FRICTION IN METAL CUTTIING

Submitted by

Arjyajyoti Goswami

02/PRD/2010

Submitted to

Dr. Reeta Wattal

CAUSE OF FRICTIONMicroscopic examination shows that even the most carefully prepared “flat” metallic surfaces consist of numerous hills and valleys. When 2 surfaces are placed together, contact is established at the summit of only a few asperities in each surface

If a normal load is applied, yielding occurs at the tips of the contacting asperities, and the real area of contact Ar increases until it is capable of supporting the applied load

For vast majority of engineering applications this real area of contact Ar is only a small fraction of the apparent area of contact Aa and is given by

Ar = Fn / σy

Fn is the normal force and σy is the yield pressure of the softer material

The adhesion resulting from the intimate metallic contact of these asperities has been termed welding, and when sliding takes place, a force is required for the continual shearing of the welded junction at the tip of these asperities

Combining the 2 equations it is found that coefficient of friction is independent of the apparent contact area , and since the ratio obtained is expected to be substantially constant for a given metal, the frictional force is proportional to the normal load.

These observations are consistent with the laws of dry friction

Therefore the total frictional force is given by

Ff = τf X Ar

Τf is the shear strength of the softer material

During metal cutting it is generally observed that the mean coefficient of friction between the chip and the tool can vary considerably and is affected by changes in cutting speed, rake angle etc

This variation in friction is due to the very high normal pressures that exists at the chip tool interface.

It causes the real area of contact to approach, or become equal to, the apparent contact area over a portion of the tool chip interface.

RELEVANCE IN METAL CUTTING

Thus under the conditions of metal cutting the Ar reaches its maximum value and is constant throughout the machining operation

The frictional force is now independent of the normal force and the ordinary laws of friction no longer apply

Under these conditions the shearing action is no longer limited to the surface asperities but takes place within the body of the softer material

Model for chip tool friction in orthogonal cutting

The real area is equal to the apparent area over the sticking region while the real area is less then the apparent area over the sliding region.

In the sliding region the coefficient of friction is constant

Through experiments it has been observed that the grinding marks on the tool were imprinted on the under surface of the chip indicating that no relative motion has taken place between the chip and the tool, thus establishing the presence of sticking region in the tool chip contact length

Presence of sticking friction was confirmed by the careful investigation of the under surface of the chip on specimen where the cutting action was suddenly stopped

Effect of sticking and sliding region

Under conditions of sticking friction , the mean angle of friction on the tool face will depend on

•the form of the normal stress distribution

•the chip tool contact length

•the mean shear strength of the chip material in the sticking region

•the coefficient of friction in the sliding region

So a single value of mean angle of friction is insufficient to describe completely the frictional conditions on the tool face

ZOREV assumed to the normal stress on the tool face to be varying as

Maximum normal stress occurs when x= lf

therefore

In the sliding region from x=0 to x= lf - lst the coefficient of friction is constant therefore distribution of shear stress is given by

In the sticking zone shear stress becomes maximum, so from x= lf - lst

So normal force Fn can be found as

Where aw is the width if the chip

And frictional force is given by

Also it can be shown that

So the final expression for frictional force is

Now the coefficient of friction in the tool face is obtained as

The mean normal stress on tool face is given by

So putting in the value of maximum normal stress in the tanβ

It has been established that Remains constant

For a wide range of unlubricated cutting conditions for a given material

Mean angle of friction is mainly dependent on the mean normal stress on the tool face and this may be used to explain the effect of change in working normal rake angle on the mean friction angle

so

As normal rake angle increases the component of resultant tool force normal to the tool face will decrease so the mean normal stress will decrease.

However the mean shear stress remains roughly constant, so increase in rake angle would be expected to increase the mean angle of friction.

results, obtained from machining copper with a high speed steel (HSS) tool

NEW APPROACHES TO ANALYSE FRICTION IN METAL CUTTING

Researchers have established that the ratio of apparent area and real area depends on whether the real areas of contact (the asperities) are elastic and on an elastic substrate, whether they are plastic and on an elastic substrate or whether they are plastic and on a plastic substrate

A1, A2—plastic asperities on an elastic base, region B—elastic asperities on an elastic base, region C—plastic asperities on a plastic base On the X axis is normal stress.

A possibly improved friction model, currently being investigated, is proposed here. A constant friction coefficient μ be replaced by one which increases with plastic strain rate:

where μ0 is the coefficient of friction in conditions in which the base is elastic and a is a coefficient that might be expected to be of the order of the un deformed chip thickness divided by the cutting speed

μ = μ0 ( 1 + a ep)

Then, μ will increase to a large multiple of μ0 within the plastically deforming secondary shear zone in metal cutting

REFERENCES1. FUNDAMENTALS OF MACHINING AND MACHINE TOOLS,

Geoffery Boothroyd and Winston.A.Knight, Third Edition, CRC Taylor and Francis 2006, pg 97-100

2. www.linkinghub.elsevier.com/retrieve/pii/S0043164805003650.pdf as retrieved on 20-3-2011 at 3:00 pm

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