Hofmann Snap-on Y2k Bedienungsanleitung

SERVICE

of the Y2k balancing platform

Seite 1 von 99

The vibratory assemblies of the Y2k balancing platform

L´

R´

L R

S´

M´

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New principle for vibratory system

– designed to reduce the effects of force relations

The disadvantages of the former solutions are the considerable effects of force relations. As a

result the plane separator circuit mostly had to form the difference between high measured

values in the transducer planes in order to calculate the unbalances present in the correction

planes. If sensitivity substantially of one transducer changed by a certain percentage under

different influences, the calculated difference, that is the reading of unbalance present in the

correction planes, would change disproportionately.

The problem of the effects of force relations will now be illustrated in Fig. 1 and the

following derived algorithms. To make the problem quite clear we assume that an unbalance

URis present in the right-hand correction plane only, this unbalance being calculated by the

plane separator circuit on the basis of data measured in the planes Rand L.

-L

Fig. 1 Illustration of the effect of force relations at an increasing distance (a+b)

Following the condition

∑Moments

the measured value Lis

()

cbaUaU

LRL +

⋅

+⋅

()

cbaU

LR+⋅

=, if .0=

Analogously the measured value Ris

() ( )

ccbaUcaU

RRL

+⋅++⋅

−=

()

ccbaU

RR++⋅

−= , if 0=

Following the condition

∑ForcesTransverse

the plane separator circuit calculates that

()

RLUR+−= .

As the measured value Lis oppositely directed to R, URis practically the difference between

the absolute measured values Land R.

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The dependence of the measured values Lfrom distance (a+b) and Rfrom distance (a+b+c)

respectively becomes obvious from the straight lines in Fig. 1. They intersect the axis in the

measuring planes. The forces in the measuring planes increase linearly with increasing

distance. It is quite obvious that the the effects of force relations increase in the ratio

ba L

+and cba R

++ respectively

with increasing distance. Consequently the mistake in the calculated unbalance URwill be

disproportionately large if the sensitivity of only one transducer changes following different

influences such as temperature, fatigue, shock, overload, vibrations in transport, humidity, etc.

The target should be to reduce the effects of force relations such that any change in the

sensitivity of one transducer does not affect unbalance readings disproportionately when

calculated by a plane separator circuit.

The disadvantages specified above are basically typical of a vibratory system with outboard

rotors. Using state-of-the-art technology an improvement is hardly possible because of given

physical restrictions.

A possibility to improve the results is the physical displacement of the right measuring plane

to outside the machine housing such as illustrated in Fig. 2. In this case the hollow space

inside the rim is used, for instance with geodyna 3001 of HWT and all machine types of

Balco. Given the rim shapes as they are displacement is quite limited and possible for one

measuring plane only.

Fig. 2 Measuring system with physical support of the rotor outside the machine housing

Seite 4 von 99

Another possibility to reduce the effects of force relations is an increased distance between

measuring planes as illustrated in Fig. 3. This condition is not always feasible for lack of

space and makes sense to a limited extent only because the left-hand measuring signal is

reduced and consequently the influence from fluctuations of measured values will increase.

Fig. 3 Measuring system with increased distance between measuring planes

Theoretically an inboard rotor with correction planes between the measuring planes such as

illustrated in Fig. 4 can be considered an improvement as well.

Fig. 4 Inboard rotor with one measuring plane on every side of the rotor

Considering state-of-the-art technology this possibility is not feasible for automotive wheels

because at least one point of support will hinder clamping of the wheels.

It is now the idea for a new vibratory system to maintain the basic concept of an outboard

rotor, but to displace the two measuring planes virtually far outside the machine housing. The

measuring planes and points of support respectively will be displaced so far outside the

machine housing that the virtual measuring planes have no physical support on the machine

housing any longer. This means that independent of physical conditions the measuring planes

may be virtually located in optimum positions along the shaft axis which could cover the

whole range of wheels to be balanced.

Seite 5 von 99

Fig. 5 System with two virtual measuring planes outside of the physical range

When the measuring planes are located in optimum positions, the virtual left-hand measuring

plane is just inside the wheel disc when the wheel is as close as possible to the housing of the

wheel balancer (see Fig. 5). In this extreme case the left-hand correction plane is slightly

displaced left of the left-hand measuring plane. Analogously the right-hand virtual measuring

plane is slightly displaced left of the right-hand correction plane in the case where the wheel

is in the remotest location relative to the housing of the wheel balancer. Apart from these

extreme cases the two correction planes are mostly located between the two virtual measuring

planes. Locations of the two measuring planes can be calculated such that the effects of force

relations are minimum over the entire range where correction planes can be located.

Virtual displacement is based on a vibratory system where the support levers are not located

in parallel, but in an angle relative to the measuring shaft as illustrated in Fig. 6.

Fig. 6 Vibratory system with virtual node of vibration

In this arrangement a node of vibration forms approximately in the point of intersection of

extended support levers. When forces act on the measuring shaft, e g centrifugal forces caused

by rotating unbalance, it comes to a vibrating deflection of the vibratory system. Magnitude

and location of such deflection also depend on the axial distance of the point of application of

the forces relative to the node of vibration. Fig. 7a illustrates that the vibratory system

responds in opposite direction of the forces applied if they are applied right of the node of

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vibration. If forces are applied left of the node of vibration such as illustrated in Fig. 7b the

vibratory system will respond in the direction of the forces applied. If, however, the forces are

applied in the node of vibration as illustrated in Fig. 7c the vibratory system will maintain a

state of rest.

The simplified Figures below do not include the springs.

Fig. 7a Deflection of vibratory system with forces applied right of the node of vibration

Fig. 7b Deflection of vibratory system with forces applied left of the node of vibration

Fig. 7c Vibratory system with forces applied in the node of vibration

The vibratory system as illustrated in Fig. 8 is the basis of a force measuring system.

Basically it would be enough to replace one of the two springs by a transducer as shown in

Fig. 8. Following Figures 7 this transducer will not supply a signal if the centrifugal force acts

on the node of vibration (point no. 1). If acting on any other points (nos. 2 and 3) the forces

will produce a signal which is proportional to aF

⋅

. The displacement of the node of vibration

as a result of the force measuring system during vibrations can be neglected.

Seite 7 von 99

312

-a a

Fig. 8 Force measuring system with one virtual point of support

In Fig. 9 two of the systems illustrated in Fig. 8 are arranged in series at different distances

relative to the node of vibration. Consequently it is possible to establish a force measuring

system for measurement of unbalances in two virtual measuring planes. The two virtual

measuring planes are located in points L and R whereas the relative physical transducers are

marked L’ and R’.

R´

L´

Fig. 9 Two systems arranged in series with different virtual points of support

If for instance a centrifugal force acts on the left-hand node of vibration L, a signal

proportional to the magnitude of the centrifugal force is supplied from transducer L’, whereas

transducer R’ does not supply a signal. On the other hand only transducer R’ will supply a

signal when the centrifugal force acts on the right-hand node of vibration R. This arrangement

is indeed a measuring system as illustrated in Fig. 4 with an outboard rotor and with

correction planes being located between the measuring planes. If forces are applied between

points L and R, the bearing forces are divided in proportion to the relative distances to the

points of support.

Figures 10 to 12 show possible alternatives.

Seite 8 von 99

L´

R´

L R

Fig. 10 Two systems arranged one above the other with different virtual points of support

S´

M´

Fig. 11 Two systems arranged in series with a parallel pair of springs

Seite 9 von 99

S´

M´

Fig. 12 Two systems arranged one above the other with a parallel pair of springs

Seite 10 von 99

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