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Contact Stress: Calculated, Fatigue Limit.

Cams wear, like bearings and gears. A cam's surface is subject to contact stress as the cam-follower passes over it.

If the cam's metallurgy is identical at all depths, then the cam would usually 'fail' at the point on the cam's surface that experiences the maximum contact-stress. Failure would be due to rolling contact fatigue. Like any machine part, the challenge is to make sure that the cam does not fail before the intended life of the machine.

 

Allowable Contact Stress, σHLim

Allowable Contact Stress is the limit of rolling contact stress that the cam steel can sustain, with a reliability of 99%, without failure by pitting for 1 life. The term 'failure from pitting-fatigue' is subjective and a source of considerable disagreement. One observer’s 'failure' may be another observer’s 'wearing-in'.

For most cam materials, N-cycles is considered to be the beginning of the endurance strength range at the 'lower knee' of the σ - N curve(S-N curve).  

The contact-force and the cam's radius-of-curvature continually change around the cam. Thus, each point on the cam will experience a different contact stress that is a result of the contact condition that prevails at that point.

We would assume the cam would fail at the point at which the contact is the most arduous and the contact-stress is a maximum. The point at which the contact-stress is a maximum is not necessarily at the point of maximum contact-force, because the cam's radius is also a factor.

Of course, we calculate the Contact Stress at all points along the Cam.

Steels: Hardness and Allowable Stress

The table below - from ISO 6336 Part 5 - shows a 'first estimation' of the Allowable Contact Stress, for 5×107 cycles for different classes of steel and heat-treatments, or for nitriding steels, 2×106 cycles.

The reliability is taken as 99%. That is to say, there is a probable risk of 1% that the cams will fail if subjected to a contact-stress equal to the stress in the table.

You can see that the Contact Stress Endurance Strength Limit is a function of the material type, quality and importantly its surface hardness.

Depth of Hardness is also important because the maximum shear-stress occurs below the surface, which is the main contribution to pitting failure.

The lubrication mode is 'mixed', and the lubricant is 'clean'.

table 1

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Modification Factors:

The permissible contact-stress is often modified - in the same way as the cam-follower life is modified - with modification factors.

Metallurgy

The allowable stress numbers are a function of melting, casting, forging and heat treating practice. Hardness, tensile strength, micro-structure and cleanliness are some criteria for determining allowable stress numbers. Allowable stress numbers in this standard are based on 107 cycles, 99 percent reliability and unidirectional loading.

Residual-Stresses

Any material having a case-core relationship is likely to have residual stresses. If properly managed, these stresses should be compressive at the surface and should enhance performance of the cam. Shot peening, case-carburizing, nitriding, and induction hardening are common methods of inducing compressive pre--stress in the surface. Grinding after heat treatment may reduce the residual compressive stresses. Care must be taken to prevent excessive reduction in hardness and changes in microstructure during the grinding process.

Life Factor

Because the Endurance Limit in the table above is for a life of 5x107 cycles, a 'Life Factor' is applied to modify the permissible stress if you want to use the cam for a shorter or longer period.

The values below show the values for 10,000,000 ;100,000, and 1000 cycles, there are also other break-points given by the S-N Curve below.

Table 2

figure 1: S-N chart to find Zn from N or N from Zn

table 3 : Equation form of S-N chart above.

You can use the equations above to find the required life-factor for a particular steep grade and number of cycles. From the Life-factor, for the steel, you can calculate the required hardness from the the equation for 'Contact Stress Endurance Limits

You can do the inverse calculation if you want to find the expected number of Number of Cycle to failure from a prescribed life factor.

The prescribed Life-factor would be found from the ratio of Application Contact-stress : Allowable Contact-Stress

The Allowable-Contact-stress  'for one life' is first established from the its Grade/Type of Steel and its Hardness. in the table above.

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Reliability Factor:

Because the Endurance Limit in the table above is for a reliability of 99%, then if you want more or less reliability, you must multiply the Allowable Contact Strength by the Reliability Factor.

Hardness Ratio: When the cam-follower is harder than cam, it is possible that the cam will be polished by the cam-roller and have its life extended. Typically, the follower should be at least + 2HRC greater than the cam.

Surface Finish: The relative surface finish is important also.

Temperature Factor: If the cam operates in an environment that is quite hot, then the Endurance of the Materials must be reduced.

Typical Cam Material Classes and Heat Treatment

Cam Steels

There are many wrought steels, cast steels, and cast-irons that you can use to manufacture a cam. You must select the steel that can match the demands of your application.

The Allowable Contact STRESS of the steel is a function of:

•The steel's chemical composition: carbon, chromium, nickel molybdenum, vanadium, aluminium...

•Its manufacturing process: cast killed, wrought killed, continuously case, hot rolled, cold rolled, sintered, powder pressed, vacuum degassed, (VAR, ESR)

•Its heat-treatment: through-hardening, quenched and tempering, carburizing, nitriding, carbonitriding, ...

•Its quality standard: kiln quality, consistency of chemical composition, 'density' of foreign-body inclusions: MX - excellent, ME - better, MQ - standard, ML - lower than average

The steels used for industrial cams are 'Wrought-Steels', 'Cast Iron and Cast Steels', 'Powder-Metallurgy (PM)' 'Tool Steels' and 'Maraging Steels'.

By far the most common are wrought-steels.

Wrought-Steels

Wrought-Steel is the general term for a carbon and alloy steel that is mechanically worked into a bar, flat, or a forging. They are available in a wide range of sizes and grades. Wrought-Steels are either Through-Hardened (carbon content between 0.3 and 0.5%) or Surface-Hardened (carbon initially not exceeding 0.25%).

Surface-Hardened: steels have a relatively thin hard 'case', which results from processes such as 'carburizing', 'nitriding', 'carbonitriding'.

Through-Hardened: steels that be considered to have the same hardness through its depth. However, in reality, they will also have hardness gradient.

Cast Irons and Cast Steels

Cast Irons (more than 2% carbon) and Cast Steels are poured into a mould that is near to the final shape of the cams. High volume engine cam-shaft are most often made this way. Cast-Iron would normally be a 'chilled' cast-iron as this gives an extremely high surface hardness that will wear.

In the fast majority of cases, the cam is manufactured from a ferrous metal - iron and steel, cast and wrought.

There are a number of classes of ferrous metals with which we can manufacture the cam:

Benefits of the different Heat-Treatment Processes

Allowable Contact Stress and Surface Hardness

Case Hardness, Case Depth, Core Strength