## 87 Wheel balancing

The wheel and tyre functions are the means to support, propel and steer the vehicle forward and backward when rolling over the road surface. In addition the tyre cushions the wheel and axle from all the shock impacts caused by the roughness of the road contour. For the wheel and tyre assembly to rotate smoothly and not to generate its own vibrations, the wheel assembly must be in a state of rotatory balance.

An imbalance of the mass distribution around the wheel may be caused by a number of factors as follows:

a) tyre moulding may not be fitted concentric on the wheel rim, b) wheel lateral run out or buckled wheel rim, c) tyre walls, crown tread thickness may not be uniform all the way round the carcass when manufactured, d) wheel lock when braking may cause excessive tread wear over a relatively small region of the tyre, e) side wall may scrape the curb causing excessive wear on one side of the tyre, f) tyre over or under inflation may cause uneven wear across the tread, g) tyre incorrectly assembled on wheel relative to valve.

Whichever reason or combination of reasons has caused the uneven mass concentration (or lack of mass) about the wheel, one segment of the wheel and tyre will become lighter and therefore the tyre portion diametrically opposite will be heavier. Hence the heavy region of the tyre can be considered as a separate mass which has no diametrically opposing mass to counteract this inbalance.

Consequently the heavier regions of the wheel and tyre assembly when revolving about its axis (the axle or stub axle) will experience a centrifugal force. This force will exert an outward rotating pull on the support axis and bearings. The magnitude of this outward pull will be directly proportional to the out of balance mass, the square of the wheel rotational speed, and inversely proportional to the radius at which the mass is concentrated from its axis of rotation.

m V2

where F = centrifugal force (N)

m = out of balance mass (kg) V = linear wheel speed (m/s) R = radius at which mass is concentrated from the axis of rotation (m)

Example If, due to excessive braking, 100 g of rubber tread has been removed from a portion of the tyre tread 250 mm from the centre of rotation, determine when the wheel has reached a speed of 160 km/h the following:

a) angular speed of wheel in revolutions per minute, b) centrifugal force.

Linear speed of wheel V = 160 X 103

or V

2666.666 m/min 2666.666

From this calculation based on a vehicle travelling at a speed of one hundred miles per hour (160 km/h) and a typical wheel size for a car, the hundred gramme imbalance of the tyre produces a radial outward pull on the wheel axis of 790 Newtons. The magnitude of this 790 Newton force can be best appreciated by converting it to weight (mass) (79 kg) and then imagine lifting and carrying 79 one kilogramme bags of sugar for some distance.

8.7.1 Cyclic movement of a heavy spot on a wheel relative to the ground (Fig. 8.50) When a road wheel rolls over a flat surface for one complete revolution, a point P on its circumference starting and finishing at ground level plots a curve known as a cycloid which represents the changing linear speed of the point P during each cycle of rotation (Fig. 8.50). For the short time point P is at ground level, its velocity remains at zero and at its highest position from the ground its forward velocity will be at a maximum. The average forward velocity of point P is at mid-height axle level, this also being the vehicle's forward speed. Thus the top of the tyre moves at twice the speed of the vehicle and in the same direction.

If point P is a heavy spot on the tyre, it will accelerate from zero to a maximum velocity for half a revolution and then decelerate to zero velocity again to complete the second half revolution. Since this spot has mass and changes its velocity, it will be subjected to a varying acceleration force which acts in a direction tangential to this curve. Consequently the direction of the inertia pull caused by this heavy spot constantly changes as the wheel moves forwards. The greatest reaction experienced on the wheel occurs within the short time the heavy spot decelerates downwards to ground level, momentarily stops, changes its direction and accelerates upwards. Hence at the end of each cycle and the beginning of the next there will be a tendency to push down and then lift up the tyre from the ground. At very low speeds this effect may be insignificant but as the vehicle speed increases, the magnitude of the accelerating force acting on this out of balance mass rises and thereby produces the periodic bump and bounce or jerking response of the tyre.

The balancing of rotating masses can be considered in two stages: firstly the static balance in one plane of revolution, this form of balance is known as static balance, and secondly the balance in more than one plane of revolution, commonly referred to as dynamic balance.

8.7.2 Static balance (Fig. 8.51) This form of imbalance is best illustrated when a wheel and tyre assembly has been mounted on the hub of a wheel balancing machine which is then spun around by hand and released. The momentum put

Fig. 8.50 Cyclic movement of a heavy spot on wheel relative to the road

into rotating the wheel tends to spin it a few times. It then stops momentarily and starts to oscillate to and fro with decreasing amplitude until eventually coming to rest. If a chalk mark is made on the tyre at its lowest point and the wheel is now turned say 90° and then released again, it will immediately commence to rotate on its own, one way and then the other way, until coming to rest with the chalk mark at the lowest point as before. This demonstrates that the heaviest part of the wheel assembly will always gravitate to the lowest position. If a small magnetic weight is placed on the wheel rim diametrically opposite the heavy side of the wheel and it has been chosen to be equivalent to the out of balance mass, then when the wheel is rotated to any other position, it remains in that position without any tendency to revolve on its own. If, however, there is still a slight movement of the wheel, or if the wheel wants to oscillate faster than before the magnetic weight was attached, then in the first case the balancing weight is too small and in the second case too large. This process of elimination by either adding or reducing the amount of weight placed opposite the heavy side of the wheel and then moving round the wheel about a quarter of a turn to observe if the wheel tries to rotate on its own is a common technique used to check and correct any wheel imbalance on one plane. When the correct balancing weight has been determined replace the magnetic weight with a clip-in weight of similar mass. With a little experience this trial and error method of statically balancing the wheel can be quick, simple and effective.

The consequences of a statically unbalanced wheel and tyre is that the heavy side of the wheel will pull radially outwards as it orbits on a fixed circular path around its axis of rotation, due to the centrifugal force created by the heavier side of the wheel (Fig. 8.51). If the swivel pins and the centre of the unbalanced mass are offset to each other,

Fig. 8.51 (a and b) Illustration of static wheel imbalance

then when the heavy spot is in the horizontal plane pointing towards the front of the vehicle a moment of force is produced (M = FR) which will endeavour to twist the stub axle and wheel assembly anticlockwise about the swivel pins (Fig. 8.51(a)). As the wheel rolls forward a further half turn, the heavy spot will now face towards the rear so that the stub axle and wheel assembly will try to swivel in the opposite direction (clockwise) (Fig. 8.5(b)). Hence with a statically unbalanced tyre the stub axle will twist about its pivot every time the heavier side of the wheel completes half a revolution between the extremities in the horizontal plane. The oscillations generated will thus be transmitted to the driver's steering wheel in the form of tremors which increase in frequency and magnitude as the vehicle's speed rises. If there is a substantial amount of swivel pin or kingpin wear, the stub axle will be encouraged to move vertically up or down on its supporting joints. This might convey vibrations to the body via the suspension which could become critical if permitted to resonate with possibly the unsprung or sprung parts of the vehicle.

8.7.3 Dynamic balance (Fig. 8.52) If a driven drum is made to engage the tread of the tyre so that the wheel is spun through a speed range there is a likelihood that the wheel will develop a violent wobble which will peak at some point as the wheel speed rises and then decreases as the speed is further increased.

This generated vibration is caused by the balance weight having been placed correctly opposite the heavy spot of the tyre but on the wheel rim which may be in a different rotational plane to that of the original out of balance mass. As a result the tyre heavy spots pull outwards in one plane while the balance weight of the wheel rim, which is being used to neutralize the heavy region of the tyre, pulls radially outwards in a second plane. Consequently, due to the offset of the two masses, a rocking couple is produced, its magnitude being proportional to the product of centrifugal force acting through one of the masses and the distance between the opposing forces (C = FX). The higher the wheel speed and the greater the distance between the opposing forces, the greater the magnitude of the rocking couple will be which is causing the wheel to wobble.

The effects of the offset statically balanced masses can be seen in Fig. 8.52(a, b and c). When the heavy spot and balancing weight are horizontal (Fig. 8.52(a)), the mass on the outside of the wheel points in the forward direction of the vehicle and the mass on the inside of the wheel points towards the rear so that the wheel will tend to twist in an anticlockwise direction about the swivel pins. With a further 180° rotation of the wheel, the weights will again be horizontal but this time the outer weight has moved to the rear and the inner weight towards the front of the vehicle. Thus the sense of the unbalanced rocking couple will have changed to a clockwise one. For every revolution of the wheel, the wheel will rock in both a clockwise and anticlockwise direction causing the driver's steering wheel to jerk from side to side (Fig. 8.52(c)). Note that when the masses have moved into a vertical position relative to the ground, the swivel pins constrain the rocking couple so that no movement occurs unless the swivel ball joints or kingpins are excessively worn.

The characteristics of the resulting wheel wobble caused by both static and dynamic imbalance can be distinguished by the steady increase in the amplitude of wheel twitching about the swivel pins with rising wheel speed in the case of static unbalanced wheels, whereas with dynamic imbalance the magnitude of wheel twitching rises to a maximum and then declines with further wheel speed increase (Fig. 8.53). Thus with dynamic imbalance, a wheel can be driven at road speeds which are on either side of the critical period of oscillation (maximum amplitude) without sensing any undue instability. If the wheel is driven within the relative narrow critical speed range violent wheel wobble results.

Slackness in the swivel pins or steering linkage ball joints with unbalanced tyres will promote excessive wheel twitch or wobble, resulting not only in the steering wheel sensing these vibrations, but causing heavy tyre tread scrub and wear.

### 8.7.4 Methods of balancing wheels

Wheel balancing machines can be of the on- or off-vehicle type. The on-vehicle wheel balancer has the advantage that it balances the wheel whole rotating wheel assembly which includes the hub, brake disc or drum, wheel and tyre. However, it is not really suitable for drive axles because the transmission drive line does not permit the wheel hub to spin freely (which is essential when measuring the imbalance of any rotating mass). Off-vehicle balancing machines require the wheel to be removed from the hub and to be mounted on a rotating spindle forming part of the balancing equipment.

Fig. 8.52(a-c) Illustration of dynamic wheel imbalance
Fig. 8.53 Relationship of wheel speed and oscillating amplitude for both static and dynamic imbalance

Balancing machine which balances statically and dynamically in two separate planes (Fig. 8.54) The wheel being balanced is mounted on the spindle of the mainshaft which is supported by a pair of spaced out ball bearings. This machine incorporates a self-aligning ball bearing at the wheel end mounted rigidly to the balancing machine frame, whereas the rear bearing is supported between a pair of stiff opposing springs which are themselves attached to the balancing machine frame. An electric motor supplies the drive to the spindle by way of the engagement drum rubbing hard against the tyre tread of the wheel assembly being balanced.

When the wheel and tyre is spun and the assembly commences to wobble about the self-aligning bearing, the restraining springs attached to the second bearing absorb the out of balance forces and the deflection of the mainshaft and spindle.

An electro-magnetic moving coil vibration detector (transducer) is installed vertically between the second bearing and the machine frame. When

Fig. 8.54 Wheel balancing machine which balances statically and dynamically in two different planes

the wheel assembly wobbles, the armature (rod) in the centre of the transducer coil moves in and out of a strong magnetic field provided by the permanent magnet. This causes the armature coil to generate a voltage proportional to the relative movement of the rod. The output signal from the detector is a direct measure of the imbalance of the wheel assembly. It is therefore fed into a compensating network which converts the signals into the required balance weight to be attached to the outside of the wheel rim in the left hand plane. These modified, but still very weak, electrical signals are then passed through a filter which eliminates unwanted side interference. They are then amplified so that they can activate the stroboscope device and the weight indicator meter.

The weight indicator meter computes the voltage amplitude signal coming from the detector and, when calibrated, indicates the size of the weight to be added to the plane of balance, in this case the outside of the wheel. Conversely, the stroboscope determines the angular phase of the balance weight on the wheel. This is achieved by the sinusoidal voltage being converted into a sharply defined bright flash of light in the stroboscope lamp. A rotating numbered transparent drum is illuminated by the stroboscope flash and the number which appears on the top of the drum relates to the phase position of the required balance weight.

Mounting of wheel on balancing machine spindle (Fig. 8.54) Mount the wheel onto the flanged multi-hole steel plate. Align the wheel stud holes with corresponding threaded holes in the flange plate and screw on the wheel studs provided. Slide the wheel hub assembly along the spindle until the inside of the wheel rim just touches the adjustable distance rod and then lock the hub to the spindle via the sleeve nut. The positioning of the wheel assembly relative to the supporting self-aligning bearing is important since the inside wheel rim now is in the same rotating plane as the centre of the bearing. Any couple which might have been formed when the balance weights were attached to the inside of the wheel rim are eliminated as there is now no offset.

Dynamic balance setting (Fig. 8.54) To achieve dynamic balance, switch on the power, pull the drive roller lever until the roller is in contact with the tyre and allow the wheel to attain full speed. Once maximum speed has been reached, push the lever so that the roller is freed from the tyre. If the wheel assembly is unbalanced the wheel will pass through a violent period of wobble and then it will steady again as the speed falls. While the wheel is vibrating, the magnitude and position of the imbalance can be read from the meter and from the stroboscope disc aperture respectively. A correction factor is normally given for the different wheel diameters which must be multiplied by the meter reading to give the actual balance weight. Select the nearest size of balance weight to that calculated, then rotate the wheel by hand to the number constantly shown on the stroboscope disc when the wheel was spinning and finally attach the appropriate balance weight to the top of the wheel on the outside (away from the machine). Thus the outer half of the wheel is balanced.

Static balance setting (Fig. 8.54) Static balance is obtained by allowing the wheel to settle in its own position when it will naturally come to rest with the heaviest point at bottom dead centre. Select a magnetic weight of say 50 grammes and place this on the inside rim at top dead centre and with this in position turn the wheel a quarter of a revolution. If the magnetic weight is excessive, the weighted side will naturally gravitate towards the bottom but if it is insufficient, the weight will rise as the wheel slowly revolves. Alter the size of the magnetic weight and repeat the procedure until there is no tendency for the wheel to rotate on its own whatever its position. The wheel is now statically and dynamically balanced and a quick check can be made by repeating the spin test for dynamic balance. Once the correct static balance weight has been found, replace the magnetic weight by a clip-on type.

Balancing machine which dynamically balances in two planes (Fig. 8.55) The machine is so constructed that the wheel being balanced is mounted on the spindle of the mainshaft which is supported by a pair of spaced out ball bearings housed in a cylindrical cradle, which itself is supported on four strain rods which are reduced in diameter in their mid region (Fig. 8.55). An electric motor supplies the drive to the mainshaft via a rubberized flat belt and pulleys.

Vibration detectors are used to sense the out of balance forces caused by the imbalance of the wheel assembly. They are normally of electromechanical moving coil type transducers. The tran-ducer consists of a small armature in the form of a stiff rod which contains a light weight coil. The rod is free to move in a strong magnetic field supplied by a permanent magnet. The armature rods are rigidly attached to the mainshaft and bearing cradle and the axes of the rods are so positioned as to coincide with the direction of vibration. The housing and permanent magnets of the detectors are mounted onto the supporting frame of the cradle. The relative vibratory motion of the armature rod to the casing causes the armature coil to generate a voltage proportional to the relative vibrational velocity.

The output signals from the two detectors are fed into a compensating network and then into the selector switch. The compensating network is so arranged that the output signals are proportional to the required balance weights in the left and right hand balancing planes respectively. The output voltages from the selector switch are very small signals and will include unwanted frequency components. These are eliminated by the filter. At the same time the signals are amplified so that they can operate the stroboscope device and both weight indicating meters. These weight indicating meters measure the amplitude of the voltage from the detectors and when calibrated indicate the actual weights to be added in each plane. The stroboscope device changes the sinusoidal voltage into a sharply defined pulse which occurs at the same predetermined point in every cycle. This pulse is converted into a very bright flash of light in the stroboscope lamp when focused on the rotating numbered transparent drum; one number will appear on the top of the apparently stationary surface. The number is a measure of the relative phase position of the voltage and is arranged to indicate the position of the required balance weight.

Dynamic balance setting in two planes (Fig. 8.55) Mount the wheel over the spindle and slide the conical adaptor towards the wheel so that its taper enters the central hole of the wheel. Screw the sleeve nut so that the wheel is centralized and wedged against the flanged hub (Fig. 8.55). Any

Fig. 8.55 Wheel balancing machine which dynamically balances in two planes

existing balance weights should now be removed and the wheel should also be brushed clean.

Before the wheel assembly is actually balanced on the machine, the two basic wheel dimensions must be programmed into the electronic network circuit. This is carried out by simply moving the wheel diameter indicator probe against the inside of the wheel rim and reading off the wheel diameter and also measuring with a caliper gauge normally provided the wheel width. The wheel diameter and wheel rim width measurements are then set by rotating the respective potentiometer knob on the display console to these dimensions so that the electronic network is altered to correct for changes in the centrifugal force and rocking couples which will vary with different wheel sizes.

Balancing machines of this type usually measure and provide correction for wheel imbalance for both static and dynamic balance with respect to both the outer and inner wheel rim rotating planes.

The start button is now pressed to energize the electric motor. As a result the drive belt will rotate the mainshaft and spin the wheel assembly under test.

First the state of wheel balance in the outer wheel rim plane of rotation is measured by pressing the outer rim weight indicator meter switch. The meter pointer will align on the scale with size of balance weight required in grammes; the stroboscope indicator window will also show a number which corresponds to the wheel position when a balance weight is to be attached.

Once the balance weight size and angular position has been recorded, the wheel assembly is brought to a standstill by pressing the stop button and then releasing it when the wheel just stops rotating.

The wheel should now be rotated by hand until the number previously observed through the stroboscope window again appears, then attach the selected size of balance weight to the top of the outer wheel rim.

The whole procedure of spinning the wheel assembly is then repeated but on the second time the inner rim weight indicator button is pressed so that the balance weight reading and the phase position of the wheel refer to the inner rim rotating plane. Again the wheel is braked, then turned by hand to the correct phase position given by the stroboscope number. Finally the required balance weight is attached, this time to the inner wheel rim at the top of the wheel.

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