﻿ Force Analysis: Contact Stress: Allowable, Permitted, Calculated

# Contact Stress: Allowable, Permissible, Nominal, Calculated

## 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 for 1-life-cycles, 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. The stress will due to the contact conditions that prevail 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 Point on 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% of 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'.

Material

Material Type

Q

u

a

l

i

t

y

Type

Contact Stress Endurance Limit MPa

99%, Rel

5x107 cycles

Hardness Range

Examples

Normalized Low Carbon Steels

&

Cast Steels

Wrought, normalized, Low Carbon Steels

ML/MQ

ME

St

1.000×HB + 190

1.520×HB + 250

110 - 210 HB

110 - 210 HB

 • St50.2, 1.0050, E295
 • St60-2, 1.0060, E335
 • St70-2, 1.0070, E360

Cast Steels

ML/MQ

ME

St

[cast]

0.986×HB + 131

1.143×HB + 237

140 - 210 HB

110 - 210 HB

 • GE200, 1.0420
 • GE240, 1.0446
 • GE300, 1.0558

Cast Irons

Black Malleable Cast Iron [pearlitic structure]

ML/MQ

GTS

[perl]

1.371×HB + 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

1.333×HB + 267

175 - 250 HB

Nodular Spheroidal Pearlitic  Bainitic Ferritic  Cast Iron

ML/MQ

GGG

1.434×HB + 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

1.500×HB + 250

200 - 300 HB

Grey

Cast Irons

ML/MQ

ME

GG

1.033×HB + 132

150 - 240 HB

 • EN-GJL-200, GG20
 • EN-GJL-300, GG30
 • EN-GJL-350, GG35
 • EN-GJL-400, GG40

1.465×HB + 122

175 - 275 HB

Through-Hardened Wrought Steels

Nominally >0.2%c.

Carbon Steels

ML

MQ

ME

V

0.963×HV+283

0.925×HV+360

0.838×HV+432

135 - 210 HV

135 - 210 HV

135 - 210 HV

 • C40E, 1.1186
 • C45E, 1.1191, 1045,

Alloy Steels

ML

MQ

ME

V

1.313×HV+188

1.313×HV+373

2.213×HV+260

200 - 360 HV

200 - 360 HV

200 - 390 HV

 • 42CrMo5, 1.7225
 • 100Cr6

Through-Hardened

Cast Steels

Nominally > 0.2%C

Carbon Steels

(Low to Medium)

ML/MQ

ME

V

[cast]

0.831×HV+300

0.951×HV+345

130 - 215 HV

130 - 215 HV

Alloy Steels

ML/MQ

ME

V

[cast]

1.276×HV+298

1.350×HV+356

200 - 360 HV

200 - 360 HV

 • G25CrMo4,
 • G34CrMo4,
 • G35CrNiMo6-6
 • G42CrMo4 :1.7231

Case Hardened

Wrought Steels

Less than 0.25% Carbon

ML

MQ

Eh

1300

1500

1650

600 - 800 HV

660 - 800 HV

660 - 800 HV

[58-64HRC]

C14E/C10R/C15E/C15R/

17Cr3 [1.7016, AISI 5115]

16MnCr5 [1.7131], 5115, 8620

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

100CrMnSi6-4 [CarboNitriding]

ME

Flame or

Induction Hardened

Wrought or Cast Steels

>0.25% Carbon

ML

MQ

ME

IF

0.740×HV+602

0.541×HV+882

0.505×HV+1013

485 - 615 HV

500 - 615 HV

500 - 615 HV

34Cr4 [1.7033] [530M32]

41Cr4, 34CrNiMo6

43CrMo4[1.3563]

Nitrided Wrought steels

Through Hardened,

Nitrided

Nitriding Steels

ML

MQ

ME

NT

1125

1250

1450

650 - 900 HV

650 - 900 HV

650 - 900 HV

EN40B, EN41B, Nitralloy, N135M

31CrMo12, 42CrMoV12, 38CrAlMo

31CrMoV9. 905M39

Through Hardening Steel

ML

MQ

ME

NV

788

998

1217

450 - 650 HV

450 - 650 HV

450 - 650 HV

32CrMoV13 [Quench And Hardened]

Wrought Steels

Nitro-Carburized

Through Hardening Steels

ML

MQ

ME

HV (nitro-carb)

0.0×HV + 650

1.167×HV + 425

0.0×HV + 950

300 - 650 HV

300 - 450 HV

450 - 650 HV

ML  - limited demands on the material quality 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.

 Material Type Abbreviation Normalized low carbon steels Structural Steels whose Ultimate Strength, σU < 800MPa Wrought normalized, low carbon steels St Cast Steels St [cast] Cast iron materials Black malleable cast iron [pearlitic structure] GTS [perl] Nodular [SPHEROIDAL] cast iron (pearlitic,  bainitic, ferritic structure) GGG [perl., bai., ferr.] Grey Cast Iron GG Through-hardened wrought steels Steels, Through Hardened and Quench and Tempered, whose  σU ≥ 800MPa Carbon Steels, Alloy Steel Heat-Treatable Steels, Carbon ≥0.2%] V Through-hardened cast steels Carbon Steels, Alloy Steels V [cast] Case-hardened wrought steels Case Hardening Steels Eh Flame or induction hardened Wrought Alloy STEELS CAST steel [C0.4%+] IF Nitrided wrought steels / nitriding steels / through-hardening steels, nitrided Nitriding Steels NT [nitr.] Through hardening steels NV [nitr.] nitro-carburized Through hardening & CASE-HARDENED STEELS NV [nitrocar.]

St  = Structural Steel σU < 800MPa [Mild Steel];

 • Normalised Structural Steel
 • Cast Structural Steel
 • Cast Alloy Steel
 • Cast Carbon Steel

V   = Through-hardening steel, through-hardened, Quench and Tempered,  σU ≥ 800MPa

 • Alloy Steel (Carbon ≥ 0.2%)
 • Carbon Steel (Carbon ≥ 0.2%)

GG = Grey Cast Iron

GGG = Spheroidal (Pearlitic, Bainitic, Ferritic) Cast Iron

GTS [perl] = Black malleable Cast Iron [pearlitic structure]

Eh = Carburized Case-Hardening Steel. Case Hardened

 • Core Hardness ≥ 30HRC
 • Core Hardness ≥ 25HRC , J=12mm < 28HRC
 • Core Hardness ≥ 25HRC , J =12mm ≥ 28HRC

IF = Steel and GGG, Flame or Induction Hardened

NT (nitr)= Gas Nitriding Steel

NV (nitr) = Through-hardening and Case-Hardened - nitrided

NV (nitro-carb) = Through-hardening and case-hardening steel - nitro-carburized

σU  <  ultimate tensile strength, approximately 3.4×BHN MPa.

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, microstructure 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.

 σHLim [@ 5×107 cycles] σHLim [@ 105 cycles] σHLim [@ 103cycles] 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 1.3 × σHLim 1.3 × σHLim Alloyed Quenched and Tempered steel, bath or gas nitrided -surface hardness 500-700HV 1000 1.3 × σHLim 1.3 × σHLim Alloyed flame or induction hardened steel - surface hardness 500 - 650 HV 0.75×HV + 750 1.6 × σHLim 4.5 × HV Alloyed quenched and tempered steel: 1.4×HV + 350 1.6 × σHLim 4.5 × HV Carbon Steel: 1.5×HV + 250 1.6 × σHLim 1.6 × σHLim These values refer to wrought steels :hot rolled or forged. For cast steel the values for σHLim are to be reduced by 15%.

 Material Group No of Load Cycles Life Factor, ZNT Group 1: St, V, GGG (perl. bain.), Eh, IF Only when a certain degree of pitting is permissible NL < 6×105 1.6 6×105 ≤ NL < 107 ZNT = 4.3739×NL -0.0756 107 ≤ NL < 109 ZNT = 3.2584×NL -0.0570 109 ≤ NL = 1010 ZNT = NL -0.004 Group 2: St, V, GGG (perl. bain.), Eh, IF No degree of pitting is tolerated NL <  105, 1.6 105 <  NL < 5×107 ZNT = 3.8198×NL -0.0756 5×107 <  NL < 1010 ZNT = NL -0.0047 Group 3: GG, GGG(ferr), NT(nitr), NV(nitr.) NL <  105,, static 1.3 NL < 2 × 106 1.0 NL = 1010 0.85 - 1.0 Group 4: NV (Nitrocar) NL <  105,, static 1.1 NL < 2 × 106 1.0 NL = 1010 0.85-1.00 These values refer to wrought steels: hot rolled or forged. For cast steel the values for σHLim are to be reduced by 15%.

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, carburising, 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:

 'Soft' or Hard' Cams Cast Irons or Cast Steels that are not normalised and tempered. They have hardnesses 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 Aluminium. Examples steels are: C45E (Ck45), 42CrMoV. Direct Hardening is by Flame or Induction Heating, followed by Quenching and Tempering. Hardnesses are in the range of 550-650HV. Compared to case carburising, 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 carbonisation 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 Carburizing 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 are often have a lower 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. Note: Copyright lost - please email with your preferred action. 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 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; low capital investment required

#### Allowable Contact Stress and Surface Hardness

 Allowable Cam Contact Hertz Stress and Maximum Shear Stress vs Cam Hardness

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 cam-followers are rolling in clean oil.

[Rule of thumb’ for the Maximum Allowable Hertz stress for racing cams made from hardened steels is about 1250 MPa. Such steels are usually hardened to Rockwell 64C or 65C.']

#### Case Hardness, Case Depth, Core Strength

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

In a homogenous material, for example a 'Through-hardened' steel, the 'Depth of ' is not important.

In case-hardened and surface hardened cams, care must be taken to make sure the Case and the Core are both strong enough. It is possible that the case is strong enough, but the core is not, and vice versa. There is a gradual transition between the hardness of the casing and that of the core.

Case: < Allowable Shear Stress [given its heat-treatment and 'hardness']

Core: at all depths< Allowable Shear Stress [given its heat-treatment and 'hardness']

Case Depth

The usual definition of Case Depth is the depth at which the hardness is greater than 550HV (Vickers Hardness) for Carburized and Carbonitrided Cams.

The depth of should be compared to the depth of the hard casing.

As a rule of thumb, Case Depth > 1.41 × Depth of Maximum Shear Stress - assuming that Maximum Shear Stress will not damage the steel when at 550HV.

A more conservative rule of thumb: Minimum Case Depth ≥ 2×b

Core Crushing

It is possible to 'Crush the Core' if the load is too high for the core and the case is too thin.

#### Definitions of 'Case Depth' depend on the Heat-Treatment.

Effective Case Depth [CHD]

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

 1 Carburized or carbonitrided parts (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 parts (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 after this limit.

 3 Nitrided parts (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 Parts have a relatively shallow depth,

Total Case Depth

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

Possible Failure from Macro-pitting and Case-Crushing

Example Failures:  The hardness profile beneath the surface gives the shear strength below the surface.

A shear stress function can fail at different depths with different hardness profiles.

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