US3177423A

US3177423A - Trigonometric store

Info

Publication number: US3177423A
Application number: US52992A
Authority: US
Inventors: Herbert M Fuldner
Original assignee: Cincinnati Milling Machine Co
Current assignee: Milacron Inc
Priority date: 1960-08-30
Filing date: 1960-08-30
Publication date: 1965-04-06
Anticipated expiration: 1982-04-06
Also published as: GB913977A; NL267022A

Description

oom m ow QOQ m 0% mok mow {k wi M INVENTOR. HE/PBER r N. FUL DNER l7 TTORNEYS H. M. FULDNER TRIGONOME'IRIC STORE Filed Aug. 30. 1960 5 O .N m O\\ U\ O u o k WN 0? April 6, 1965 United States Patent 3,177,423 TRHGQNOMETREC STGRE Herbert M. Fuldner, Fort Thomas, Ky, assignor to The Cincinnati Milling Machine Company, Cincinnati, (Phio, a corporation of Ohio Filed Aug. 30, 1960, Ser. No. 52,992 6 Claims. (Cl. 323-435) This invention relates to a converter for transforming digital information into analog voltages which are representative of the desired positions to be assumed by the numerical controlled element of a machine tool. More particularly, the invention relates to a circuit for converting digital information into angular data corresponding to the rotation of a shaft, the converted data being in the form of quadrature voltages which are proportional to the sine and cosine of the angle of rotation.

It is known to provide trigonometric stores of the type which convert digital input information into angular data such as sine and cosine voltages and thereafter to apply these voltages to the quadrature windings of a resolver which serves as the error detecting device of a servo system. One such device is shown and described in the US. Patent to Tripp, No. 2,849,668, granted August 26, 1958, for Automatic Machine Control. The purpose of the present invention is to simplify the prior art apparatus by reducing the size and number of transformers and switches required thereby reducing the cost and complexity of the system. A further purpose of the present invention is to combine a system of 36 segments or bites with a system of 18 bites so as to obtain in one system the advantages of the two individual systems. This is accomplihsed by providing a sine-cosine transformer with five 18 taps on either side of a center tap. The output of the transformer is obtained by a tap switch which advanoes in 36 steps. Each 18 segment of the 36 step is then individually interpolated into five equal parts to obtain the 3.6 increments. These increments are in turn divided into ten equal parts to obtain the .36 increments.

Accordingly, it is an object of the present invention to provide an improved type of trigonometric store which is simpler and less costly to construct than former devices of this character.

Another object of the invention is to provide a trigonometric store having a tapped sine-cosine transformer of relatively few turns while'providing a high degree of accuracy in the synthesis of the sine and cosine voltages.

Another object of the invention is to provide a trigonometric store which utilizes split linear interpolation for the subdivision of the angles represented by the sine and cosine Voltages derived from t aps on a sine-cosine transformen Another object of the invention is to proivde a digitalto-angular data converter which has all the advantages of a system employing 36 segments while affording the accuracy of a system employing 18 segments.

With these and other objects in view which will become apparent from the following description, the invention includes certain novel features of construction and combination of parts, the essential elements of which are set forth in the appended claims, and a preferred form or embodiment of which will hereinafter be described with reference to the drawings which accompany and form a part of this specification.

In the drawings:

FIG. 1 is a diagram of the trigonometric store as incorporated in a servo system.

FIG. 2 is a diagram of the switching circuit used to I change'the connections from one pair of switch banks to another.

EJ711423 Federated Apr. 6, 1965 In the-circuit shown in the accompanying drawings, an AC. reference voltage is applied to terminals 10 and 11 which are connected by conductors to the

end terminals

12 and 13 of a tapped autotransformer 14. Since, in the present apparatus, the autotransformer is required to serve as a low-impedance, precision voltage divider, it is preferably a toroidal type transformer designed for minimum flux leakage between turns. As shown, the transformer is wound on an annular core 15 and is provided with a grounded center tap and eight intermediate taps 17, which are appropriately spaced to provide voltages which are proportional to the sine and cosine of 0, 18, 36, 54, 72, and 90 on either side of the center tap, the sine of 0 being equal to the cosine of 90, the sine of 18 being equal to the cosine of 72, the sine of 36 being equal to thecosine of 54, etc.

In designing the transformer 14 it was found that in order to provide voltages which were accurate to within one part in 100,000 of the sine and cosine voltages required, a transformer of approximately 100,000 turns would be required. Since such a transformer would be not only very costly but also of very high impedance due to the amount of wire required, it was necessary to devise some other means for obtaining the desired degree of accuracy. In the present instance this has been accomplished by the use of a second toroidal transformer 20 having an annular core 21 on which is wound a primary winding 22 and eight secondary windings 23. The secondary windings are inserted in the leads from the taps 17 and thereby act to insert correcting voltages which either add to or subtract from the voltages provided by the taps. To maintain the proper phase relation between the injected voltages and the voltages from the taps, and also to maintain the proper amount of voltage injection regardless of variations in the supply voltage, the primary winding 22 is excited from a winding 24 wound on the core 15 of the autotransformer.

In the present embodiment of the invention, the transformer 14 is provided with 252 turns, i.e., 126 turns on either side of the center tap 100, and the taps for

sine

18, 36, 54 and 72 are tapped at 39, 74, 102 and turns respectively, on either side of the center tap. The primary winding of transformer 20 is provided with 48 turns and the secondary windings connected to terminals E, D, C, B have 3, +3, -3 and -8 turns, respectively, as do also the secondary windings connected to terminals G, H, I, and K, respectively. The signs as used above indicate that the secondary windings are poled to subtract their voltages from those provided by the transformer taps, while the sign indicates that this winding'is poled to add its voltage to that provided by the tap. The winding 24 which excites the primary winding of transformer 20 is comprised of a single turn wound on the core 15. It will be appreciated that multiples of the given numbers of turns will provide the same voltages at the terminals AL but with a higher impedance.

Accordingly, when the terminals 10 and 11 are energized from a source of reference voltage, terminals 25, marked A-L will be supplied with voltages which are proportional to the plus and minus values of the sine and cosine of 0, 18, 36, 54 72 and 90.

Assuming that the feedback unit connected to the machine tool element which, in the present instance, is assumed to be a slide, is one which is subject to angular displacement such as, for example, a resolver, and that .1 inch movement of the slide produces one revolution or 360 rotation of the feedback unit, then each 36 of displacement of the unit will equal .01 inch movement of the slide. Thus, 36 divisions of the transformer 14, such as between terminals F and D, D and B, etc. Will represent .01 inch of slide movement. Since, in the present ap enemas 1 In other words, the voltage between taps on the winding 29 is ten times as great as the voltage between taps on the winding 30. This is for the purpose of enabling the voltage between adjacent terminals A, B, C, D, etc. to be dividedinto five equal parts by winding 29 with each. of these divisions then being further resolved into ten equal parts by the winding 30. The means for connecting the taps in the proper order to provide the desired resolution of voltages comprises three multi-bank switches 138, 258 and 3S8. These may be manually settable selector switches or, alternatively they may take the form of step ping switches controlled from a punched tape and tape reader in a well-known manner.

As above noted, the switches are provided with multiple banks of contacts which are designated by letter suffixes such as C, B, E, etc. As herein illustrated, the switch bank llSS-C has ten contacts numbered 9, inclusive, which contacts are connected to the terminals in the order indicated by the letter designations beside the contacts, namely, F, D, B, B, D, F, H, K, K, H. It will be noted that these are alternate terminals. in other'words, the wiper of bank lSS-C advances in 36 bites.

Bank D of switch 158 has its ten contacts 0-9 connect ed to the terminals 25 as indicated by the letter designation beside the contacts, namely, E, C, A, C, E,G, J, L, J, and G. These too it will be noted are alternate terminals on the transformer. However these terminals lie between the terminals to which the contacts of bank 1SS-C are connected, i.e., the order of connection has been advanced 18. terminals'D, B, B, D, F, H, K, K, H and B. These are the same terminals to which the contacts of banks lSS-C are connected but the order of connection has been advanced 36. Hence, when the wipers of switch 183 are on 0, a wire d2 connected to the wiper or" bank C will be Bank E of switch 188 has ten contacts connected to per end of winding 29 and a voltage proportional to the sine of 36 will be supplied to the lower end of the winding. The voltage impressed across the winding 29 represents, therefore, the angular span from 18 to 36 in terms of the sine function, and thisspan is divided into five equal parts by the taps 74-73 representing the digits .005 to .009. Each of these divisions is in turn divisable into ten equal parts by the taps on winding 30.

When the thousandths digit changes from 9 to 0, relay 20R is again deenergized and wires 92 and 94 are again connected to wires 74 and '70, thereby again connecting the first 18 segment of the 36 bite to the winding 29. It will now be seen that each step of switch KSSVCQIIE- sponds to a 36 bite and that each bite is divided into two 18 segments.

The approximate value of the cosine of 195.12" is derived in a similar fashion from the sine-cosine voltages 7 provided at the terminals A-L. For this purpose there is connected to ground, a wire 9 connected to the wiper of bank D will be supplied with a potential proportional to the sine of 18 and a wire 95 connected to the wiper of bank B will be supplied with a potential proportional to the sine of 36. The wires 92', 9 2- and 95 are connected to a pair of wires '74 and 79 through the contacts of a I switching relay ZCR. When the relay is deenergized, the wires 92 and 94 are connected to the wires '74 and '79, respectively, which, in turn, are connected to the terminals of the winding 29 on transformer-2h. Hence, a volt age proportional to the value of sine 18 is impressed across the winding 2?.

The taps of winding 29 are connected by wires 74 -725 to the contacts 0-9' of a switch bank LESS-D. As indicated on the drawing, wire 74 is connected to the contacts 0 and 5, wire '75 is connected to contacts 1 and 6, etc. '1 .e taps of winding 30 are connected to the contacts 0-9 of a switch bank dSS-C, and a wire 91 connects the wiper of this bank with the wiper of bank ZSS-D. An output con ductor $1 is connected to the end of winding 3d which is connected to the 0 contacts of switch bank SSS-C and provides anoutput voltage which, referenced to ground,

is approximately proportional to the sine of the angle corresponding to the decimal amount setup on the switches 188, 253 and 38S. When these switches are set to the positions indicated in the drawings, i.e., .0542 inch, the

corresponding angle is 195.12. Whenthe thousandths digit'changes from 4 to 5, relay ZCR is energized through bank C of switch 285 (FIG. 2 thereby connecting wire 94 to wire 74 andwire 95 to wire 79; Hence, a voltage 2 proportional to the sine of 18 will be supplied to the-up provided a second toroidal transformer 33 which may be identical to the trmsforrner 28 and, like this transformer, has a pair of linearly tapped windings Maud 35 wound on an annular core .36. The winding 34 is divided into five sections of twenty turns each and the winding '35 is divided into ten sections of two turns each so that the voltage between taps on winding Ed is ten times as great i as the, voltage between taps on winding 35.

The data input meansfor the cosine system includes additional banks of contacts on the switches 13S, 23S and 388. For example, banks F, G, and H of switch 183 are connected to terminals A-L according to the same scheme as used for the sine functions but displaced to provide voltages which are proportional to the cosine of the angle. When relay ZCR is deenergized, wires 1% and 104 are connected to wires )6 and 1.02, which, in turn, are connected to the upper and lower ends of the winding 34. Hence, a voltage proportional to the cosine value of the first 18 segment of a 36 bite wiil be impressed across the winding 34. The five taps of this winding are connected by wires 96-101 to the contacts 09'of a switch bank ZSS- E, wire 96 being connected to contacts 0 and 5. wire 97 being connected to contacts 1 and 6, etc. The taps of winding 35 are connected to the contacts 09 of a switch bank ESS-D and a wire 116 connects the wiper of this bank with the wiper of bank ZSS-E. An output conductor 1536 is connected to the 0 end of winding 35 and true sine and cosine values of the 3.6 and 36 angular 7 increments which correspond to the .001 inch and .0001 inch movements of the slide. It has been discovered, however, that the ratio of the sine and cosine values, i.e the tangent function of the angle, is remarkably accurate in spite of this approximation. This resultsfromthe fact that when the sine and cosine values thus produced are supplied to the quadrature windings of a sine-cosine type of feedback unit, such as a resolver, it is the ratio of the sine and cosine values which determines the position taken up by the device." Hence, it is responsive to the tangent of the angle andby use of the transformers 1d and 2b, as described, which produce very nearly true values of the sine and cosine functions at 18 intervals, it is possible with the present system to obtain values of thetangent function which are accurate to within two minutes of angle. Since two minutes is equal to approximately .00001inch of slide movement, the trigonometric store herein described is well within the limits of accuracy needed; for controlling slide movement to the nearest ,0001inch. A seven-fold increase in accuracy is obtainable by the use of 18 increments in place of 36 increments. In

other words,;had a 36 bite system per se been used Vin place of the combined 18 and 36 system disclosed herein, the values of the tangent function would have been accurate only to within 14 minutes or .00007 inch of slide movement. Since it is desirable in the present control system to maintain an accuracy of .0001 inch of slide movement, the factor of safety using a straight 36 system would be undesirably small.

As shown in FIG. 1, the sine and cosine voltages are applied to the

guadrature windings

70, 71 of a resolver 72 which is also provided with a rotor winding 73. The two leads 84 and 85 from this winding are connected to a pair of input terminals on a servo-amplifier 86. The output of the servoamplifier is connected by leads 87 and 88 to the control winding 89 of a two-phase electric servomotor 90. This motor also is provided with a reference voltage winding 91 and runs in one direction or the other depending on the phase of the voltage supplied to the winding 89 in a well-known manner. The armature of the motor is drivingly connected, as indicated by the dashed line 107, to the slide 93 which is to be positioned in accordance with the input data supplied to the trigonometric store. The rotor of the resolver is also arranged to be driven by the slide through an angle of 36 for each .01 inch movement of the slide as is indicated by the dashed line 108.

When the rotor of the resolver is turned by the motor to a position in which the voltage across the

leads

84 and 85 is reduced to zero, then the output of the servoamplifier will also be reduced to zero, and the servomotor will be deenergized. This will stop the slide 93 in the position required by the input data.

While the present system has been shown applied to a single information channel only, namely the fine channel of a control system, it will be appreciated that the principles of the invention may be applied with equal advantage to the other information channels of the control system, for example, to the coarse and medium channels, in accordance with the known practices of the prior art.

Having thus described the invention in connection with one possible form or embodiment thereof and having used, therefore, certain specific terms and language herein, it is to be understood that the present disclosure is illustrative rather than restrictive and that changes and modifications may be resorted to without departing from the spirit of the invention as defined by the claims which follow.

What is claimed is:

1. A trigonometric store for a positioning system comprising a function generating transformer including a plurality of voltage taps selected to provide a series of voltages proportional to the values of the sine and cosine of angles spaced at 18 intervals, an interpolating transformer having two linearly tapped windings each capable of dividing a voltage impressed thereacross into equal voltage increments, one of said windings having ten times as many turns between taps as the other winding, switch means for connecting a selected pair of adjacent taps on said function generating transformeracross said one winding, and additional switch means for connecting a selected tap on said one winding with a selected tap on said other winding to thereby cause a voltage to be impressed on one end of said other winding which is approximately proportional to the value of the sine or cosine of the angle represented by the setting of said switch means.

2. A trigonometric store comprising a function generating transformer having a plurality of voltage taps selected to provide a series of voltages approximately proportional to the value of the sine and cosine of a plurality of equally spaced angles, an injection transformer having a single primary winding and a plurality of secondary windings each having one end connected to a tap on said function generating transformer, a winding on said function generating transformer for energizing said primary winding, an interpolating transformer having a linearly tapped winding for dividing a voltage impressed thereacross into equal voltage increments, switch means for connecting the other ends of a selected pair of adjacent secondary windings across said linearly tapped winding, and additional switch means for selecting a voltage from any one of the taps of said linearly tapped winding to thereby provide a voltage which is approximately proportional to the value of the sine or cosine of the angle represented by the setting of said switch means.

3. A trigonometric store comprising an autotransformer of two hundred fifty-two turns with a center tap and first, second, third, and fourth taps at 39, 74, 102 and 120 turns on either side of the center tap, an injection transformer having a primary winding of forty-eight turns and first, second, and third and fourth secondary windings each having one end connected to a corresponding tap on said autotransformer and having -3, +3, -3 and -8 turns respectively, and a winding of one turn, or a multiple thereof, on said autotransformer connected to said primary Winding for energizing the same.

4. The trigonometric store of claim 3 including an interpolating transformer having a linearly tapped winding for dividing a voltage impressed thereacross into equal voltage increments, switch means for connecting the other ends of a selected pair of adjacent secondary windings across said linearly tapped winding, and additional switch means for selecting a voltage from anyone of the taps of said linearly tapped winding to thereby provide a voltage which is approximately proportional to the value of the sine or cosine of the angle represented by the setting of said switch means.

5. A trigonometric store comprising a function generating transformer having a plurality of voltage taps selected to provide -a series of voltages proportional to the values of the sine and cosine of angles spaced at 18 intervals from 0 to and from 0 to 90, an interpolating transformer having a linearly tapped winding capable of dividing a voltage impressed thereacross into equal voltage increments, switch means for selectively connecting either of two pairs of three adjacent taps on said function generating transformer across said linearly tapped winding, additional switch means cooperating with the taps on said linearly tapped winding, and means controlled by said additional switch means for causing said first mentioned switch means to disconnect one of said pairs of taps from across said linearly tapped winding and to connect the other of said pairs of taps thereacross.

6. The trigonometric store of claim 5 wherein said first mentioned switch means includes a switch having at least three banks of contacts with successive contacts on each of the three banks connected to alternate taps on said function generating transformer and with the corresponding contacts of each bank connected to taps spaced 18 apart.

References Cited by the Examiner UNITED STATES PATENTS 1,667,752 5/28 Thomas 323-43.5 2,200,979 5/40 Blume 323-435 2,201,642 5/40 Bauer 323-435 2,849,668 8/58 Tripp 323-435 3,042,307 7/62 Booth et a1. 235-197 X LLOYD MCCOLLUM, Primary Examiner. ORIS L. RADER, Examiner.

Claims

1. A TRIGONOMETRIC STORE FOR A POSITIONING SYSTEM COMPRISING A FUNCTION GENERATING TRANSFORMER INCLUDING A PLURALITY OF VOLTAGE TAPS SELECTED TO PROVIDE A SERIES OF VOLTAGES PROPORTIONAL TO THE VALUES OF THE SINE AND COSINE OF ANGLES SPACED AT 18* INTERVALS, AN INTERPOLATING TRANSFORMER HAVING TWO LINEARLY TAPPED WINDINGS EACH CAPABLE OF DIVIDING A VOLTAGE IMPRESSED THEREACROSS INTO EQUAL VOLTAGE IMCREMENTS, ONE OF SAID WINDINGS HAVING TEN TIMES AS MANY TURNS BETWEEN TAPS AS THE OTHER WINDING, SWITCH MEANS FOR CONNECTING A SELECTED PAIR OF ADJACENT TAPS ON SAID FUNCTION GENERATING TRANSFORMER ACROSS SAID ONE WINDING, AND ADDITIONAL SWITCH MEANS FOR CONNECTING A SELECTED TAP ON SAID ONE WINDING WITH A SELECTED TAP ON SAID OTHER WINDING TO THEREBY CAUSE A VOLTAGE TO BE IMPRESSED ON ONE END OF SAID OTHER WINDING WHICH IS APPROXIMATELY PROPORTIONAL TO THE VALUE OF THE SINE OR COSINE OF THE ANGLE REPRESENTED BY THE SETTING OF SAID SWITCH MEANS.