General Design Information > Cam-Mechanism Design > Design Analysis > Force Analysis: Cam: Fatigue Limit

Contact Stress: Calculated, Fatigue Limit,

Cams wear, like bearings and gears.

A Cam-Profile wears because it is subject to a contact-stress as a Follower-Roller rolls over it. The cam would usually fail at the point 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.

Contact Stress Endurance Limit

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

1 Life is typically 5 × 107 (50 million cycles), but not always (Note, for Follower-Rollers, 1 life is always a rotation of 1 × 106 ( 1 million cycles)).

For most cam materials, a life is considered to be the beginning of the endurance strength, at the lower-knee of its σ - N curve (also called its S-N curve).

We assume the cam fails at the point at which the contact-stress is a maximum.

We have seen that the contact-stress is a function of the contact-force, material properties, and the radii-of-curvature of both follower-profile and cam-profile.

Usually, both the contact-force and the radius-of-curvature of a cam-profile continually change. Therefore, each point along the cam-profile experiences a different contact-stress. We must, therefore, calculate the contact-stress at all points along the cam-profile.

Hardness and Allowable Stress

Table 1- from ISO 6336 Part 5 - shows a first estimation of the Hardness required for and Contact Stress Endurance Limit at 5×107 cycles for different classes of steel and heat-treatments, and for nitriding steels at 2×106 cycles.

You can see that the Contact Stress Endurance Strength Limit is a function of the Steel type, Steel quality, and Steel Surface Hardness.

E.g. the Endurance Limit of a Normalized Low Carbon Steel with ME quality, that has a Brinell Hardness of 150HB is equal to 1.520HB+250= 478Mpa

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

Depth of Hardness is also important because the maximum shear-stress is below the surface.

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

table 1 (from ISO 6336-5)

Steel / Cast Iron Categories	Material Type (Abbreviation)	Steel Quality*	Contact Stress Endurance Limit MPa 99%, Rel 5×107 cycles	Hardness Range	Example Steels NOT from ISO 6336 Examples that we have assigned to the different steel and cast-iron categories. Please check that your steel is in the correct-category.
Normalized Low Carbon Steels & Cast Steels (St (cast))	Wrought**,normalized, Low Carbon Steels (St)	ML/MQ	1.000HB + 190	110 - 210 HB***	St50.2, 1.0050, E295 St60-2, 1.0060, E335 St70-2, 1.0070, E360
	Wrought**,normalized, Low Carbon Steels (St)	ME	1.520HB + 250	110 - 210 HB
	Cast Steels (St (cast))	ML/MQ	0.986HB + 131	140 - 210 HB	GE200, 1.0420 GE240, 1.0446 GE300, 1.0558
	Cast Steels (St (cast))	ME	1.143HB + 237	140 - 210 HB	GE200, 1.0420 GE240, 1.0446 GE300, 1.0558
Cast Irons	Black Malleable Cast Iron (pearlitic structure) (GTS (perl))	ML/MQ	1.371HB + 143	135 - 250 HB	EN-GJMB-350-10 : HB 150 EN-GJMB-500-5 : HB 165-215 EN-GJMB-600-2 : HB 195-245 EN-GJMB-700-2 : HB 240-290
		ME	1.333HB + 267	175 - 250 HB
	Nodular Spheroidal Pearlitic Bainitic Ferritic Cast Iron (GGG (perl, bai, ferr))	ML/MQ	1.434HB + 211	175 - 300 HB	EN-GJS-400-15 : HB 135-180 EN-GJS-500-14 : HB 170-215 EN-GJS-600-10 : HB 190-230 EN-GJS-700-2 : HB 210-305 EN-GJS-800-2 : HB 240-335 EN-GJS-900-2
		ME	1.500HB + 250	200 - 300 HB
	Grey Cast Irons (GG)	ML/MQ	1.033HB + 132	150 - 240 HB	EN-GJL-200, GG20 EN-GJL-300, GG30 EN-GJL-350, GG35 EN-GJL-400, GG40
	Grey Cast Irons (GG)	ME	1.465HB + 122	175 - 275 HB
Through-Hardened Wrought** Steels Nominally >0.2%C	Carbon Steels (V)	ML	0.963HV+283	135 - 210 HV	EN8 / 080M40. C40E, 1.1186 C45E, 1.1191, 1045,
		MQ	0.925HV+360	135 - 210 HV
		ME	0.838HV+432	135 - 210 HV
	Alloy Steels (V)	ML	1.313HV+188	200 - 360 HV	EN19T/709M40T, 42CrMo5, 1.7225, 4140
		MQ	1.313HV+373	200 - 360 HV
		ME	2.213HV+260	200 - 390 HV
Through-Hardened Cast Steels Nominally > 0.2%C	Carbon Steels (Low to Medium) (V (cast))	ML/MQ	0.831HV+300	130 - 215 HV	100Cr6 (52100, Ws#1.3505. SUJ2)
	Carbon Steels (Low to Medium) (V (cast))	ME	0.951HV+345	130 - 215 HV	100Cr6 (52100, Ws#1.3505. SUJ2)
	Alloy Steels (V (cast))	ML/MQ ME	1.276HV+298 1.350HV+356	200 - 360 HV 200 - 360 HV	G25CrMo4, G34CrMo4, G35CrNiMo6-6 G42CrMo4 :1.7231
Case Hardened Wrought Steels	< 0.25%C (Eh)	ML	1300	600 - 800 HV	C14E/C10R/C15E/C15R/ 14NiCr4, 1.5752, EN36B/655M13 17Cr3 (1.7016, AISI 5115) 16MnCr5 (1.7131), 590M17 18CrMo4 20MnCr5 (1.7147) 15NiCr13 (1.5752) 17CrNi6-6 (1.5918) 18CrNiMo7-6 (1.6587) 20NiCrMo2-2, 22CrMoS3-5 18NiCrMo5 17NiCrMo6-4, EN36 - 1.5752 - 14NiCr4, SAE8620, 14NiCrMo13-4, AISI 9310, 1.6657 655M13 EN39B/835M15, 15NiCrMo16-5, SNCM815.
		MQ	1500	660 - 800 HV
		ME	1650	660 - 800 HV (58-64HRC)
Flame or Induction Hardened Wrought or Cast Steels	>0.25%C (IF)	ML MQ ME	0.740HV+602 0.541HV+882 0.505HV+1013	485 - 615 HV 500 - 615 HV 500 - 615 HV	34Cr4 (1.7033) (530M32) 41Cr4, 34CrNiMo6 43CrMo4(1.3563)
Nitrided Wrought steels	Nitriding Steels (NT(nitr.))	ML	1125	650 - 900 HV	EN40B, EN41B, Nitralloy, N135M 31CrMo12, 42CrMoV12, 38CrAlMo 31CrMoV9. 905M39
		MQ	1250	650 - 900 HV
		ME	1450	650 - 900 HV
Through Hardened, Nitrided	Through Hardening Steels NV(nitr.))	ML MQ ME	788 998 1217	450 - 650 HV 450 - 650 HV 450 - 650 HV	32CrMoV13 (Quench And Hardened)
Wrought Steels Nitro-Carburized	Through Hardening Steels (NV(nitrocar)	ML	0.0HV + 650	300 - 650 HV	100CrMnSi6-4 (CarboNitriding)
		MQ	1.167HV + 425	300 - 450 HV
		ME	0.0HV + 950	450 - 650 HV
* ML, MQ, ME - consult with your steel re-seller, request the Steel's Specification (Data-Sheet from the Steel manufacturer. ML - limited demands on the material quality, number and type of inclusions, and on the material heat treatment process during gear manufacture. MQ - requirements met by experienced manufacturers at moderate cost ME - requirements realized when a high degree of operating reliability is required. Refer to ISO 3663-Part 5 for more details of ML, MQ, ME steels qualities. Wrought refers to all manufacturing processes that manipulate the shape of the material without melting it. Hot and Cold rolling are the two common processes. Wire drawing, deep drawing, extrusion are others processes. * HB - Brinell Hardness, HV - Vickers Hardness

Modification Factors:

The allowable contact-stress is often modified - in the same way as the Follower-Roller 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 are compressive at the surface and should enhance the 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

The Endurance Contact-Stress Limit is for a life of 5x107 cycles.

When the actual Contact-Stress is not equal to the Endurance Contact-Stress, you can use the ratio of Actual to Endurance Contact Stress as a Life Factor. Then use that to find the actual Life of the Cam. Each Steel type has a maximum and minimum ratio above and below which the Life-Factor does not apply.

Alternatively, Table 2 shows the allowable stress for 10,000,000 ;100,000, and 1000 cycles, there are also other break-points given by the S-N Curve below.

Table 2


Alloyed case hardened steels (surface hardness 58-63 HRC):
- of specially approved high grade:	1650	2500	3100
- of normal grade:	1500	2400	3100
Nitrided steel, gas nitrided - surface hardness 700-800 HV	1250
Alloyed Quenched and Tempered steel, bath or gas nitrided -surface hardness 500-700HV	1000
Alloyed flame or induction hardened steel - surface hardness 500 - 650 HV	0.75.HV + 750		4.5 × HV
Alloyed quenched and tempered steel:	1.4.HV + 350		4.5 × HV
Carbon Steel:	1.5.HV + 250
These values refer to wrought steels, hot-rolled or forged. For cast steel, reduce by 15%.

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

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

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

Material Group	Range of Load Cycles	Life Factor in the Range, ZNT
Group 1: St, V, GGG (perl. bain.), Eh, IF Only when a ~15% of pitting is permissible



Group 2: St, V, GGG (perl. bain.), Eh, IF No pitting allowed		1.6
		ZNT = 3.8218×NL -0.075629
		ZNT = NL -0.0047
Group 3: GG, GGG(ferr), NT(nitr), NV(nitr.)		Break Point: 1.3
		1 × Life: 1.0
		Extended Life: 1.0 > 0.85
Group 4: NV (Nitrocar)		Break Point: 1.1
		1 × Life: 1.0
		Extended-Life 1.00 > 0.85

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 cycles 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.

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, aluminum...

•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 mold 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:

'Soft' or Hard' Cams

Cast Irons or Cast Steels that are not normalized and tempered.

Hardness in the range of 100-360HB.

Surface Hardened Cams

These cams use Direct Hardening Steels. The carbon content is the range of 0.3 to 0.45%, with and without alloying elements, typically Chromium, Nickel, Molybdenum, Vanadium and Aluminum.

Examples steels are: C45E (Ck45), 42CrMoV.

Direct Hardening is by Flame or Induction Heating, followed by Quenching and Tempering.

Hardness in the range of 550-650HV.

Compared to case-carbonizing, there is less distortion with flame and induction hardening.

Case Carburized Surface Hardened Cams

The carbon content of plain and alloy steels is increased by carbonization at 850-950ºC, to achieve a carbon content of 0.7% to 0.9% in the outer case of the cam. After quenching and tempering, the surface hardness can be in the range of 650-750HV.

Case Hardening processes include Carburzing and Carbonitriding (not Nitriding)

Example steels are: 18CrNiMo7-6, 16MnCr5.

A minimum case depth will be a function of the size of the cam and the depth of maximum shear stress.

Nitrided Cams

Nitriding of plain carbon, alloy and nitriding steels is carried out at 500-550ºC with ammonia for gas nitriding to form hard carbides close to the surface. Because the temperature is low and there is no need for quenching, there is much less distortion, if any, of the cam. This may mean there is no need for grinding the surface after heat treatment.

The hard case, of up to 850HV, is relatively shallow.

Example Steels are: 32AlCrMo4, 34CrAl6, 31CrMoV9,

Nitrided surfaces often have lower coefficient-of-friction than other surfaces and also there is some corrosion resistance.

Benefits of the different Heat-Treatment Processes

Carburizing

Hard, highly wear-resistant surface (medium case depths); excellent capacity for contact load; good bending fatigue strength; good resistance to seizure; excellent freedom from quench cracking; low-to-medium cost steels required; high capital investment required

Carbonitriding

Hard, highly wear-resistant surface (shallow case depths); fair capacity for contact load; good bending fatigue strength; good resistance to seizure; good dimensional control possible; excellent freedom from quench cracking; low-cost steels usually satisfactory; medium capital investment required; improved salt corrosion resistance

Nitriding

Hard, highly wear-resistant surface (shallow case depths); fair capacity for contact load; good bending fatigue strength; excellent resistance to seizure; excellent dimensional control possible; good freedom from quench cracking (during pretreatment); medium-to-high-cost steels required; medium capital investment required; improved salt corrosion resistance.

The depth of hardness with Gas-Nitriding is a function of the hours and the steel.

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Induction hardening

Hard, highly wear-resistant surface (deep case depths); good capacity for contact load; good bending fatigue strength; fair resistance to seizure; fair dimensional control possible; fair freedom from quench cracking; low-cost steels usually satisfactory; medium capital investment required

Flame hardening

Allowable Contact Stress and Surface Hardness

GDI-HardnessvsAllowableContactStress-400

Rule of Thumb

Through Hardened Steels; Range of Brinell Hardness; HB = 180 – 400, Grade of Steel: 'Grade 1, (ME,MQ); Reliability, 99% Statistical Reliability; Number of Cycles: 1x107

Allowable Contact Stress ~ 2.41HB +237 (MPa )

If you want 10 - 100 million cycles than increase the HB Hardness by 15 –20%.

The image shows typical Allowable Maximum Contact Stress and Allowable Maximum Contact Shear Stress values against Brinell, Vickers and Rockwell 'C' Hardness Scales.)

The values assume the Follower-Roller rolls in clean oil.

Case Hardness, Case Depth, Core Strength

Importance of Depth of Hardening / Core Strength and Depth of Maximum Shear Stress.

The depth of is not important with homogenous materials. For example, a Through-Hardened steel.

However, with case-hardened and surface hardened cams, it is possible that the case is strong enough, but the core is not, and vice versa.

The Allowable Shear Stress will vary with depth, because the hardness will vary with depth.

Case: < Allowable Shear Stress (function of material and hardness )

Core: < Allowable Shear Stress (function of material and hardness)

Case Depth

For Carburized and Carbonitrided Cams, the Case Depth is the depth at which the hardness is greater than 550HV (-see also Definitions of Case-Depth, below)

The depth of Maximum Shear-Stress, , should be compared to the Case-Depth from the surface

As a rule of thumb,

Case Depth > assuming that Maximum Shear Stress will not damage the steel when the Hardness is 550HV.

Core Crushing

If the Hardness reduces rapidly after the Case-Depth, it is possible to Crush the Core when the Shear or a Principal Stress is greater than the steel strength. Hardness rapidly falls with Induction and Flame Hardening.

Definitions of Case Depth.

Effective Case Depth (CHD)

The definition of Effective Case Depth is a dependent on the heat treatment process.

1.Carburized or Carbonitrided Cams (EN ISO 2639)

Hardness Limit = 550 HV.

CHD (Eht) = Distance from surface to a point where the hardness is 550 HV.

Hardness tends to gradually drop off, depending in the core hardness.

2.Induction or Flame Hardened Cams (EN 10328, ISO 3754)

Hardness Limit = 80% x (Minimum) surface hardness.

CHD (Rht) = Distance from surface to point where hardness is 80% of the (minimum) surface hardness.

Hardness tends to drop rapidly at a depth slightly greater than this limit.

3.Nitrided Cams (DIN 50190-3)

Hardness Limit = Core Hardness + 50 HV.

CHD (Nht, NCD) = (Max.) Distance from the surface to the point where hardness is 50HV above core hardness.

Nitrided cams have a relatively shallow case depth, but a gradual hardness gradient.

Total Case Depth

The depth at which the hardness becomes the same as the core hardness.

GDI-ContactFatigueStrength-vs-Hardness