GB2323932A - Wheel balancing apparatus using positive feedback to cause torsional instability - Google Patents

Abstract

A machine for detecting the state of unbalance of a "rigid" wheel in 2 planes has - as its central component - an arbour 1 designed to be torsionally flexible but laterally rigid. The arbour 1 carries a wheel at each end - one of these being the trial wheel 3 which is required to be balanced and the other being a well-balanced reaction inertia 6. The arbour is coupled to a motor 9 or torsional actuator which is capable of exerting small torques on it in such a manner as to excite the first torsional resonance. Instability of a positive-feedback control system around the motor is used to cause the torsional resonance to become excited. When the arbour is undergoing substantial torsional oscillations, the effect of significant instantaneous angular accelerations combined with the presence of unbalance causes forces to exist on the arbour from the wheels. These forces cause the bearings which support the arbour to move (or deform) and the movement (or deformation) is detected and used to deduce the unbalance.

Description

APPARATUS FOR BALANCING WHEELS USES POSITIVE FEEDBACK TO CAUSE TORSIONAL INSTABILITY.

Summarv of the Many wheels which rotate about their principal axis at finite speeds require to be balanced in order to minimise the net transverse forces appearing at the bearings and the net movements of the wheel. Balancing requires the addition (or removal) of mass at points on the wheel. The conventional method for determining where corrective mass should be added (or removed) and how large these masses should be involves spinning the wheel and measuring either the movements at the bearings or the reaction forces tending to hold the bearings still in space. This invention describes a machine which uses a different principle to determine what the corrective masses should be and where they should be placed.

Background to the Invention.

The inertial balancing of rotating parts has been an issue since the industrial revolution and machines have long been available to perform this function. The balancing of wheels is a special subset of the area of balancing cylindrical rotors which is itself a subset of the whole set of balancing activity. This categorisation is now explained.

The distinction between the balancing of rotors which can be called cylindrical and other general balancing situations begins with a clarification of what the term cylindrical means in this context. A cylindrical rotor, for the present purposes, is one which can be turned about its principal axis (its axis of rotation) by some fraction of a revolution (less than one-half), and be indistinguishable from its previous state. Clearly, no rotor is perfectly cylindrical in this sense because of mechanical tolerances but many are very close.

Within the set of cylindrical rotors there is a special subset which might be referred to as rigid rotors. In absolute terms nothing is totally rigid. However there is a clear criterion for determining whether a rotor is rigid and this is based on a comparison of the maximum rated rotation speed of the rotor and the first transverse resonance frequency of the rotor in rigid bearings. Every rotor has some maximum intended rotational speed and this is usually well down. The first transverse resonance frequency of the rotor in rigid bearings can be determined accurately from calculation in many cases or from test. Resonance frequencies are normally expressed in Hz but can be given in cycles per minute. Rated rotational speed is normally expressed in revolutions (or cycles) per minute but it can be given in Hz. If the two figures are compared in the same system of units and if the resonance frequency is several times (typically 4 times) greater than the highest rated speed, then the rotor can be classed as being rigid. Rigid rotors can be balanced well by applying unbalance corrections in only two planes.

Within the set of rigid rotors, there is a further subset which can be called wheels. The distinction between a wheel and any other rigid rotor is based on a comparison of the axial length of the rotor compared with the outer diameter of the rotor. Very narrow wheels can be adequately balanced using single-plane balancing. It can easily be shown that the dynamic moments which can exist tend to be relatively unimportant if the wheel is axially shallow.

This invention relates to an apparatus for balancing wheels which is suitable for both occasional and production balancing of wheels in two planes.

The normal method used for balancing wheels involves spinning the wheel up to some steady angular speed and measuring either the reaction forces on the bearings acting to keep the shaft position relatively constant or measuring the displacements which occur at the bearings. This requires a substantial input of energy, has safety implications in many cases and invariably has significant levels of noise associated with it.

In the proposed new method for balancing, the wheel is caused to have high angular accelerations about its principal axis. These accelerations are cyclic and come about through deliberately exciting the first torsional resonance frequency of a torsional system of which the wheel being balanced forms one part. Another inertia of similar value is present to act as a reaction wheel and the two inertias are connected by a spindle or "arbour" which is deliberately made to be torsionally flexible but laterally stiff. The maximum amount of energy given to the wheel is a very small fraction of the energy which would normally be supplied to spin the wheel for balancing. As a result, the motor and associated gear can be much smaller than would otherwise be the case and the time taken for achieving a good reading of unbalance can still be substantially smaller than the time taken to accelerate the wheel up to balancing speed.

Moreover, the machine is intrinsically safe since no part ever moves at high velocity and power requirements are also very modest. The machine is inherently quiet since the normal velocity of all exposed surfaces is near zero. The principle of operation is explained in the following section after which follows a description of the machine with drawings.

Principle of Operation.

Consider the infinitely thin wheel shown in Fig. 1. If a measurement of unbalance force, Fu, is made whilst a rigid wheel is undergoing substantial angular acceleration, then.

Fu = mr(o2 sr - mra Et Here, sr is the unit vector in the radial direction as defined before and is the unit vector in the direction of the tangent which points in the direction of positive circumferential acceleration of the center of gravity of the wheel. The symbols Q and a denote angular velocity (radls) and angular acceleration respectively. For a given combination of Q and a, the magnitude of force is IFul and y is the angle which this force makes with the radius containing the actual wheel centre of gravity.

IFul = mr ( Q2 + ar5 tan(y) = a / co Exaggerated impression of wheel's uncorrected c.o.g

Clearly, it is possible to determine the state of unbalance of a thin wheel using any combination of angular velocity and angular acceleration. This invention proposes that angular acceleration alone would be used predominantly. Since the radial forces caused by an unbalance are influenced by the square of angular velocity whereas the influence of angular acceleration is only a direct proportion, it is evident that high levels of angular acceleration must be achieved in order to produce detectable forces. These accelerations are achieved by incorporating the wheel into a system which has a lightly damped torsional resonance and then exciting this system so that it rings spontaneously at a relatively high frequency.

Consider now that the wheel is caused to have torsional oscillations with instantaneous angular position 0(t), and corresponding angular velocity Q(t) and angular acceleration a(t). If the angular position is varying sinusoidally with respect to time between - @ and e, then it is possible to express 0(t), Q(t) and a(t) as follows: 0(t) = e sin(ot) , Q(t) = .e cos(ot), a(t) = 2.e sin(ot) The quantity Q2(t) oscillates between 0 and Cj)2.62 with a frequency of 2O.

By contrast, a(t) oscillates between 2.e and o)2.O with a frequency ofo.

For all practical cases, e is a very small angle (orders of magnitude less than 1). In these circumstances angular velocity would make a negligible contribution to the lateral forces acting on the wheel. However, even if the Q2 contribution is measurable, it can be separated out from the contribution made by the acceleration using the difference in frequencies of the two components.

For an infinitely thin wheel, unbalance can only exist in one plane and needs to be corrected only in 1 plane. This in turn requires measurements in only one plane. For a (rigid) wheel with finite axial depth, unbalance can be considered to exist in two planes. Angular acceleration can still be used to translate the unbalances into measurable forces or displacements but measurements must then be taken in two planes.

The Frequency of Torsional Vibrations is limited bv rigidity of the Wheel and the Arbour.

The assembly of reaction-wheel, arbour and trial-wheel is itself a cylindrical rotor according to the definition above. Cylindrical rotors have the useful property that the vibration modes of the freely suspended rotor can be separated into uncoupled families . lateral modes and torsionalhaxial modes.

The balancing operation is made much simpler if the following conditions hold: (a) the entire assembly of arbour, reaction-inertia and trial-wheel is effectively "laterally rigid" for frequencies below and up to the first non-zero torsional natural frequency. In practice, this means that the first non-zero lateral resonance frequency of the free-free arboür+wheels system is more than, say, 4 times greater than the first non-zero torsional resonance frequency.

(b) the dominant source of torsional flexibility within the arbour+wheels system occurs in the central section of the arbour.

(c) the "bearings + bearing-supports" items offer negligible torsional resistance to motion compared with the absolute torsional stiffness for frequencies and amplitudes of torsion of the order which occur in the test.

(d) the outer frame (including the support struts between outer and inner frames) does not "complicate" the lateral dynamics of the system for frequencies up to 4 times greater than the torsional resonance frequency.

Specific Embodiment.

This embodiment of the invention is illustrated using five figures labelled 1-5.

Fig. l shows an overview of the complete wheel-balancing unit.

Fig. 2 shows a more detailed view of the central portion of the apparatus comprising arboursupport, arbour, reaction wheel and trial-wheel.

Fig. 3 shows one possible realisation for the central portion of the arbour which achieves an arbour having high lateral stiffness but low torsional stiffness.

Fig. 4 shows a possible arrangement for the "bearing and bearing-support" unit.

Fig. 5 is a schematic illustrating the interaction of the torsional and lateral system.

The following parts are referenced (consistently) in Fig.s 1 and 2.

(1) The arbour.

(2) The quick-release locking clamp.

(3) The Wheel to be balanced (the "trial wheel").

(4) The combined "Bearing + Bearing Support" unit.

(5) The Arbour-Support frame.

(6) The Reaction Wheel (7) Support Struts.

(8) Outer Frame (9) Torsional Actuator ('Motor).

(10) Rigid Part ofthe Arbour. (Part ofitem (1)) (11) Strips of spring steel. (Part ofitem (1)) (12) Binding ring for holding locking segments. (Part of item (1)) (13) Locking segments for clamping strips in place. (Part of item (1)) (14) Inner steel surface of"bearing+bearing support". (Part of item (4)) (15) Outer steel surface of"bearing+bearing support". (Part of item (4)) (16) Flexible rubber core of"bearing+bearing support". (Part of item (4)) (17) Accelerometer on "bearing+bearing support". (Part of item (4)) The description of this specific embodiment of the invention begins with Fig. 1. An arbour (1) is at the centre of the device and has integral tapered adaptors at top and bottom which mate with the trial-wheel (3) and a reaction wheel (6) respectively. The trial-wheel (3) is held firmly down onto the tapered adapter at the top of the arbour by a quick-release clamp (2). The reaction-wheel is held onto its adaptor by a more permanent means such as a nut on a threaded section at the end of the arbour.

Fig. 2 shows that the arbour (1) is suspended within the arbour-support frame (5) through two units called "bearing and bearing-supports" (4). These items are designed to allow relatively free angular motion about any axis (especially the principal axis of the machine - shown as vertical in Fig.s 1 and 2). They combine some level of lateral restraint with 2-directions of measurement capability built into each item. Depending on the level of lateral restraint actually provided, these measurements may be measurements of force or measurements of deflection.

The engineering requirements on the rest of the system are much more easily met if the "bearing and bearing-support" units present a relatively low level of lateral stiffness to the arbour+wheels assembly and if displacements are measured.

Fig. 3 shows a possible realisation of the arbour which achieves high lateral stiffness and low torsional stiffness at the same time. The torsional flexibility is achieved through the spring strips (11) which are held in place at each end on the rigid parts ofthe arbour (10) using a system of locking segments (12) and a holding band (13). In torsion the spring strips take-up a small amount of twist coupled with some bending in their flexible planes. However, for the unit to achieve any lateral deformation in one plane, some of the strips would have to undergo a combination of shear and bending in their stiff planes.

Fig. 4 shows a possible realisation of the "bearing + bearing support" units comprising a rubber moulding bonded into a steel case and having acceleration sensors oriented to measure in two orthogonal directions. The units have steel inner- and outer- surfaces (14) and (15) and they permit torsional movement by having a rubber core (16) which is very flexible torsionally.

They are also very flexible in the lateral sense. Accelerations of the inner surface (14) of the bearing support are measured in the two lateral directions using accelerometers (17) mounted on this subcomponent.

The connection between arbour-support frame (5) and outer frame (8) is achieved through support struts (7). A small motor (9) is mounted at the bottom of the outer frame (8) with vertical orientation. The shaft of the motor is coupled rigidly to the bottom end of the arbour.

The motor contains an internal means of detecting angular velocity and the velocity signal is fed back through a positive feedback element of adjustable gain in order to achieve instability.

Fig. 5 is a schematic showing the way in which the torsional system interacts with the lateral system and illustrating what signals are taken into the computer to evaluate unbalance.

Claims (1)

1. CLAMPS.

   (1) A wheel-balancing apparatus which contains an arbour onto which are mounted two wheels (one reaction wheel and the trial wheel) such that the system of arbour-plus-wheels is comparatively rigid laterally and comparatively flexible torsionally which apparatus uses torsional oscillations ofthe arbour-plus-wheels to cause sufficient angular accelerations that the unbalances present on the trial wheel can be detected as forces or deflections at the supports of the arbour.

   (2) A wheel balancing apparatus such as described in (1) which uses variable gain positivefeedback of a velocity signal in closed-loop control around the motor or actuator which acts on the arbour in order to cause the system to oscillate spontaneously.

   (3) A wheel-balancing apparatus such as described in (1) or (2) in which the arbour does not have true "bearings" in the sense that they do not permit indefinite rotation of the arbour but which has instead deformable supports which present very little additional torque to the arbour - compared to its internal torque - when the arbour is undergoing torsional oscillation.

   (4) A wheel-balancing apparatus such as described in (1) or (2) or (3) in which the measurements used for detecting the unbalance may be measures of acceleration of the arbour at each of its points of support in the two lateral directions.

   (5) A wheel-balancing apparatus such as described in (1) or (2) or (3) in which the measurements used for detecting the unbalance may be measures of force exerted by the arbour on its surrounding structure as it tries to move in response to the unbalance forces.

   (6) A wheel-balancing apparatus such as described in any of claims (1) to (5) above in which the attachment of the trial wheel to the arbour is via a tapered adaptor which holds the wheel firmly when a quick-release clamp is locked on pressing the trial wheel down onto the taper.