Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
DEVICE FOR REGULATING LINEAR MOTION
The invention relates to a de~ice for regulating linear motion of
a driven component part, particularly of a driven part of a machine
tool, along at least two correlated paths corresponding to axes X
and Y, whereby the motion along respective axes is performed by
separate drive units. ~he term "component part" in this context
is meant in quite a general sense, that is, the compenent part
can be for example an exactly guided tool such as a milling cutter
or a grinding disk or an accurately guided part of a measuring in-
O strument. Also, the term "axes" is to be interpreted in its broadestmeaning, which may denote both physical rotary axles arranged at an
angle one to another as well as orthogonal-coordinate axes or
axes correlated at another angle, along which a linear function of
the component part is generated.
In control technology a frequently occurring problem is how to
perform a linear function
Sy = M Sx (Equation 1)
along the axes x and y. In this equation it is assumed that the
x-axis is the master or leadi~g axis and the y-axis is the
O follower axis. In Equation 1, Sx denotes the track predetermined
by the master axis X and M ;is a real constant which is predeter-
mined by the displacement process to be made. The path along the
y-axis is to be regulated in position in such a manner tha~ the
Equation 1 is a]ways fulfilled.
~r,
5 ~
In practice, several proposals have already been made in order
to realize such a linear motion regulation by means of regulating
circuits. Such prior-art proposals, however, require very high
expenditures for the actual regulating circuit, whereby the regu-
lating process itself is inaccurate and too slow for practical use.
It is therefore a general object of the present invention to
overcome the above mentioned disadvantages.
More particularly, it is an object of the invention to provide
an improved device for regulating linear motions of the afore-
described kind which enables to achieve a high precision of theregulating process.
Another object of this invention is to provide such an improved
device which requires less circuit units and is less expensive
to manufacture.
In keeping with these objects and others which will become
apparent hereafter, one feature of the invention resides, in a
device of the aforedescribed kind, in a combination which com-
prises at least two drive units for displacing the component part
along respective x- and y-axes, one of the drives being a master
drive and the other a follower drive, mechanically coupled sensors
for generating timing signals corresponding to the actual displace-
ment of respective drive units, a counter coupled to the actual
displacement sensors to determine from the timing signals a regula-
ting difference signal of corresponding sign, a position regulator
connected between the counter and the drive units to regulate the
follower drives in response to movements of the master drive.
The substantial advantage of this invention resides in the fact
that the regulating difference is determined with correct sign by
means of a counter and a relatively simple hardware, so that the
regulating difference can be directly applied to the drive on the
guided axis.
The novel features which are considered characteristic for the
invention are set forth in particular in the appended claims. The
invention itself, however, both as to its construction and its
method of operation, together with additional objects and advantages
thereof, will be best understood from the following description of
specific embodiments when read in connection with the accompanying
drawing.
Fig. 1 is a block circuit diagram of the device of this inven-
tion generating a regulating difference value;
Fig. 2 is a time plot of two phase-shifted timing signals genera-
ted by the actual displacement sensors and a time plot of forward
and backward signals derived from the timing signals;
Fig. 3 is a block diagram of an exemplary application of the
device of this invention; and
Fig. 4 is another embodiment of the device of this invention
for regulating the linear movements of a component part along
a plurality of axes.
It is essential for this invention to determine the regulating
difference
Xd = M ~ S - S (Equation 2)
L
The determined regulating difference is directly applied to a
digital or via a D/A-converter to an analog position regulator
for regulating the linear movement along the follower y-axis, as
will be explained in detail below in connection with Figs. 1 and 3.
The circuit for determining the regulating difference is assembled
exclusively of electronic digital modules constructed by TTl and
CMOS technology.
Referring to Fig. 1, two timing pulses Ax, Bx and Ay, By are
applied to corresponding inputs of digital recovering circuits
1 and 2. The shape of the timing pulses A and s is illustrated
in thetime plot of Fig. 2. The two phase-shifted timing pulses
are delivered for example by incremental actual displacement
sensors which are mechanically coupled to the tracks or axes
X and Y. Specifically, an incremental actual displacement sensor
is assigned to the x-axis and the other sensor to the y-axis.
Each pair of phase-shifted timing pulses Ax, Bx and Ay, sy is
subjected to a digital recovery in the circuits 1 and 2. The
restoration or recovery in the modules 1 and 2 is made by a shift
register and corresponding auxiliary logic circuits, so that the
recovery time is determined by the iength of the shift register
and by the timing of the shifting operations. The modules for
performing these functions are integrated circuits of known con-
struction. The purpose of these integrating circuits is to elimin-
ate interfering impulses whose duration is smaller than the
recovery time. The recovery time also determines the minimum time
period between two flanks of the output pulses at the units 1 and 2.
.12~
The outputs of ~he units l and 2 are connected to corresponding
inputs of a device 3`for switching over fast/slow timing pulses.
By means of data selectors, the timing pulses at the master track
when a desired timing pulse ratio Mpl between the follower and
master axes is less then l, are fed to unit 4. ~he unit 4 serves
for generation of fast leading and trailing pulses, whereas the unit
5 serves for the generation of slow leading and trailing timing
pulses for the guided or follower track. When the desired timing
pulse ratio Mpl between the follower and master axes is greater than
l, then the leading and trailing timing pulses are applied by the
switching device 3 to the unit 5 for generating slow leading and
trailing pulses, whereas as mentioned before, when the ratio is less
than l, the timing pulses are switched over to the unit 4 for
generating fast leading and trailing pulses. The switchover from
fast to slow leading pulses is controlled by a control signal applied
to the device 3 via conduit 14. The output signal from the switchover
device 3 is applied to the units 4 and 5 via conduits As, Bs and
Al, Bl.
Units 4 and 5 contain monostable multivibrators which produce, in
dependence upon the rising and falling flanks of the restored two-
phase timing signals, the leading timing signals Vs, Vl and trailing
timing signals Rs~ ~l The shape of the leading and trailing
timing pulses V, R is also illustrated in Fig. 2.
The slow leading and trailing timing pulses Vl, Rl from the
output of unit 5 are applied directly to a switching module 8,
which switches over leading or trailing timing pulses. It will
be seen from Fig. l that the fast timing pulses Vs~ Rs are also
applied to ~he switchover module 8 via programmable dividers 6
and 7. Conduits 15, leading to control inputs of modules 4 and 5
--5--
~ ~Sl
for generating fast and slow leading and trailing pulses, feed
blocking pulses to respective modules 4 and 5 so that, in depen-
dence on the presence or absence of a signal in the ~onduit 15,
the generation of the fast or slow leading and trailing pulses
Vs~ Rs or V1, Rl is either released or suppressed.
The programmable dividers 6, 7 include cascaded digital modules,
preferably BCD- or binary dividers. A time multiplier Mp is con-
nected via conduit 17 to respective programmable dividers 6 and 7.
The number of digits of the applied pulse ~ultiplier Mp signal is
determined by the required aCcuracy and determine in turn the
number of cascaded modules. ~he pulse multiplying singal Mp must
be transferred in total. The sign must be applied separately from
the switchover of timing pulses Vf~ Rf~. The time pulse multi-
plier Mp is always less than or equal to 1. It is dimensioned such
that the aforementioned Equation 1 converts into the following
Equations 3 and 4, depending on the sign of the pulse multiplier.
(~PV = ~PR ) = + [Mpl PVx] + [Mpl x
(Equa~ion 3)
[M 2 ' ~PVy] ~ [Mp2 ~PRy] + (~PVX x
(Equation 4)
wherein
~PVX y = the su~ of all leading pulses for the x- or
y-axls
~PRX y = the sum of all trailing pulses for the x- or
y-axis
Mpl = the pulse multiplier following/~leading = desired
O timing pulse ratio between follower/master axis
(in total)
,-i Mp2 = MP2 = l/Mpl
--6--
[m] = the largest integer < m, or the smallest integer
> m, where m is an arbitrary real number which
is valid for both values and depends on the
preset pulse multiplier Mp and the sum of timing
pulses applied in the two programmable dividers.
The dividers also perform the rounding off of the
digits.
The above equation 3 is realized when the follower axis is the
faster one. According to the actual case, the pulse multiplier
applies to the programmable dividers is Mp = Mpl or = Mp2.
At the output of the programmable dividers, the leading and
trailing pulses VsM and RsM are delivered. The following
equations are valid:
?~PVSM = [Mp ~pvs] (Equation 5)
?~PRSM = [Mp ~P s] (Equation 6)
wherein
?~PA = the sum of all pulses of the timing signal A
[m]* = the greater integer < m, or the smallest
integer > m.
Which of the two values is applicable depends on
the preset Mp and on the sum of impulses applied
in the two dividers. The dividers make a corres-
ponding rounding off.
A data selector cooperates with the module 8 for switching over
leading/follower timing pulses. The data selector is controlled
by control signals from conduit 14, which is also applied to the
fast/slow switching module 3. The switchover is carried out such
that the timing pulses VsM, RSM from the output of the programmable
dividers 6, 7 and the pulses Vl, Rl from the output of the module 5
cause during the switchover the timing pulses of the leading axis to
reach the outputs Vf, Rf and the timing pulses of the follower axes
to reach the outputs Vg, R of the module 8. The subscript f means
leading, and the subscript g means guided.
The outputs Vf, Rf are connected to a module 10 for desynchronizing
and generating leading pulses, and the outputs Vg, Rg are connected
to a further module 11 for desynchronizing and generating follower
pulses. The modules 10 and 11 include D-flip-flops triggered by
flanks of the phase-shifted timing pulses Tl, T2 from a timing pulse
generator 9. In this manner, it is achieved that the alternation of
flanks at the outputs of the flip-flops, which are assigned to
different axes, do not occur simultaneously. A simultaneous change-
over of the flanks at the D-flip-flops pertaining to one axis is
prevented by the digital recovery process.
For the actual operation, the following conditions must be main-
tained: The duration of a period of a recovery cycle must be less
than 1/4 of the period of the incoming two-phase timing pulses at
their maximum frequency. The recovery time must be less than 1/2
of the period of the two-phase timing pulses at their maximum fre-
quency. The duration of timing pulses Vf, Rf and Vl, Rl must be
less than or equal to the minimum recovery time. The duration of
the period of the timing pulses Tl, T2 must be less than the dura-
tion of the timing pulses Vf, Rf and Vl, Rl. The duration of the
subsequently generated pulses Vf~, Rf~ and Vg~, Rg~ must be less
than the minimum time between the triggering flanks of timing
tZl ~
signals Tl and T2. The outputs of the D-flip-flops are connected
to a circuit which produces from the rising flanks a short low
pulse. In this manner, the timing pulses Vf~, Rf~ and Vg~, R
are generated.
The modules 10 and 11 for desynchronization are connected to a
further module 12 for the switchover of timing pulses, which in
turn is connected to a sign-pulse multiplier VZ by circuit 19.
The outputs V~, R~ of the timing pulse switch 12 are connected to
forward-backward counter 13, whose output delivers the regulating
difference signal xdy.
In response to the sign-pulse multiplier VZ, a switching network
performs a switchover according to a table given below and produces
thus the signals V~, R~.
TABLE
VZ V~ R~
r ¦ Rg~ A Vf~¦ Vg~ ~ Rf~ ¦
VZ = 1 neg. sign
1 Rg~ ~ Rf~ Vg~ ~ Vf~ VZ = 0 pos. sign
The input for fGrward counting of counter 13 is connected to the
signal V~, and the backward counting input is connected to the sig-
nal R~. The counting result ZE is in the form of a binary number.
In order to evaluate this counting result, two conditions (a) and
(b), which will be explained below, are to be distinguished. The
following equation is always applicable.
~f'~
ZE = ~PV~ - ~PR~ (Equation 7)
At VZ = 0 (positive sign), the following relationships apply:
=o = ~PRg~ + ~PVf~ - ~PVg~ - ~PRf~ =
( g~ - ~PVg~) + (~PVf~ - ~PRf~) =
5= (~PVf~ - ~PRf~ PVg~ - ~PRg~) (Equation 8)
At V2 = 1 (negative signj, the following relationship applies:
IVZ=1 = ~PRg~ + ~PRf~ - ~PVg~ - ~PVf~ =
= (~PRf~ - ~PVf~ PVg~ - ~PRg~) (Equation 9)
At this point, it is necessary to distinguish the aforementioned
two conditions:
Case (a):
If the leading axis is faster, then by combining Equations 8
and 9 with Equations 5 and 6, there results:
Z a¦Væ=0 ([ pl ~PVX][Mpl ~PRX]) - (~PVy - ~PR )
(Equation 10)
ZEalVZ=l ([ pl ~PRX][Mpl ~PVX]) - (~PVy - ~PR )
(Equation 11)
wherein in case (a)
Vx = Vs; R = R
Vy = Vl; Ry = Rl
From Equations 10 and 11, it is evident that in the counter an
approximate regulating difference in pulses is present with the
correct sign. The following consideration will show how accurately
the counting result corresponds to the real regulating difference.
--10--
L
Without rounding-off errors in the two dividers, the desired or
nominal value would be preset with the accuracy of + 1 pulse.
Assuming that each of the two dividers produces a maximum rounding-
off error of _ 1 (which in fact is smaller), then it follows that
the nominal value is preset with an accuracy of + 3 pulses. The
actual value is generated with an accuracy of + 1 pulse. Hence,
the following equation applies:
~ZE - 4) < xdyp < (ZEa (Equation A)
From the Equation A lt follows that in the case (a) the guided axis
or track can be positioned by a digital regulator with an accuracy
of + 4 pulses.
Case (b):
If the guided axis is faster, then by combining Equations 8 and
9 with Equations 5 and 6, there results:
15ZEb¦VZ=0 x x) ([Mp2 ~PVy] - [Mp2 ~PR ])
(Equation 12)
b¦VZ=l x x) ([Mp2 ~PVy] - [Mp2 ~PR ])
(Equation 13)
wherein in case (b)
Vx = Vl; R = R
V = V ; R = R
From Equations 12 and 13 it is evident that in this case the
counting result is not an approximately regulating difference in
pulses. By means of a consideration similar to that of the case
(a), it will be found that:
*) - *)
(LZE M 11 ~ 4 I MP11 ) ' Xdyp < (¦ZEb pll pl
(Equation B)
This means that in the case (b) the guided axis can be positioned
only with an accuracy of + 4 Mpl pulses, wherein MP1 ~ 1.
*)
lm~ = the largest integer < m
rm-l = the smallest interger > m
Since in case (b) the pulses of the guided axis are subdivided,
the regulating path of the y-axis undergoes a change which has to
be considered in the design of the regulator. The case (b) can be
obviated when the pulses pertaining to the guiding axis are suitably
multiply when Mpl < 1. Accordingly, the condition for the case ~a)
is created.
As mentioned before, at the output 21 of the rorward-backward
counter 13 a regulating difference xdy is delivered. A reverted
signal Clear xdy is fed back to the clear input of the counter 13
via couduit 20. For the sake of completeness it will be also men-
tioned that via conduit 16 a Clear signal is applied to the dividers
6 and 7, and the timing pulse generator 9 received input clock
pulses via conduit 18.
In Fig. 2, arrow 22 the range of leading or forward pulses and
array 23 denotes the range of trailing or backwards pulses.
Fig. 3 illustrates by way of an example the application of the
device of this invention. In this embodiment, there are employed
two D.C. drives M whose rotary movement is subject to linear
regulation of this invention. For this purpose there are provided
35 i
two incremental sensors 29, 30 which supply the regulating differ-
ence generator 28 with pulses Sx and Sy from which the regulating
difference is generated. The regulating difference generator 28 is
supplied at its input 31 with a pulse multiplying signal Mp to pro-
duce from the above pulses Sx and Sy the counting result ZE in the
manner as described in connection with the device of Fig. 1. The
counting result is applied to a digital position regulator 27 which
produces y-rotary speed nominal value nSOlly~ These y-rotary speed
desired or nominal values are then applied via a D/A-converter 26
to an analog y-rotary speed regulator 24. The desired x-rotary
speed values nSOllX of the guiding axis are supplied directly to an
analog x-rotary speed regulator 25, so that the nominal or desired
x-rotary speed values nSOllx determined rotary speed of both
direct-current electric motors M. The counting results correspond
to the aforedescribed equations 10-13. From Fig. 3 it is evident
that each of the rotary speed regulators 24 and 25 is provided
with a tacho generator G. It will also be noted that control
signals are applied to the regulating different generator 28 via
a conduit 32.
The present invention is not limited to the aforedescribed
embodiments and may also find a useful application in other
types of constructions differing from the types described above,
according to the desired field of application. In general, the
invention is applicable in all constructions where a linear
motion regulation between two axes is required, that is where a
differential can be created. The fields of application of this
invention are, for example, gear-cutting technology, grinding
~21~
technology, or gear measurement. Moreover, the invention is also
applicable to motion~regulation in measuring technology for pro-
viding correction values. The latter application is advantageous
for example in the case where, for the measuring purposes, the
axes are to be moved according to a linear function with such a
high accuracy which cannot be achieved by conventional regulating
means. By means of this invention, it is possible to determine
such a correction value which can be included in the computation
of the measured value. Furthermore, the invention is not limited
to the regulation of two axes, but it is suitable also for regulat-
ing a greater number of axes in dependence on a master axis, or
vice versa for regulating one axis in dependence on several axes.
Fig. 4 shows a block circuit diagram of another embodiment of
this invention, namely for a linear motion regulation of an axis
L5 in dependence on one to three axes. The overall circuit consists
essentially of four similar timing pulse multipliers 33 arranged
side-by=side. For the sake of simplicity only one of these devices
33 has been delimited by a dash-dot line. A summer 34 for generating
the regulating difference has its inputs connected to each of the
O timing pulse multipliers 31 and delivers at its output the reyulat-
ing difference xdl.
Each of the axes whose linear motion is to be regulated (total
of four axes in Fig. 4) cooperates with a non-illustrated incre-
mental actual displacement sensor which delivers respectively
two-phase timing pulses Al, Bl, A2, B2, A3, B3, A4, B4. These
pairs of phase-shifted pulses are processed in digital recovery units
35-38 to remove any interferences. Similarly as in the example
of Fig. 1, the digital recovery units 35-38 include shift regis-
ters and corresponding additional logic circuits. The digital
-14-
5:~.
recovery units 35-38 are supplied with restoring pulses TEl, TE2,
TE3 and TE4. The restored timing pulses at the output of each of
the units 35-38 are processed in units 39-42 into a leading or
forward pulses Vl to V4 and into trailing or backward pulses Rl
to R4. For this purpose, switchover or blocking pulses PSl, PS2,
PS3 and PS4 are applied to the control input of the switchover
units 39. The resulting forward pulses Vl to V4 and backward
pulses R1 to R4 are subsequently applied to the programmable
dividers 43-- 46 or 47-50 and are multiplied by pulse multipliers
Mpl to Mp4. The resulting subdivided timing pulses VMl to VM4 and
RMl to RM4 are applied to respective units or modules 51-54 where
the switchover of the sign of these pulses is performed.
The sign switchover is made as follows:
- sign pulse multiplier Vzx =
VAx = VMx
RAx = RMX
- sign pulse multiplier Vzx = 1:
VAx = RMX
RAx = VMx
Hence, the pulses VAx RAX are the time pulses Vx~ Rx multiplied
by Mpx and signed. At the control inputs of sign switches 51-54
are supplied with sign multiplifaction signals VZl to VZ4. The
programmable dividers 43-50 have their control inputs supplied
with multiplying signals Mpl and with clear signals CTl to CT4.
The forward or leading pulses VAl to VA4 and the backward or
trailing pulses RAl to RA4 at the outputs of sign switches 51-54
are applied to the common summer 34 where the sum or regulation
difference is generated. The summer 34 includes the module 55
for desynchronization and pulse generation, to which the outputs
of all timing pulse multipliers are connected. The incoming
timing pulses VAl to VA4 or RAl to RA4 are compared with eight
phast-shifted pulses To to T7 and unified into forward pulses
and backward pulses ~R. The forward pulses V and the backward
pulses R are supplied to counting inputs of a forward-backward
counter 59, the latter being also provided with a loading input
63 and a signal input 64 connected via a module 58 for an offset
addition to a module 56 for generating timing pulses. Reference
numberal 57 indicates an input for control pulses for the timing
pulse generator, and reference numerals 61 and 62 indicate, re-
spectively, inputs for an offset signal and a load signal applied
to the offset adder 58. The output ~f the counter 59 is connected
to a storage unit 60.
In counter 59, when disregarding the offset addition, the
following sum is generated:
S = _ pl 1] [Mpl~PRl]) + (Equation 14)
+ ( [Mp2 ~:PV2 ] - [Mp2 ~:PR2 ] )
+ ([Mp3~PV3] - [Mp3~PR3])
+ ([Mp4~PV4] - [Mp4~PR4]) +
-16-
In Equation 14
PVl PV2, PV3, PV4 are forward pulses for the four axes;
PRl, PR2, PR3, PP~4 are backward pulses for the four axes;
[m] denotes the largest integer < m or the smallest
integer ~ m; and
Mpl, Mp2, Mp3, Mp4 are pulse multipliers.
The timing pulse generator delivers 10 phase-shifted consecutive
pulses To~T9 and a regulating pulse T4' which in a subsequent digi-
tal regulator can serve as a sensing pulse.
By means of the offset addition in module 58 it is made possible
to add to the computation result of the counter an offset without
losing pulses; in this manner a relative position regulation on
the guided drive is performed. The loading of the result of the
addition is executed by the pulse Tg.
The device according to this embodiment of the invention enables
to regulate an axis in dependence on the three additional axes
according to the equations:
Sl = M2S2 (Equation 15)
Sl = M2S2 + M3 3 (Equation 16)
Sl = M2S2 + M3S3 + M4S4 (Equation 17)
S2, S3 and S4 are displacements predetermined for three of the
axes. M2, M3 and M4 are real constants determined by the particu-
lar motion to be regulated.
In counter 59 a regulating difference xdl according to Equation
14 is determined, whereby the pulse multiplier M < 1 is selected
such that one of Equations 15, 16 or 17 is fulfilled. This regu-
lating difference xdl can be applied directly to a digital posi-
tion regulator for the axis in question.
While the invention has been illustrated and described as em-
bodied in specific examples of linear motion regulators, it is
not intended to be limited to the details shown, since various
modifications and structural changes may be made without departing
in any way from the spirit of the present invention.
Without further analysis, the foregoing will so fully reveal
the gist of the present invention that others can, by applying
current knowledge, readily adapt it for various applications
without omitting features that, from the standpoint of prior
art, fairly constitute essential characteristics of the generic
or specific aspects of this invention.
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