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J. Hugel

Balancing Grinding Wheels

Introduction

Owners of tool and cutter grinders know that at least the larger wheels usually are not very

well balanced and produce bothering vibrations. I therefore provide for those wheels in the

mounting flange 12 evenly distributed holes, threaded M5 as seen in Figure 1. The holes

are identified by numbers from zero to eleven and the masses for balancing are setscrews.

Figure 1: Grinding wheel with threaded holes in the flange for balancing with setscrews

But what is an unbalance exactly? A circular disk or wheel, mounted perpendicular on a

shaft is balanced if the axis of rotation meets the centre of mass (CM). If the axis however

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has the distance e from the CM and the disk with the mass M is turned with the rotational

speed n a centrifugal force 2(2 )F n M eπ= ⋅ ⋅ ⋅ ⋅ is generated. The product u M e= ⋅ is

called the static unbalance or better is named force unbalance. There exists a second kind

of unbalance, the torque unbalance, which usually is negligible if unbalanced grinding

wheels are regarded. The classical method to identify and compensate force unbalances is

shown in Figure 2, the shaft is rested on two rails with knife edges and as long as the

wheel is not balanced the CM points down and the system acts as a pendulum. A more

modern design is shown in Figure 31, the four light weighted disks are supported by ball

bearings and balancing here is performed by two equal masses in a circular slot, seen in

the photo. The masses for compensation are shifted until the grinding wheel has no longer

the tendency to turn into a certain position and becomes indifferently stable.

Figure 2: Balancing apparatus for grinding wheels

1 Courtesy Baitella AG, Zürich. <http://www.baitella.com/>

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Figure 3: A modern balancing stage

Building such a stage would be not very difficult, but the grinding wheels of the QUORN,

STENT and other tool and cutter grinders are mounted on stub arbours and these would ask

for a more complicated equipment. But there is another way to balance grinding wheels.

The rotating unbalance forces excite vibrations which disappear for the balanced wheel.

Touching the machine with the finger or thumb nail very sensitively indicates the

existence of vibrations however judging its magnitudes is very uncertain. Albeit finding

the right mass and its angular position for compensation with the finger only is possible in

principle but the procedure would be very longwinded and cumbersome. A suitable sensor

for measuring the vibrations’ magnitude supports essentially the balancing process and

then this becomes simple and straight forward as we’ll see. It is absolutely not necessary

to have the more sophisticated equipment found in industry and trade which only helps to

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balance a rotor much faster but not more accurate than by the much more simpler

approach regarded here.

Vibration Sensors

If a grinding machine is excited to vibrations by an unbalance the oscillations observed

have different magnitudes and phase angles at different locations but the frequency is

always the same, identical with the rotational speed n. Normally the most intensive

vibrations are found in the vicinity of the spindle bearings. In balancing technology the

specifications are based on the RMS values2 of the oscillations’ velocities. Tool grinders

should be balanced to a speed not much higher than v = 1 mm/s; a finger tip can detect

vibrations as low as 0.1 mm/s. Sensors are available for the vibrations speed, but also for

the displacement x and acceleration a; balancing in principle is possible with any of these

devices. Measuring the acceleration however has some advantages. The most important

feature is fact that no reference basis is necessary and the sensors simply can be attached

to the grinding machine, even with putty or tapes. The now available Micro Electro-

Mechanical Systems (MEMS), based on semiconductor technologies are accurate, cheap,

and easy to handle, to the authors experience they are very suitable for balancing grinding

wheels. The sensors are small chips; typical representatives are the ADXL103 from

Analog Devices3 or the SCA610 from VTI Technologies4. The shockproof VTI sensor is

seen in a plastic case in Figure 4, the author used the special type SCA610-C13H1G which

is also available ready for application with the chip encapsulated in a little box from

aluminium as KAS 804 03A from KELAG5. The supply voltage for the SCA610 is 5 Volt

DC; in the vertical position the earth’s acceleration of gravity is measured, the output

voltage is either 3.8 V if the sensor points down or 1.2 V in the opposite direction. These

values can be used for calibration regarding the earth’s acceleration 29.81 /g m s= ± . In

the horizontal position the sensor is not biased by the gravitation and best applied for

measuring the vibrations from unbalances. The steady state output voltage is 2.5 V DC.

2 Root Mean Square 3 <http://www.analog.com/ 4 <http://www.vti.fi/> 5 <http://www.kelag.ch/>

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Superimposed are the AC-signals from the vibrations and these only are interesting, its

separation from the DC offset with a capacitor is very simple.

Figure 4: The sensor SCA610 in a plastic case

Figure 5: Signals for acceleration and speed recorded with a test stand

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The acceleration signal directly could be recorded by an oscilloscope or a true RMS-AC-

meter. However converting the acceleration a into a speed signal v has some advantages;

the noise becomes lower and the measuring results can be compared with the

recommendations of the standards for unbalances. In Figure 5 a record is shown. The blue

acceleration signal is converted into the yellow speed signal, the frequency is 100 Hz

equivalent to 6000 RPM.

The green rectangular signal is from a half black and half white reference track on the

shaft and picked up by a reflective light sensor; this is used for triggering the oscilloscope

but also could be applied for phase measurements.

Per definition the acceleration is the derivative of the speed and then inversely the speed v

is received from the acceleration signal a by integration; practically this signal processing

is performed by a simple low pass filter. For harmonic signals the speed v is the

acceleration divided by the circular frequency: /(2 )a nν π= ⋅ ⋅ and this special relation is

valid for amplitudes or RMS-values.

Figure 6: Electrical scheme for measuring the vibration’s velocity

In Figure 6 the electrical scheme for measuring the vibration’s speed with the KAS 804 or

SCA 610 is seen. The supply voltage is 12 V and converted by a voltage regulator to

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precisely 5 V. The sensor’s output is connected to the low pass filter, the combination of

resistor R1 and capacitor C3. Capacitor C4 already was mentioned and separates the AC-

signal from the DC offset. The voltage meter shall indicate the RMS value; a suitable

multimeter, ready available, may be used or a RMS-DC converter chip6 together with a

DC meter. This was realized in the Vibroscope Figure 7 which contains the complete

circuit of Figure 6 and additionally the electronic circuit for a reflective light sensor. The

device is calibrated, 1 V output voltage at C3 is equivalent to 10 mm/s RMS.

Figure 7: The Vibroscope

A RMS meter efficiently suppresses the noise as long as this is weaker than the vibration

signal. In course of the balancing procedure, the unbalance together with the related

vibrations are reduced. Then the filtering effect of the RMS meter disappears more and

more until the unbalance and noise signal have the same order of magnitude. Now

balancing is finished; it makes no sense to try to proceed to finer limits. If the result is not

satisfying it would be necessary first to reduce the mechanical noise which is generated by

other moving components, e.g. the motor or belt.

6 For example LTC 1966 from Linear Technology <http://www.linear.com/>

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Balancing a Grinding Wheel

Balancing always starts with an initial run to record the vibration signal vI. If then a test

unbalance is set arbitrarily in one hole, the vibration my become increased or reduced. In

the first case however the mass then should be set in the opposite hole to receive in any

case a reduced signal. Now the mass and its position is varied until the minimum vibration

signal is received. Normally it is necessary to set masses into two or more holes. One

reason is that the initial unbalance is not exactly in line with the direction of one of the

twelve holes and then two masses at two adjacent positions are necessary for

compensation. Secondly the maximum mass of one hole may be insufficient to

compensate the unbalance and then adjacent additional holes are used. For safety reasons

the set screws must not protrude from the rim. Thirdly it may happen that the minimum

unbalance of the shortest screw is too high for compensation, then two masses in opposite

holes, set to different depths must be applied.

Figure 8: Diagram of the vibration signal for different test runs

This trial and error procedure sound very complicated but isn’t in reality. Within a very

short period a good feeling is acquired how to proceed step by step. The author and others

have balanced grinding wheels by this method, very seldom more than ten test runs were

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necessary to be successful. It should be taken in mind, absolute perfection is neither

possible, nor necessary.

There is no intention to discuss in this short article the systematic methods for balancing

with a minimum of test runs by an analytical determination of the unbalance’s magnitude

and position. But to get some more insight how balancing works it shall now be assumed

that 12 test runs are performed with the same test unbalance successively set into the holes

0 to 11. Then a diagram can be plotted as seen in Figure 8;. the minimum unbalance in

this case is at position 2.8 and this means that for compensation the total mass must be

split; 80% for hole No.3 and 20% for hole No.2.

The minimum unbalance however can be under- or over-compensated. In the first case the

compensating mass must be increased and in the second reduced. The situation is clarified

with the signal vI from the initial test run. In the first case the initial unbalance is vI = (vmax

- vmin)/2; the maximum vmax and minimum vmin have the same distance from vI. In the

second case it is vI = (vmax + vmin)/2; the minimum vmin is less distant from vI than the

maximum vmax. With the test unbalance uT the total unbalance for compensation is in the

first case uC = uT·vI /(vI - vmin) and in the second uC = uT·vI /(vI + vmin).

The method presented here of course is not restricted to grinding wheels and could also be

applied for balancing other components as motors, locomotive wheels etc.; it would be

very interesting to hear from others experiences.

The Vibroscope

The Vibroscope in Figure 7 was designed to support the balancing of grinding wheels my

measuring the RMS values of the speed as already explained. Additionally outputs are

provided for demonstrating the vibration signal by an oscilloscope. The device was built

for our Society to demonstrate at exhibition stands how simple it is to balance grinding

wheels. Building the Vibroscope is a simple and interesting project. This is described

completely in a little booklet, available from the SMEE membership secretary Mike

Kapp. Included are all electrical schemes, layouts and lists of parts. Also some more

details are explained on the theoretical background and the more systematic procedures of

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balancing. These are supported by Excel worksheets which are provided together with

detailed instructions on a CD. The booklet together with the CD are sold for £ 10.00 plus

p.p.; printing as well as the CD was sponsored and the total revenue will support the

renovation fund for Marshall House.