
t
P KW  E
 2 P 2R    2 P 
A 2  ~  2 
x
k  t 
Moens-Korteweg wave speed
C
R  ~ Et 
k  2 
2 
R 
25

~
W
Et 

t W  K  2   W k
2
R
R 

Wave propagation in artery wall
wave speed c
Wall-blood
wave
L/2

c
f
c
disturbance
R 
Et 
k



2 
R2 
Section behaves like a cylindrical
shell of n=0 mode (membrane
mode)
Critical condition: when the resonance frequency of the cylindrical
membrane of length L   / 2 coincides with c / f
26
Artery wall as a cylindrical shell
natural frequency when n=0
and m=1
Circular cylinder shell
simply supported
m=1
Equations of motion
N xx 1 N x
 2u x

 h 2  0
x
a 
t
N x 1 N Q 3
 2u


 h 2  0
x
a 
a
t
Qx 3 1 Q 3 N
 2 u3


 h 2  0
x
a 
a
t
Assumed solution
m x
cos n(   )
L
m x
U ( x, )  B sin
sin n(   )
L
m x
U 3 ( x, )  C sin
cos n(   )
L
U x ( x, )  A cos
27
Rough estimation of resonance condition
of a typical rat tail artery
E  30 kPa
f vs f(m=1,n=0)
  1050kg / m3
0.0014
h  0.1m m
r  0.8m m
  0.5
c
 2L
f
c
L
2f
0.0016
Length (m)
0.0012

0.001
0.0008
f
0.0006
f(m=1,n=0)
0.0004
0.0002
0
0
fn1, m0  f (L)
f(n=0,m=1)
1000
2000
3000
4000
5000
6000
Freqnecy (Hz)
Critical Frequencies, f* = 950Hz, 1850Hz
The above is only a very preliminary estimation
•Data should be refined
•Is the surrounding tissue has a more added mass effect or
Winkler foundation effect?
28
Comparison of Various Lumped Parameter
Hand-Arm Models
Lumped parameter
hand-arm model
me2
A compact tool
me2
e
e
M tool
M tool
Vibration response
of hand-held tool
Vibration response of
free-suspended tool
Comparison of the prediction of the pair by the model and
measurement to qualitatively evaluate hand-arm models
29
Research Plan
• Select models to compare.
• Collect acceleration data for two or three
tools.
• Use data to determine input force to apply to
models.
• Simulate response of models.
• Compare simulated response to measured
response of hand-held tool.
30
Hand-Arm Models
• Models vary in complexity
from 1 DOF to many
DOFs.
• Various values for
constants are available for
the different models.
31
Data Collection
• Acceleration data collected for:
– Free suspended
– Held in hands
• Test procedure is with grinder running freely.
32
Sample Acceleration Data
RSS, Accel 1
Acceleration, m/s 2
250
Accelerometer Data, Accel 1, X axis
200
150
200
150
100
100
Acceleration, m/s 2
50
50
0
0
0
-50
500
1000
1500
2000
Sample #
-100
-150
-200
Data collected for DeWalt
handheld DW818 grinder
-250
0
500
1000
1500
2000
Sample #
2500
3000
3500
33
2500
3000
Open Discussions
• Refinement of the models
• Expansion or simplification of the models
• Possible validations
– Direct / indirect validations
– Qualitative / quantitative validations
• Application ideas
• Criticisms and suggestions
34