# Cam: Lubrication and Film Thickness Ratio

## Lubrication for Cams and Gears

Reasons to lubricate cam and cam-followers with the correct lubricant are to:

 1 Reduce abrasive and adhesive wear between the cam and the follower.
 2 Increase the life of the cam and the cam-follower.
 3 Reduce temperature, and to prevent scuffing between the cam and follower.
 4 Remove contaminants, when there is also an oil filtration system.
 5 Reduce noise.

Especially for cams with flat-faced cam-followers:

 1 Reduce friction and wear between the cam and cam-follower.
 2 Limit the temperature rise caused by rolling and sliding friction.

### Film Thickness Ratio, λ:

Film Thickness Ratio, λ:

$\frac{1}{{R}_{e}}=\frac{1}{{R}_{1}}+\frac{1}{{R}_{2}}$

h = Thickness of Lubricant Film

Rqt = Combined Surface Roughness of Cam and Follower

We can see that the Film Thickness Ratio is conceptually simple.

It is a ratio of two dimensions: the Oil's Film Thickness and the height of surface asperities defined by Cam and Cam-Follower surface roughness.

 • Film Thickness Ratio = 1, the cam's surface asperities just about touch the cam-follower's surface asperities through an oil film of the similar dimension.
 • Film Thickness Ratio > 1, the contact of the asperities becomes less likely.
 • Film Thickness Ratio <1, contact is more likely or even certain.

Thus, the Film Thickness Ratio is a reasonable indication of the likelihood of cam wear and fatigue.

 Film Thickness Ratio Failure Characteristic 3.0 < λ < 4.0 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 , but is usually avoided. λ < 1.0 Surface scoring, smearing or deformation occurs at the cam surface and is followed by wear. Film-Thickness Ratio is closely related to the 'Mode-of-Lubrication, Aiso'. Film Thickness is often less-than 1 micrometer (<0.001mm). When we compare its thickness dimension to typical contaminants, we can see that cleanliness of the oil, cam, and cam-follower are important. Filter Ratings versus Life example

#### h, Thickness of Lubricant Film

Formula for Film Thickness

 The calculation of the Film Thickness between a cam and follower can be simplified into an equivalent arrangement of two cylinders that roll together, as shown above. Derived by Dowson and Higginson. Applies to isothermal conditions Parameter Units α= Pressure exponent of lubricant viscosity (m2/N) or (Pa-1) (kinematic viscosity × density) (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. Simplified Film Thickness Formula 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. If you cannot change the cam design to change Re or ue, the only parameter you can change is the operating dynamic viscosity, η, of the lubricant. Units (Ns/m^2) (m/s) (m)

Entrainment Velocity, Ue

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

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 Entrainment Velocity drops, for example, at start-up.

Cam and Rolling Cam-Follower

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

When there cam-follower rolls without slipping Uc = Uf

Ue = Uc or Uf

Cam and Flat-Faced Follower

For Flat-Faced Followers, the entrainment velocity is the velocity of the cam surface relative to the contact point.

Entrainment Velocity can reverse its sign and also become zero for some part of the cam's rotation, at which time the Film Thickness will collapse.

Ue = (Uc + Uf ) / 2.

Clearly, in this case, the Uf = 0

Equivalent Radius of Curvature of Cam and Follower, Re

 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 at each point as: The equivalent Radius-of-Curvature, Re will be used to calculate the Film Thickness Ratio 'in Release 13'.

Dynamic Viscosity,η & Kinematic Viscosity, ν

 Kinematic-Viscosity, mm2/s (centiStoke) = Dynamic Viscosity (1Poise)  / Density (g/cm3)

#### Rqt :Combined Surface Roughness

 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 to Root-Mean-Square roughness, Rq, from the more commonly used Centre-Line-Average roughness, Ra, use: Rq = 1.3 * Ra. Commercial Cam-Follower ≈ 0.2Ra ; Ground Cam ≈ 0.4Ra ; Good milling and or wire-cutting≈ 0.8Ra

### Regime  of Lubrication

There are four different modes of lubrication that can be identified for self pressure generating lubricated contacts.

REGIME 1: Hydrodynamic Lubrication : occurs mainly in Plain Bearings.

λ > 5

The load carrying surfaces are separated by a relatively thick film of lubricant. Metal-to-metal contact does not occur. 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.

REGIME 2: Elasto-hydrodynamic Boundary Lubrication : common in Gears and Bearings.

3 < λ < 5

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

REGIME 3: Mixed-Boundary-Lubrication : common for cam sliding and rolling cam-followers.

0.5 < λ < 3

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 Elasto-hydrodynamic Film and partly by Solid Contact between the high spots of the cam and follower surfaces. Some surface 'glazing' may occur (polishing).

REGIME 4: Boundary-Lubrication

λ < 0.5

Boundary lubrication is the condition when the oil film is insignificant and there is asperity contact. The load is not supported by the oil. Rather, there is solid contact between the surfaces. The physical and chemical properties of the films at the contacting surfaces become important, while the properties of the bulk oil are not. EP (Extreme Pressure) Additives (see below: AW and EP Additives) should be in the lubrication. The EP additives adhere to the surfaces or chemically modified them. The solid-film will also have low shear-strength. Smearing and wear are much more likely with boundary lubrication.

AW (anti-wear) and EP (extreme-pressure) Additives

In practice, a cam and cam-roller will often have an oil-film thickness below the optimum. In this condition, the hydrodynamic film is not developed and a mixed or boundary condition is present, the asperities on the interacting surfaces start to contact and the temperature rises.

This is where AW and EP Additives may be used.

AW and EP additives react with the surfaces forming tribolayers that prevent direct contact between the sliding surfaces. Usually, anti-wear agents have a lower activation temperature than the extreme-pressure ones.

The distinction between anti-wear and extreme-pressure additives is not very clear. Some are classified as AW in one application and EP in another, and some have both functions. AW additives are designed to deposit surface films under moderate contact pressures whereas EP additives are much more reactive and are used when the contact pressures are very high in order to prevent modes of failure like scuffing.

The three most common temperature activated EP additives are chlorine, phosphorus and sulphur. They are activated by reacting with the metal surface when the temperature is elevated. The chemical reaction between the EP additive and the metal surface forms a new compound that acts as a barrier to reduce friction, wear and the possibility of welding. These EP additives are effective over different temperature ranges;

 Chloro-paraffins 180-450°C Phosphorus compounds 200-700°C Sulphur compounds 600-1000°C

The non-temperature dependent overbased sulphonate EP additives operate by a different mechanism. Although the film formation is similar to the temperature dependent additives. The sulphonates contain a colloidal carbonate salt dispersed within the overbased sulfonate and during the interaction with iron the colloidal carbonate forms a film that can act as a barrier between the metal surfaces.

More technically: Common AW and EP additives are organo-sulfur and organo-phosphorus compounds; organic polysulfides, phosphates dithiophosphates and dithiocarbamates. In the 1930’, zinc dialkydithiophosphates (ZDDP) was introduced initially to prevent bearing corrosion. However, it was found to have good anti-oxidant and anti-wear abilities.

### Striebeck Curve

Striebeck Curve shows Wear; Film Thickness; Coefficient-of-Friction as a function of the Viscosity, Velocity, Load

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 (with a sliding cam-follower) 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.

### Fatigue Life as a function of Film Thickness Ratio

 There is a rapid increase in cam and cam-follower fatigue life if the Film Thickness Ratio becomes greater the 1. What is Beta ( β ) Ratio? Beta ratio (ß) is a formula used to calculate the filtration efficiency of a particular fluid filter using base-data obtained from multi-pass testing. In a multi-pass test, fluid is continuously injected with a uniform amount of contaminant (i.e., ISO medium test dust), then pumped through the filter unit being tested. Filter efficiency is determined by monitoring oil contamination levels upstream and downstream of the test filter at specific times. An automatic particle counter is used to determine the contamination level. Through this process an upstream to downstream particle count ratio is developed, known as the beta ratio. The formula used to calculate the beta ratio is: β(x)= particle count in upstream oil / particle count in downstream oil. E.g. : β4(x)= 200 200 times fewer particles, size of 4μm, downstream than there are upstream of a filter. This means it is 99.5% efficient.

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