CENTERLESS GRINDING (Part 2)

Forces Active in Centerless Grinding

Why does the workpiece not jump out of the grinding gap? Why does the workpiece rotate with almost the same surface speed as the regulating wheel? Moreover, why does the workpiece not spin up to the same surface speed as the grinding wheel? The diagram below illustrates the forces in action within the grinding gap.

Illustration 16

The diagram shows the forces in action at the three contact points of the workpiece. At the grinding point, the acting forces are the tangential cutting force Ft and the concomitant radial pressure Fr1. The ratio Fr1 / Ft varies wildly, depending on whether we are dealing with a roughing or ?nishing process and whether the grinding wheel is sharp and newly dressed or worn and dull. The radial pressure Fr1 acting on the regulating wheel is 1.5 to 4 times greater than the tangential cutting force Ft. This ratio prevents the grinding wheel from accelerating the workpiece.

The forces which act on the workblade are the normal pressure Fa and the concomitant frictional force μa x Fa. The coef?cient of friction μa depends on the grinding ?uid in use and the matching of the workblade and workpiece materials. On average, the coef?cient of friction μr is equal to 0.1 to 0.15. The steeper the blade angle β, the smaller the frictional value μr is between the workpiece and regulating wheel.

The magnitude of the normal pressure force Fa is given by the component forces of the grinding pressure and the workpiece weight in the direction of Fa. The forces that act on the regulating wheel are the radial pressure exerted by regulating wheel Fr2 and the peripheral force Fu. Here too, the radial pressure exerted by regulating wheel Fr2 is the sum of the component forces of the grinding pressure and the workpiece weight in the direction of Fr2 . To prevent slipping between the workpiece and control wheel, the regulating wheel Fu's peripheral force must correspond to the equation Fu< μr x Fr2, where μr is the frictional value between the workpiece and regulating wheel.

Grinding Gap Geometry and Height-of-Workpiece above Wheel Center

The grinding and regulating wheels' contact points are determined by the height above the center of the workpiece. The radii of the two wheels form the two angles γR and γS across the centerline. The resulting angle γ is designated as the tangent angle and bears a considerable in?uence on a workpiece's rounding. The tangent angle γ is directly related to the workpiece height ?h?. Trials have shown that angles γ of 6.3°, 8°, and 11° have produced a positive in?uence in the rounding process.

Ft - μa x Fa ± μr x Fr2 = 0

The positive sign (+) represents the case in which the regulating wheel drives the workpiece. Generally, the regulating wheel slightly decelerates the workpiece, in which case the negative sign (-) is used. Under the influence of the cutting force, the force component in direction Fr2 is increased, the frictional force μa x Fa is overcome, and the workpiece begins to turn with the regulating wheel's surface speed.

 Although in through-feed grinding, the regulating wheel is inclined, the inclination angle is mostly so small that it has been ignored in the cross-section diagram. Therefore, the contact lines have been reduced to contact points, and the angle γR represents a theoretical average value.

Illustration 17

 However, when confronted with small workpiece diameters, space constraints mean that it is not always possible to maintain such angles. The experience of another machine tool builder (Mikrosa), based on a workblade angle of 30°, has shown the following angles to be bene?cial for the rounding process: 6°30', 8°15' and 12°.

 Calculation of the Height-above-Center ?h?

Although a high position of the workpiece center above the centerline (value ?h?), and as large as possible a tangent angle γ, speeds up the rounding of a workpiece, it must be borne in mind that there are limits to the application of these rules. To illustrate this point, see the following diagram that shows the tangent angle γ to be made up of the two tangential lines that touch the workpiece's contact points at the grinding wheel and regulating wheel. As the height-above-center increases, so does the tangent angle. Clearly, there is a point at which the workpiece tends to lift off the workblade or begin to vibrate or even jump out of the grinding gap altogether. The tangent angle γ depends on the diameters of the grinding and regulating wheels and the workpiece, and the height-above-center ?h?. As previously mentioned, an angle γ of 11 degrees may lead to conditions conducive to quick rounding, which prevent the workpiece from jumping out of the grinding gap.

Illustration 18

Illustration 19

Illustration 20

Another parameter to consider is the workblade. First, the support angle has to be established. As a rule, this angle is chosen to be around 30°. Larger angles may exert too much pressure on the workblade and may lead to vibrations in the process.

Materials for Workblades

• Plunge grinding:
• Generally, tungsten carbide tipped steel blades (increasingly also PCD)
• Through-feed grinding of short pieces:
• Tungsten carbide tipped steel blades (PCD)
• Through-feed grinding of long pieces (bar grinding)
• - gray cast iron
• For bar grinding stainless steel:
• - bronze tipped steel blades.

The Workblade’s Support Angle

Illustration 21

 Another parameter to consider regarding the workblade is its width to the workpiece diameter, as shown in the following graphic.

Illustration 22

Illustration 23

Illustration 24

Important Grinding Parameters

The Regulating Wheel and the Speed Ratio qs

The speed ratio qs between the grinding wheel's surface speed and the workpiece is one of the most important parameters determining the grinding process.

Illustration 25

The setting values for the speed ratio qs correspond to those of conventional cylindrical grinding between centers:

Roughing          =           50 to 60

Standard            =           60 to 90

Finishing            =          90 to 120

The regulating wheel determines the speed ratio qs between the grinding wheel and the workpiece. The regulating wheel's surface speed corresponds more or less to that of the workpiece. Small deviations caused by slippage can be ignored for practical purposes.

The speed ratio qs is calculated as follows: 

vc = surface speed of grinding wheel in m/s or sfpm

vr = surface speed of regulating wheel in m/s or sfpm

A speed ratio of 60, for example, means that the surface speed of the grinding wheel is 60 times higher than that of the regulating wheel.

The Speci?c Material Removal Rate Q'w

Centerless Plunge Grinding

The speci?c material removal rate, known as Q-Prime or Q'w, represents the material removal rate in mm3 of 1 mm grinding wheel width in one second. Looking at 1 mm grinding wheel width allows a direct comparison between different grinding processes.

Illustration 26

vfr = speed of infeed of regulating wheel in mm/min

Q′w Guidelines for centerless plunge grinding

Roughing           3.5 to 8.0 mm3 / mm/s

Finishing             1.0 to 1.5 mm3 / mm/s

Fine finishing    0.2 to 1.0 mm3 / mm/s

The formula for calculating Q'w is as follows:

 The factor "1/2" is used because the workpiece center moves half the plunge infeed distance.

vfr = infeed speed of the regulating wheel in mm/min

dW = workpiece diameter

 As with standard plunge grinding, the plunge approach is divided into several sections with a rapid approach to safety distance, then a switch-over to a lower speed until contact. There are several steps with switch-over points from the point of contact and slowing feed-rates at each of those points until the final size has been reached, as shown in the following graphic.

Illustration 27

Feed-rate Vfa for Through Grinding 

The control wheel's inclination achieves the feed-rate of the workpiece across the grinding to the grinding wheel.

Illustration 28

 The regulating wheel's inclination in its horizontal axis by the angle α generates an axial movement, the feed-rate vfa. The correct dressing operation must consider the workpiece diameter, the dressing operation's height above the center, and the dressing angle.

Illustration 29

Specific Material Removal Rate Q'Prime Trough Grinding

The specific material removal rate, known as Q-Prime or Q'w represents the material removal rate in mm3 of 1 mm grinding wheel width in one second. Looking at 1 mm grinding wheel width allows a direct comparison between different grinding processes.

Illustration 30

 Q'w Guidelines for centerless through grinding

Roughing           3.5 to 8.0 mm3 / mm/s

Finishing             1.0 to 1.5 mm3 / mm/s

Fine finishing    0.2 to 1.0 mm3 / mm/s

 ae = depth of cut

dw = diameter of workpiece

dw= grinding wheel rpm

Dressing of the Regulating Wheel

Dressing the centerless grinding wheel is identical to dressing a cylindrical grinding wheel. Nevertheless, as centerless wheels tend to be very wide, the selection of dressing diamonds is more limited. Single point diamonds are not suitable, as they would wear across the wide wheel section. Hence, the selection is limited to multi-point diamonds, blade dressers, or rotary dressers.

The regulating wheel, however, is often dressed with a single-point diamond dresser. In this case, the dressing takes place at the back of the wheel, and the center height of the workpiece concerning the centerline of both the grinding and regulating wheel must be taken into account. This avoids any possible geometrical distortion that may occur if dressing took place in the centerline.

The regulating wheel is every bit as important as the grinding wheel. Every error of form or error of rotation will be transferred onto the workpiece. The regulating wheel:

• Regulates the surface speed of the workpiece.
• Determines the final workpiece size on the basis of its applied pressure and its infeed.
• Determines the feed rate of the workpiece on the basis of its angle of inclination.

Illustration 31

Illustration 32

Illustration 33

Function of the Regulating Wheel

Illustration 34

Errors at Grinding Gap Inlet and Outlet Guide Blocks

The grinding gap areas of inlet and outlet guide blocks substantially influence the final accuracy of workpieces. This is all the more important when the workpieces feature an asymmetrical mass distribution. The resulting geometrical deviations on workpieces indicate whether to correct the inlet or outlet guide blocks to achieve optimal results. The workpieces are guided through the grinding gap by the workblade, the regulating and grinding wheels, and the inlet and outlet guide blocks. Any of these guiding elements may induce a positional change of a workpiece, leading to a greater material removal at a certain spot on the workpiece.

Grinding wheel = position 1

Regulating wheel = position 2

Guide block inlet side = position 3

Guide block outlet side = position 4

Errors and Counter Measures

 The following illustrations A to F show different resulting workpiece shapes depending on the guide blocks' alignment. For this purpose, it has been assumed that the workblade was straight and perfectly aligned to the grinding wheel.

 Illustration 35

Shape A:

This illustrates a perfectly ground cylindrical shape with the guide blocks in perfect alignment.

 Shape B:

Overall high stiffness is of paramount importance; otherwise, deviations, as illustrated, may occur as in B. Here, the wheel edge at the back of the grinding wheel (left side) is the determining factor in regards to the size. The workpiece, which is transported with each revolution, gets a left-handed spiral ground into its desired cylindrical shape.

 Shapes C and D:

Here, the misalignment of the guide blocks 3 and 4 leads respectively to concave or convex results,

although the regulating and grinding wheels are perfectly aligned. The misalignment of the guide blocks 3 and 4 may also occur if the workpieces are too heavy.

 Shapes E and F: Here, the guide blocks 3 and 4 are only misaligned on one side of the grinding wheel and lead to a one-sided taper. Influences on workpiece form errors may occur in combination, making it more difficult to recognize and correct them.

Measures for Error Corrections

1. Improving roundness

·        Increase the surface speed of the regulating wheel (plunge grinding)

·        Reduce the angle of inclination (through-feed grinding)

·        Increase height-over-center

·        Check dressing diamond for wear

·        Increase dressing feed rate vd

·        Reduce dressing cycles

·        Use coarser grit size, or softer and/or a more aggressive grinding wheel

·        Check whether the end-face faces of workpieces are at a right angle

2. Variation in diameter (spread)

·        Adjust gauge (if applicable)

·        Check that spread does not come from out-of-roundness or taper

·        Check that spread does not come from great variations in grinding allowances

·        Check if there is sufficient grinding fluid supply

·        Check dressing diamond for wear

3. Cylindricity (Parallelism)

·        Reduce dressing feed-rate vd across the grinding wheel (plunge grinding)

·        Adjust the position of the regulating wheel in relation to the workblade (through-feed)

·        Check whether the grinding wheel cuts across its entire width (through-feed grinding)

·        Re-dress the regulating wheel (through-feed and plunge grinding)

·        Check copying dressing template for accuracy and positioning (plunge grinding)

·        Check the workblade for burrs, wear, and dirt (mainly plunge grinding)

·        Reduce dressing intervals

·        Select a harder grinding wheel or a finer grit size

·        Check dressing diamond for wear

4. Straightness

·        Adjust the position of the regulating wheel in relation to the workblade (through-feed)

·        Check whether the grinding wheel cuts across its entire width (through-feed grinding)

·        Check contact line (through-feed grinding)

·        Increase the number of grinding passes (lower depth of cut ae)

·        Check workpiece for crookedness before and after grinding (tension and spring-back)

·        Check dressing diamond for wear

5. Surface quality

·        Check grinding wheel selection

·        Reduce dressing feed-rate vd across grinding wheel (plunge grinding)

·        Increase grinding time (plunge grinding)

·        Reduce angle of inclination of regulating wheel (through-feed grinding)

·        Use finer grit size

·        Check the workblade for burrs, wear, and dirt (mainly plunge grinding)

·        Check grinding wheel for imbalance

·        Check whether there is ample grinding fluid supply.

·        Check grinding fluid for lubricating effect and whether filtration is adequate

·        rpm of regulating wheel may be too high

·        Add extra grinding pass (through-feed grinding)

·         

6. Profile errors in plunge grinding

·        Adjust the setting of the dressing slide

·        Reduce dressing feed-rate vd across grinding wheel (plunge grinding)

·        Reduce dressing interval

·        Select a harder grinding wheel or a finer grit size

·        Check whether grinding allowance is even

·        Check copying dressing template for accuracy (plunge grinding)

7. Chatter Marks

·        Workpiece too high above center

·        Check grinding wheel for imbalance

·        Support angle on workblade is excessive

·        Workblade is too thin or warped

·        The grinding wheel is not appropriately dressed as dressing diamond is worn

·        The grinding wheel is too hard or too fine

·        Dressing feed-rate vd is too slow

·        The material removal rate is excessive

·        Workblade is too long for a given grinding wheel

·        The grinding wheel is not correctly mounted on the wheel flange

8. Burning

·        Increase depth of cut ae

·        Reduce grinding time

·        Increase through-feed rate vfa

·        Use coarser grit size or softer grinding wheel

·        Increase grinding fluid supply or optimize nozzle position

·        Check dressing diamond for wear 

This article is based on the handbook (Handbook Centerless Grinding, 2009) the author , Walter Graf, wrote while working for Winterthur Technology Group (later 3M). 

Walter Graf, The Philosopher's Grindstone, Copyright 2021