CN110617783A - Turntable eccentric error measuring method based on photoelectric detection modulation period particle swarm optimization - Google Patents
Turntable eccentric error measuring method based on photoelectric detection modulation period particle swarm optimization Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/26—Measuring arrangements characterised by the use of optical techniques for measuring angles or tapers; for testing the alignment of axes
- G01B11/27—Measuring arrangements characterised by the use of optical techniques for measuring angles or tapers; for testing the alignment of axes for testing the alignment of axes
- G01B11/272—Measuring arrangements characterised by the use of optical techniques for measuring angles or tapers; for testing the alignment of axes for testing the alignment of axes using photoelectric detection means
Abstract
The invention relates to a method for measuring eccentric errors of a turntable by particle swarm optimization of photoelectric detection modulation period, which adopts a modulation signal period photoelectric detection device of a rotary optical gate, counts and continuously measures the period value of a modulation signal of the turntable in each modulation period through a counter, and determines the eccentric amount and the eccentric position of the turntable by particle swarm optimization according to the relationship equation between the period value and the angle corresponding to a scribing line or a tooth uniformly distributed on the turntable and the eccentric amount and the eccentric position angle of the turntable, thereby providing a basis for coaxial adjustment of turntable parts. The device is simple and convenient, easy to operate, easy to realize and high in precision, provides a high-efficiency and high-precision measuring device and method for detecting the eccentric error of the turntable parts, and is suitable for measuring the eccentric error of the reticle circumference or part installation of the turntable parts with uniformly distributed reticles or teeth on the circumferences of a circular grating, a mechanical modulation disc, a photoelectric encoder code disc and the like.
Description
Technical Field
The invention relates to a method for measuring installation errors of rotary disc parts such as a circular grating, a mechanical modulation disc, a photoelectric encoder code disc and the like. In particular to a method for measuring the eccentricity and eccentric position of the installation of scribed line circumferences or parts of turntable parts with uniformly distributed scribed lines or teeth on the circumferences.
Background
When the parts such as the turnplate (the rotating disc) are installed, the installation error of the parts and the rotating shaft exists, and the coaxiality error is mainly caused by the eccentricity of the parts such as the turnplate and the rotating shaft. The error directly affects the working stability of the turntable and the precision of the output signal, so the detection and debugging of the error are necessary works for producing turntable parts. The existing eccentricity measurement method for the turntable-like component usually adopts a least square method of the contour of the circumferential edge of the turntable to obtain an eccentricity error, such as: two-dimensional coordinate measuring method, yellow 21180, and other < machine vision precision measurement system research > [ J ]. optical technology, 2004,30(4): 491-; a three-coordinate measuring method, Lijunfeng et al < compensation algorithm for mounting eccentricity of worm based on three-coordinate measurement >. New technology and new process 2010,1:34-37, obtaining the coordinates of the circumferential edge of an object through a three-coordinate measuring instrument, establishing a space coordinate system of a part, and determining the center of a circle by using a least square method so as to calculate the eccentricity of the object. The accuracy of the above method depends on the accuracy of the instrument measuring the circumferential edge. For turntable parts with evenly distributed scribed lines or teeth on the circumference, the eccentricity of the scribed line circumference or part mounting is also measured and corrected by adopting a photoelectric detection technology. Such as: the methods of the invention include (GPT-1 type grating eccentricity adjustment tester 2003,24(2), 171-; a method for detecting the eccentric error of the circular grating is provided: the method comprises the steps of acquiring 2 paths of sinusoidal signals by adopting double reading heads at two ends of a circular grating diameter pair, and orthogonally synthesizing the two paths of sinusoidal signals into a Lissajous figure through an oscilloscope to determine the phase difference of the 2 paths of signals, so as to detect the eccentricity and the eccentricity direction of the circular grating. The method can be used for measuring the eccentric error of a high-density uniform reticle disc, but a matched reading head is required to obtain 2 paths of sinusoidal signals, an oscilloscope or other equipment capable of synthesizing Lissajous figures is required, and the measurement accuracy is not high for reticle or turntable parts with fewer teeth. Highly-bin et al propose an error compensation and parameter identification method for a circular grating angle sensor [ J ] optical precision engineering, 2010,18(8): 1966-. The method can compensate the eccentricity error in real time, but a reading device needing matching extracts the rotation angle of the disc, and the size and the direction of eccentricity are not determined.
Disclosure of Invention
The present invention aims to provide a photoelectric detection device using the modulation signal period of the rotary optical gate, which measures the continuous period values of the modulation signal of the rotary disc, optimizes the particle swarm to obtain the installation eccentricity and the eccentric position, and provides a basis for the coaxial adjustment of the rotary disc parts.
The purpose of the invention is realized by the following technical scheme:
a method for measuring the eccentric error of rotary disk by photoelectric detection of modulation period and particle swarm optimization includes such steps as using the photoelectric detector for modulation signal period of rotary optical gate to make the ith graduation line or tooth pitch of rotary disk rotate at the detection position A for TiThe equation of (a) is:
wherein: i is 1,2, …, n, which is the sequence number of the modulation signal period; n is the number of scribed lines or teeth of the turntable part; f. of0Is the rotational speed (Hz) of the turntable. The included angle and the rotating speed are both anticlockwise positive.
A method for measuring eccentricity error of a turntable by photoelectric detection modulation period particle swarm optimization includes that a microprocessor unit 10 counts the whole period of each modulation signal when a zero detection signal is received effectively to obtain a count value s of the modulation signal in each whole period, wherein the count frequency is fcRepeatedly go inAfter m (m is more than or equal to n, n is the number of disc teeth or scribed lines of the turntable part) cycles of continuous rows, obtaining cycle count values s of m modulation cyclesi(ii) a Obtaining the eccentricity e and the eccentricity position theta of the rotary table through particle swarm optimization,
the method comprises the following steps:
A. the photoelectric detection device sets a measurement cycle number m value, the number of disc teeth of a turntable part or a reticle number n, wherein m is more than or equal to n; setting the measurement period number i of the current modulation signal to be 0; the counter is clear 0;
B. c, judging whether to start measurement according to whether the zero detection signal is effective, if so, setting a counter control signal to be effective, and entering the step C; otherwise, repeating the step;
C. judging whether each modulation whole period starts or ends according to whether the modulation signal is a period starting point, and if not, repeatedly judging; if yes, then:
if i is 0, namely the beginning of the 1 st period of the modulation signal, i is 1, the counter starts counting;
if 0<i<m, i.e. the end of the i-th cycle of the modulated signal, obtaining the count s of the i-th cycleiThe counter is clear 0; the beginning of the i +1 th period of the modulation signal, i is i +1, and the counter counts again;
D. judging whether the detection is finished: if i is m, ending the detection, turning to the step E, otherwise, returning to the step C;
E. calculating a period value of each period of the modulation signal:
wherein: f. ofcCounting the frequency for a timer; i is 1,2, …, m is the sequence number of the modulation signal period;
F. and (4) solving the eccentricity e and the eccentric position theta of the rotary table through particle swarm optimization.
The method for solving the eccentricity e and the eccentric position theta of the rotary table through particle swarm optimization comprises the following steps of:
a. defining particle parameters and optimizing intervals: defining a particle position P (k, theta) by taking parameters k as e/a and theta as a two-dimensional space, and determining an optimization interval W as [ 0-0.1; 0-2 pi ], and the interval lengths are respectively 0.001 to 0.k and pi/100 to 100 [ delta ] theta ];
b. defining the fitness function as:
c. determining a starting value: randomly taking values in each parameter optimization interval to form a starting position P1(t)＝[kt，θt]Z times, wherein z is a positive integer; defining z starting positions, t ═ 1,2, … …, z; defining a starting speed V for each position1(t)＝[Δk，Δθ]/b，b>1; z starting positions P to be defined1The corresponding data is substituted into the adaptive function formula (3) to obtain z f1(t) selecting the minimum value f1minThe corresponding position is taken as the initial global optimum position Pop(1)；S1(t)＝P1(t) setting an iteration stop time, an iteration stop threshold and a convergence threshold for the initial individual optimal position of the tth particle, wherein the iteration time j is 1;
d. update speed and position: defining a non-negative number as the inertial weight coefficient w, in combination with the optimum position Pop(j) And Sj(t) optimizing the velocity of each particle to obtain a new position velocity Vj+1(t)：
Vj+1(t)＝wVj(t)+c1r1(Sj(t)-Pj(t))+c2r2(Pop(j)-Pj(t)) (4)
Wherein: c. C1、c2Is a learning factor, is a non-negative number; r is1、r2Is distributed in [0,1 ]]A random number in between, and a random number,
updating the position of each particle to Pj+1(t)：
Pj+1(t)＝Pj(t)+Vj(t) (5)
Judgment of Pj+1(t) for each new position whether the elements are within the optimization space W, if Pj+1(t) if an element is not in W, the element isThe value remains the value of the last position; if yes, continuing;
every new position Pj+1(t) substituting the adaptive function formula (3) to obtain the fitness f corresponding to the z new positionsj+1(t) fitness value f of its previous global optimumjminComparing, and taking the minimum value f in z +1 fitness valuesj+1minAs a new global optimum position Pop(j+1)；
Determining a new individual optimum position S for each particlej+1(t): the current individual optimal position S of each particle is takenj(t) and New position Pj+1(t) fitness function fsj(t) and fj+1(t) the position corresponding to the minimum value;
e. and (3) judging: if fj+1minLess than the iteration stop threshold and fj+1min-fjminIf | is less than the convergence threshold, or j +1 is equal to the iteration number, the particle swarm parameter optimization is finished, and PopThe two-dimensional element value of (j +1) is the optimum values of k and theta; otherwise, j is j + 1; returning to the step d;
f. calculating the eccentricity e
e＝ka； (6)
g. And (6) ending.
Has the advantages that: the invention provides a method for measuring the installation eccentricity and the eccentric position of turntable parts, which provides a basis for the coaxial adjustment of the turntable parts. A photoelectric detection device is adopted, a coaxial motor of a tested turntable is driven by direct current stabilized current to obtain a modulation signal, and the eccentricity position of the turntable are determined by particle swarm optimization according to the period value of the modulation signal and the relation equation between the period value and the angle corresponding to the carved line or the tooth uniformly distributed on the turntable as well as the eccentricity and the eccentricity position angle of the turntable. Compared with the existing method, the detection device is simple, the measurement speed is high, the detection precision is high, and the detection cost is low.
Description of the drawings:
FIG. 1 is a block diagram of a photoelectric detection device for modulation period of a turntable
FIG. 2 is a front view of the mounting position of the turntable to be measured
FIG. 3 is a top view of the mounting position of the turntable to be measured
FIG. 4 is a flow chart of a turntable eccentricity error measurement method based on photoelectric detection modulation period particle swarm optimization
FIG. 5 is a flowchart of a periodic particle swarm optimization algorithm
1 rotary table, 2 shafts, 3 zero pins, 4 detection positions A, 5 modulation photoelectric pair tubes, 6 motors, 7 current stabilizing power supplies, 8 zero photoelectric pair tubes, 9 shaping circuits, 10 microprocessor units, 11 upper computers/peripherals
The specific implementation mode is as follows:
the following detailed description is made with reference to the accompanying drawings and examples:
a method for measuring eccentric errors of a turntable by photoelectric detection modulation period particle swarm optimization is characterized in that a modulation signal period photoelectric detection device of a rotary optical gate is adopted, as shown in figure 1, the device comprises an upper computer or a peripheral device, a photoelectric detection circuit and a rotary optical gate mechanism, wherein the photoelectric detection circuit is connected with the upper computer or a keyboard and the peripheral device for display through a data communication interface or a data line, the photoelectric detection circuit is respectively aligned with a zero position pin 3 of the rotary optical gate mechanism and a detection position A (4) of a turntable 1 to be detected through two photoelectric geminate transistors and is connected with the rotary optical gate mechanism, and A is the position of a disk tooth or a reticle of a turntable part; the photoelectric detection circuit is formed by connecting a shaping circuit 9 with a zero photoelectric pair tube 8 and a modulation photoelectric pair tube 5 respectively, and the shaping circuit 9 is connected with an upper computer through a processor unit 10; the rotary optical shutter mechanism is characterized in that a rotating shaft O of a tested turntable component is coaxially and fixedly connected with a direct current motor 6 through a coupler, and is connected with the direct current motor 6 through a power line current stabilizing power supply 7, a zero position pin 3 is installed on a connecting shaft 2 of the motor and the turntable component, and the position relation between the axial center O of the connecting shaft 2, the axial center B of the zero position pin 3 and a detection position A (4) is in a measurement initial state, namely a zero position, as shown in figures 2 and 3: the three parts are coplanar, the distance between O and A is a, the distance between B and O is perpendicular to O and A, the actual axis of the rotating disc is O ', the distance between O ' and O in the plane of the rotating disc is the eccentric amount of the rotating disc, the included angle theta between a straight line OO ' and OA in zero position measurement is an eccentric position angle, the detection position A is ensured to be on the initial edge of a scale or tooth of the rotating disc when the zero position is measured during installation,
when the turntable parts rotate at a constant speed around the rotating shaft O, the ith scale line or pitch of the turntable part is detectedPosition A over time TiThe equation of (a) is:
wherein: i is 1,2, …, n, which is the sequence number of the modulation signal period; n is the number of the carved lines or teeth of the turntable parts; f. of0The rotating speed (Hz) of the rotating disc, and the included angle and the rotating speed are both anticlockwise positive.
A method for measuring eccentricity error of rotary table by photoelectric detection modulation period particle swarm optimization includes counting each modulation signal in whole period by microprocessor unit 10 when zero detection signal is received effectively to obtain count value s of modulation signal in each whole period with counting frequency fcRepeating m (m is more than or equal to n, n is the number of disc teeth or scribed lines of the turntable part) cycles continuously, and obtaining cycle count values s of m modulation cyclesi(ii) a The eccentricity e and the eccentric position theta of the rotary table are obtained through particle swarm optimization, the realization process is shown in figures 4 and 5,
the method comprises the following steps:
A. the photoelectric detection device sets a measurement cycle number m value, the number of disc teeth of a turntable part or a reticle number n, wherein m is more than or equal to n; setting the measurement period number i of the current modulation signal to be 0; the counter is clear 0;
B. c, judging whether to start measurement according to whether the zero detection signal is effective, if so, setting a counter control signal to be effective, and entering the step C; otherwise, repeating the step;
C. judging whether each modulation whole period starts or ends according to whether the modulation signal is a period starting point, and if not, repeatedly judging; if yes, then:
if i is 0, namely the beginning of the 1 st period of the modulation signal, i is 1, the counter starts counting;
if 0<i<m, i.e. the end of the i-th cycle of the modulated signal, obtaining the count s of the i-th cycleiThe counter is clear 0; the beginning of the i +1 th period of the modulation signal, i is i +1, and the counter counts again;
D. judging whether the detection is finished: if i is m, ending the detection, turning to the step E, otherwise, returning to the step C;
E. calculating a period value of each period of the modulation signal:
wherein: f. ofcCounting the frequency for a timer; i is 1,2, …, m is the sequence number of the modulation signal period;
F. and (4) solving the eccentricity e and the eccentric position theta of the rotary table through particle swarm optimization.
The method for solving the eccentricity e and the eccentric position theta of the rotary table through particle swarm optimization comprises the following steps of:
a. defining particle parameters and optimizing intervals: defining a particle position P (k, theta) by taking parameters k as e/a and theta as a two-dimensional space, and determining an optimization interval W as [ 0-0.1; 0-2 pi ], and the interval lengths are respectively 0.001 to 0.k and pi/100 to 100 [ delta ] theta ];
b. defining the fitness function as:
c. determining a starting value: randomly taking values in each parameter optimization interval to form a starting position P1(t)＝[kt，θt]Z times, wherein z is a positive integer; defining z starting positions, t ═ 1,2, … …, z; defining a starting speed V for each position1(t)＝[Δk，Δθ]/b，b>1; z starting positions P to be defined1The corresponding data is substituted into the adaptive function formula (3) to obtain z f1(t) selecting the minimum value f1minThe corresponding position is taken as the initial global optimum position Pop(1)；S1(t)＝P1(t) setting an iteration stop time, an iteration stop threshold and a convergence threshold for the initial individual optimal position of the tth particle, wherein the iteration time j is 1;
d. update speed and position: defining a non-negative number as the inertial weight coefficient w, in combination with the optimum position Pop(j) And Sj(t) for each particle velocityOptimized to obtain new position speed Vj+1(t)：
Vj+1(t)＝wVj(t)+c1r1(Sj(t)-Pj(t))+c2r2(Pop(j)-Pj(t)) (4)
Wherein: c. C1、c2Is a learning factor, is a non-negative number; r is1、r2Is distributed in [0,1 ]]A random number in between, and a random number,
updating the position of each particle to Pj+1(t)：
Pj+1(t)＝Pj(t)+Vj(t) (5)
Judgment of Pj+1(t) for each new position whether the elements are within the optimization space W, if Pj+1(t) if an element is not within W, holding the value of the last position with the value of the element; if yes, continuing;
every new position Pj+1(t) substituting the adaptive function formula (3) to obtain the fitness f corresponding to the z new positionsj+1(t) fitness value f of its previous global optimumjminComparing, and taking the minimum value f in z +1 fitness valuesj+1minAs a new global optimum position Pop(j+1)；
Determining a new individual optimum position S for each particlej+1(t): the current individual optimal position S of each particle is takenj(t) and New position Pj+1(t) fitness function fsj(t) and fj+1(t) the position corresponding to the minimum value;
e. and (3) judging: if fj+1minLess than the iteration stop threshold and fj+1min-fjminIf | is less than the convergence threshold, or j +1 is equal to the iteration number, the particle swarm parameter optimization is finished, and PopThe two-dimensional element value of (j +1) is the optimum values of k and theta; otherwise, j is j + 1; returning to the step d;
f. calculating the eccentricity e
e＝ka； (6)
g. And (6) ending.
Claims (3)
1. Photoelectric detection modulation period particle swarm optimizationThe method for measuring eccentricity error of rotary disk is characterized by that when the rotary disk component is uniformly rotated by means of rotating shaft O, the ith scribed line or tooth pitch of the rotary disk component is rotated for a time T at detection position A of photoelectric detection device in the period of modulation signaliThe equation of (a) is:
wherein: i is 1,2, …, n, which is the sequence number of the modulation signal period, i.e. the scale line or the pitch on the turntable part; n is the number of scribed lines or teeth of the turntable part; f. of0The rotating speed Hz of the rotating shaft O; a is the distance between the detection position A and the rotating shaft O; e is the eccentric amount of the turntable relative to the rotating shaft O; theta is the eccentric position angle of the turntable; both the angle and the rotational speed are counterclockwise positive.
2. Method for measuring eccentricity error of a turntable by particle swarm optimization with photoelectric detection of modulation cycles according to claim 1, wherein the microprocessor unit (10) counts the whole cycle of each modulation signal at the beginning of the effective reception of the null detection signal, and obtains the count value s of the modulation signal in each whole cycle with the counting frequency fcRepeating m cycles, wherein m is more than or equal to n, n is the number of disc teeth or scribed lines of the turntable part, and obtaining a cycle count value s of m modulation cyclesi(ii) a Obtaining the eccentricity e and the eccentricity position theta of the rotary table through particle swarm optimization,
the method comprises the following steps:
A. the photoelectric detection device sets a measurement cycle number m value, the number of disc teeth of a turntable part or a reticle number n, wherein m is more than or equal to n; setting the measurement period number i of the current modulation signal to be 0; the counter is clear 0;
B. c, judging whether to start measurement according to whether the zero detection signal is effective, if so, setting a counter control signal to be effective, and entering the step C; otherwise, repeating the step;
C. judging whether each modulation whole period starts or ends according to whether the modulation signal is a period starting point, and if not, repeatedly judging; if yes, then:
if i is 0, namely the beginning of the 1 st period of the modulation signal, i is 1, the counter starts counting;
if 0<i<m, i.e. the end of the i-th cycle of the modulated signal, obtaining the count s of the i-th cycleiThe counter is clear 0; the beginning of the i +1 th period of the modulation signal, i is i +1, and the counter counts again;
D. judging whether the detection is finished: if i is m, ending the detection, turning to the step E, otherwise, returning to the step C;
E. calculating a period value of each period of the modulation signal:
wherein: f. ofcCounting the frequency for a timer; i is 1,2, …, m is the sequence number of the modulation signal period;
F. and (4) solving the eccentricity e and the eccentric position theta of the rotary table through particle swarm optimization.
3. The method for measuring the eccentricity error of the turntable by the particle swarm optimization of the photoelectric detection modulation period according to claim 2, wherein the method for solving the eccentricity e and the eccentricity position θ of the turntable by the particle swarm optimization comprises the following steps:
a. defining particle parameters and optimizing intervals: defining a particle position P by taking the parameters k as e/a and theta as a two-dimensional space, and determining an optimization interval W as [ 0-0.1; 0-2 pi ], and the interval lengths are respectively 0.001 to 0.k and pi/100 to 100 [ delta ] theta ];
b. defining the fitness function as:
c. determining a starting value: randomly taking values in each parameter optimization interval to form a starting position P1(t)＝[kt，θt]Z times, wherein z is a positive integer; defining z starting positions, t ═ 1,2, … …, z; defining a starting speed V for each position1(t)＝[Δk，Δθ]/b，b>1; will be provided withZ defined starting positions P1The corresponding data is substituted into the adaptive function formula (3) to obtain z f1(t) selecting the minimum value f1minThe corresponding position is taken as the initial global optimum position Pop(1)；S1(t)＝P1(t) setting an iteration stop time, an iteration stop threshold and a convergence threshold for the initial individual optimal position of the tth particle, wherein the iteration time j is 1;
d. update speed and position: defining a non-negative number as the inertial weight coefficient w, in combination with the optimum position Pop(j) And Sj(t) optimizing the velocity of each particle to obtain a new position velocity Vj+1(t)：
Vj+1(t)＝wVj(t)+c1r1(Sj(t)-Pj(t))+c2r2(Pop(j)-Pj(t)) (4)
Wherein: c. C1、c2Is a learning factor, is a non-negative number; r is1、r2Is distributed in [0,1 ]]A random number in between, and a random number,
updating the position of each particle to Pj+1(t)：
Pj+1(t)＝Pj(t)+Vj(t) (5)
Judgment of Pj+1(t) for each new position whether the elements are within the optimization space W, if Pj+1(t) if an element is not within W, holding the value of the last position with the value of the element; if yes, continuing;
every new position Pj+1(t) substituting the adaptive function formula (3) to obtain the fitness f corresponding to the z new positionsj+1(t) fitness value f of its previous global optimumjminComparing, and taking the minimum value f in z +1 fitness valuesj+1minAs a new global optimum position Pop(j+1)；
Determining a new individual optimum position S for each particlej+1(t): the current individual optimal position S of each particle is takenj(t) and New position Pj+1(t) fitness function fsj(t) and fj+1(t) the position corresponding to the minimum value;
e. and (3) judging: if fj+1minLess than the iteration stop threshold and fj+1min-fjminIf | is less than the convergence threshold, or j +1 is equal to the iteration number, the particle swarm parameter optimization is finished, and PopThe two-dimensional element value of (j +1) is the optimum values of k and theta; otherwise, j is j + 1; returning to the step d;
f. calculating the eccentricity e
e＝ka； (6)
g. And (6) ending.
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| CN115014244A (en) * | 2022-05-30 | 2022-09-06 | 吉林大学 | Method for measuring eccentric angle of rotary table by continuous modulation period and transposition compensation |
| CN115096215A (en) * | 2022-05-30 | 2022-09-23 | 吉林大学 | Turntable eccentricity angle measurement method based on full-period modulation signal period |
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| 王智宏等: "基于粒子群寻优的光谱仪波长误差修正方法", 《仪器仪表学报》 * |
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112414322A (en) * | 2020-11-11 | 2021-02-26 | 中国计量大学 | Turntable positioning error separation method |
| CN112414322B (en) * | 2020-11-11 | 2022-02-18 | 中国计量大学 | Turntable positioning error separation method |
| CN115014244A (en) * | 2022-05-30 | 2022-09-06 | 吉林大学 | Method for measuring eccentric angle of rotary table by continuous modulation period and transposition compensation |
| CN115096215A (en) * | 2022-05-30 | 2022-09-23 | 吉林大学 | Turntable eccentricity angle measurement method based on full-period modulation signal period |
| CN115014244B (en) * | 2022-05-30 | 2023-03-10 | 吉林大学 | Method for measuring eccentricity angle of turntable by continuous modulation period and transposition compensation |
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