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Helixyn position control
Helixyn Position Control D. J. MYNALL Introduction Helixyn is the name given to an electromechanical transducer which, while applicable to precise linear measurement and control in general, was developed in the first place particularly for automatic positioning of machine tool movements from numerical input data. An integral part of Helixyn position control systems is the digital-analogue converter which is used to translate the numerical input into related voltages required by the Helixyn. The purpose of this paper is to describe the particular Helixyn and digital-analogue converter types which have received intensive development and to outline the manner in which their combination may be used in complete systems for machine tool control, both for static positioning and for continuous, coordinated, simultaneous control of several movements. The order of accuracy of the control system itself, i.e. its possible contribution to overall error in the end-product, considered separately from machine tool and servo imperfections, is 0'0001 in. (0'0025 mm). The Helixyn has the same field of application as the Farrand Linear Inductosyn and bears a superficial resemblance to the Canadian Westinghouse NuItrax; its differences from these two devices are noted later. Helixyn Description Leading dimensions-The Helixyn comprises a cylindrical bar 1·75 in. (4'5 cm) in diameter, at present made in lengths up to 50 in. (130 cm), and a short cylindrical sleeve 4 in. (10 cm) long, which moves co-axially along the bar but not in contact with it. The radial clearance between the members is 0·030 in. (0'75 mm). The lengths given above are those which are electrically effective, and do not include provision for mounting. The two parts are mounted on the machine tool for direct pickup of the relative linear movement which is to be controlled. Sleeve-The essential part of the sleeve is a tube of bonded fibreglass of about 0'1 in. (2'5 mm) radial thickness which is copper plated to a thickness of 0'0005 in. (0'013 mm). The inside surface of the sleeve has four helical grooves of the same hand cut through the metal film, from end to end of the sleeve, by means of a thin grinding wheel. The grooves are uniformly interlaced in the same pattern as a four-start thread. The grinding wheel leaves gaps of about 0·005 in. (0' 13 mm) between metal-plated lands of about 0·020 in. (0'5 mm) width, measured in the axial direction. The axial lead of the system, i.e. the pitch of anyone of the helices, is accurately 0·1024 in. (2'6 mm). The plating on the end surfaces of the sleeve is divided so as to leave the four metal helices insulated from each other and from the plating on the outside of the sleeve. The remaining portions of the end plating serve as means for making connections to the helices and to the outer screen. Bar-The bar consists basically of a cylindrical steel tube on the outside surface of which a tube of fibreglass insulation is firmly bonded. The insulation is of about 0'1 in. (2'5 mm) radial thickness, as in the sleeve, and is copper plated in the
same way. Helical grooves are also ground through the plating, with the same lead and hand as those on the sleeve and leaving the same width of conductor (measured axially) but with the following difference: three (not four) helices are interlaced uniformly in the fashion of a three-start thread. It follows that the gaps between conductors are somewhat wider than those on the sleeve, being about 0·013 in. (0'33 mm).
Operation Electrostatic coupling is used between sleeve and bar. Alternating or impulsive voItages (all of the same form but, in general, of different magnitudes and/or sign) are applied to the four helices on the sleeve. Either a.c. of frequency 10 kc/s or pulses of 50 to 100 [LS duration are used for excitation. The system is not critical with regard either to frequency or waveform. If the helices are numbered 1-4 in sequence along the sleeve then the voItages applied to them are proportional to cos 8, sin 8, - cos 8 and - sin 8, respectively, 8 being determined by and proportional to a digital input (by means described under the heading Digital-analogue Converter). A range of 27T radians in 8 exhausts all possible distinct inputs, and corresponds to a relative movement of sleeve and bar, equal to the lead of the HeIixyn. The system is thus cyclic in its action in the same way as a conventional synchro. The type of electrostatic field set up in the air gap is shown diagrammatically in Figure 1(a-c) for three particular values of8. 3
2
3
2
4
4
a
(a)
c
A
2
1
(b)
A
C
B
2
4
3
8 4
3
7[fl~f C
A
C
8
A
1234
6
Figure 1.
A
4
234
a
c
"TT
8
(c) 8
0
B
c
TT
2
A
Cross-sections of air-gap field
The diagrams represent cross-sections of part of the conductor system by a plane which contains the axis of the system, and are to be considered as 'snapshots' taken at any instant when the field is finite, irrespective of how the voItages are varying. Helices on the bar have been lettered A, Band e, and have been assumed held at zero potential. Further, A and B have been placed in each diagram so as to pick up equal f1uxes. ] t
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follows that if A and B are freed from ground they will develop equal voitages and that the difference voltage between them will be zero; it is this difference voltage which is taken as the output from the Helixyn and used to sense positions indicated by B, and, hence, by the numerical input. If the axial displacement of the bar relative to the sleeve is represented by cp, where cp is zero in Figure l(a) and increases to 217 as the bar moves through one space-cycle (Helixyn lead) to the right, then it is clear, from conditions of symmetrY, that cp = B when B is a multiple of 17/4. Moreover, when B is not a multiple of 17/4, cp is at least approximately equal to B; therefore, to some determinable level of accuracy, we may say that cp = B -in other words, the voltage null positions indicate displacements directly proportional to the numerical input. Another series of voltage nulls is obtained when cp = B+17; these are equally usable, but lead to no ambiguity when the Helixyn is part of a position-finding servo system, since one set only will give stable settings.
Basic systematic error The approximation, rather than equality, of cp to B when B is not a multiple of 17/4 gives a positioning error which exists even for a perfectly constructed Helixyn. The design must, therefore, be such that this error is acceptably small. Space forbids full description of the pertinent theory, but the line of attack may be indicated as follows. If we start by expressing the voltage induced on A by the voltage on 1 as e.cos B[ao+
n~1 an cos n(cp-17/3)]
(e, ao, an constant), as we may, because this voltage must be an even function of cp-17/3, it is then possible without introducing further constants to write down similar Fourier series for the voltages induced on A by 2, 3 and 4. These series may be added to give the resultant voltage induced on A. The same thing can be done for the voltage induced on B, and the difference between these results gives a Fourier series which, when equated to zero, relates Band cp when the output voltage is nulled. Using the fact that cp is known to be nearly equal to B, it is possible to derive the closely approximate explicit result cp
= B-~[assin48-a7sin88-(al!-au)sin 128- ... ] al
realization of the design; these set the allowable tolerances in manufacture to the required order of accuracy of performance.
Cyclic errors due to departure from design Most significant sources of cyclic error-In an actual Helixyn, cyclic positioning errors might result from the separation between centre-lines of conductors being incorrect (conductor spacing error) or the widths of conductors being incorrect (conductor width error). From a theoretical analysis, it emerges that the two effects described below are the most significant, because it would be uneconomic or impracticable to insist on manufacturing tolerances fine enough to render them negligible. (a) Spacing error of sleeve conductors so that the effective centre of the 1,3 pair is not 17/2 from the 2,4 pair (nonorthogonality). The error in cp is ex cos 28, where 2ex is the departure from orthogonality. (b) Total width of the 1,3 pair of sleeve conductors being different from the total width of the 2, 4 pair (interchannel unbalance). The error in cp is f1 sin 28, where 2f1 is the fractional unbalance between channels. The recognition of these effects in test results is simple, since there is no other source contributing appreciable second harmonic to the cyclic error. In addition, they can be distinguished one from the other by their respective cosine and sine forms. Elimination of second harmonic cyclic error-Second harmonic components in the cyclic error curve are reduced to zero by using pre-set trimming potentiometers in conjunction with a pair of transformers in the supply circuit to the sleeve, as shown in Figure 2. The trimmers are marked on the diagram to correspond with the effects, listed above, for which they compensate.
cos~lne
channel
In[~:
(1)
Examination of the working shows that ao vanishes from this result because a voltage difference is taken between A and B, all coefficients with even subscripts vanish because of the arrangement and method of excitation of the sleeve, and all coefficients with subscript 3m (m = 1, 2, 3 ... ) vanish because helices A and B are spaced by 217/3 radians. It is sufficient for the present purpose to determine, from the nature of the electrostatic field, a limit to the values which lan/all may attain. Again, only the result may be quoted: this is, under justifiable simplifying assumptions which hold in the region of interest,
(217 d/L) lanl < 2sinhsinh(217n d/L) al
(2)
where d/ L is the ratio of the gap between bar and sleeve to the helical lead of the conductors. In the present instance, las/a.j < 0'0012, la7/a.j < 0'00003, and so on. The peak error arising from as cannot, therefore, exceed 0'0012.0'1024/217 in. = 20 fL in. (0'5 fL), and the other terms are negligible. It remains to examine possible errors due to imperfect
Figure 2.
Trimmer (a) introduces compensating non-orthogonality (cross-feed from the sine to the cosine channel) into the supply to the sleeve, and trimmer (b) alters the gain of the cosine channel relative to the sine channel to give compensating unbalance. The required sense of connection of the trimmer windings and the settings of the trimmers are determined by a systematic test procedure and the settings then sealed. The adjusted transformers and the sleeve are henceforth regarded as a unit, the parts of which are not to be separated.
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Use of relative rotation of sleeve and bar Cam correction-Measurable cumulative error will generally be present in the pattern of a long Helixyn bar. When the utmost precision is desired, cancellation of this cumulative error is achieved by mounting the Helixyn sleeve so that it is rotatable about its axis through a limited angle, this rotation being controlled by a radius arm moving in contact with a longitudinal cam which is fixed with respect to the mounting of the bar. Due to the helical pattern of the conductors, a rotation of 0·36° is equivalent to an axial movement of 0'0001 in. (0'0025 mm). The magnification between axial movement and change of cam profile is, for example, 125 times at 2 in. (5 cm) radius. Cam correction may also be used to compensate for certain types of systematic error in the machine which the Helixyn controls.
Temperature coefficient of bar The bar has the same coefficient of expansion with temperature as the steel tube which forms its structural basis, as nearly as could be measured, that is, 10 x 10- 6 per 0c. Performance It has been found on test that the Helixyn behaves as would be expected from theory, and it has been possible to devise a technique for manufacture which gives residual cyclic errors less than ±0'0001 in. (0'0025 mm). The second harmonic error trims need no attention other than initial alignment. At the time of writing, Helixyns have been installed on a machine tool in a laboratory test for about a year and have given no trouble apart from one open-circuited end connection. Experience gained so far indicates that settings are stable and repeatable.
Fine datum setting-In order to make an arbitrarily chosen longitudinal position of bar and sleeve correspond to a particular value of 8, the bar may be made rotatable about its axis. Provision for rotation through slightly more than one revolution is sufficient.
Digital-analogue Converter General description-The function of the digital-analogue converter is to provide the voltages required to excite the Helixyn sleeve. The voltages are variable in amplitude under control of a numerical input set up on switches or relays. It is important that the ratio of the two voltages be closely approximate to tan (8+ E), where (J is an angle which is proportional to the numerical input, and E is a constant (which may be zero). It is less important that the individual voltages be separately closely proportional to sin (8+ E) and cos (8+ E) respectively. A range of 21T radians in 8 must correspond to the axial lead of the Helixyn conductors, and intermediate positions in this range must be defined by the numerical input to about onethousandth part of this range. The essential part of the digital-analogue converter consists of a relatively low-impedance resistive network which is switched in accordance with the numerical input to develop the required voltages when supplied with an a.c. or impulsive electrical input. In part of the network the switching of the circuit is arranged to effect a variation of resistances which is linear with respect to the numerical input, the required development of a tangent ratio being obtained by the way in which the linearly varying resistors are connected in the network. Basic circuit-To appreciate how the required ratios are produced it is helpful first to consider the basic circuit shown in Figure 3, and then to consider how the circuit may be economically switched to give the desired result. With the values marked in the diagram it is easy to show that x Es/Ec = 1+(I-x)(0'26823+0'29443x)
Electrical parameters Inter-electrode capacitances- From the circuit aspect, the Helixyn is a multi-electrode variable capacitor. When used as described, the number of distinct electrodes is seven (counting the screen on the sleeve, the steel tube in the bar and conductor C as one electrode, since all these are connected to ground). The number of direct capacitances between these seven electrodes is 21, and academically they should all be considered to vary with
Sleeve conductor to ground Between adjacent sleeve conductors Between non-adjacent sleeve conductors Bar conductor to ground Between bar conductors Sleeve conductor to bar conductor
75 160 75 50 per in. (20 per cm) 33 per in. (13 per cm) 15+ 14 cos oft
l where'" radians is the axial displacement of a particular pair of electrodes)
Input and output capacitances-From the capacitances listed above, it may be deduced that a round value for the capacitance load of the sleeve presented to the full secondary winding of each input transformer (Figure 2) is 300 fLfLF. The null voltage is taken from the bar via a 1: 1 ratio transformer with a floating primary winding. The output capacitance through which the open-circuit null voltage is effectively applied to the output transformer is (30+ 78K) fLfLF, where K is the length of the bar in in. or (30+31k) fLfLF, where k is the length of the bar in cm.
and, further, by direct calculation, to plot the difference
, I
Basic conversion circuit:
..---.._ _
Inverse voltage transfer and sensitivity-Again from the capacitances listed, it may be deduced that the ratio
-nl~
,------'_--<>-'
liE
power] 11 input
Maxim.um voltage input per channel is 2'5 + 4.8K or 2·5 + 1'9k MaXImum o.c. voltage from bar ' and that the maximum input voltage per channel required to give 1 mY o.c. voltage output for 0·0001 in. (0'0025 mm) misalignment from null is 0'4+0'79K or 0·4+0·31k.
091101 R .n.
Figure 3.
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Basic circuit 01 digital-analogue converter
HELIXYN POSmON CONTROL
tan- 1 (Es/Ec) - (7T/4)x against x. With the circuit proportions given in Figure 3, the difference between tan- 1 (Es/Ec) and (7T/4)x is extremely small, so that if Es and Ec are used as excitation voltages for the Helixyn sleeve, the axial field shift with x will be closely proportional to x. For a 0·1024 in. (2·6 mm) Helixyn lead the peak errors due to the approximation are within ± 4 fJ.in. (± 0·1 fJ.). There are considerable variants of the circuit of Figure 3, this circuit being the latest product of an extensive search for simple circuits in which the trigonometric ratio required is sufficiently approximated by a rational algebraic function of the input number--circuit elements themselves varying linearly with that number. It is shown in a later subsection how x may be varied under control of a numerical input and how the range zero to 7T/4 radians in the space-phase output can be extended to cover the complete space-cycle of 27T radians. Source resistance for constant sensitivity-When the circuit of Figure 3 is supplied from a voltage source the value of (Ec 2 + El)! rises as x varies from 0 to 1. On the other hand, when the supply is a current source there is a variation in the reverse direction. In some applications, Ec and Es are required individually to be approximate to cos 8 and sin 8, respectively, in addition to having the correct ratio. When this is so, there should be no variation of (E/+ El)! with x, and this condition can be approximated by supplying the network with an actual or effective source resistance of value 3·49682R n: this keeps the variation of (Ec 2 + Es2)t within ± 2 per cent of the mean value. Numerically variable potentiometer-The most economical switching is obtained if the space-cycle (Helixyn lead) is divided into a number of equal parts which is a power of 2, and successive parts are numbered in the cyclic progressive binary code (Gray code). Figure 4 shows a particular example of this
Switch positions correspond
pow~
InPu:J
,, ,I
I
I
I
I
6
4
3 21
116·61
I
433· 74 (Resistor values in .0.)
Figure 4.
Digital- analogue converter for c.P. binary code
switching which is used in Helixyn control. Here, R has been chosen equal to 128 n and the cycle has been divided into 1,024 (= 210) distinct steps, requiring 10 binary digits to specify a particular position. The switches are numbered from 0 to 9 to correspond with the significance of digits of the input code, o being the least significant and 9 the most significant. Space does not permit listing all the 1,024 different settings, but it may easily be verified that a c.p. binary input number N(O ,,;; N ,,;; 1,023) will present voltages Ec and Es to the Helixyn sleeve which correspond in sign and relative magnitude to a spacephase angle of (N + O· 5)/ 1,024 27T radians. Because tht Helixyn lead is 0·1024 in. (2·6 mm) and this distance is divided into 1,024 steps, it is clear that the least digital steps in N correspond exactly to 0·0001 in. (approximately 0·0025 mm).
In practice, the 0·5 n resistors are reduced in value to allow for the finite contact resistance of the switch or relay contacts. A circuit (not shown) similar to Figure 4, but somewhat less economical in components, may be used when it is required to accept a pure binary input. Performance-In practice, it has appeared that these circuits give the desired performance and are stable, no adjustment having yet been called for after initial trimming of the precision resistors to correct value. Excitation of conventional synchros-It is practicable to excite conventional resolver synchros from the digital-analogue converter circuit of Figure 3, provided that step-down transformers are used in order to avoid destroying the accuracy of the network. The step-down ratio will vary according to the design of the synchro, but may be of the order of 40: 1. Null voltage sensitivities of the same order as those obtained from a Helixyn supplied through 1: 1 transformers are still obtainable under these conditions. Conventional synchros supplied in this manner may be used for coarse positioning, as described below. Helixyn Positioning Systems General-The 0·1024 in. (2·6 mm) lead of the Helixyn was chosen to allow binary operation of the digital-analogue converter, as this permits use of the simpler types of converter and also results in economy in digital computing circuits which may be called for where the input data has to undergo arithmetical modification before actuating the digital-analogue converter. The way in which the binary input is automatically derived from the decimal form in which it normally occurs, and other features of complete Helixyn positioning systems, are briefly described below. Coordinate setting-For static positioning over ranges of movement much greater than one Helixyn space-cycle, coarse positioning and intermediate positioning resolver synchros, geared together and effectively geared to the Helixyn, are used in the earlier part of the positioning sequence to bring the movement within non-ambiguous range of the Helixyn system. The synchros and the Helixyn belonging to a particular coordinate all receive information in turn from a single digital-analogue converter. This converter is supplied with pure binary information from a shifting register to which it is permanently connected at the more significant end. The shifting register is initially set up to contain the binary equivalent (in units of 0·0001 in.) of the complete decimal input which defines the desired position. The coarse synchro takes information from the more significant digits of the binary number, through the digital-analogue converter, and operates a servo system to bring the movement within non-ambiguous range of the intermediate synchro. When the misalignment is within pre-determined limits, control is automatically transferred to the intermediate synchro and the digits appropriate to its range of action are moved in the shift register so that they become the input to the digital-analogue converter. When the intermediate synchro brings the misalignment within non-ambiguous range of the Helixyn, a similar shift of control takes place and final positioning is achieved by the Helixyn. Prior to the above action the required initial binary content of the shift register has been set up by shifting binary coded decimal digits of the input number into the register one by one, the most significant digit first. Each time a digit is shifted into the register the contents of the register (if any) are moved out, multiplied by ten in a simple serial computing circuit and added
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to the incoming binary cOded decimal digit; this builds up the required binary equivalent of the decimal input. The successive binary coded decimal digits of the input may be provided manually from a keyboard or read in automatically from a punched paper tape. The system is economical in components because the shifting register and its associated circuits are used over and over again in sequence, and are also used for two distinct purposes, namely, decimal to binary conversion and effective switching of different parts of the number to the digital-analogue converter. In this application the converter is supplied with 10 kc/s a.c. excitation.
Continuous, coordinated control-In continuous control, coarse and intermediate positioning is not needed, since each movement remains continuously under non-ambiguous direction from its associated Helixyn. The system which has been developed uses sampled position information in each of three coordinates. The position samples are derived from the drawing data by automatic digital computing, the description of which is outside the scope of this paper. No decimal to binary conversion problem exists in the position control system, because this conversion takes place in the process of computing the position samples. At present the sampling period in anyone of the coordinates is 16 mS, which is adequate for present needs but may be raised in the future. The sampling epochs for the different coordinates are interlaced in time-division multiplex and are recorded in binary notation on tin. (6 mm) wide magnetic tape, together with synchronizing and checking data. The tape also carries digital information which may be used to modify the position samples (during control) to allow the use of a cutter which is not to nominal diameter, or may be used to take a roughing cut with allowance for finishing. In addition, the tape carries miscellaneous information to allow automatic control of servo power, locking of machine movements, etc. All the information is carried on four parallel tracks and the tape is read at 7'5 in./sec (19 cm/sec). In the circuits which handle the information read from the tape, considerable economy is possible because the signals are in time-division multiplex. A single digital-analogue converter handles information for all three coordinates, actually in sequence but effectively continuously. Similarly, a single computing circuit effects tool diameter correction for the two coordinates which are involved. Impulsive sampling of position misalignment is used, taking advantage of the wide-band characteristics of the Helixyns and the common digital-analogue converter. A valuable feature of the synchro-like nature of Helixyn control is that it cannot accumulate error. Occasional in-
correct position samples may occur, due to magnetic tape dropouts or drop-ins, but these will, in general, have no sensible effect on the finished product. Advantage is taken of this feature to arrange that automatic digital checking circuits do not direct the equipment to shut down unless fault indications occur with significant frequency.
Performance-The coordinate setting system described has not yet been applied to a machine tool, but laboratory equipment has shown the system to operate and to give extremely stable and repeatable positioning to the expected order of accuracy. The continuous control system is being used for three coordinate control of a vertical-spindle milling machine, in the laboratory, and will shortly be put into use under factory conditions. The control system has been shown to work as described. Precise absolute accuracy tests are not yet completed, but good surface finish and repeatability have been shown from the outset. Devices Related to the Helixyn Linear Inductosyn-The Linear Inductosyn of Farrand Controls, Inc. is similar to the Helixyn in that a slider is excited by a pair of currents, just as the Helixyn sleeve is excited by a pair of voltages, and a null voltage is taken from an assembly of scales corresponding to the Helixyn bar. Magnetic coupling is used. However, it is somewhat less economical to supply precisely controlled currents than similarly controlled voltages and the rotary feature of the Helixyn, of use in fine datum setting and cam correction, is not present. The space cycle of the Inductosyn is 0·1 in., and it would not suit the position control systems described earlier. Nultrax-The Nultrax of Canadian Westinghouse Co., Ltd., is superficially similar to the Helixyn in that it has cylindrical bar and sleeve elements bearing helical conductors. Coupling is magnetic. There is, however, no real similarity to the Helixyn in use, since the Nultrax bar and sleeve must be rotated with respect to each other to obtain fine position setting, and this involves the provision of a subservo to convert the numerical input to a corresponding rotation. The author gratefully acknowledges the work done by his colleagues in helping to develop Helixyn control from an idea to practical realization. Thanks are also due to the Board of Directors of the British Thomson-Houston Co., Ltd., and the Executive of the Associated Electrical Industries Limited, Electronic Apparatus Division, for permission to publish this paper.
Summary
Helixyn is the name given to a position-measuring element which has been developed for automatic positioning of machine tool movements from numerical input data. The order of accuracy of the device is 0·0001 in. (0'0025 mm), including conversion of input data from numerical form. The measuring unit comprises a cylindrical bar, somewhat longer than the distance over which control is required, and a short cylindrical sleeve which moves along the bar but not in contact with it. The two parts are mounted on the machine tool so as to pick up directly the relative movement which is to be controlled. In the form on which development has been concentrated, the sleeve consists basically of a tube of insulating material, the inside surface of which supports four distinct helical conducting paths which
are disposed with equal axial spacing so as to form a regular interlaced pattern. The bar consists of three interlaced helical conducting paths carried on a layer of insulation bonded firmly to a steel tube. The lead of the helices on the bar is the same as that on the sleeve, and the design is such that the variation of capacitance between each sleeve conductor and each bar conductor is closely sinusoidal when plotted against relative axial movement. The sleeve conductors are supplied with a.c. or impulsive voltages of relative sign and magnitude set by a relay-switched resistor network. The numerical input controls the switching in such a way that the electrostatic field between sleeve and bar remains substantially constant in form but takes up an axial position relative to the sleeve bearing a linear relation to the numerical input.
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HELIXYN POSITION CONTROL
Sommaire Helixyn est le nom donne a un element de mesure de position, qui a ete etudie pour le positionnement automatique des mouvements de machines-outils, en partant de donnees d'entn:e numeriques. L'ordre de grandeur de la precision du dispositif est de 0,0025 mm, y compris la conversion des donnees d'entree a partir de leur forme numerique. L'element de mesure comprend un barreau cylindrique un peu plus long que la distance sur laquelle la commande est desiree, et un court manchon a glissiere, qui se deplace le long du barreau, mais sans contact avec lui. Les deux pieces sont montees sur la machine outil, de fac;on a detecter directement le mouvement relatif qui doit ctre controle. Dans la forme sous laquelle l'application a ete faite, le manchon consiste en principe en un tube de materiau isolant, dont la surface interieure supporte quatre trajectoires helicoid ales conductrices, qui sont disposees avec un espacement axial egal, de fa90n a former un
modele regulierement entrelace. Le barreau consiste en trois trajectoires conductrices helicoldales entrelacees supportees par une couche d'isolant solidement collee sur un tube d'acier. Le pas des helices sur le barreau est le mcme que celui des helices sur le manchon et la forme est telle que la variation de capacitance entre chaque conducteur du manchon et chaque conducteur du barreau est tres exactement sinusoldale en fonction du mouvement axial relatif. Les conducteurs du manchon sont alimentes avec des tensions alternatives ou impulsionnelles, dont les signes et amplitudes relatifs sont regles par un reseau de resistances commutees par relais. Les entrees numeriques controlent la commutation de telle fac;on que le champ electrostatique entre manchon et barreau reste de forme sensiblement constante mais prenne une position axiale par rapport au manchon qui soit en relation lineaire avec l'entree numerique.
Zusammenfassung , Helixyn' ist ein Me13glied zur Lageregelung an Werkzeugmaschinen mit numerischer Eingabe. Die Genauigkeit des Gerates liegt in der Grol3enordnung von 0,0025 mm, einschliel3lich Umwandlung der numerischen Eingabewerte. Das Me13glied besteht aus einer zylindrischen Stange, die etwas langer ist als der Einstellbereich, sowie einer kurzen zylindrischen Buchse, die sich entIang der Stange bewegt, diese aber nicht beriihrt. Die beiden Teile erfassen die zu regelnde Relativbewegung. Der Buchsenkorper aus Isolierstoff tragt an der Oberfiache der
II-A.R.e.4
Bohrung vier isolierte und in gleichem axialen Abstand angeordnete spiralformige Leiter. Die Stange tragt eine Isolierschicht, in die drei ineinander gewickelte spiralformige Leiter eingebettet sind. Die Kapazitatsanderungen zwischen jeder Leiterspirale in der Buchse und jedem Leiter auf der Stange verlaufen weitgehend sinusformig. Die Spiralleiter in der Buchse werden mit Impuls- oder reinen Wechselspannungen gespeist. Die Impu)sspannungen werden von einem relaisgesteuerten Netzwerk geliefert.
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same way. Helical grooves are also ground through the plating, with the same lead and hand as those on the sleeve and leaving the same width of conductor (measured axially) but with the following difference: three (not four) helices are interlaced uniformly in the fashion of a three-start thread. It follows that the gaps between conductors are somewhat wider than those on the sleeve, being about 0·013 in. (0'33 mm).
Operation Electrostatic coupling is used between sleeve and bar. Alternating or impulsive voItages (all of the same form but, in general, of different magnitudes and/or sign) are applied to the four helices on the sleeve. Either a.c. of frequency 10 kc/s or pulses of 50 to 100 [LS duration are used for excitation. The system is not critical with regard either to frequency or waveform. If the helices are numbered 1-4 in sequence along the sleeve then the voItages applied to them are proportional to cos 8, sin 8, - cos 8 and - sin 8, respectively, 8 being determined by and proportional to a digital input (by means described under the heading Digital-analogue Converter). A range of 27T radians in 8 exhausts all possible distinct inputs, and corresponds to a relative movement of sleeve and bar, equal to the lead of the HeIixyn. The system is thus cyclic in its action in the same way as a conventional synchro. The type of electrostatic field set up in the air gap is shown diagrammatically in Figure 1(a-c) for three particular values of8. 3
2
3
2
4
4
a
(a)
c
A
2
1
(b)
A
C
B
2
4
3
8 4
3
7[fl~f C
A
C
8
A
1234
6
Figure 1.
A
4
234
a
c
"TT
8
(c) 8
0
B
c
TT
2
A
Cross-sections of air-gap field
The diagrams represent cross-sections of part of the conductor system by a plane which contains the axis of the system, and are to be considered as 'snapshots' taken at any instant when the field is finite, irrespective of how the voItages are varying. Helices on the bar have been lettered A, Band e, and have been assumed held at zero potential. Further, A and B have been placed in each diagram so as to pick up equal f1uxes. ] t
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follows that if A and B are freed from ground they will develop equal voitages and that the difference voltage between them will be zero; it is this difference voltage which is taken as the output from the Helixyn and used to sense positions indicated by B, and, hence, by the numerical input. If the axial displacement of the bar relative to the sleeve is represented by cp, where cp is zero in Figure l(a) and increases to 217 as the bar moves through one space-cycle (Helixyn lead) to the right, then it is clear, from conditions of symmetrY, that cp = B when B is a multiple of 17/4. Moreover, when B is not a multiple of 17/4, cp is at least approximately equal to B; therefore, to some determinable level of accuracy, we may say that cp = B -in other words, the voltage null positions indicate displacements directly proportional to the numerical input. Another series of voltage nulls is obtained when cp = B+17; these are equally usable, but lead to no ambiguity when the Helixyn is part of a position-finding servo system, since one set only will give stable settings.
Basic systematic error The approximation, rather than equality, of cp to B when B is not a multiple of 17/4 gives a positioning error which exists even for a perfectly constructed Helixyn. The design must, therefore, be such that this error is acceptably small. Space forbids full description of the pertinent theory, but the line of attack may be indicated as follows. If we start by expressing the voltage induced on A by the voltage on 1 as e.cos B[ao+
n~1 an cos n(cp-17/3)]
(e, ao, an constant), as we may, because this voltage must be an even function of cp-17/3, it is then possible without introducing further constants to write down similar Fourier series for the voltages induced on A by 2, 3 and 4. These series may be added to give the resultant voltage induced on A. The same thing can be done for the voltage induced on B, and the difference between these results gives a Fourier series which, when equated to zero, relates Band cp when the output voltage is nulled. Using the fact that cp is known to be nearly equal to B, it is possible to derive the closely approximate explicit result cp
= B-~[assin48-a7sin88-(al!-au)sin 128- ... ] al
realization of the design; these set the allowable tolerances in manufacture to the required order of accuracy of performance.
Cyclic errors due to departure from design Most significant sources of cyclic error-In an actual Helixyn, cyclic positioning errors might result from the separation between centre-lines of conductors being incorrect (conductor spacing error) or the widths of conductors being incorrect (conductor width error). From a theoretical analysis, it emerges that the two effects described below are the most significant, because it would be uneconomic or impracticable to insist on manufacturing tolerances fine enough to render them negligible. (a) Spacing error of sleeve conductors so that the effective centre of the 1,3 pair is not 17/2 from the 2,4 pair (nonorthogonality). The error in cp is ex cos 28, where 2ex is the departure from orthogonality. (b) Total width of the 1,3 pair of sleeve conductors being different from the total width of the 2, 4 pair (interchannel unbalance). The error in cp is f1 sin 28, where 2f1 is the fractional unbalance between channels. The recognition of these effects in test results is simple, since there is no other source contributing appreciable second harmonic to the cyclic error. In addition, they can be distinguished one from the other by their respective cosine and sine forms. Elimination of second harmonic cyclic error-Second harmonic components in the cyclic error curve are reduced to zero by using pre-set trimming potentiometers in conjunction with a pair of transformers in the supply circuit to the sleeve, as shown in Figure 2. The trimmers are marked on the diagram to correspond with the effects, listed above, for which they compensate.
cos~lne
channel
In[~:
(1)
Examination of the working shows that ao vanishes from this result because a voltage difference is taken between A and B, all coefficients with even subscripts vanish because of the arrangement and method of excitation of the sleeve, and all coefficients with subscript 3m (m = 1, 2, 3 ... ) vanish because helices A and B are spaced by 217/3 radians. It is sufficient for the present purpose to determine, from the nature of the electrostatic field, a limit to the values which lan/all may attain. Again, only the result may be quoted: this is, under justifiable simplifying assumptions which hold in the region of interest,
(217 d/L) lanl < 2sinhsinh(217n d/L) al
(2)
where d/ L is the ratio of the gap between bar and sleeve to the helical lead of the conductors. In the present instance, las/a.j < 0'0012, la7/a.j < 0'00003, and so on. The peak error arising from as cannot, therefore, exceed 0'0012.0'1024/217 in. = 20 fL in. (0'5 fL), and the other terms are negligible. It remains to examine possible errors due to imperfect
Figure 2.
Trimmer (a) introduces compensating non-orthogonality (cross-feed from the sine to the cosine channel) into the supply to the sleeve, and trimmer (b) alters the gain of the cosine channel relative to the sine channel to give compensating unbalance. The required sense of connection of the trimmer windings and the settings of the trimmers are determined by a systematic test procedure and the settings then sealed. The adjusted transformers and the sleeve are henceforth regarded as a unit, the parts of which are not to be separated.
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Use of relative rotation of sleeve and bar Cam correction-Measurable cumulative error will generally be present in the pattern of a long Helixyn bar. When the utmost precision is desired, cancellation of this cumulative error is achieved by mounting the Helixyn sleeve so that it is rotatable about its axis through a limited angle, this rotation being controlled by a radius arm moving in contact with a longitudinal cam which is fixed with respect to the mounting of the bar. Due to the helical pattern of the conductors, a rotation of 0·36° is equivalent to an axial movement of 0'0001 in. (0'0025 mm). The magnification between axial movement and change of cam profile is, for example, 125 times at 2 in. (5 cm) radius. Cam correction may also be used to compensate for certain types of systematic error in the machine which the Helixyn controls.
Temperature coefficient of bar The bar has the same coefficient of expansion with temperature as the steel tube which forms its structural basis, as nearly as could be measured, that is, 10 x 10- 6 per 0c. Performance It has been found on test that the Helixyn behaves as would be expected from theory, and it has been possible to devise a technique for manufacture which gives residual cyclic errors less than ±0'0001 in. (0'0025 mm). The second harmonic error trims need no attention other than initial alignment. At the time of writing, Helixyns have been installed on a machine tool in a laboratory test for about a year and have given no trouble apart from one open-circuited end connection. Experience gained so far indicates that settings are stable and repeatable.
Fine datum setting-In order to make an arbitrarily chosen longitudinal position of bar and sleeve correspond to a particular value of 8, the bar may be made rotatable about its axis. Provision for rotation through slightly more than one revolution is sufficient.
Digital-analogue Converter General description-The function of the digital-analogue converter is to provide the voltages required to excite the Helixyn sleeve. The voltages are variable in amplitude under control of a numerical input set up on switches or relays. It is important that the ratio of the two voltages be closely approximate to tan (8+ E), where (J is an angle which is proportional to the numerical input, and E is a constant (which may be zero). It is less important that the individual voltages be separately closely proportional to sin (8+ E) and cos (8+ E) respectively. A range of 21T radians in 8 must correspond to the axial lead of the Helixyn conductors, and intermediate positions in this range must be defined by the numerical input to about onethousandth part of this range. The essential part of the digital-analogue converter consists of a relatively low-impedance resistive network which is switched in accordance with the numerical input to develop the required voltages when supplied with an a.c. or impulsive electrical input. In part of the network the switching of the circuit is arranged to effect a variation of resistances which is linear with respect to the numerical input, the required development of a tangent ratio being obtained by the way in which the linearly varying resistors are connected in the network. Basic circuit-To appreciate how the required ratios are produced it is helpful first to consider the basic circuit shown in Figure 3, and then to consider how the circuit may be economically switched to give the desired result. With the values marked in the diagram it is easy to show that x Es/Ec = 1+(I-x)(0'26823+0'29443x)
Electrical parameters Inter-electrode capacitances- From the circuit aspect, the Helixyn is a multi-electrode variable capacitor. When used as described, the number of distinct electrodes is seven (counting the screen on the sleeve, the steel tube in the bar and conductor C as one electrode, since all these are connected to ground). The number of direct capacitances between these seven electrodes is 21, and academically they should all be considered to vary with
Sleeve conductor to ground Between adjacent sleeve conductors Between non-adjacent sleeve conductors Bar conductor to ground Between bar conductors Sleeve conductor to bar conductor
75 160 75 50 per in. (20 per cm) 33 per in. (13 per cm) 15+ 14 cos oft
l where'" radians is the axial displacement of a particular pair of electrodes)
Input and output capacitances-From the capacitances listed above, it may be deduced that a round value for the capacitance load of the sleeve presented to the full secondary winding of each input transformer (Figure 2) is 300 fLfLF. The null voltage is taken from the bar via a 1: 1 ratio transformer with a floating primary winding. The output capacitance through which the open-circuit null voltage is effectively applied to the output transformer is (30+ 78K) fLfLF, where K is the length of the bar in in. or (30+31k) fLfLF, where k is the length of the bar in cm.
and, further, by direct calculation, to plot the difference
, I
Basic conversion circuit:
..---.._ _
Inverse voltage transfer and sensitivity-Again from the capacitances listed, it may be deduced that the ratio
-nl~
,------'_--<>-'
liE
power] 11 input
Maxim.um voltage input per channel is 2'5 + 4.8K or 2·5 + 1'9k MaXImum o.c. voltage from bar ' and that the maximum input voltage per channel required to give 1 mY o.c. voltage output for 0·0001 in. (0'0025 mm) misalignment from null is 0'4+0'79K or 0·4+0·31k.
091101 R .n.
Figure 3.
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Basic circuit 01 digital-analogue converter
HELIXYN POSmON CONTROL
tan- 1 (Es/Ec) - (7T/4)x against x. With the circuit proportions given in Figure 3, the difference between tan- 1 (Es/Ec) and (7T/4)x is extremely small, so that if Es and Ec are used as excitation voltages for the Helixyn sleeve, the axial field shift with x will be closely proportional to x. For a 0·1024 in. (2·6 mm) Helixyn lead the peak errors due to the approximation are within ± 4 fJ.in. (± 0·1 fJ.). There are considerable variants of the circuit of Figure 3, this circuit being the latest product of an extensive search for simple circuits in which the trigonometric ratio required is sufficiently approximated by a rational algebraic function of the input number--circuit elements themselves varying linearly with that number. It is shown in a later subsection how x may be varied under control of a numerical input and how the range zero to 7T/4 radians in the space-phase output can be extended to cover the complete space-cycle of 27T radians. Source resistance for constant sensitivity-When the circuit of Figure 3 is supplied from a voltage source the value of (Ec 2 + El)! rises as x varies from 0 to 1. On the other hand, when the supply is a current source there is a variation in the reverse direction. In some applications, Ec and Es are required individually to be approximate to cos 8 and sin 8, respectively, in addition to having the correct ratio. When this is so, there should be no variation of (E/+ El)! with x, and this condition can be approximated by supplying the network with an actual or effective source resistance of value 3·49682R n: this keeps the variation of (Ec 2 + Es2)t within ± 2 per cent of the mean value. Numerically variable potentiometer-The most economical switching is obtained if the space-cycle (Helixyn lead) is divided into a number of equal parts which is a power of 2, and successive parts are numbered in the cyclic progressive binary code (Gray code). Figure 4 shows a particular example of this
Switch positions correspond
pow~
InPu:J
,, ,I
I
I
I
I
6
4
3 21
116·61
I
433· 74 (Resistor values in .0.)
Figure 4.
Digital- analogue converter for c.P. binary code
switching which is used in Helixyn control. Here, R has been chosen equal to 128 n and the cycle has been divided into 1,024 (= 210) distinct steps, requiring 10 binary digits to specify a particular position. The switches are numbered from 0 to 9 to correspond with the significance of digits of the input code, o being the least significant and 9 the most significant. Space does not permit listing all the 1,024 different settings, but it may easily be verified that a c.p. binary input number N(O ,,;; N ,,;; 1,023) will present voltages Ec and Es to the Helixyn sleeve which correspond in sign and relative magnitude to a spacephase angle of (N + O· 5)/ 1,024 27T radians. Because tht Helixyn lead is 0·1024 in. (2·6 mm) and this distance is divided into 1,024 steps, it is clear that the least digital steps in N correspond exactly to 0·0001 in. (approximately 0·0025 mm).
In practice, the 0·5 n resistors are reduced in value to allow for the finite contact resistance of the switch or relay contacts. A circuit (not shown) similar to Figure 4, but somewhat less economical in components, may be used when it is required to accept a pure binary input. Performance-In practice, it has appeared that these circuits give the desired performance and are stable, no adjustment having yet been called for after initial trimming of the precision resistors to correct value. Excitation of conventional synchros-It is practicable to excite conventional resolver synchros from the digital-analogue converter circuit of Figure 3, provided that step-down transformers are used in order to avoid destroying the accuracy of the network. The step-down ratio will vary according to the design of the synchro, but may be of the order of 40: 1. Null voltage sensitivities of the same order as those obtained from a Helixyn supplied through 1: 1 transformers are still obtainable under these conditions. Conventional synchros supplied in this manner may be used for coarse positioning, as described below. Helixyn Positioning Systems General-The 0·1024 in. (2·6 mm) lead of the Helixyn was chosen to allow binary operation of the digital-analogue converter, as this permits use of the simpler types of converter and also results in economy in digital computing circuits which may be called for where the input data has to undergo arithmetical modification before actuating the digital-analogue converter. The way in which the binary input is automatically derived from the decimal form in which it normally occurs, and other features of complete Helixyn positioning systems, are briefly described below. Coordinate setting-For static positioning over ranges of movement much greater than one Helixyn space-cycle, coarse positioning and intermediate positioning resolver synchros, geared together and effectively geared to the Helixyn, are used in the earlier part of the positioning sequence to bring the movement within non-ambiguous range of the Helixyn system. The synchros and the Helixyn belonging to a particular coordinate all receive information in turn from a single digital-analogue converter. This converter is supplied with pure binary information from a shifting register to which it is permanently connected at the more significant end. The shifting register is initially set up to contain the binary equivalent (in units of 0·0001 in.) of the complete decimal input which defines the desired position. The coarse synchro takes information from the more significant digits of the binary number, through the digital-analogue converter, and operates a servo system to bring the movement within non-ambiguous range of the intermediate synchro. When the misalignment is within pre-determined limits, control is automatically transferred to the intermediate synchro and the digits appropriate to its range of action are moved in the shift register so that they become the input to the digital-analogue converter. When the intermediate synchro brings the misalignment within non-ambiguous range of the Helixyn, a similar shift of control takes place and final positioning is achieved by the Helixyn. Prior to the above action the required initial binary content of the shift register has been set up by shifting binary coded decimal digits of the input number into the register one by one, the most significant digit first. Each time a digit is shifted into the register the contents of the register (if any) are moved out, multiplied by ten in a simple serial computing circuit and added
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to the incoming binary cOded decimal digit; this builds up the required binary equivalent of the decimal input. The successive binary coded decimal digits of the input may be provided manually from a keyboard or read in automatically from a punched paper tape. The system is economical in components because the shifting register and its associated circuits are used over and over again in sequence, and are also used for two distinct purposes, namely, decimal to binary conversion and effective switching of different parts of the number to the digital-analogue converter. In this application the converter is supplied with 10 kc/s a.c. excitation.
Continuous, coordinated control-In continuous control, coarse and intermediate positioning is not needed, since each movement remains continuously under non-ambiguous direction from its associated Helixyn. The system which has been developed uses sampled position information in each of three coordinates. The position samples are derived from the drawing data by automatic digital computing, the description of which is outside the scope of this paper. No decimal to binary conversion problem exists in the position control system, because this conversion takes place in the process of computing the position samples. At present the sampling period in anyone of the coordinates is 16 mS, which is adequate for present needs but may be raised in the future. The sampling epochs for the different coordinates are interlaced in time-division multiplex and are recorded in binary notation on tin. (6 mm) wide magnetic tape, together with synchronizing and checking data. The tape also carries digital information which may be used to modify the position samples (during control) to allow the use of a cutter which is not to nominal diameter, or may be used to take a roughing cut with allowance for finishing. In addition, the tape carries miscellaneous information to allow automatic control of servo power, locking of machine movements, etc. All the information is carried on four parallel tracks and the tape is read at 7'5 in./sec (19 cm/sec). In the circuits which handle the information read from the tape, considerable economy is possible because the signals are in time-division multiplex. A single digital-analogue converter handles information for all three coordinates, actually in sequence but effectively continuously. Similarly, a single computing circuit effects tool diameter correction for the two coordinates which are involved. Impulsive sampling of position misalignment is used, taking advantage of the wide-band characteristics of the Helixyns and the common digital-analogue converter. A valuable feature of the synchro-like nature of Helixyn control is that it cannot accumulate error. Occasional in-
correct position samples may occur, due to magnetic tape dropouts or drop-ins, but these will, in general, have no sensible effect on the finished product. Advantage is taken of this feature to arrange that automatic digital checking circuits do not direct the equipment to shut down unless fault indications occur with significant frequency.
Performance-The coordinate setting system described has not yet been applied to a machine tool, but laboratory equipment has shown the system to operate and to give extremely stable and repeatable positioning to the expected order of accuracy. The continuous control system is being used for three coordinate control of a vertical-spindle milling machine, in the laboratory, and will shortly be put into use under factory conditions. The control system has been shown to work as described. Precise absolute accuracy tests are not yet completed, but good surface finish and repeatability have been shown from the outset. Devices Related to the Helixyn Linear Inductosyn-The Linear Inductosyn of Farrand Controls, Inc. is similar to the Helixyn in that a slider is excited by a pair of currents, just as the Helixyn sleeve is excited by a pair of voltages, and a null voltage is taken from an assembly of scales corresponding to the Helixyn bar. Magnetic coupling is used. However, it is somewhat less economical to supply precisely controlled currents than similarly controlled voltages and the rotary feature of the Helixyn, of use in fine datum setting and cam correction, is not present. The space cycle of the Inductosyn is 0·1 in., and it would not suit the position control systems described earlier. Nultrax-The Nultrax of Canadian Westinghouse Co., Ltd., is superficially similar to the Helixyn in that it has cylindrical bar and sleeve elements bearing helical conductors. Coupling is magnetic. There is, however, no real similarity to the Helixyn in use, since the Nultrax bar and sleeve must be rotated with respect to each other to obtain fine position setting, and this involves the provision of a subservo to convert the numerical input to a corresponding rotation. The author gratefully acknowledges the work done by his colleagues in helping to develop Helixyn control from an idea to practical realization. Thanks are also due to the Board of Directors of the British Thomson-Houston Co., Ltd., and the Executive of the Associated Electrical Industries Limited, Electronic Apparatus Division, for permission to publish this paper.
Summary
Helixyn is the name given to a position-measuring element which has been developed for automatic positioning of machine tool movements from numerical input data. The order of accuracy of the device is 0·0001 in. (0'0025 mm), including conversion of input data from numerical form. The measuring unit comprises a cylindrical bar, somewhat longer than the distance over which control is required, and a short cylindrical sleeve which moves along the bar but not in contact with it. The two parts are mounted on the machine tool so as to pick up directly the relative movement which is to be controlled. In the form on which development has been concentrated, the sleeve consists basically of a tube of insulating material, the inside surface of which supports four distinct helical conducting paths which
are disposed with equal axial spacing so as to form a regular interlaced pattern. The bar consists of three interlaced helical conducting paths carried on a layer of insulation bonded firmly to a steel tube. The lead of the helices on the bar is the same as that on the sleeve, and the design is such that the variation of capacitance between each sleeve conductor and each bar conductor is closely sinusoidal when plotted against relative axial movement. The sleeve conductors are supplied with a.c. or impulsive voltages of relative sign and magnitude set by a relay-switched resistor network. The numerical input controls the switching in such a way that the electrostatic field between sleeve and bar remains substantially constant in form but takes up an axial position relative to the sleeve bearing a linear relation to the numerical input.
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HELIXYN POSITION CONTROL
Sommaire Helixyn est le nom donne a un element de mesure de position, qui a ete etudie pour le positionnement automatique des mouvements de machines-outils, en partant de donnees d'entn:e numeriques. L'ordre de grandeur de la precision du dispositif est de 0,0025 mm, y compris la conversion des donnees d'entree a partir de leur forme numerique. L'element de mesure comprend un barreau cylindrique un peu plus long que la distance sur laquelle la commande est desiree, et un court manchon a glissiere, qui se deplace le long du barreau, mais sans contact avec lui. Les deux pieces sont montees sur la machine outil, de fac;on a detecter directement le mouvement relatif qui doit ctre controle. Dans la forme sous laquelle l'application a ete faite, le manchon consiste en principe en un tube de materiau isolant, dont la surface interieure supporte quatre trajectoires helicoid ales conductrices, qui sont disposees avec un espacement axial egal, de fa90n a former un
modele regulierement entrelace. Le barreau consiste en trois trajectoires conductrices helicoldales entrelacees supportees par une couche d'isolant solidement collee sur un tube d'acier. Le pas des helices sur le barreau est le mcme que celui des helices sur le manchon et la forme est telle que la variation de capacitance entre chaque conducteur du manchon et chaque conducteur du barreau est tres exactement sinusoldale en fonction du mouvement axial relatif. Les conducteurs du manchon sont alimentes avec des tensions alternatives ou impulsionnelles, dont les signes et amplitudes relatifs sont regles par un reseau de resistances commutees par relais. Les entrees numeriques controlent la commutation de telle fac;on que le champ electrostatique entre manchon et barreau reste de forme sensiblement constante mais prenne une position axiale par rapport au manchon qui soit en relation lineaire avec l'entree numerique.
Zusammenfassung , Helixyn' ist ein Me13glied zur Lageregelung an Werkzeugmaschinen mit numerischer Eingabe. Die Genauigkeit des Gerates liegt in der Grol3enordnung von 0,0025 mm, einschliel3lich Umwandlung der numerischen Eingabewerte. Das Me13glied besteht aus einer zylindrischen Stange, die etwas langer ist als der Einstellbereich, sowie einer kurzen zylindrischen Buchse, die sich entIang der Stange bewegt, diese aber nicht beriihrt. Die beiden Teile erfassen die zu regelnde Relativbewegung. Der Buchsenkorper aus Isolierstoff tragt an der Oberfiache der
II-A.R.e.4
Bohrung vier isolierte und in gleichem axialen Abstand angeordnete spiralformige Leiter. Die Stange tragt eine Isolierschicht, in die drei ineinander gewickelte spiralformige Leiter eingebettet sind. Die Kapazitatsanderungen zwischen jeder Leiterspirale in der Buchse und jedem Leiter auf der Stange verlaufen weitgehend sinusformig. Die Spiralleiter in der Buchse werden mit Impuls- oder reinen Wechselspannungen gespeist. Die Impu)sspannungen werden von einem relaisgesteuerten Netzwerk geliefert.
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