Contact Stress: Allowable, Permissible, Nominal, Calculated

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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, 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

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);

normalized 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, 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


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%.

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

SigmaH-SNCurve-SMALL

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

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%.

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.


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.

Reliability Gears

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:

'Soft' or Hard' Cams

Cast Irons or Cast Steels that are not normalized 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-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 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 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

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

Click to Expand / Collapse

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.


Case Hardness, Case Depth, Core Strength

Depth of Hardness and Shear-Stress

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 Tmax is not important.

In 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: Tmax < Allowable Shear Stress (proportional to Hardness and material)

Core: Tauat all depths< Allowable Shear Stress (proportional its Hardness and material)

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, Tmax, should be compared to the Case-Depth of the hard casing.

As a rule of thumb, Case Depth > 2 × Depth of Maximum Shear Stress - assuming that Maximum Shear Stress will not damage the steel when at 550HV.

Core Crushing

If the Hardness reduces rapidly after the Case-Depth, as you find with Induction and Flame Hardening, it is possible to 'Crush the Core' if the Shear or a Principal Stress is greater than the steel can resist.

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 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 or at a depth slightly greater than 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, but a gradual hardness gradient.

Total Case Depth

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

Possible Failure from Macro-pitting and Case-Crushing

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.