Transcript Pairing Down Robotics Safety Tests

Robotics Safety Tests for new
ISO standard
Samson Phan
Conclusions
HIC
• WAM “human safe” robot
shows less high HIC
number for collisions
• HIC numbers for all tests
too low for serious
damage
• Neck Constraint Matters
CLI
• Bimodal distributtion
shows CLI too insensitive
for robot-human collision
R2 =
0.3871
Can we reduce the number of
injury criterias?
Elimination of other scenarios
• Unconstrained
scenarios
– All energy goes into
deformation or plastic
yielding instead of
acceleration of the
target.
• Eliminate very sharp
planforms
– Designers are
competent
– Care given to not give
knives
– How sharp is “sharp?”
Proposed Model
• Quasi-static
– Stress wave traversal
(Timoshenk & Goodier, 1951)
• Inconsequential skin
– Thickness of layer << contact
length
• Hertzian pressure distribution
• Coupling between tangential
and normal forces based only
on friction, not deformation (q
(x)=u p(x))
•Pressure distribution p0(1-x2/a2)
(hertz pressure)
•Friction induced tangential forces
Collision Parameter->KE ->deflection-> pressure->shear stress
Quasi-static Assumption?
Material
Young’s
Modulus
Density
Wavespeed
Skin
4.2E5
1750 kg/m3
1600
Muscle
126E3
1060 kg/m3
10.9
Bone
18E18
1500 kg/m3
1.8974E8
m/s
c0 
E

Inconsequential skin thickness?
• Skin thickness: 2-4.5 mm
• Bone thickness (skull): 410 mm
• Muscle thickness
Sliding Contact
q(x,y)=µ p(x,y)
Q/µP
Bhushan
2001
Tangential velocity inclusion
• Assume sufficient
tangential velocity to
induce sliding
Vx ≥ µ Vz
Model Development
Energy (Before collision)
• Tangential Velocity
• Vertical Velocity
• Limiting case
– Vx = µ Vz
1
1
2
Einitial  mi vi , x  mi vi2, y
2
2
1
 mi 1   vi2, y
2
Energy (After Collision)
• Velocity (Vx, Vy)
• Deflection in robot (Erobot)
• Deformation of tissue
Wdeformation  Erobot
Model Development
Kinetic Energy of Robot to Tissue
deflection (for solids of revolute)
3
*2
d max 16 RE
1
2
mi 1   vi , y  
d  Erobot
0
2
9
1
8 2.5 * 0.5
mi 1   vi2, y  d max
E R  Erobot
2
15
 Erobot  151   mi vi2 
 (eq1)
d max  
0.5 *
16R E


Hertzian Theory of Contact for Solids of
revolution
(sphere)
a
p0 R
*
(eq2)
2E
d  ap0 (eq3)
0.4
Neglect dissipative losses
(sound, heat, etc) and Erobot
for worst case scenario
mi = mass matrix of robot
vi = velocity matrix of robot
R = relative curvature (1/R)=(1/R1 + 1/R2)
1/E* = (1-v1^2)/E1 + (1-v2^2)/E2
p0 = max pressure at given instance
d = deflection
P = total load compressing solid
Contact Mechanics
• Combine eq (2) & (3):
d
p0 p0 R
*
*

 p R
2
2
0
*2
2E 2E
4E
• Equate with eq (1):
0.4
2
2
2
 p0 R  151   mi vi 
4E
*2



16R
0.5
E



*
• Solve for p0
 151   mi vi2 

p0  
0.5 *
 16R E 
0.4
 4E *2   151   mi vi2 

 2   
0.5 *
  R   16R E 
0.2
 2E * 


0.5 
 R 
Failure criteria
• Von Mises Yield at
surface for u >0.3
p0  (1  2v) 2

J 
3
3 
Assumptions
• Spherical rigid
manipulator
• quasi-static

(1  2v)(2  v)
(16  4v  7v )

 
  • negligible plane
4
4

orientation change
• negligible skin thickness
(doesn’t affect contact
dynamics)
2
1/ 2
Hamilton 1983
Onset of Yield
Material property function
10
Wassink et al
10
8
10
µ = 0.4
6
10
µ = 0.8
4
10
0.1
10
8
0.05
6
4
robot radii
0
2
0
velocity
Kind of like boxing…
Another approach…
• Allowable amount of
soft tissue damage?
• OSHA mandated
levels?
• Same set of
equations to visualize
volume
How about non spherical
impactors?
4:1
1:4
b B
 
a  A
2 / 3
 R' 
 
 R" 
2 / 3
Impedence (m,E,w)
Impedance as a performance
and safety parameter
m
s
w
60 Hz
Epidermis spinosum
• Weakest shear layer
in skin.
• Blistering and
abrasions: layer that
separates.
• Shear layer failure
may be more
predictive of injury
than tension or Von
Mises yield criterion
Dropping Stuff…
2 in drop
140
120
100
80
with
60
without
40
20
0
N=10
avg
N=4