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The development of a multi-turn absolute encoder—a new concept in accordance with a design insensitive to accuracy
The d e v e l o p m e n t of a multi turn absolute encoder a n e w c oncept in accordance w i t h a design insensitive to accuracy T. Tsukada*and T. Kanada** A new design concept of a multi-turn absolute rotary encoder which is insensitive to the accuracy of encoder components is proposed. This new design does not demand high accuracy of the encoder structure other than the fundamental pattern to produce the least significant digit. The allowable error in the encoder structure is compensated by electronic light circuits. This absolute encoder has been applied to the measurement of height position in a cylindrical form-measuring system. The new encoders can be connected in series by reduction gears whose accuracy is fairly rough, so that a multi-turn device is realized. The allowable tolerances in the encoder structure are presented.
Keywords: multi-turn absolute encoder, error compensation, logic circuits
If an absolute rotary encoder is connected in series by, for example, a lead screw, we can measure the absolute rotary position or movement of a table without considering a special setting such as a linear scale encoder. However, the measuring range of a general absolute encoder is one revolution of the encoder. Hence, if we want to know a longrange position, reduction gears should be applied with the encoder. Though high accuracy is required of the reduction gears, sufficient accuracy is not guaranteed by this method. There is a design concept by which the degree of accuracy necessary in the components is reduced without necessarily incurring loss of final function of the equipment, This is referred to as 'design insensitive to accuracy' in this paper. For example, in a magnetic disc of computer memory, the recording density is increased by making the distance between the writing/reading head and the disc as small (order of 0.1 /Jm) as possible. However, it is very difficult to achieve such a spatial relation by a rigid structure, and it would be very expensive. The head is, in fact, floating on the air rotating with the disc surface. The initial objective of controlling the floating distance can be achieved by the use of a spring. Another example is given by the method of size measurement according to Abbe's principle. When the measuring scale is located along the size direction to be measured, the effect of location error of the scale will be generally * Tokyo Institute of Technology, Department of Mechanical Engineering for Production, Oh-okayama 2-12- I, Meguro-ku, Tokyo 152,Japan ** Kanto Gakuin University, Department of Mechanical Engineering, Mutsuura 4834, Kanazawa-ku, Yokohama236, Japan
66
neglected. High accuracy of mechanical structure can be dispensed with not only in the abovementioned cases but also with regard to the maximum material principal of drawing (symbolized by (~) and so on. The application of such a design concept will reduce manufacturing cost. By means of this design concept, the required function of a multi-turn absolute rotary encoder can be realized without demanding high accuracy in the reduction gears. In this study, a mechanism producing a signal of absolute rotary angle and simple electronic logic circuits were developed for a multi-turn rotary encoder according to the above-mentioned design concept. This absolute encoder has been fitted in a cylindrical form-measuring machine developed by the authors 1, along with an absolute rotary encoder on the market, to provide information on the position of the sensor. The output from the multiturn encoder is input to a microcomputer, and its measuring range is adjusted to the cylindrical formmeasuring machine.
Principle of absolute rotary encoder Fig 1 shows a generating pattern of 4 bits by means of W, X, Y, and Z tracks for 16 different signals. In this pattern, because of the relative positioning error of the detecting device, the signal phase gaps such as At1 and A t 2 in Fig 2 occur. Hence, the signals '0' between '1" and '2', or '7" between '3' and '4', are caused by, respectively, At1 or At2. This is an error arising from the change of two or more bits at the same time. In order to prevent this phenomenon from occurring, the grey code in Table 1, whose bit change is unique, will generally
0141-6359/88/020066-05/S03.00 © 1988 Butterworth & Co (Publishers) Ltd
APRIL 1 988 VOL 10 NO 2
Tsukada and Kanada--multi-turn encoder
15
0
be applied. However, it is rather doubtful whether a multi-turn device with connecting reduction gears in series can be realized using conventional principles.
New principle of pattern generation
Let us consider a method for generating a correct signal, assuming that there are location errors of the detecting device and positioning errors of each pattern on the rotary plate, such as in Fig 1. Consider the lower 2 bits, namely the Y and Z tracks. Firstly, assume that the signal Sz of the least significant bit (Z track) is generated regularly by a correct pattern. The neighbouring Y track has two signals, Sy~ and SY2, of different phase as shown in Fig 3. The signal width (rotary angle) and the position (phase) are settled to satisfy the following criterion against Sz:
12
11
0 < A ~ n < ~, 8
7
}1
I]
(1)
Eq (1) is realized on the mechanical structure, and the regular signal Sy of the Y track is obtained by the following logic:
F/g1 Generating pattern for binary code
Z track ~
n=1,2,3,4
1]
Sy = {(NOT Sz)
AND SY1} OR {Sz AND Sy,}
= ~'~Z"SY 1 -~-Sz" SY 2
- - ~ - - Z~t1
(2)
The above logical operators NOT, AND, and OR are simply given by the electronic logic circuits (eg TTL). As long as the criterion of Eq (1) is satisfied, the errors of the mechanical structure do not affeqt the signal Sv when using Eq (2). Fig 4 shows the locations of the detecting devices for Sy~ and Sy2, satisfying Eq (1). Fig 5 shows an example of logical processing for Eq (2) by means of TTL 2.
Y track
X track
Decimal I Fig2
¢,
Error due to generating pattern
Table I
Decimal and bit pattern
Ztrack Sz I I I I I
Binary Decimal
Grey
W
X
Y
Z
W
X
Y
Z
0 1 2 3 4 5 6 7
0 0 0 0 0 0 0 0
0 0 0 0 1 1 1 1
0 0 1 1 0 0 1 1
0 1 0 1 0 1 0 1
0 0 0 0 0 0 0 0
0 0 0 0 1 1 1 1
0 0 1 1 1 1 0 0
0 1 1 0 0 1 1 0
8 9 10 11 12 13 14 15
1 1 1 1 1 1 1 1
0 0 0 0 1 1 1 1
0 0 1 1 0 0 1 1
0 1 0 1 0 1 0 1
1 1 1 1 1 1 1 1
1 1 1 1 0 0 0 0
0 0 1 1 1 1 0 0
0 1 1 0 0 1 1 0
SZ'SY1
I
Sz'Sy2
l
S'Z" Sy1 + SZ'Sy2 I Correct signal for Y track
I 4
Direction of rotation Fig 3
PRECISION ENGINEERING
1[
Structure of non-error generation
67
Tsukada and Kanada--multi-turn encoder A~ 3 A~ 1
Position o f S,, sensor ,I
i,
Regular position of , J - Y t r a c k sensor I_
,
Position of Sy1 sensor
where ~ is a coefficient• For example, the most significant bit of the first stage absolute encoder changes by 2'/turn, and the least significant bit of the second stage absolute encoder, 2*/turn; then, the reduction ratio is 2' 1/2'. Hence, 2= 1 / ( 2 ' 2 ' )
of Y track
F/g4 Positions of sensor for pattern reading NOT logic (SN7404) (SN7432)
SzO •
I ~
S
multi-turn
absolute
The multi-turn absolute rotary encoder so developed has been applied to a cylindrical form-measuring machine to provide information on the axial position of the sensor, as shown in Fig 7. The required specifications are presented in Table 2. In order to satisfy these specifications by one absolute encoder,
A~ 3
SyiO
If r = 1 and k = 8, then the allowable error is about 0.7 °. The allowable error becomes larger when k becomes smaller, and the number of stages increases, without a loss of the final function of the encoder. The developed encoder
P r o x y position o f Sy2 sensor
~
(4)
r
nth stage absolute
rotary
encoder
y Reduction
gears box
Sy20 First
stage absolute
rotary
encoder
AND logic (SN7408)
F g5 Electronic logic circuits for generating Sv
Fig 6 Module-structured multi-turn encoder Second stage absolute encoder
Insensitivity to accuracy of the new encoder
First stage absolute encoder
".\
The Z track in Fig 2 generates 24 signals per revolution. The total accuracy, involving location errors of the detecting devices and positioning errors of the pattern, of the neighbouring Y track is as follows, using the symbols in Fig 4:
Reference / plate
0 < A~ < 2~z/24 = 22.5 ° For the X track,
Chuck
0
' Air bearing ~
If the pattern of the Z track is correctly made and detected, the required accuracy of the other patterns is remarkably reduced. Therefore, the most severe accuracy of the pattern for 2 n signals is 2~/2n= ~/2 n-l, except for the least significant bit pattern. When the absolute encoder is connected with the reduction gears as shown in Fig 6, the allowable error of the second stage absolute encoder is as follows: 0 < A~ < 2~,~z
68
(3)
rv ) ~oto¢
=
'
r
DC se!-vo rrlotor
encoder
Fig 7 Developed absolute encoder in a cylindrical form-measuring machine
APRIL 1988 VOL 10 NO 2
Tsukada and Kanada--multi-turn encoder Table 2
Vcc (pc 5v)
Required specification
Pitch of lead screw Resolution Required range (decimal) Required number of bits
• ~
1.5 mm 0.05 mm 0-4400 13
~ Schmitt-trigger inverter (SN7414)
8 - b i t g r e y code absolutq e n c o d e r
5-bit binary code absolute encoder
I~
•
O Sy1
ooved rotating plate
Photosensor
~...~$.:
~l' ; ',;i
'
Input
Photo-sensor
~
Reduction
Grooved
pattern
gears
revolution
Fig 8 Combination with the commercial absolute encoder
Vcc
Fig 9 Mechanism of generating S~I and Sy2signals
Grey code input
A
0
r~]~l
0
l
[-c3-I
_i
021
0
r I.
~ ~
_I -~
022 °23
0 0
I
C
~
~ 1
0
NAND logic (SN7437)
020
![
Ao
DJ
°24 025
BO
027
Binary output (hexadecimal 4 bytes)
OC
Grey to binary logic (CI)
0 C 0 0 0 0
Binary code input
1~2
i
T
029 210
0 0
211
0 0
~
0 0
Logic '0' input ~I
~
0 212 J" ]"
0213 O 214 o 215
sy,
OSy
Sy2O Logic for Sy (C2)
Fig 10 Developed circuits for hexadecimal 4 bytes
PRECISION ENGINEERING
69
Tsukada and K a n a d a - - m u l t i - t u r n encoder
a reduction ratio of about 1:150 would be required for the gears; this would be very expensive. Therefore, the combination of a commercial 8-bit grey code absolute encoder and the absolute encoder so developed (5-bit, binary) has been designed as shown in Fig 8. The former encoder is connected in series with a lead screw by reduction ratio of 1 5:1 28. Further, the latter encoder is connected in series with the above axis reduced by 1:20. The allowable error for this set of encoders is z ~ = 9 ° from Eq (3). The final function can be obtained with relatively rough reduction gears. The latter encoder structure is realized in a grooved cylinder made of aluminium. The grooves are detected by the photosensor, as in Fig 9. Its signal is Schmitt-triggered by 1-1"L. Then, the signals of SY1 and Sy2 are obtained. Fig 10 shows the transforming circuits of the 8bit grey code and 5-bit binary encoders for microcomputer processing. The role of the circuit C1 is the transformation from grey to binary codes; C2 is the same as in Fig 6.
Conclusions In this research, a multi-turn absolute rotary encoder w a s developed according to a design insensitive to accuracy. The main conclusions are as follows.
70
(1)
(2)
(3)
(4)
(5)
A structure having phase difference between two detecting devices for pattern is considered. In this way, a binary absolute encoder can be realized. Its accuracy depends on only the least significant bit pattern generation. By means of the above structure and with the help of logical processing of the signals, the required accuracy for the mechanical structure can be remarkably reduced. According to the design concept of this research, multi-turn devices can be easily realized without demanding high accuracy of the mechanical components. The allowable limits of error for the developed multi-turn absolute encoder components are presented. Further, the electronic logic circuits have been designed. This newly developed multi-turn absolute rotary encoder can be combined with a commercial incremental rotary encoder to form a long-range scale detector. This reduces the cost/performance ratio.
References
1 Tsukada T. et al Measurementof cylindrical form errors using a noncontact detector. Precision Eng, 1982, 4(3), 153-158 2 The bipo/ar digital integrated circuits data book for design engineers, Parts 1 and 2, Texas Instruments Co Ltd, 1982
APRIL 1988 VOL 10 NO 2
Keywords: multi-turn absolute encoder, error compensation, logic circuits
If an absolute rotary encoder is connected in series by, for example, a lead screw, we can measure the absolute rotary position or movement of a table without considering a special setting such as a linear scale encoder. However, the measuring range of a general absolute encoder is one revolution of the encoder. Hence, if we want to know a longrange position, reduction gears should be applied with the encoder. Though high accuracy is required of the reduction gears, sufficient accuracy is not guaranteed by this method. There is a design concept by which the degree of accuracy necessary in the components is reduced without necessarily incurring loss of final function of the equipment, This is referred to as 'design insensitive to accuracy' in this paper. For example, in a magnetic disc of computer memory, the recording density is increased by making the distance between the writing/reading head and the disc as small (order of 0.1 /Jm) as possible. However, it is very difficult to achieve such a spatial relation by a rigid structure, and it would be very expensive. The head is, in fact, floating on the air rotating with the disc surface. The initial objective of controlling the floating distance can be achieved by the use of a spring. Another example is given by the method of size measurement according to Abbe's principle. When the measuring scale is located along the size direction to be measured, the effect of location error of the scale will be generally * Tokyo Institute of Technology, Department of Mechanical Engineering for Production, Oh-okayama 2-12- I, Meguro-ku, Tokyo 152,Japan ** Kanto Gakuin University, Department of Mechanical Engineering, Mutsuura 4834, Kanazawa-ku, Yokohama236, Japan
66
neglected. High accuracy of mechanical structure can be dispensed with not only in the abovementioned cases but also with regard to the maximum material principal of drawing (symbolized by (~) and so on. The application of such a design concept will reduce manufacturing cost. By means of this design concept, the required function of a multi-turn absolute rotary encoder can be realized without demanding high accuracy in the reduction gears. In this study, a mechanism producing a signal of absolute rotary angle and simple electronic logic circuits were developed for a multi-turn rotary encoder according to the above-mentioned design concept. This absolute encoder has been fitted in a cylindrical form-measuring machine developed by the authors 1, along with an absolute rotary encoder on the market, to provide information on the position of the sensor. The output from the multiturn encoder is input to a microcomputer, and its measuring range is adjusted to the cylindrical formmeasuring machine.
Principle of absolute rotary encoder Fig 1 shows a generating pattern of 4 bits by means of W, X, Y, and Z tracks for 16 different signals. In this pattern, because of the relative positioning error of the detecting device, the signal phase gaps such as At1 and A t 2 in Fig 2 occur. Hence, the signals '0' between '1" and '2', or '7" between '3' and '4', are caused by, respectively, At1 or At2. This is an error arising from the change of two or more bits at the same time. In order to prevent this phenomenon from occurring, the grey code in Table 1, whose bit change is unique, will generally
0141-6359/88/020066-05/S03.00 © 1988 Butterworth & Co (Publishers) Ltd
APRIL 1 988 VOL 10 NO 2
Tsukada and Kanada--multi-turn encoder
15
0
be applied. However, it is rather doubtful whether a multi-turn device with connecting reduction gears in series can be realized using conventional principles.
New principle of pattern generation
Let us consider a method for generating a correct signal, assuming that there are location errors of the detecting device and positioning errors of each pattern on the rotary plate, such as in Fig 1. Consider the lower 2 bits, namely the Y and Z tracks. Firstly, assume that the signal Sz of the least significant bit (Z track) is generated regularly by a correct pattern. The neighbouring Y track has two signals, Sy~ and SY2, of different phase as shown in Fig 3. The signal width (rotary angle) and the position (phase) are settled to satisfy the following criterion against Sz:
12
11
0 < A ~ n < ~, 8
7
}1
I]
(1)
Eq (1) is realized on the mechanical structure, and the regular signal Sy of the Y track is obtained by the following logic:
F/g1 Generating pattern for binary code
Z track ~
n=1,2,3,4
1]
Sy = {(NOT Sz)
AND SY1} OR {Sz AND Sy,}
= ~'~Z"SY 1 -~-Sz" SY 2
- - ~ - - Z~t1
(2)
The above logical operators NOT, AND, and OR are simply given by the electronic logic circuits (eg TTL). As long as the criterion of Eq (1) is satisfied, the errors of the mechanical structure do not affeqt the signal Sv when using Eq (2). Fig 4 shows the locations of the detecting devices for Sy~ and Sy2, satisfying Eq (1). Fig 5 shows an example of logical processing for Eq (2) by means of TTL 2.
Y track
X track
Decimal I Fig2
¢,
Error due to generating pattern
Table I
Decimal and bit pattern
Ztrack Sz I I I I I
Binary Decimal
Grey
W
X
Y
Z
W
X
Y
Z
0 1 2 3 4 5 6 7
0 0 0 0 0 0 0 0
0 0 0 0 1 1 1 1
0 0 1 1 0 0 1 1
0 1 0 1 0 1 0 1
0 0 0 0 0 0 0 0
0 0 0 0 1 1 1 1
0 0 1 1 1 1 0 0
0 1 1 0 0 1 1 0
8 9 10 11 12 13 14 15
1 1 1 1 1 1 1 1
0 0 0 0 1 1 1 1
0 0 1 1 0 0 1 1
0 1 0 1 0 1 0 1
1 1 1 1 1 1 1 1
1 1 1 1 0 0 0 0
0 0 1 1 1 1 0 0
0 1 1 0 0 1 1 0
SZ'SY1
I
Sz'Sy2
l
S'Z" Sy1 + SZ'Sy2 I Correct signal for Y track
I 4
Direction of rotation Fig 3
PRECISION ENGINEERING
1[
Structure of non-error generation
67
Tsukada and Kanada--multi-turn encoder A~ 3 A~ 1
Position o f S,, sensor ,I
i,
Regular position of , J - Y t r a c k sensor I_
,
Position of Sy1 sensor
where ~ is a coefficient• For example, the most significant bit of the first stage absolute encoder changes by 2'/turn, and the least significant bit of the second stage absolute encoder, 2*/turn; then, the reduction ratio is 2' 1/2'. Hence, 2= 1 / ( 2 ' 2 ' )
of Y track
F/g4 Positions of sensor for pattern reading NOT logic (SN7404) (SN7432)
SzO •
I ~
S
multi-turn
absolute
The multi-turn absolute rotary encoder so developed has been applied to a cylindrical form-measuring machine to provide information on the axial position of the sensor, as shown in Fig 7. The required specifications are presented in Table 2. In order to satisfy these specifications by one absolute encoder,
A~ 3
SyiO
If r = 1 and k = 8, then the allowable error is about 0.7 °. The allowable error becomes larger when k becomes smaller, and the number of stages increases, without a loss of the final function of the encoder. The developed encoder
P r o x y position o f Sy2 sensor
~
(4)
r
nth stage absolute
rotary
encoder
y Reduction
gears box
Sy20 First
stage absolute
rotary
encoder
AND logic (SN7408)
F g5 Electronic logic circuits for generating Sv
Fig 6 Module-structured multi-turn encoder Second stage absolute encoder
Insensitivity to accuracy of the new encoder
First stage absolute encoder
".\
The Z track in Fig 2 generates 24 signals per revolution. The total accuracy, involving location errors of the detecting devices and positioning errors of the pattern, of the neighbouring Y track is as follows, using the symbols in Fig 4:
Reference / plate
0 < A~ < 2~z/24 = 22.5 ° For the X track,
Chuck
0
' Air bearing ~
If the pattern of the Z track is correctly made and detected, the required accuracy of the other patterns is remarkably reduced. Therefore, the most severe accuracy of the pattern for 2 n signals is 2~/2n= ~/2 n-l, except for the least significant bit pattern. When the absolute encoder is connected with the reduction gears as shown in Fig 6, the allowable error of the second stage absolute encoder is as follows: 0 < A~ < 2~,~z
68
(3)
rv ) ~oto¢
=
'
r
DC se!-vo rrlotor
encoder
Fig 7 Developed absolute encoder in a cylindrical form-measuring machine
APRIL 1988 VOL 10 NO 2
Tsukada and Kanada--multi-turn encoder Table 2
Vcc (pc 5v)
Required specification
Pitch of lead screw Resolution Required range (decimal) Required number of bits
• ~
1.5 mm 0.05 mm 0-4400 13
~ Schmitt-trigger inverter (SN7414)
8 - b i t g r e y code absolutq e n c o d e r
5-bit binary code absolute encoder
I~
•
O Sy1
ooved rotating plate
Photosensor
~...~$.:
~l' ; ',;i
'
Input
Photo-sensor
~
Reduction
Grooved
pattern
gears
revolution
Fig 8 Combination with the commercial absolute encoder
Vcc
Fig 9 Mechanism of generating S~I and Sy2signals
Grey code input
A
0
r~]~l
0
l
[-c3-I
_i
021
0
r I.
~ ~
_I -~
022 °23
0 0
I
C
~
~ 1
0
NAND logic (SN7437)
020
![
Ao
DJ
°24 025
BO
027
Binary output (hexadecimal 4 bytes)
OC
Grey to binary logic (CI)
0 C 0 0 0 0
Binary code input
1~2
i
T
029 210
0 0
211
0 0
~
0 0
Logic '0' input ~I
~
0 212 J" ]"
0213 O 214 o 215
sy,
OSy
Sy2O Logic for Sy (C2)
Fig 10 Developed circuits for hexadecimal 4 bytes
PRECISION ENGINEERING
69
Tsukada and K a n a d a - - m u l t i - t u r n encoder
a reduction ratio of about 1:150 would be required for the gears; this would be very expensive. Therefore, the combination of a commercial 8-bit grey code absolute encoder and the absolute encoder so developed (5-bit, binary) has been designed as shown in Fig 8. The former encoder is connected in series with a lead screw by reduction ratio of 1 5:1 28. Further, the latter encoder is connected in series with the above axis reduced by 1:20. The allowable error for this set of encoders is z ~ = 9 ° from Eq (3). The final function can be obtained with relatively rough reduction gears. The latter encoder structure is realized in a grooved cylinder made of aluminium. The grooves are detected by the photosensor, as in Fig 9. Its signal is Schmitt-triggered by 1-1"L. Then, the signals of SY1 and Sy2 are obtained. Fig 10 shows the transforming circuits of the 8bit grey code and 5-bit binary encoders for microcomputer processing. The role of the circuit C1 is the transformation from grey to binary codes; C2 is the same as in Fig 6.
Conclusions In this research, a multi-turn absolute rotary encoder w a s developed according to a design insensitive to accuracy. The main conclusions are as follows.
70
(1)
(2)
(3)
(4)
(5)
A structure having phase difference between two detecting devices for pattern is considered. In this way, a binary absolute encoder can be realized. Its accuracy depends on only the least significant bit pattern generation. By means of the above structure and with the help of logical processing of the signals, the required accuracy for the mechanical structure can be remarkably reduced. According to the design concept of this research, multi-turn devices can be easily realized without demanding high accuracy of the mechanical components. The allowable limits of error for the developed multi-turn absolute encoder components are presented. Further, the electronic logic circuits have been designed. This newly developed multi-turn absolute rotary encoder can be combined with a commercial incremental rotary encoder to form a long-range scale detector. This reduces the cost/performance ratio.
References
1 Tsukada T. et al Measurementof cylindrical form errors using a noncontact detector. Precision Eng, 1982, 4(3), 153-158 2 The bipo/ar digital integrated circuits data book for design engineers, Parts 1 and 2, Texas Instruments Co Ltd, 1982
APRIL 1988 VOL 10 NO 2