﻿ Force-Analysis: Cam: Lubrication and Suface Finish

Force-Analysis: Cam: Lubrication and Suface Finish

Lubrication for Cams and Gears

Reasons to lubricate cams are to:

 1 Reduce friction between the cam and cam-follower, reduce wear.
 2 Limit the temperature rise caused by rolling and sliding friction.
 3 Remove contaminants - with an oil filtration system.
 4 Significantly improve the life of the Cam and the Cam-Follower

A lubricant is needed with most cam systems, especially those with a sliding follower.

The ratings determined by these formulae are valid only if the gear teeth are operated with a lubricant of proper viscosity and additives for the load, speed and surface finish, and if there is a sufficient quantity of lubricant supplied to the gear teeth and bearings to lubricate and maintain an acceptable operating temperature.

Film Thickness Ratio, λ:

The Film Thickness Ratio, λ, is defined as:

The greater the Film Thickness Ratio, λ, the less 'contact' there is between the surfaces of the cam and cam-follower.

We will see that the Film-Thickness Ratio is closely related to the 'Mode-of-Lubrication'.

 Film Thickness Ratio Failure Characteristic 3 > λ Minimal wear and long life can be expected. 1.5 < λ < 3.0 Surface glazing may occur and there is a risk of sub-surface originated pitting. 1 < λ < 1.5 Surface distress and pitting may occur λ < 1.0 Surface scoring, smearing or deformation occurs at the cam surface and is followed by wear.

The two parameters that we need to calculate the Film Thickness Ratio are:

Thickness of Lubricant Film, h

The calculation of the Lubricant Film Thickness for a cam and follower system can be simplified into an equivalent arrangement of two cylinders that roll together, as shown above.

 Formula for Film Thickness Derived by Dowson and Higginson. Applies to isothermal conditions [m^2/N] [Ns/m^2] [m/s] [m/s^2] [m] [m] [m] [N] [m]

The formula can be used for cam-followers that do not roll perfectly. It gives a good result provided that the entrainment velocity, the equivalent radius-of-curvature, and contact load are known at each position for the machine cycle. Of course, all these are known by MechDesigner.

The equation can be simplified. You will notice that the exponents for Equivalent Modulus, E', [0.03] and the Load per unit width of cylinder, P/b. [0.13] are not very high. Also, for oil lubrication, the pressure exponent of viscosity does not change much.

Thus, the equation can be simplified to use only three parameters:

 Simplified Film Thickness Formula [Ns/m^2] [m/s] [m] If you cannot change the cam design to change Re or ue, the only parameter you can change is the viscosity, η, of the lubricant.

Viscosity

 The viscosity, η, of the lubricant can be found from its viscosity-temperature curve.

Entrainment Velocity

To generate Hydrodynamic separation of the two surfaces, any lubrication must fulfil two requirements.

 1 There must be a mechanism for delivering the lubricant in sufficient quantity to flood the inlet of the contact.
 2 There must be a sufficient entrainment velocity to carry the lubricant into the contact to generate the necessary hydrodynamic film.

The latter condition, by definition requires the contacting surfaces to be in motion with at least one surface moving from the direction of lubricant supply and at sufficient speed to generate a thick enough hydrodynamic film.

The image to the left shows elastohydrodynamic lubrication between the cam-profile and cam-follower roller, running with the same surface velocity with a fully flooded inlet.

It is important to remember that the lubrication film thickness is weakly dependent on the load between the two bodies. Thus, once the film is established, increasing the load will not usually destroy it.

The lubrication may collapse if the surfaces happen to be moving in the opposite directions, or both have zero velocity. For example, at start-up.

Entrainment Velocity: Cams and Followers

Ue = (Uc + Uf ) / 2. : the average of the cam and the roller at the surface.

When there two bodies roll without slipping Uc = Uf

Thus, the entrainment velocity is the contact speed of the Cam or the Roller.

Ue = Uc or Uf . It is easier to calculate the Uc.

For Cam-Follower Rollers, the entrainment velocity is very close to the surface speed of the cam.

Flat-Faced Followers

For Flat-Faced Followers, the entrainment velocity is the average of:

 • the velocity of the cam surface relative to the contact point

and

 • the velocity of the follower surface relative to the contact point

It can reverse in sign, especially for flat faced followers, and also be zero for a part of the cam rotation. Thus, there is concern that the boundary lubrication will fail.

Ue = (Uc + Uf ) / 2.

Clearly, in this case, the UcUf

 The Radius-of-Curvature of the Cam and the Cam-Follower are known at each point in the machine cycle. Thus we can calculate the equivalent radius as: The equivalent Radius-of-Curvature, Re is used to calculate the Film Thickness Ratio 'in Release 13'

Combined Surface Roughness, Rqt

 The combined surface roughness is derived from the roughness of the cam and the cam-follower: The cam's roughness, Rqc, and cam-follower's roughness, Rqf, both use the Root-Mean-Square (RMS) roughness values. To approximately convert from the 'Root-Mean-Square' roughness, Rq, from the more commonly used 'Centre-Line-Average' roughness, Ra, use: Rq = 1.3 * Ra.

Mode of Lubrication

The four modes of lubrication are: i) hydrodynamic, ii) elastohydrodynamic, iii) partial or mixed iv) boundary.

Four different forms of lubrication can be identified for self pressure generating lubricated contacts: i) hydrodynamic, ii) elastohydrodynamic, iii) partial or mixed iv) boundary.

Mode 1: Hydrodynamic Lubrication

Hydrodynamic or full film lubrication is the mode when the load carrying surfaces are separated by a relatively thick film of lubricant. This is a stable regime of lubrication and metal-to-metal contact does not occur during the steady state operation of the bearing. The lubricant pressure is self generated by the moving surfaces drawing the lubricant into the wedge formed by the bounding surfaces at a high enough velocity to generate the pressure to completely separate the surfaces and support the applied load.

This is possible when the contact area is substantial and conformal and convergent. The viscous lubricant is 'entrained' by the relative motion of the cam and follower. The load is supported by the hydrodynamic pressure generated in the film.

Hydrodynamic Lubrication occurs in Plain Bearings,

Mode 2: Elastohydrodynamic Boundary Lubrication

The lubricant is introduced and entrained into the contact area by the relative motion of the cam and follower and then it is maintained there because its viscosity increases significantly due to the high pressure. The load and pressure is high enough to elastically deflect the contact area (metal actually moves). This helps to make the contact more conformal, and will assist lubricant entrapment.

The cam and follower is separated by a very thin film of lubricant. The contact is a small area and under extremely high pressure.

Elastohydrodynamic Lubrication is common in Cam-Profile and Cam-Follower applications, Gears and Bearings.

Mode 3: Mixed Boundary Lubrication

Partial or mixed lubrication regime deals with the condition when the speed is low, the load is high or the temperature is sufficiently large to significantly reduce lubricant viscosity – when any of these conditions occur, the tallest asperities of the bounding surfaces will protrude through the film and occasionally come in contact.

The load is partly supported by an Elastohydrodynamic Film and partly by Solid Contact between the high spots of the cam and follower surfaces. Some surface 'glazing' may occur (polishing).

Mixed Boundary Lubrication is common mode for cam sliding and rolling cam-followers.

Mode 4: Boundary Lubrication

λ < 0.5

The load between the cam and follower is not supported by 'pressurised' lubrication liquid films. The load is carried by solid contact between the cam surfaces. The surfaces are usually covered by a solid film that adheres to them, or there are chemically modified or converted surface layers, all with a relatively low shear strength.  Surface smearing and wear likely to occur.

Boundary lubrication is the condition when the fluid films are negligible and there is considerable asperity contact. The physical and chemical properties of thin surface films are of significant importance while the properties of the bulk fluid lubricant are insignificant.

Striebeck-Curve shows the relative Coefficient-of-Friction as a function of the Viscosity, Velocity, Load with the Mode of Lubrication.

Striebeck Curve

Elastohydrodynamic Boundary Lubrication is the best you can usually get for a cam and follower system. However, because the relative speeds might reduce to zero, and even become negative, the lubricant entrainment will stop and the pressure will drop. At this point in the cycle, only Mixed Boundary Lubrication will exist.

Obviously, if a cam and follower is to be run without lubricant – especially a sliding contact follower - then wear and life depend on the material properties: especially its scuffing resistance and self lubricating properties. Cam systems without lubricant are obviously suitable only for light loads or speeds. In this case, cams with roller followers, rather than sliding followers, are preferred, for obvious reasons.

When a design choice must be made for the surface finish and whether to use anti-wear additives in the lubricant, it is necessary to make an estimate of the film thickness between the cam and follower at each point in the machine cycle.

Wear Pattern as a function of Film Thickness Ratio

 λ < 1 Surface smearing, deformation, abrasive wear 1 ≤ λ < 1.5 Smoothing of Rough Areas, Spallation 1.5 ≤ λ < 3 Some smoothing of rough area 3 ≤ λ < 4 Minimal wear 4 ≤ λ Full separation by EHL film

Fatigue Life as a function of Film Thickness Ratio

 As expected, Fatigue Life improves with the Film Thickness Ratio, λ.. A typical improvement function is shown in the image to the left.

LUBRICATION OF GEARS and CAMS

To avoid difficulties such as wear and premature failure, the correct lubricant must be chosen.

Methods of Lubrication

There are three lubrication methods in general use:

 1 Grease lubrication.
 2 Splash lubrication (oil bath method).
 3 Forced oil circulation lubrication.

There is no single best lubricant and method. Choice depends upon tangential speed (m/s) and rotating speed (rpm). At low speed, grease lubrication is a good choice. For medium and high speeds, splash lubrication and forced circulation lubrication are more appropriate, but there are exceptions. Sometimes, for maintenance reasons, a grease lubricant is used even with high speed.

Table 1 presents lubricants, methods and their applicable ranges of speed.

The following is a brief discussion of the three lubrication methods.

Grease Lubrication

Grease lubrication is suitable for any gear or cam system that is open or enclosed. It is usually applied to low speed, or when the cams or gears are exposed to the product, pack or packaging running on a machine. There are three major points regarding grease:

 1 Choosing a lubricant with suitable viscosity. A lubricant with good fluidity is especially effective in an enclosed system.
 2 Not suitable for use under high load and continuous operation. The cooling effect of grease is not as good as lubricating oil. So it may become a problem with temperature rise under high load and continuous operating conditions.
 3 Proper quantity of grease. There must be sufficient grease to do the job. However, too much grease can be harmful, particularly in an enclosed system. Excess grease will cause agitation, viscous drag and result in power loss.

Splash Lubrication

Splash lubrication is used with an enclosed system. The rotating gears splash lubricant onto the gear system and bearings. It needs at least 3 m/s tangential speed to be effective. However, splash lubrication has several problems, two of them being oil level and temperature limitation.

 1 Oil level.

There will be excessive agitation loss if the oil level is too high. On the other hand, there will not be effective lubrication or ability to cool the gears if the level is too low. Table 2 shows guide lines for proper oil level. Also, the oil level during operation must be monitored, as contrasted with the static level, in that the oil level will drop when the gears are in motion. This problem may be countered by raising the static level of lubricant or installing an oil pan.

 2 Temperature limitation.

The temperature of a gear system may rise because of friction loss due to gears, bearings and lubricant agitation. Rising temperature may cause one or more of the following problems:

 • Lower viscosity of lubricant.
 • Deformation of housing, gears and shafts.
 • Decreased backlash.

New high-performance lubricants can withstand up to 80 to 90°C. This temperature can be regarded as the limit. If the lubricants temperature is expected to exceed this limit, cooling fins should be added to the gear box, or a cooling fan incorporated into the system.

Forced-Circulation Lubrication

Forced-circulation lubrication applies lubricant to the contact portion of the teeth by means of an oil pump. There are drop, spray and oil mist methods of application.

 1 Drop method:

An oil pump is used to suck-up the lubricant and then directly drop it on the contact portion of the gears via a delivery pipe.

 2 Spray method:

An oil pump is used to spray the lubricant directly on the contact area of the gears.

 3 Oil mist method:
 • Lubricant is mixed with compressed air to form an oil mist that is sprayed against the contact region of the gears. It is especially suitable for high-speed gearing.
 • Oil tank, pump, filter, piping and other devices are needed in the forced-lubrication system. Therefore, it is used only for special high-speed or large gear box applications. By filtering and cooling the circulating lubricant, the right viscosity and cleanliness can be maintained. This is considered to be the best way to lubricate gears.

Cam Lubricants

An oil film must be formed at the contact surface between the cam and roller to minimize friction and to prevent dry metal-to-metal contact. The lubricant should have the properties listed in Table 3.

Viscosity of Lubricant

The correct viscosity is the most important consideration in choosing a proper lubricant. The viscosity grade of industrial lubricant is regulated in JIS K 2001. Table 4 expresses ISO viscosity grade of industrial lubricants.

 • JIS K 2219 regulates the gear oil for industrial and automobile use. Table 5 shows the classes and viscosities for industrial gear oils.
 • JIS K 2220 regulates the specification of grease which is based on NLGI viscosity ranges. These are shown in Table 6.
 • Besides JIS viscosity classifications, Table 7 contains AGMA viscosity grades and their equivalent ISO viscosity grades.

Selection of Lubricant

It is practical to select a lubricant by following the catalog or technical manual of the manufacturer. Table 8 is the application guide from AGMA 250.03 "Lubrication of Industrial Enclosed Gear Drives".

Table 9 is the application guide chart for worm gears from AGMA 250.03.

Table 10 expresses the reference value of viscosity of lubricant used in the equations for the strength of worm gears in AGMA 405-01.

Table 1 Range of Typical Speed (m/s) for Spur and Bevel Gears

 No Lubrication Type Range of Tangential Speeds [m/s] 0 5 10 15 20 25 1 Grease 2 Splash 3 Forced Circulation Applies to 'Oil Mist', Circulating Oil, 'Oil Jets'.

Description

1

Correct and

Proper Viscosity

Lubricant should maintain a proper viscosity to form a stable oil film at the specified temperature and speed of operation.

2

Anti-scoring Property

Lubricant should have the property to prevent the scoring failure of tooth surface while under high-pressure of load.

3

Oxidization and Heat Stability

A Good lubricant should not oxidized easily and must perform in moist and high-temperature environment for long duration.

4

Water Anti-affinity Property

Moisture tends to condense due to temperature change, when the gears are stopped. The lubricant should have the property of isolating moisture and water from lubricant.

5

Anti-foam

Property

If the lubricant foams under agitation, it will not provide a good oil film. Anti-foam property is a vital requirement.

6

Anti-corrosion Property

Lubrication should be neutral and stable to prevent corrosion from rust that may mix into the oil.

Table 4 ISO Viscosity Grade of Industrial Lubricant (JIS K 2001)

The correct viscosity is the most important consideration in choosing a proper lubricant. The viscosity grade of industrial lubricant is regulated in JIS K 2001.

 ISO Viscosity Grade Kinematic Viscosity Center Value 10-6m²/s (cSt) (40ºC) Kinematic Viscosity Range 10-6m²/s (cSt) (40ºC) More Than Less than ISO VG 2 2.2 1.98 2.42 ISO VG 3 3.2 2.88 3.52 ISO VG 5 4.6 4.14 5.06 ISO VG 7 6.8 6.12 7.48 ISO VG 10 10 9 11.0 ISO VG 15 15 13.5 16.5 ISO VG 22 22 19.8 24.2 ISO VG 32 32 28.8 35.2 ISO VG 46 46 41.4 50.6 ISO VG 68 68 61.2 74.8 ISO VG 100 100 90 110 ISO VG 150 150 135 165 ISO VG 220 220 198 242 ISO VG 320 320 288 352 ISO VG 460 460 414 506 ISO VG 680 680 612 748 ISO VG 1000 1000 900 1100 ISO VG 1500 1500 1350 1650

Table 5 Industrial Gear Oil

 Types of Industrial Gear Oil Usage Class One ISO VG  32 ISO VG  46 ISO VG  68 ISO VG   100 ISO VG   150 ISO VG   220 ISO VG   320 ISO VG   460 Mainly used in a general and lightly loaded enclosed gear system Class Two ISO VG    68 ISO VG   100 ISO VG   150 ISO VG   220 ISO VG   320 ISO VG   460 ISO VG   680 Mainly used in a general medium to heavily loaded enclosed gear system

 NLGI No. Viscosity Range State Application No 000 445...475 Semi-Liquid For Central Lubrication Systems No  00 400...430 Semi-Liquid No   0 335...385 Very Soft Paste Automotive Chassis No   1 310...340 Soft Paste No   2 265...295 Medium Firm Paster Ball and Roller Bearing General Use No   3 220...250 Semi-hard Paste Automobile Wheel Bearing No   4 175...205 Hard Paste Sleeve Bearing (Pillow Block) No   5 130...165 Very Hard Paste No   6 85....115 Very Hard Paste

 AGMA No. of Gear Oil ISO Viscosity Grades R & O Type EP Type 1  2  3  4  5  6 7 comp  8 comp      8A comp  9 2 EP 3 EP 4 EP 5 EP 6 EP 7 EP 8 EP   9EP VG 46  VG 68  VG 100  VG 150  VG 220  VG 320  VG 460  VG 680  VG 1000  VG 1500

Table 8 Recommended Lubricants by AGMA

It is practical to select a lubricant by following the catalog or technical manual of the manufacture. This table is the application guide from AGMA 250.03 "Lubrication of Industrial Enclosed Gear Drives".

 Gear Type Size of Gear Equipment (mm) Ambient temperature ºC -10 ... 16 10 ... 52 AGMA No. Parallel Shaft System Single Stage Reduction Center Distance (Output Side) Less than 200 200 ... 500 more than 500 2 to 3 2 to 3 3 to 4 3 to 4 4 to 5 4 to 5 Double Stage Reduction Less than 200 200 ... 500 More than 500 2 to 3 3 to 4 3 to 4 3 to 4 4 to 5 4 to 5 Triple Stage Reduction Less than 200 200 ... 500 More than 500 2 to 3 3 to 4 4 to 5 3 to 4 4 to 5 5 to 6 Planetary Gear System Outside Diameter of Gear Casing Less than 400 More than 400 2 to 3 3 to 4 3 to 4 4 to 5 Straight and Spiral Bevel Gearing Cone Distance Less than 300 More than 300 2 to 3 3 to 4 4 to 5 5 to 6 Gear-motor 2 to 3 4 to 5 High Speed Gear Equipment 1 2

Table 9 Recommended Lubricants for Worm Gears by AGMA

 Types of Worm Center Distance mm Rotating Speed of Worm rpm Ambient Temperature, ºC Rotating Speed of Worm rpm Ambient Temperature, ºC -10 ... 6 10 ... 52 -10 ... 16 10 ... 52 Cylindrical Type <150 150 ... 300 300 ... 460 460 ... 600 600< 700< 450< 300< 250< 200< 7 Comp 8 Comp 700< 450< 300< 250< 200< 8 Comp 7 Comp Throated Type <150 150 ... 300 300 ... 460 460 ... 600 600< 700< 450< 300< 250< 200< 8 Comp 8A Comp 700< 450< 300< 250< 200< 8 Comp

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