Hofmann Snap-on Y2k User manual

SERVICE
of the Y2k balancing platform
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The vibratory assemblies of the Y2k balancing platform
L´
R´
L R
S´
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.
c
L
b
a
R
-L
RR
U
UR
UR
L
U
Fig. 1 Illustration of the effect of force relations at an increasing distance (a+b)
Following the condition
0=
∑Moments
the measured value Lis
()
cbaUaU
LRL +
⋅
+⋅
=
or
()
cbaU
LR+⋅
=, if .0=
L
U
Analogously the measured value Ris
() ( )
ccbaUcaU
RRL
+
+⋅++⋅
−=
or
()
ccbaU
RR++⋅
−= , if 0=
L
U
Following the condition
0=
∑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
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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.
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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.
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312
-a a
F
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’.
LR
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.
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L´
R´
L R
Fig. 10 Two systems arranged one above the other with different virtual points of support
S´
S
M´
Fig. 11 Two systems arranged in series with a parallel pair of springs
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S´
S
M´
Fig. 12 Two systems arranged one above the other with a parallel pair of springs
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