Crash Mechanics for automotive courses.pdf

Crash mechnaics

1. Geometry
Meshed Model
Boundary
Conditions
Material Laws
Kinematics
Crash
Mechanics
Crash Mechanics Ref; 010
CRASH MECHANICS

2. Equations

3. Newton’s First Law
(law of inertia)
An object at rest tends to stay at rest 
and an object in motion tends to stay 
in motion unless acted upon by an 
unbalanced force.

4. Newton’s Second Law
(F=ma)
Force equals mass times acceleration.

5. Newton’s Third Law (For every action equal and opposite reaction)
For every action there is an equal and
opposite reaction.

6. Newton’s Laws of Motion
For every action equal there is an
equal and opposite reaction

7. The Equations
They are called the 'suvat' equations because the q uantities s, u, v, a and t are used in the
equations, with four of the symbols used in each eq uation.
s = displacement (measured in metres)
u = initial velocity (measured in metres per second , ms-1)
v = final velocity (also measured in ms-1)
a = acceleration (measured in metres per second per second, ms-2)
t = time (measured in seconds, s)
The equations are:
v = u + at
s = ½*(u+v)t
s = ut+ ½*at
2
v
2
= u
2
+ 2as

8. Graphs of Motion

9. Graphs of Motion
•The gradient of a position - time graph (x vs. t) gi ves the velocity.
•The gradient of a velocity - time graph (v vs. t) gi ves the acceleration.
•The area under a velocity - time graph (v vs. t) giv es the displacement.
•The area under an acceleration - time graph ( avs. t) gives the velocity.

10. Graphs of Motion -Velocity
Increasing Acceleration Decreasing Acceleration Constant Deceleration
t
V
15
200
t
V
5
16
8
Area under line = 15 x 200
Displacement
= 3000 m
Area under line = (5 x 8) + (0.5 x 8 x 5)
Displacement
= 60 m

11. Graphs of Motion -
Displacement
Increasing Speed
Decreasing Speed

12. Frame of Reference &
Relative Velocity The frame of reference is the point of view from wh ich a system
is observed
The velocity of an object is frame dependent.
C’s right
C’s left

13. Momentum
•If an object is
moving
then it has momentum.
This can be calculated;
•Which one has more momentum?
Momentum = Mass x Velocity
P = m * v
kgm/s = kg m/s
Momentum is a
vector
quantity
Mass (kg) Velocity
(m/s)
Car 1000 5
Motorcycle 200 30

14. Change in Momentum
•Change in momentum is calculated by looking at
final and initial momentums.
•
∆∆∆∆p= p
f–p
i
–∆∆∆∆p: change in momentum
–p
f: final momentum
–p
i: initial momentum
•In which case is the magnitude
of the momentum change greatest?
•In which case is the change
in the magnitude of the
momentum greatest?

15. Impulse •Impulse
is the
product of
an external
force and time,
which
results in a
change in momentum
of a particle or system.
•J= Ft and J= ∆P
•Therefore Ft= ∆P
•Units:
N s
or
kg m/s
(same as momentum)
Impulse (J) on a graph
F(N)
t (ms)
0 1 2 3 4
0
1000
2000
3000
area under curve

16. Impulsive Forces
•Usually
high magnitude
,
short
duration
.
•Suppose the ball hits the bat at 90
mph and leaves the bat at 90 mph,
what is the magnitude of the
momentum change?
•What is the change in the
magnitude of the momentum?

17. External versus internal
forces
•External forces:
forces coming from outside the system of
particles whose momentum is being considered.
–External forces change the momentum of the system.
•Internal forces:
forces arising from interaction of particles
within a system.
–Internal forces cannot change momentum of the syste m.

18. An external force in golf
•The club head exerts an
external impulsive force
on the ball and changes
its momentum.
•The acceleration of the
ball is greater because
its mass is smaller.
The System

19. An internal force in pool •The forces the balls exert
on each other are internal
and do not change the
momentum of the system.
•Since the balls have equal
masses, the magnitude of their
accelerations is equal.
The System

20. Applying the Principle of
Conservation of Linear Momentum
•Decide which objects are included in the
system
•Relative to the system, identify the internal
and external forces.
•Verify that the system is isolated
•Set the final momentum of the system equal
to its initial momentum.
–Remember that the momentum is a vector

21. Conservation of Momentum •Momentum conserved in one and two
dimensions
P
i= P
f

22. Collisions
•When two moving objects make contact with each othe r, they
undergo a
collision
.
•Conservation of momentum is used to analyze all col lisions.
•Newton’s Third Law is also useful. It tells us that the force
exerted by body A on body B in a collision is equal and
opposite to the force exerted on body B by body A.

23. Collisions
•During a collision, external
forces are ignored.
•The time frame of the
collision is very short.
•The forces are impulsive
forces (high force, short
duration).

24. Collision Types
•Elastic collisions
–Also called “hard” collisions
–No deformation occurs, no kinetic energy lost
•Inelastic collisions
–Deformation occurs, kinetic energy is lost
•Perfectly Inelastic (stick together)
–Objects stick together and become one object
–Deformation occurs, kinetic energy is lost

25. Elastic Collisions
An elastic collision is a collision where both mome ntum and
kinetic energy is conserved
G
eoG
m
G
etrG
eyoG
mtrG
my
M
eo M
m
M
etr M
eyo M
mtr M
my
Momentum conservation
Kinetic energy
conservation

26. Inelastic Collisions
An inelastic collision is where momentum is conserv ed but
kinetic energy is not conserved
G
eo G
m

M
e≠ M
m

Momentum conservation
Kinetic energy NOT
conserved

27. 2D-Collisions (Assumption for the Assignment –next session)
•Momentum in the x-direction is conserved.
–ΣP
x(before) = ΣP
x(after)
•Momentum in the y-direction is conserved.
–ΣP
y(before) = ΣP
y(after)
•Treat x and y coordinates independently.
–Ignore x when calculating y
–Ignore y when calculating x

28. Definition Of Centre Of
Mass
•The center of mass is a point that
represents the average location for the
total mass of a system
•The center of mass will remain constant
during a collision

29. Centre Of Mass
2 1
22 11
m m
xm xm
x
cm
+
+
=

30. Velocity of the center of
mass
Λ
Λ
+ +
+
+
= ∆
2 1
22 11
m m
vm vm
v
cm
2 1
2 2 1 1
m m
x m x m
x
cm
+
∆
+
∆
= ∆

31. Velocity of the center of
mass
•In an isolated system, the
total linear momentum
does not change.
•Therefore, the velocity of
the center of mass does
not change.
2 1
22 11
m m
vm vm
v
cm
+
+
=

32. Car Crashes & Physics

33. Kamal’s Model

34. Vehicle Structures

35. Problem
Analyze the behavior of the system composed of the two springs
loaded by external forces as shown above
Given
F
1x , F
2x,F
3xare external loads. Positive directions of the forces
are along the positive x-axis
k
1and k
2are the stiffnesses of the two springs
k
1
k
2
F
1x
F
2x
F
3x
x
An FE based approach

36. In Series, Parallel & at angle

37. Car Crashes & Biology

38. Tolerance & Survivability

39. Industrial Application

41. Defining an Engineering Problem

42. CAE Model

43. CAE Model

44. CAE Model

45. CAE Model

46. CAE Model

47. CAE Model

48. Thank you for listening …………..