Topic 3 Contact Mechanics Flashcards
What can excessive contact stress or deformation lead to
overload wear rolling contact fatigue seizure loss of tolerance
What is the Hertz theory of elastic contact
- 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
What are the Hertz model of contact assumptions
- 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
Most frequently used contact parameters are
- Contact area dimensions
- Maximum and average contact pressure
- Stress distribution in the contact
- position of he maximum shear stress below the surface
What does a point contact occur between
two balls and two cylinders of the same radius at right angles
What does a line contact be occur between
two parallel cylinders
Where do ellipitical contacts occur
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
Why is it important to identify correct contact model
Ensure using correct equations as different contacts have different stress distribution
When does the maximum contact stress occur
Below the surface
Whats wrong with Hertzian contact model
Most engineering contacts violate the hertz assumptions, but contact mechanics under these conditions become complex and numberical methods are needed
How does friction and sliding contacts impact the hertrizan contact theory
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
What happens when mu = 0.25 for contact shear stresses
Will cause the shear stress to reach the surface of the contact
What happens at yield in contact mechanics
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
Hardness H may be related to Yield strength Y by what equation
H=2.7Y
Draw a diagram of what actually happens in contact mechanics with a rough surface
see powerpoint
What happens in rough contacts
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
What techniques are used for determining contact area and pressure experimentally
photoelastic techniques
pressure sensitive film
contact resistance
ultrasound
What is the equation for reduced radius
1/R’ = 1/R1 + 1/R2
What is the equation for reduced modulus
1/E* = (1-v1^2)/E1 + (1-v2^2)/E2
What is the radius of a flat plate
infinitity i.e 1/R = 0
What is the difference between po and pavg
po is the maximum contact pressure and p average is the average contact pressure
If the po is greater than yield strength what is worth noting when calculating the contact stresses
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
Whats the difference between a and b in an elliptical point contact
a is the long ellipitical dimension and b is the short dimension
What is the area of an ellipse
pi * a * b
How do you convert load in a ball bearing to load on a single ball
Use stravic equation P = 5F/z where z is the number of balls carrying a radial load
In a ball bearing contact what is the reduced radius equal to
1/R’ = 1/Ry + 1/Rx
What is the x direction in a ball bearing
x is in the direction of motion therefore along the track radius
Which direction is the longer dimension of the ellipse formed in a ball bearing contact
in the y direction i.e. along the groove radius
What does P’ refer to in a line contact
load per unit length
