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Synchronization precision compensation technology of dual-driving feed mechanism
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Procedia Manufacturing 26 (2018) 87–94 Procedia Manufacturing 00 (2017) 000–000 www.elsevier.com/locate/procedia
46th SME North American Manufacturing Research Conference, NAMRC 46, Texas, USA 46th SME North American Manufacturing Research Conference, NAMRC 46, Texas, USA
Synchronization precision compensation technology of dual-driving Synchronization precision compensation technology of dual-driving feed mechanism Manufacturing Engineering Societyfeed International Conference 2017, MESIC 2017, 28-30 June mechanism 2017, Vigo (Pontevedra), Spain Lu Honga,b, Yang Yongfeia*, Fan Weia, Wang Shaojunc , Wang Yufua, Xu Yifana Lu Honga,b, Yang Yongfeia*, Fan Weia, Wang Shaojunc , Wang Yufua, Xu Yifana
Wuhan University of Technology, Wuhan, China, 430070 4.0: Trade-off Costing modelsFirst foraffiliation, capacity optimization in Industry Second affiliation, Laboratory of Hubei Province for DigitalWuhan, Manufacture, First Key affiliation, Wuhan University of Technology, China, Wuhan, 430070China, 430070 Third affiliation, Southeast Missouri University ，Cape Girardeau, efficiency USA, MOChina, 63701430070 Second affiliation, Key Laboratory of HubeiState Province for Digital Manufacture, Wuhan, between used capacity and operational a
b b
a
c c
Third affiliation, Southeast Missouri State University ，Cape Girardeau, USA, MO 63701
A. Santanaa, P. Afonsoa,*, A. Zaninb, R. Wernkeb * Yang Yongfei. T el.:13697349223. E-mailYongfei. address:[email protected] * Yang el.:13697349223. a E-mail address: [email protected] University of Minho, 4800-058 Guimarães, Portugal b Unochapecó, 89809-000 Chapecó, SC, Brazil Abstract Abstract The dual-driving feed mechanism (DDFM ) has good feeding precision and reliability, but its synchronization error is unavoidable. Abstract The dual-driving feed mechanism (DDFM good feeding precision and reliability, but itsfor synchronization error is unavoidable. A brand-new compensation strategy called) has active compensation is proposed in this paper DDFM . The position errors of two A brand-new compensation strategy called compensation is proposed in this paper for DDFM . The position errors of two axes are measured in advance and they areactive compensated to the control instructions respectively before feeding to eliminate the Under the concept ofreduce "Industry 4.0", production will be to the be principle increasingly interconnected, error.are This strategy will the synchronization error inprocesses . Firstly, the pushed DDFM and of synchronization axes measured in advance and they are compensated toDDFM the control instructions respectively before feeding to eliminateerror the information based ontheareduce real time basis and, necessarily, much. Firstly, more efficient. Inand this optimization error. This strategy will the synchronization error DDFM the DDFM thecontext, principlecapacity of synchronization error are introduced. Then, simulation analysis of the activeincompensation strategy is carried out. Furthermore, the position error of goes beyond the traditional aimsynchronization ofanalysis capacity contributing alsois for organization’s profitability and error value. are introduced. Then, the simulation ofmaximization, the active compensation strategy carried out. Furthermore, the the position of DDFM is measured. Finally, the precision of active compensation strategy is compared against master slave Indeed, lean management and continuous improvement approaches suggest optimization of control. is The results show the effectiveness of the proposed active compensation strategy. DDFM measured. Finally, the synchronization precision of active compensation strategycapacity is compared against the instead master slave control. The results theof effectiveness of the proposed compensation maximization. Theshow study capacity optimization andactive costing models isstrategy. an important research topic that deserves © 2018 The Authors. Published by Elsevier contributions from both the practical andB.V. theoretical perspectives. This paper presents and discusses a mathematical © 2018 The Authors. Published by Elsevier B.V. © 2018for Thecapacity Authors. Published by Elsevier B.V. Peer-review under responsibility ofthe the scientific committee NAM RI/SM E. American model management based on different costing models and TDABC). A generic modelConference. has been Peer-review under responsibility of scientific committee ofofthe 46th SME(ABC North Manufacturing Research Peer-reviewand under responsibility of the scientific committee NAM RI/SM E. towards the maximization of organization’s developed it was used to analyze idle capacity and toofdesign strategies Keywords: mechanism; synchronization active compensation simulation. and it is shown that capacity value. TheDual-driving trade-off feed capacity maximization vs error; operational efficiencystrategy; is highlighted Keywords: Dual-driving feed mechanism; synchronization error; active compensation strategy; simulation. optimization might hide operational inefficiency.
© 2017 The Authors. Published by Elsevier B.V. 1. Introduction large load, good structure stiffness, small motor inertia, Peer-review under responsibility of the scientific committee of the Manufacturing Engineering Society International Conference 1. Introduction large load, good structureerror stiffness, small motorbetween inertia, but the synchronization is unavoidable 2017.
but the synchronization error component is unavoidable between With the increasing demand of high speed and high two axes. As a transmission of precision With the increasing demand of high speed and high two axes. As a transmission component of precision precision in modern industry, dual-driving feed CNC equipment, the precision of feed mechanis m Keywords: Cost Models; ABC; TDABC; Capacity Management; Idle Capacity; Operational Efficiency precision modern is industry, dual-driving feed CNC equipment, the precision of feed mechanis m mechanismin(DDFM) adopted in precision CNC directly determines the performance of CNC mechanism [1, (DDFM) adopted in directly of CNC equipment 2]. Theis worktable is precision driven by CNC dual equipment.determines Therefore, the it is performance of great significance to equipment The worktable is driven by dual equipment. it is error of great significance to 1. Introduction [3]. motor and [1, dual2].screw in the same direction. The research the Therefore, synchronization of DDFM motor and dual performance, screw in thesuch sameas withstanding direction. The research the synchronization error of DDFM [3]. DDFM has good a DDFM has of good such as withstanding a for companies and their management of extreme importance The cost idleperformance, capacity is a fundamental information 2351-9789 2018 The Authors. Published by Elsevier in modern©production systems. In general, it isB.V. defined as unused capacity or production potential and can be measured Peer-review under of the scientific committee of NAMRI/SME. 2351-9789 2018responsibility The Authors. Published by available Elsevier B.V. in several ©ways: tons of production, hours of manufacturing, etc. The management of the idle capacity Peer-review underTel.: responsibility of the scientific committee NAMRI/SME. * Paulo Afonso. +351 253 510 761; fax: +351 253 604of 741 E-mail address: [email protected]
2351-9789 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the Manufacturing Engineering Society International Conference 2017. 2351-9789 © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the 46th SME North American Manufacturing Research Conference. 10.1016/j.promfg.2018.07.011
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Lu Hong et al. / Procedia Manufacturing 26 (2018) 87–94 Author name / Procedia Manufacturing 00 (2018) 000–000
Scholars have proposed many methods to reduce the synchronization error. The most previous control of DDFM is mechanical rigid coupling [4]. However, the synchronization performance of DDFM heavily depends on the machining and assembly precision, which are hard to guarantee. So, the synchronization control of DDFM has changed from the mechanical method to the electrical control, such as electronic virtual main shaft control, cross coupling control, fuzzy PID control, and neural network control. The electronic virtual main shaft control is used to solve the problem based on the master-slave control [5].Cross coupling control was first proposed by Koren. The position difference and velocity difference of two axes are taken as feedback signals to compensate [6]. Fuzzy control was first proposed by L. A. Zadeh, a famous professor at the University of California in the United States. The error signal is input into the fuzzy controller, and the accurate output is obtained through the analysis [7]. Neural network control is also used in DDFM controlling in recent years [8]. A new control approach is also developed which is to stabilize speed tracking of each motor while synchronizing its motion with other motors' motions so that differential speed errors amongst multiple motors converge to zero [9].These control algorithms above are complex, and the dynamic synchronization performance is not good enough. They are difficult to apply in industry practice. A coupling control approach of dual axes is called “master-slave” control which has been widely adopted in industry practice for its simple structure. The position or velocity signal of the master motor is used as a reference command to the slave, which generates an unavoidable delay between the dual-driving systems and the load disturbance imposed on the slave axis cannot affect the master, which causes a poor synchronous performance in the load disturbance situation. Therefore, this paper presents the active compensation strategy. This paper is organized as follows. Section 2 introduces DDFM and the principle of synchronization error. The simulation analysis of the active compensation strategy is carried out in section 3. In section 4, the position error of DDFM is measured, and the synchronization precision of active compensation strategy is compared against the master slave control. Conclusions are drawn in section 5.
2. DDFM and its synchronization error 2.1. Single driving feed mechanism The transmission precision of the ball screw driving feed mechanism seriously affects the performance of the machine tool. The traditional CNC machine tool adopts single motor and single ball screw to drive the worktable. Its dynamic simplified model is shown in Fig.1. x
θ1
k1 k2 M c
Fig.1. Simplified dynamic model of single ball screw driving feed mechanism As shown in Fig.1, the ball screw driving feed mechanism is equivalent to the stiffness and damping unit, and the worktable is equivalent to a mass block M. The displacement of worktable is x, and the dynamic expression is as follows.
mx cx k1 x F
(1)
Where m is the quality of mass M, k 1 and c are the axial driving stiffness and damping of the ball screw, and F is the equivalent axial force to promote the worktable. F can be obtained by the following formula.
P F k2 h 1 x 2
(2)
Where Ph is the ball screw lead, 𝜃𝜃1 is the output of motor, and k 2 is the equivalent axial stiffness . Through the above analysis of the ball screw driving feed mechanism, the mechanical transfer function diagram of single ball screw driving feed mechanism can be obtained, as shown in Fig.2. k2
P k2 h 2
F
c 1 x 1 x m s
1 s
x
k1
Fig.2. Mechanical transfer function diagram of single ball screw driving feed mechanism
Lu Hong et al. / Procedia Manufacturing 26 (2018) 87–94 Author name / Procedia Manufacturing 00 (2018) 000–000
2.2. The analysis of synchronization error in DDFM
mx c1 x1 k3 x1 c2 x2 k4 x2 F1 F2
θ1
k3
θ
k1
L M θ2
x
k2
x2
J F1L c1 x1 k3 x1 L F2 L c2 x2 k4 x2 L
c1
(4) Where J is the rotational inertia of the worktable to the center of gravity, and L is the vertical distance fro m the screw to the center of gravity. 𝐹𝐹1 , 𝐹𝐹2 can be obtained by the following formula.
k4
c2
P F1 k1 h 1 x1 2 P F2 k2 h 2 x2 2
Fig.3. Simplified model of DDFM As shown in Fig.3, because of the diversity of motors, the angular displacements of the two motors are different. The worktable will be twisted, and the twist angle is 𝜃𝜃. The ball screw driving mechanism is equivalent to the stiffness and damping units, and the worktable is equivalent to a mass block M [10]. When the worktable is driving by the two motors, the outputs of two motors are 𝜃𝜃1 and 𝜃𝜃2 , and the displacement of the worktable are 𝑥𝑥 1 and𝑥𝑥 2. x is the displacement of the gravity center. There is one mass block M in the simplified model, so, the only one inertial force mx exist in the expression. Its dynamic expression in the x-y plane is as follows.
x1 x L x2 x L
2
c1s
k3 k3 L
P k1 h 2
k2
Ph 2
F1
F2
(5) (6)
Where Ph is the ball screw lead, 𝜃𝜃1 , 𝜃𝜃2 are the output of motor, and 𝑘𝑘1 , 𝑘𝑘2 are the equivalent axial stiffness. In addition, the following geometric relations can be obtained.
k1
1
(3)
Where m is the quality of mass M, and 𝑘𝑘3 , 𝑘𝑘4 , 𝑐𝑐1 , 𝑐𝑐2 are the axial driving stiffness and damping of the ball screw. 𝐹𝐹1 , 𝐹𝐹2 are the equivalent axial force to promote the worktable. Considering the twist of the worktable around Z axis, the following twist balance expression is established.
The DDFM researched in this paper uses dual motor with dual ball screw to drive the worktable in the same direction. The simplified dynamic model of DDFM is shown in Fig.3.
x1
89 3
L
1 x 1 x 1 x m s s
L
k4 L
c2 s
k4
x1
1 1 J s
c1sL
c2 sL
k2
Fig.4. Mechanical transfer function diagram of DDFM
L 1 s L
x2
(7) (8)
Lu Hong et al. / Procedia Manufacturing 26 (2018) 87–94 Author name / Procedia Manufacturing 00 (2018) 000–000
90 4
The mechanical transfer function diagram of DDFM can be obtained, as shown in Fig.4. Many differences exist between two axes, such as the outputs of two motors, the axial driving stiffness and damping and the equivalent axial stiffness. The installation and interference also affect the synchronization precision of DDFM. Synchronization error exists unavoidably. 3. The principle of active compensation strategy 3.1. The principle of active compensation strategy The main control method of DDFM is the masterslave control currently. As mentioned in section 1, the output of the master axis is the input of the salve axis . There is a delay between two axes all the time. When the slave axis is disturbed, it cannot be fed back to the master axis. So the synchronization error will occur between the two axes unavoidably. The active compensation strategy is proposed in this paper, which means the position errors are compensated to the two control instructions respectively before feeding to eliminate the error. Firstly, the position error of two axes must be measured in advance when the DDFM feeds at arbitrary speed, starting position and stroke. The method of error measurement is shown in Fig.5. The target position is entered into the controller. The position error is the difference between the target position and the actual position measured by grating ruler.
Target location
Transmission 1
Grating ruler
+
Transmission 2
Grating ruler
+
-
Controller
Error 1
Error 2
-
Fig.5. The method of position error measurement When the stroke is fixed, changing the starting position x, the position error function can be fitted by least square method as follows.
e x ax3 bx 2 cx d
(9)
The position error at arbitrary starting position can be calculated based on the function above. Furthermore, the position error compensation mat rix A is established as follows.
e11 x A= e x m1
e1n x emn x
(10)
𝑒𝑒𝑖𝑖𝑖𝑖 (𝑥𝑥) is the position error model. It represents the position error when the feed mechanism is feeding from the starting position x at the speed of i mm/s, and the stroke is j mm. The position errors of two axes are compensated to the respective control instructions before feeding through the error compensation mat rix A. The principle of active compensation strategy is shown in Fig.6. Compensation matrix A1
+
Transmission 1
Output 1
+
Control instruction
+ Compensation matrix A2
+
Transmission 2
Output 2
Fig.6. The principle of active compensation strategy In this strategy, the two axes are independent of each other. The synchronization precision can be guaranteed by improving the positioning precision of the two axes respectively through the active compensation. The mechanical error of the DDFM is also included in the active compensation. 3.2. Simulation According to the principle of active compensation strategy, the simulation analysis of active compensation is carried out. The simulation model is established in MATLAB / Simulink as shown in Fig.7. Simulation process is as follows . The simulation control instruction causes the feed mechanism feeding at an arbitrary position 6, when the stroke is 10 mm at a speed of 10 mm/s. The mechanical transmission error is loaded into the output of two axes respectively through the S-Function in the form of interference. The position and synchronization error of two axes are recorded by the oscilloscope. The position error of two axes is calculated, which is the distance between the actual position and the target position 16. The calculated position errors are compensated to the control instructions of two axes respectively. The simulation model of master slave control is also established in Fig.8.
Lu Hong et al. / Procedia Manufacturing 26 (2018) 87–94 Author name / Procedia Manufacturing 00 (2018) 000–000
91 5
Fig.7. Simulation model of active compensation strategy
Amplitude/mm
Amplitude/mm
Fig.8. Simulation model of master slave control
Time/s
Time/s
(a) Master slave control (b) Active compensation strategy Fig.9. Comparison of simulation results The simulation results are compared in Fig.9. In the and the red line represents the synchronization error figure, the blue line represents the position of the axis between the two axes. X1, the pink line represents the position of the axis X2, Comparing the results in Fig.9, the feed mechanism can be precisely positioned at the target position 16 at
Hong et al. / Procedia Manufacturing 26000–000 (2018) 87–94 Author Lu name / Procedia Manufacturing 00 (2018)
92 6
the active compensating strategy, and the synchronization error between two axes is 0. In the master slave control, the axis X1 and axis X2 are the master and slave axis respectively. There is a delay between two axes and the synchronization error between two axes exists all the time.
Axis X1
4. Experiment In order to verify the active compensation strategy, the experiment is carried out based on the DDFM shown in Fig.10.The dual motor and dual ball screw are used to drive the worktable at the same direction, and the grating ruler is used as the position detecting device.
Axis X2
Grating Ruler
Motor X2
Motor X1
Fig.10. Dual-driving feed mechanism starting position, 10 mm is fed at the speed of 5 mm/s 4.1. Position error of DDFM respectively. The position errors of two axes are recorded. The stroke of the feed mechanism is 230 mm. The position error of DDFM is measured firstly to Considering the effect of the clearance when the initial compensate. In this section, 10 mm is taken as an position is 0, the measurement takes 5, 6, 7, 8, and 9 example to measure the position error when the stroke as the starting position respectively. Averaging is fixed. A series of equidistant points within the stroke multiple measurements, the position errors of two axes of DDFM are taken as the starting positions. At each in each starting position are shown in Table 1, Table 2. Table 1. Position error of axis X1 Starting position
T arget stroke/mm
Actual stroke/mm
1
2
3
4
5
5
10
9.9351
9.9355
9.9361
9.9356
6
10
9.9986
9.9989
9.9998
9.9995
7
10
9.9968
9.9976
9.9986
8
10
9.9993
9.9997
10.001
9
10
9.9985
9.9990
9.9979
Table 2. Position error of axis X2
Average/mm
Position error/mm
9.9347
9.9354
-0.0046
9.9987
9.9991
-0.0009
9.9972
9.9983
9.9977
-0.0023
9.9996
9.9999
9.9999
-0.0001
9.9988
9.9988
9.9986
-0.0014
Average/mm
Position error/mm
Starting position
T arget stroke/mm
Actual stroke/mm
1
2
3
4
5
5
10
9.9975
9.9971
9.9965
9.9968
9.9971
9.9970
-0.0030
6
10
10.0008
10.001
10.000
10.0015
10.0007
10.0008
0.0008
7
10
9.9958
9.9970
9.9957
9.9963
9.9962
9.9962
-0.0038
8
10
9.9967
9.9958
9.9960
9.9965
9.9970
9.9964
-0.0036
9
10
9.9999
9.9989
9.9997
9.9986
9.9994
9.9993
-0.0007
Lu Hong et al. / Procedia Manufacturing 26 (2018) 87–94 Author name / Procedia Manufacturing 00 (2018) 000–000
4.2. Experiment of active compensation strategy The position errors measured in 4.1 will be compensated to the control instructions of two axes. The compensation program is as follows. The same as the measurement, the position 5, 6, 7, 8 and 9 are taken as the starting position when the stroke is 10 mm at a speed of 5 mm/s respectively. Then the position errors X1 axis positioning error
+
are compensated to the two control instructions respectively before feeding. Measuring the displacement of two axes by grating ruler ， the synchronization error of DDFM in the feed process can be obtained. The principle of experiment is shown in Fig.11. Synchronization error between two axes at the active compensation strategy is compared with it at the master slave control.
X1 axis displacement
+
+ +
Transmission 2
X2 axis displacement
Synchronization error/mm
Fig.11. The principle The synchronization error curve of DDFM can be obtained by importing the measurement results into MATLAB. Starting position 5 is taken as an example. When the stroke is 10 mm at a speed of 5 mm/s, the synchronization error in feeding process is shown in Fig.12.
X:559 Y:-0.005741
Sampling number/time
(a) Active compensation strategy Synchronization error/mm
Grating ruler
+
Target location X2 axis positioning error
Transmission 1
93 7
Synchronization error
Grating ruler
of experiment The maximu m synchronization error in feeding process can be obtained by Fig.12. The synchronization error at starting position 6,7,8,9 can be obtained by the same method. The maximu m synchronization errors at the active compensation strategy and the master slave control are shown in Table 3. Table 3. The maximu m synchronization error /mm Starting position /mm
Stroke /mm
Master slave control
Active compensation
5
10
-0.006466
-0.005741
6
10
-0.007038
-0.006084
7
10
-0.006924
-0.005932
8
10
-0.00885
-0.007362
9
10
-0.00679
-0.005646
As shown in Table 3, when the stroke is 10 mm at a speed of 5 mm/s, the active compensation strategy can effectively reduce the synchronization error compared with the master slave control at the different starting positions. The results show the effectiveness of the proposed active compensation strategy. 5. Conclusions
X:693 Y:-0.006466
Sampling number/time
(b) Master slave control Fig.12. Synchronization error of DDFM
A brand-new active compensation strategy is proposed in this paper. Firstly, the DDFM and the principle of synchronization error are introduced. Then the simulation analysis is carried out based on the principle of active compensation strategy. Finally , compared with master slave control, the active compensation strategy is verified by experimen t .
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Lu Hong et al. / Procedia Manufacturing 26 (2018) 87–94 Author name / Procedia Manufacturing 00 (2018) 000–000
Active compensation strategy can enhance the synchronization precision of DDFM. The position errors measured is limited in this work. In the following research, all the position error of the DDFM will be measured and an automatic compensation software will be developed. Acknowledgements This work is supported by the Excellen t Dissertation Cultivation Funds of Wuhan University of Technology (No.2017-YS-030). References [1] S. K. Jeong, S. S.You. Precise position synchronous control of multi-axis servo system. Mechatronics, 18 (2008) 129-140. [2] C. Li, B. Yao, X. Zhu, Q. Wang. Adaptive Robust Synchronous Control with Dynamic Thrust Allocation of Dual Drive Gantry Stage. IEEE/ASME International Conference on Advanced Intelligent Mechatronics, (2014) 316-321. [3] B. Sencer, T . Mori, E. Shamoto. Design and application of a sliding mode controller for accurate motion synchronization of dual servo systems. Control Engineering Practice, 21(11), (2013) 1519-1530. [4] H. K. Park, S. S. Kim, J. M. Park,D. Hong, T .Y.Cho. Design of a Dual-Drive Mechanism for Precision Gantry. KSME International Journal, 16(12), (2002) 1664-1672. [5] M. A. Valenzuela,R. D. Lorenz. Electronic line-shafting control for paper machine drives. IEEE T ransactions on Industry Applications, 37(1), (2000) 158–164. [6] Y. Koren. Cross-coupled biaxial computer control for manufacturing systems. Journal of Dynamic Systems Measurement & Control, 102(4), (1980) 265–272. [7] A. F. Amer, E. A. Sallam, W. M. Elawady. Fuzzy precompensated fuzzy self-tuning fuzzy PID controller of 3 DOF planar robot manipulators. IEEE/ASME International Conference on Advanced Intelligent Mechatronics, (2011) 599604. [8] M. Bouziane, M Abdelkader. A neural network based speed control of a dual star induction motor. International Journal of Electrical & Computer Engineering, 4(6), (2014) 953-961. [9] D. Zhao, C. Li, J. Ren. Speed synchronization of multiple induction motors with adjacent cross coupling control. IEEE Conference on Decision & Contol, 4(1), (2009) 6805-6810. [10]Y. Cheng. Non-synchronous error and modeling of dual-drive system in gantry-type machine tools with travelling bridge. Journal of Mechanical Engineering, 49(13), (2013) 174-182.
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Procedia Manufacturing 26 (2018) 87–94 Procedia Manufacturing 00 (2017) 000–000 www.elsevier.com/locate/procedia
46th SME North American Manufacturing Research Conference, NAMRC 46, Texas, USA 46th SME North American Manufacturing Research Conference, NAMRC 46, Texas, USA
Synchronization precision compensation technology of dual-driving Synchronization precision compensation technology of dual-driving feed mechanism Manufacturing Engineering Societyfeed International Conference 2017, MESIC 2017, 28-30 June mechanism 2017, Vigo (Pontevedra), Spain Lu Honga,b, Yang Yongfeia*, Fan Weia, Wang Shaojunc , Wang Yufua, Xu Yifana Lu Honga,b, Yang Yongfeia*, Fan Weia, Wang Shaojunc , Wang Yufua, Xu Yifana
Wuhan University of Technology, Wuhan, China, 430070 4.0: Trade-off Costing modelsFirst foraffiliation, capacity optimization in Industry Second affiliation, Laboratory of Hubei Province for DigitalWuhan, Manufacture, First Key affiliation, Wuhan University of Technology, China, Wuhan, 430070China, 430070 Third affiliation, Southeast Missouri University ，Cape Girardeau, efficiency USA, MOChina, 63701430070 Second affiliation, Key Laboratory of HubeiState Province for Digital Manufacture, Wuhan, between used capacity and operational a
b b
a
c c
Third affiliation, Southeast Missouri State University ，Cape Girardeau, USA, MO 63701
A. Santanaa, P. Afonsoa,*, A. Zaninb, R. Wernkeb * Yang Yongfei. T el.:13697349223. E-mailYongfei. address:[email protected] * Yang el.:13697349223. a E-mail address: [email protected] University of Minho, 4800-058 Guimarães, Portugal b Unochapecó, 89809-000 Chapecó, SC, Brazil Abstract Abstract The dual-driving feed mechanism (DDFM ) has good feeding precision and reliability, but its synchronization error is unavoidable. Abstract The dual-driving feed mechanism (DDFM good feeding precision and reliability, but itsfor synchronization error is unavoidable. A brand-new compensation strategy called) has active compensation is proposed in this paper DDFM . The position errors of two A brand-new compensation strategy called compensation is proposed in this paper for DDFM . The position errors of two axes are measured in advance and they areactive compensated to the control instructions respectively before feeding to eliminate the Under the concept ofreduce "Industry 4.0", production will be to the be principle increasingly interconnected, error.are This strategy will the synchronization error inprocesses . Firstly, the pushed DDFM and of synchronization axes measured in advance and they are compensated toDDFM the control instructions respectively before feeding to eliminateerror the information based ontheareduce real time basis and, necessarily, much. Firstly, more efficient. Inand this optimization error. This strategy will the synchronization error DDFM the DDFM thecontext, principlecapacity of synchronization error are introduced. Then, simulation analysis of the activeincompensation strategy is carried out. Furthermore, the position error of goes beyond the traditional aimsynchronization ofanalysis capacity contributing alsois for organization’s profitability and error value. are introduced. Then, the simulation ofmaximization, the active compensation strategy carried out. Furthermore, the the position of DDFM is measured. Finally, the precision of active compensation strategy is compared against master slave Indeed, lean management and continuous improvement approaches suggest optimization of control. is The results show the effectiveness of the proposed active compensation strategy. DDFM measured. Finally, the synchronization precision of active compensation strategycapacity is compared against the instead master slave control. The results theof effectiveness of the proposed compensation maximization. Theshow study capacity optimization andactive costing models isstrategy. an important research topic that deserves © 2018 The Authors. Published by Elsevier contributions from both the practical andB.V. theoretical perspectives. This paper presents and discusses a mathematical © 2018 The Authors. Published by Elsevier B.V. © 2018for Thecapacity Authors. Published by Elsevier B.V. Peer-review under responsibility ofthe the scientific committee NAM RI/SM E. American model management based on different costing models and TDABC). A generic modelConference. has been Peer-review under responsibility of scientific committee ofofthe 46th SME(ABC North Manufacturing Research Peer-reviewand under responsibility of the scientific committee NAM RI/SM E. towards the maximization of organization’s developed it was used to analyze idle capacity and toofdesign strategies Keywords: mechanism; synchronization active compensation simulation. and it is shown that capacity value. TheDual-driving trade-off feed capacity maximization vs error; operational efficiencystrategy; is highlighted Keywords: Dual-driving feed mechanism; synchronization error; active compensation strategy; simulation. optimization might hide operational inefficiency.
© 2017 The Authors. Published by Elsevier B.V. 1. Introduction large load, good structure stiffness, small motor inertia, Peer-review under responsibility of the scientific committee of the Manufacturing Engineering Society International Conference 1. Introduction large load, good structureerror stiffness, small motorbetween inertia, but the synchronization is unavoidable 2017.
but the synchronization error component is unavoidable between With the increasing demand of high speed and high two axes. As a transmission of precision With the increasing demand of high speed and high two axes. As a transmission component of precision precision in modern industry, dual-driving feed CNC equipment, the precision of feed mechanis m Keywords: Cost Models; ABC; TDABC; Capacity Management; Idle Capacity; Operational Efficiency precision modern is industry, dual-driving feed CNC equipment, the precision of feed mechanis m mechanismin(DDFM) adopted in precision CNC directly determines the performance of CNC mechanism [1, (DDFM) adopted in directly of CNC equipment 2]. Theis worktable is precision driven by CNC dual equipment.determines Therefore, the it is performance of great significance to equipment The worktable is driven by dual equipment. it is error of great significance to 1. Introduction [3]. motor and [1, dual2].screw in the same direction. The research the Therefore, synchronization of DDFM motor and dual performance, screw in thesuch sameas withstanding direction. The research the synchronization error of DDFM [3]. DDFM has good a DDFM has of good such as withstanding a for companies and their management of extreme importance The cost idleperformance, capacity is a fundamental information 2351-9789 2018 The Authors. Published by Elsevier in modern©production systems. In general, it isB.V. defined as unused capacity or production potential and can be measured Peer-review under of the scientific committee of NAMRI/SME. 2351-9789 2018responsibility The Authors. Published by available Elsevier B.V. in several ©ways: tons of production, hours of manufacturing, etc. The management of the idle capacity Peer-review underTel.: responsibility of the scientific committee NAMRI/SME. * Paulo Afonso. +351 253 510 761; fax: +351 253 604of 741 E-mail address: [email protected]
2351-9789 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the Manufacturing Engineering Society International Conference 2017. 2351-9789 © 2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the 46th SME North American Manufacturing Research Conference. 10.1016/j.promfg.2018.07.011
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Lu Hong et al. / Procedia Manufacturing 26 (2018) 87–94 Author name / Procedia Manufacturing 00 (2018) 000–000
Scholars have proposed many methods to reduce the synchronization error. The most previous control of DDFM is mechanical rigid coupling [4]. However, the synchronization performance of DDFM heavily depends on the machining and assembly precision, which are hard to guarantee. So, the synchronization control of DDFM has changed from the mechanical method to the electrical control, such as electronic virtual main shaft control, cross coupling control, fuzzy PID control, and neural network control. The electronic virtual main shaft control is used to solve the problem based on the master-slave control [5].Cross coupling control was first proposed by Koren. The position difference and velocity difference of two axes are taken as feedback signals to compensate [6]. Fuzzy control was first proposed by L. A. Zadeh, a famous professor at the University of California in the United States. The error signal is input into the fuzzy controller, and the accurate output is obtained through the analysis [7]. Neural network control is also used in DDFM controlling in recent years [8]. A new control approach is also developed which is to stabilize speed tracking of each motor while synchronizing its motion with other motors' motions so that differential speed errors amongst multiple motors converge to zero [9].These control algorithms above are complex, and the dynamic synchronization performance is not good enough. They are difficult to apply in industry practice. A coupling control approach of dual axes is called “master-slave” control which has been widely adopted in industry practice for its simple structure. The position or velocity signal of the master motor is used as a reference command to the slave, which generates an unavoidable delay between the dual-driving systems and the load disturbance imposed on the slave axis cannot affect the master, which causes a poor synchronous performance in the load disturbance situation. Therefore, this paper presents the active compensation strategy. This paper is organized as follows. Section 2 introduces DDFM and the principle of synchronization error. The simulation analysis of the active compensation strategy is carried out in section 3. In section 4, the position error of DDFM is measured, and the synchronization precision of active compensation strategy is compared against the master slave control. Conclusions are drawn in section 5.
2. DDFM and its synchronization error 2.1. Single driving feed mechanism The transmission precision of the ball screw driving feed mechanism seriously affects the performance of the machine tool. The traditional CNC machine tool adopts single motor and single ball screw to drive the worktable. Its dynamic simplified model is shown in Fig.1. x
θ1
k1 k2 M c
Fig.1. Simplified dynamic model of single ball screw driving feed mechanism As shown in Fig.1, the ball screw driving feed mechanism is equivalent to the stiffness and damping unit, and the worktable is equivalent to a mass block M. The displacement of worktable is x, and the dynamic expression is as follows.
mx cx k1 x F
(1)
Where m is the quality of mass M, k 1 and c are the axial driving stiffness and damping of the ball screw, and F is the equivalent axial force to promote the worktable. F can be obtained by the following formula.
P F k2 h 1 x 2
(2)
Where Ph is the ball screw lead, 𝜃𝜃1 is the output of motor, and k 2 is the equivalent axial stiffness . Through the above analysis of the ball screw driving feed mechanism, the mechanical transfer function diagram of single ball screw driving feed mechanism can be obtained, as shown in Fig.2. k2
P k2 h 2
F
c 1 x 1 x m s
1 s
x
k1
Fig.2. Mechanical transfer function diagram of single ball screw driving feed mechanism
Lu Hong et al. / Procedia Manufacturing 26 (2018) 87–94 Author name / Procedia Manufacturing 00 (2018) 000–000
2.2. The analysis of synchronization error in DDFM
mx c1 x1 k3 x1 c2 x2 k4 x2 F1 F2
θ1
k3
θ
k1
L M θ2
x
k2
x2
J F1L c1 x1 k3 x1 L F2 L c2 x2 k4 x2 L
c1
(4) Where J is the rotational inertia of the worktable to the center of gravity, and L is the vertical distance fro m the screw to the center of gravity. 𝐹𝐹1 , 𝐹𝐹2 can be obtained by the following formula.
k4
c2
P F1 k1 h 1 x1 2 P F2 k2 h 2 x2 2
Fig.3. Simplified model of DDFM As shown in Fig.3, because of the diversity of motors, the angular displacements of the two motors are different. The worktable will be twisted, and the twist angle is 𝜃𝜃. The ball screw driving mechanism is equivalent to the stiffness and damping units, and the worktable is equivalent to a mass block M [10]. When the worktable is driving by the two motors, the outputs of two motors are 𝜃𝜃1 and 𝜃𝜃2 , and the displacement of the worktable are 𝑥𝑥 1 and𝑥𝑥 2. x is the displacement of the gravity center. There is one mass block M in the simplified model, so, the only one inertial force mx exist in the expression. Its dynamic expression in the x-y plane is as follows.
x1 x L x2 x L
2
c1s
k3 k3 L
P k1 h 2
k2
Ph 2
F1
F2
(5) (6)
Where Ph is the ball screw lead, 𝜃𝜃1 , 𝜃𝜃2 are the output of motor, and 𝑘𝑘1 , 𝑘𝑘2 are the equivalent axial stiffness. In addition, the following geometric relations can be obtained.
k1
1
(3)
Where m is the quality of mass M, and 𝑘𝑘3 , 𝑘𝑘4 , 𝑐𝑐1 , 𝑐𝑐2 are the axial driving stiffness and damping of the ball screw. 𝐹𝐹1 , 𝐹𝐹2 are the equivalent axial force to promote the worktable. Considering the twist of the worktable around Z axis, the following twist balance expression is established.
The DDFM researched in this paper uses dual motor with dual ball screw to drive the worktable in the same direction. The simplified dynamic model of DDFM is shown in Fig.3.
x1
89 3
L
1 x 1 x 1 x m s s
L
k4 L
c2 s
k4
x1
1 1 J s
c1sL
c2 sL
k2
Fig.4. Mechanical transfer function diagram of DDFM
L 1 s L
x2
(7) (8)
Lu Hong et al. / Procedia Manufacturing 26 (2018) 87–94 Author name / Procedia Manufacturing 00 (2018) 000–000
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The mechanical transfer function diagram of DDFM can be obtained, as shown in Fig.4. Many differences exist between two axes, such as the outputs of two motors, the axial driving stiffness and damping and the equivalent axial stiffness. The installation and interference also affect the synchronization precision of DDFM. Synchronization error exists unavoidably. 3. The principle of active compensation strategy 3.1. The principle of active compensation strategy The main control method of DDFM is the masterslave control currently. As mentioned in section 1, the output of the master axis is the input of the salve axis . There is a delay between two axes all the time. When the slave axis is disturbed, it cannot be fed back to the master axis. So the synchronization error will occur between the two axes unavoidably. The active compensation strategy is proposed in this paper, which means the position errors are compensated to the two control instructions respectively before feeding to eliminate the error. Firstly, the position error of two axes must be measured in advance when the DDFM feeds at arbitrary speed, starting position and stroke. The method of error measurement is shown in Fig.5. The target position is entered into the controller. The position error is the difference between the target position and the actual position measured by grating ruler.
Target location
Transmission 1
Grating ruler
+
Transmission 2
Grating ruler
+
-
Controller
Error 1
Error 2
-
Fig.5. The method of position error measurement When the stroke is fixed, changing the starting position x, the position error function can be fitted by least square method as follows.
e x ax3 bx 2 cx d
(9)
The position error at arbitrary starting position can be calculated based on the function above. Furthermore, the position error compensation mat rix A is established as follows.
e11 x A= e x m1
e1n x emn x
(10)
𝑒𝑒𝑖𝑖𝑖𝑖 (𝑥𝑥) is the position error model. It represents the position error when the feed mechanism is feeding from the starting position x at the speed of i mm/s, and the stroke is j mm. The position errors of two axes are compensated to the respective control instructions before feeding through the error compensation mat rix A. The principle of active compensation strategy is shown in Fig.6. Compensation matrix A1
+
Transmission 1
Output 1
+
Control instruction
+ Compensation matrix A2
+
Transmission 2
Output 2
Fig.6. The principle of active compensation strategy In this strategy, the two axes are independent of each other. The synchronization precision can be guaranteed by improving the positioning precision of the two axes respectively through the active compensation. The mechanical error of the DDFM is also included in the active compensation. 3.2. Simulation According to the principle of active compensation strategy, the simulation analysis of active compensation is carried out. The simulation model is established in MATLAB / Simulink as shown in Fig.7. Simulation process is as follows . The simulation control instruction causes the feed mechanism feeding at an arbitrary position 6, when the stroke is 10 mm at a speed of 10 mm/s. The mechanical transmission error is loaded into the output of two axes respectively through the S-Function in the form of interference. The position and synchronization error of two axes are recorded by the oscilloscope. The position error of two axes is calculated, which is the distance between the actual position and the target position 16. The calculated position errors are compensated to the control instructions of two axes respectively. The simulation model of master slave control is also established in Fig.8.
Lu Hong et al. / Procedia Manufacturing 26 (2018) 87–94 Author name / Procedia Manufacturing 00 (2018) 000–000
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Fig.7. Simulation model of active compensation strategy
Amplitude/mm
Amplitude/mm
Fig.8. Simulation model of master slave control
Time/s
Time/s
(a) Master slave control (b) Active compensation strategy Fig.9. Comparison of simulation results The simulation results are compared in Fig.9. In the and the red line represents the synchronization error figure, the blue line represents the position of the axis between the two axes. X1, the pink line represents the position of the axis X2, Comparing the results in Fig.9, the feed mechanism can be precisely positioned at the target position 16 at
Hong et al. / Procedia Manufacturing 26000–000 (2018) 87–94 Author Lu name / Procedia Manufacturing 00 (2018)
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the active compensating strategy, and the synchronization error between two axes is 0. In the master slave control, the axis X1 and axis X2 are the master and slave axis respectively. There is a delay between two axes and the synchronization error between two axes exists all the time.
Axis X1
4. Experiment In order to verify the active compensation strategy, the experiment is carried out based on the DDFM shown in Fig.10.The dual motor and dual ball screw are used to drive the worktable at the same direction, and the grating ruler is used as the position detecting device.
Axis X2
Grating Ruler
Motor X2
Motor X1
Fig.10. Dual-driving feed mechanism starting position, 10 mm is fed at the speed of 5 mm/s 4.1. Position error of DDFM respectively. The position errors of two axes are recorded. The stroke of the feed mechanism is 230 mm. The position error of DDFM is measured firstly to Considering the effect of the clearance when the initial compensate. In this section, 10 mm is taken as an position is 0, the measurement takes 5, 6, 7, 8, and 9 example to measure the position error when the stroke as the starting position respectively. Averaging is fixed. A series of equidistant points within the stroke multiple measurements, the position errors of two axes of DDFM are taken as the starting positions. At each in each starting position are shown in Table 1, Table 2. Table 1. Position error of axis X1 Starting position
T arget stroke/mm
Actual stroke/mm
1
2
3
4
5
5
10
9.9351
9.9355
9.9361
9.9356
6
10
9.9986
9.9989
9.9998
9.9995
7
10
9.9968
9.9976
9.9986
8
10
9.9993
9.9997
10.001
9
10
9.9985
9.9990
9.9979
Table 2. Position error of axis X2
Average/mm
Position error/mm
9.9347
9.9354
-0.0046
9.9987
9.9991
-0.0009
9.9972
9.9983
9.9977
-0.0023
9.9996
9.9999
9.9999
-0.0001
9.9988
9.9988
9.9986
-0.0014
Average/mm
Position error/mm
Starting position
T arget stroke/mm
Actual stroke/mm
1
2
3
4
5
5
10
9.9975
9.9971
9.9965
9.9968
9.9971
9.9970
-0.0030
6
10
10.0008
10.001
10.000
10.0015
10.0007
10.0008
0.0008
7
10
9.9958
9.9970
9.9957
9.9963
9.9962
9.9962
-0.0038
8
10
9.9967
9.9958
9.9960
9.9965
9.9970
9.9964
-0.0036
9
10
9.9999
9.9989
9.9997
9.9986
9.9994
9.9993
-0.0007
Lu Hong et al. / Procedia Manufacturing 26 (2018) 87–94 Author name / Procedia Manufacturing 00 (2018) 000–000
4.2. Experiment of active compensation strategy The position errors measured in 4.1 will be compensated to the control instructions of two axes. The compensation program is as follows. The same as the measurement, the position 5, 6, 7, 8 and 9 are taken as the starting position when the stroke is 10 mm at a speed of 5 mm/s respectively. Then the position errors X1 axis positioning error
+
are compensated to the two control instructions respectively before feeding. Measuring the displacement of two axes by grating ruler ， the synchronization error of DDFM in the feed process can be obtained. The principle of experiment is shown in Fig.11. Synchronization error between two axes at the active compensation strategy is compared with it at the master slave control.
X1 axis displacement
+
+ +
Transmission 2
X2 axis displacement
Synchronization error/mm
Fig.11. The principle The synchronization error curve of DDFM can be obtained by importing the measurement results into MATLAB. Starting position 5 is taken as an example. When the stroke is 10 mm at a speed of 5 mm/s, the synchronization error in feeding process is shown in Fig.12.
X:559 Y:-0.005741
Sampling number/time
(a) Active compensation strategy Synchronization error/mm
Grating ruler
+
Target location X2 axis positioning error
Transmission 1
93 7
Synchronization error
Grating ruler
of experiment The maximu m synchronization error in feeding process can be obtained by Fig.12. The synchronization error at starting position 6,7,8,9 can be obtained by the same method. The maximu m synchronization errors at the active compensation strategy and the master slave control are shown in Table 3. Table 3. The maximu m synchronization error /mm Starting position /mm
Stroke /mm
Master slave control
Active compensation
5
10
-0.006466
-0.005741
6
10
-0.007038
-0.006084
7
10
-0.006924
-0.005932
8
10
-0.00885
-0.007362
9
10
-0.00679
-0.005646
As shown in Table 3, when the stroke is 10 mm at a speed of 5 mm/s, the active compensation strategy can effectively reduce the synchronization error compared with the master slave control at the different starting positions. The results show the effectiveness of the proposed active compensation strategy. 5. Conclusions
X:693 Y:-0.006466
Sampling number/time
(b) Master slave control Fig.12. Synchronization error of DDFM
A brand-new active compensation strategy is proposed in this paper. Firstly, the DDFM and the principle of synchronization error are introduced. Then the simulation analysis is carried out based on the principle of active compensation strategy. Finally , compared with master slave control, the active compensation strategy is verified by experimen t .
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Lu Hong et al. / Procedia Manufacturing 26 (2018) 87–94 Author name / Procedia Manufacturing 00 (2018) 000–000
Active compensation strategy can enhance the synchronization precision of DDFM. The position errors measured is limited in this work. In the following research, all the position error of the DDFM will be measured and an automatic compensation software will be developed. Acknowledgements This work is supported by the Excellen t Dissertation Cultivation Funds of Wuhan University of Technology (No.2017-YS-030). References [1] S. K. Jeong, S. S.You. Precise position synchronous control of multi-axis servo system. Mechatronics, 18 (2008) 129-140. [2] C. Li, B. Yao, X. Zhu, Q. Wang. Adaptive Robust Synchronous Control with Dynamic Thrust Allocation of Dual Drive Gantry Stage. IEEE/ASME International Conference on Advanced Intelligent Mechatronics, (2014) 316-321. [3] B. Sencer, T . Mori, E. Shamoto. Design and application of a sliding mode controller for accurate motion synchronization of dual servo systems. Control Engineering Practice, 21(11), (2013) 1519-1530. [4] H. K. Park, S. S. Kim, J. M. Park,D. Hong, T .Y.Cho. Design of a Dual-Drive Mechanism for Precision Gantry. KSME International Journal, 16(12), (2002) 1664-1672. [5] M. A. Valenzuela,R. D. Lorenz. Electronic line-shafting control for paper machine drives. IEEE T ransactions on Industry Applications, 37(1), (2000) 158–164. [6] Y. Koren. Cross-coupled biaxial computer control for manufacturing systems. Journal of Dynamic Systems Measurement & Control, 102(4), (1980) 265–272. [7] A. F. Amer, E. A. Sallam, W. M. Elawady. Fuzzy precompensated fuzzy self-tuning fuzzy PID controller of 3 DOF planar robot manipulators. IEEE/ASME International Conference on Advanced Intelligent Mechatronics, (2011) 599604. [8] M. Bouziane, M Abdelkader. A neural network based speed control of a dual star induction motor. International Journal of Electrical & Computer Engineering, 4(6), (2014) 953-961. [9] D. Zhao, C. Li, J. Ren. Speed synchronization of multiple induction motors with adjacent cross coupling control. IEEE Conference on Decision & Contol, 4(1), (2009) 6805-6810. [10]Y. Cheng. Non-synchronous error and modeling of dual-drive system in gantry-type machine tools with travelling bridge. Journal of Mechanical Engineering, 49(13), (2013) 174-182.