Topic 3 Contact Mechanics

Question 1

What can excessive contact stress or deformation lead to

Answer 1

overload
wear
rolling contact fatigue
seizure
loss of tolerance

Question 2

What is the Hertz theory of elastic contact

Answer 2

• Two curved bodies loaded together contact at a single point or along a line
• Elastic deformation occurs and contact is made over a finite area
• An analytical method for determing the size of this region was first described by heinrich Hertz

Question 3

What are the Hertz model of contact assumptions

Answer 3

• The materials in contact are homogenous and the yield stress is not exceeded
• Contact load is causd by the load which is normal to the contact, which effectively means that there are no tangential forces acting between the solids
• The size of the contact is small compared to the size of the curved bodies
• The contactings solids are at rest and in equilibrium
• The effects of surface roughness are negligble

Question 4

Most frequently used contact parameters are

Answer 4

• Contact area dimensions
• Maximum and average contact pressure
• Stress distribution in the contact
• position of he maximum shear stress below the surface

Question 5

What does a point contact occur between

Answer 5

two balls and two cylinders of the same radius at right angles

Question 6

What does a line contact be occur between

Answer 6

two parallel cylinders

Question 7

Where do ellipitical contacts occur

Answer 7

When two cylinder are crossed or a moving ball is in contact with inner ring of a bearing or two gear teeth are in contact

Question 8

Why is it important to identify correct contact model

Answer 8

Ensure using correct equations as different contacts have different stress distribution

Question 9

When does the maximum contact stress occur

Answer 9

Below the surface

Question 10

Whats wrong with Hertzian contact model

Answer 10

Most engineering contacts violate the hertz assumptions, but contact mechanics under these conditions become complex and numberical methods are needed

Question 11

How does friction and sliding contacts impact the hertrizan contact theory

Answer 11

When friction is bigger than tangential force Qmu*P sliding will occur, contact stress distributions are now due to both pressure and frictional tractions, moves shear stress towards surface

Question 12

What happens when mu = 0.25 for contact shear stresses

Answer 12

Will cause the shear stress to reach the surface of the contact

Question 13

What happens at yield in contact mechanics

Answer 13

yields occurs initially at a location sub-surface

• region of plasticity initiall contained by an elastic region
• if load increases further, place region grows
• full plasticity when the plastic region reaches the surface

Question 14

Hardness H may be related to Yield strength Y by what equation

Answer 14

H=2.7Y

Question 15

Draw a diagram of what actually happens in contact mechanics with a rough surface

Answer 15

see powerpoint

Question 16

What happens in rough contacts

Answer 16

Rough interface acts like a compliant layer
Asperity peaks outside the nominal ‘Hertzian’ contact area may touch
Local pressure peaks at each asperity contact, but the average pressure over the contact will be reduced

Question 17

What techniques are used for determining contact area and pressure experimentally

Answer 17

photoelastic techniques
pressure sensitive film
contact resistance
ultrasound

Question 18

What is the equation for reduced radius

Answer 18

1/R’ = 1/R1 + 1/R2

Question 19

What is the equation for reduced modulus

Answer 19

1/E* = (1-v1^2)/E1 + (1-v2^2)/E2

Question 20

What is the radius of a flat plate

Answer 20

infinitity i.e 1/R = 0

Question 21

What is the difference between po and pavg

Answer 21

po is the maximum contact pressure and p average is the average contact pressure

Question 22

If the po is greater than yield strength what is worth noting when calculating the contact stresses

Answer 22

If po, the maximum contact pressure, is greater than the yield strength there will be plastic deformation occuring, Hertz contact theory breaks down when significant plastic deformation

Question 23

Whats the difference between a and b in an elliptical point contact

Answer 23

a is the long ellipitical dimension and b is the short dimension

Question 24

What is the area of an ellipse

Answer 24

pi * a * b

Question 25

How do you convert load in a ball bearing to load on a single ball

Answer 25

Use stravic equation P = 5F/z where z is the number of balls carrying a radial load

Question 26

In a ball bearing contact what is the reduced radius equal to

Answer 26

1/R’ = 1/Ry + 1/Rx

Question 27

What is the x direction in a ball bearing

Answer 27

x is in the direction of motion therefore along the track radius

Question 28

Which direction is the longer dimension of the ellipse formed in a ball bearing contact

Answer 28

in the y direction i.e. along the groove radius

Question 29

What does P’ refer to in a line contact

Answer 29

load per unit length