Abstract
The reliability of the prediction model and test scheme for the positioning accuracy of the cycloid reducer is very important. This paper proposes an efficient bidirectional drive tooth contact analysis (BDTCA) model that can simultaneously analyze the forward transmission error (TE), the reverse TE, and the global lost motion (GLM) of a cycloid drive, considering a variety of manufacturing and assembly errors (including pin assembly error). The results of the BDTCA case studies show that the sensitivity of the pin radius error to the GLM considering pin assembly error is twice that of the sensitivity without considering pin assembly error. Therefore, the influence of pin assembly error on the GLM cannot be ignored. The equivalent error model for BDTCA is established based on Latin hypercube sampling and template measurement, and the positioning accuracy of 50,000 reducer virtual prototypes is predicted. According to the positioning accuracy requirements, the tolerance allocation is optimized by using the discrete particle swarm optimization algorithm, and the qualified rate after optimization is significantly improved. A bidirectional drive test (BDT) scheme is proposed according to the BDTCA model. By comparing with the traditional hysteresis curve test, the superiority of the BDT scheme and the rationality of the tolerance allocation optimization are proved. The sensitivity of the pin radius error to the GLM is obtained through a comparison BDT, which verifies the correctness of the BDTCA model considering pin assembly error. This BDTCA model provides more reliable theoretical guidance for the design and manufacture of cycloid reducers.
Issue Section:
Design of Direct Contact Systems
References
1.
Lin
, Y.
, Sun
, W.
, He
, G.
, and Zhang
, Z.
, 2021
, “Overview of Robotic Reducer Testing Technology
,” J. Phys.: Conf. Ser.
, 2002
(1
), p. 012025
. 2.
Ivanović
, L.
, Devedžić
, G.
, Ćuković
, S.
, and Mirić
, N.
, 2012
, “Modeling of the Meshing of Trochoidal Profiles With Clearances
,” ASME J. Mech. Des.
, 134
(4
), p. 041003
. 3.
Xu
, L. X.
, 2018
, “A Dynamic Model to Predict the Number of Pins to Transmit Load in a Cycloidal Reducer With Assembling Clearance
,” Proc. IMechE. Part C: J. Mech. Eng. Sci.
, 233
(12
), pp. 4247
–4269
.4.
Artyomov
, I. I.
, Tchufistov
, E. A.
, and Tchufistov
, O. E.
, 2019
, “Stress Loading and Losses of Power in the Pin-Roller Gearing With Clearances
,” IOP Conf. Ser.: Mater. Sci. Eng.
, 537
(3
), p. 032091
. 5.
Jiang
, N.
, Wang
, S.
, Xie
, X.
, Yuan
, X.
, Yang
, A.
, and Zhang
, J.
, 2022
, “A Vectorial Modification Methodology Based on an Efficient and Accurate Cycloid Tooth Profile Model
,” Precis. Eng.
, 73
(1
), pp. 435
–456
. 6.
Zhang
, C.
, Dong
, H.
, Wang
, D.
, and Cheng
, Y.
, 2021
, “Tolerance Synthesis for Lost Motion Requirement of Planetary Gear Train Based on a Mechanism Model
,” Mech. Mach. Theory
, 164
(1
), p. 104405
. 7.
Qiu
, Z.
, and Xue
, J.
, 2021
, “Review of Performance Testing of High Precision Reducers for Industrial Robots
,” Measurement
, 183
(1
), p. 109794
. 8.
Pham
, A.-D.
, and Ahn
, H.-J.
, 2021
, “Rigid Precision Reducers for Machining Industrial Robots
,” Int. J. Precis. Eng. Manuf.
, 22
(8
), pp. 1469
–1486
. 9.
Pham
, A. D.
, and Ahn
, H. J.
, 2018
, “High Precision Reducers for Industrial Robots Driving 4th Industrial Revolution: State of Arts, Analysis, Design, Performance Evaluation and Perspective
,” Int. J. Precis. Eng. Manuf. Green Technol.
, 5
(4
), pp. 519
–533
. 10.
Huang
, X.
, and Zhang
, J.
, 2020
, “Analysis of Geometric Characteristics of Cycloidal Transmission
,” IOP Conf. Ser.: Mater. Sci. Eng.
, 751
(1
), p. 012059
. 11.
Gorla
, C.
, Davoli
, P.
, Rosa
, F.
, Longoni
, C.
, Chiozzi
, F.
, and Samarani
, A.
, 2008
, “Theoretical and Experimental Analysis of a Cycloidal Speed Reducer
,” ASME J. Mech. Des.
, 130
(1
), p. 112604
. 12.
Sensinger
, J.
, 2013
, “Efficiency of High-Sensitivity Gear Trains, Such as Cycloid Drives
,” ASME J. Mech. Des.
, 135
(7
), p. 071006
. 13.
Malhotra
, S. K.
, and Parameswaran
, M. A.
, 1983
, “Analysis of a Cycloid Speed Reducer
,” Mech. Mach. Theory
, 18
(6
), pp. 491
–499
. 14.
Shuting
, L.
, 2014
, “Design and Strength Analysis Methods of the Trochoidal Gear Reducers
,” Mech. Mach. Theory
, 81
(1
), pp. 140
–154
. 15.
Efremenkov
, E. A.
, Kobza
, E. E.
, and Efremenkova
, S. K.
, 2015
, “Force Analysis of Double Pitch Point Cycloid Drive With Intermediate Rolling Elements and Free Retainer
,” Appl. Mech. Mater.
, 756
(1
), pp. 29
–34
. www.scientific.net/AMM.756.2916.
Hsieh
, C. F.
, 2014
, “Dynamics Analysis of Cycloidal Speed Reducers With Pinwheel and Nonpinwheel Designs
,” ASME J. Mech. Des.
, 136
(9
), p. 091008
. 17.
Blanche
, J. G.
, and Yang
, D. C. H.
, 1989
, “Cycloid Drives With Machining Tolerances
,” ASME J. Mech. Transm. Autom. Des.
, 111
(3
), p. 337
. 18.
Yang
, D. C. H.
, and Blanche
, J. G.
, 1990
, “Design and Application Guidelines for Cycloid Drives With Machining Tolerances
,” Mech. Mach. Theory
, 25
(5
), pp. 487
–501
. 19.
Hidaka
, T.
, Wang
, H. Y.
, Ishida
, T.
, Matsumoto
, K.
, and and Hashimoto
, M.
, 1994
, “Rotational Transmission Error of K-H-V Planetary Gears With Cycloid Gear: 1st Report, Analytical Method of the Rotational Transmission Error
,” Trans. Jpn. Soc. Mech. Eng. C
, 60
(570
), pp. 645
–653
. 20.
Li
, X.
, He
, W.
, Li
, L.
, and Schmidt
, L. C.
, 2004
, “A New Cycloid Drive With High-Load Capacity and High Efficiency
,” ASME J. Mech. Des.
, 126
(4
), pp. 683
–686
. 21.
Hwang
, Y. W.
, and Hsieh
, C. F.
, 2007
, “Geometric Design Using Hypotrochoid and Nonundercutting Conditions for an Internal Cycloidal Gear
,” ASME J. Mech. Des.
, 129
(4
), pp. 413
–420
. 22.
Li
, Y. H.
, Li
, W.
, and He
, W. D.
, 2011
, “RV Reducer Backlash Analysis Based on Robust Design
,” Appl. Mech. Mater.
, 148–149
(1
), pp. 418
–421
. www.scientific.net/AMM.148-149.41823.
Xu
, L.
, and Yang
, Y.
, 2016
, “Dynamic Modeling and Contact Analysis of a Cycloid-Pin Gear Mechanism With a Turning Arm Cylindrical Roller Bearing
,” Mech. Mach. Theory
, 104
(1
), pp. 327
–349
. 24.
Li
, X.
, Li
, C.
, Wang
, Y.
, Chen
, B.
, and Lim
, T.
, 2017
, “Analysis of a Cycloid Speed Reducer Considering Tooth Profile Modification and Clearance-Fit Output Mechanism
,” ASME J. Mech. Des.
, 139
(3
), p. 033303
. 25.
Xu
, L. X.
, Chen
, B. K.
, and Li
, C. Y.
, 2019
, “Dynamic Modelling and Contact Analysis of Bearing-Cycloid-Pinwheel Transmission Mechanisms Used in Joint Rotate Vector Reducers
,” Mech. Mach. Theory
, 137
(1
), pp. 432
–458
. 26.
Sun
, X.
, Han
, L.
, and Wang
, J.
, 2019
, “Design and Transmission Error Analysis of CBR Reducer
,” ASME J. Mech. Des.
, 141
(8
), p. 082301
. 27.
Sun
, X.
, and Han
, L.
, 2019
, “A New Numerical Force Analysis Method of CBR Reducer With Tooth Modification
,” J. Phys.: Conf. Ser.
, 1187
(3
), p. 032053
. 28.
Wang
, H.
, Shi
, Z.-Y.
, Yu
, B.
, and Xu
, H.
, 2019
, “Transmission Performance Analysis of RV Reducers Influenced by Profile Modification and Load
,” Appl. Sci.
, 9
(19
), p. 4099
. 29.
Wu
, K. Y.
, Shih
, Y. P.
, and Lee
, J. J.
, 2020
, “Kinematic Error Analysis of the Rotor Vector Gear Reducer With Machining Tolerances
,” J. Braz. Soc. Mech. Sci. Eng.
, 42
(11
), pp. 1
–16
.30.
Liu
, C.
, Shi
, W.
, Xu
, L.
, and Liu
, K.
, 2021
, “A Novel Approach to Calculating the Transmission Accuracy of a Cycloid-Pin Gear Pair Based on Error Tooth Surfaces
,” Appl. Sci.
, 11
(18
), p. 8671
. 31.
Li
, X.
, Tang
, L.
, He
, H.
, and Sun
, L.
, 2022
, “Design and Load Distribution Analysis of the Mismatched Cycloid-Pin Gear Pair in RV Speed Reducers
,” Machines
, 10
(8
), p. 672
. 32.
Li
, L.
, 1984
, “The Modification Manner for Tooth Profile and Analysis of Forces on the Cycloid Disk of a Cycloid Speed Reducer
,” Chin. J. Mech. Eng.
, 22
(1
), pp. 40
–49
.33.
Li
, L.
, Guan
, T.
, Wang
, Z.
, Liu
, Y.
, Wei
, Y.
, and Wan
, C.
, 1990
, “The Computer Aided Design of Cycloid Drive
,” Chin. J. Mech. Eng.
, 3
(2
), pp. 221
–231
.34.
Lin
, W. S.
, Shih
, Y. P.
, and Lee
, J. J.
, 2014
, “Design of a Two-Stage Cycloidal Gear Reducer With Tooth Modifications
,” Mech. Mach. Theory
, 79
(1
), pp. 184
–197
. 35.
Ren
, Z. Y.
, Mao
, S. M.
, Guo
, W. C.
, and Guo
, Z.
, 2017
, “Tooth Modification and Dynamic Performance of the Cycloidal Drive
,” Mech. Syst. Signal Process.
, 85
(1
), pp. 857
–866
. 36.
Li
, A.
, and Deng
, 2020
, “A New Tooth Profile Modification Method of Cycloidal Gears in Precision Reducers for Robots
,” Appl. Sci.
, 10
(4
), p. 1266
. 37.
Huang
, J.
, Li
, C.
, Zhang
, Y.
, Wang
, Y.
, and Chen
, B.
, 2021
, “Transmission Error Analysis of Cycloidal Pinwheel Meshing Pair Based on Rolling–Sliding Contact
,” J. Braz. Soc. Mech. Sci. Eng.
, 43
(1
), p. 7
. 38.
Su
, J.
, Jiang
, C.
, Zhang
, H.
, and Nie
, S.
, 2021
, “Error Analysis and Compensation of Cycloid Gear Form Grinding Based on Multi-body System Error Topology Theory
,” J. Braz. Soc. Mech. Sci. Eng.
, 44
(1
), p. 14
. 39.
Han
, L.
, and Guo
, F.
, 2016
, “Global Sensitivity Analysis of Transmission Accuracy for RV-Type Cycloid-Pin Drive
,” J. Mech. Sci. Technol.
, 30
(3
), pp. 1225
–1231
. 40.
Sun
, X.
, Han
, L.
, Ma
, K.
, Li
, L.
, and Wang
, J.
, 2018
, “Lost Motion Analysis of CBR Reducer
,” Mech. Mach. Theory
, 120
(1
), pp. 89
–106
. 41.
Wang
, J.
, Luo
, S.
, and Su
, D.
, 2016
, “Multi-Objective Optimal Design of Cycloid Speed Reducer Based on Genetic Algorithm
,” Mech. Mach. Theory
, 102
(1
), pp. 135
–148
. 42.
Yang
, M.
, Zhang
, D.
, Cheng
, C.
, and Han
, X.
, 2021
, “Reliability-Based Design Optimization for RV Reducer With Experimental Constraint
,” Struct. Multidiscipl. Optim.
, 63
(4
), pp. 2047
–2064
. 43.
Sensinger
, J. W.
, 2010
, “Unified Approach to Cycloid Drive Profile, Stress, and Efficiency Optimization
,” ASME J. Mech. Des.
, 132
(2
), p. 024503
. 44.
Wang
, C.
, and Mao
, K.
, 2021
, “Design of High Power Density for RV Reducer
,” J. Braz. Soc. Mech. Sci. Eng.
, 43
(6
), p. 291
. 45.
Wang
, Y.
, Qian
, Q.
, Chen
, G.
, Jin
, S.
, and Chen
, Y.
, 2017
, “Multi-Objective Optimization Design of Cycloid Pin Gear Planetary Reducer
,” Adv. Mech. Eng.
, 9
(9
), pp. 1
–10
.46.
Lin
, K.-S.
, Chan
, K.-Y.
, and Lee
, J.-J.
, 2018
, “Kinematic Error Analysis and Tolerance Allocation of Cycloidal Gear Reducers
,” Mech. Mach. Theory
, 124
(1
), pp. 73
–91
. 47.
Hang
, X. U.
, Shi
, Z.
, Bo
, Y. U.
, and Wang
, H.
, 2019
, “Dynamic Measurement of the Lost Motion of Precision Reducers in Robots and the Determination of Optimal Measurement Speed
,” J. Adv. Mech. Des. Syst. Manuf.
, 13
(3
), p. JAMDSM0044
. 48.
Litvin
, F. L.
, and Feng
, P. H.
, 1996
, “Computerized Design and Generation of Cycloidal Gearings
,” Mech. Mach. Theory
, 31
(7
), pp. 891
–911
. 49.
Lai
, T.-S.
, 2006
, “Design and Machining of the Epicycloid Planet Gear of Cycloid Drives
,” Int. J. Adv. Manuf. Technol.
, 28
(7–8
), pp. 665
–670
. 50.
Shin
, J. H.
, and Kwon
, S. M.
, 2006
, “On the Lobe Profile Design in a Cycloid Reducer Using Instant Velocity Center
,” Mech. Mach. Theory
, 41
(5
), pp. 596
–616
. 51.
Freudenstein
, F.
, Tsai
, L. W.
, and Maki
, E. R.
, 1984
, “The Generalized Oldham Coupling
,” ASME J. Mech. Des.
, 106
(4
), pp. 475
–481
.52.
Pham
, A. D.
, Tran
, T. L.
, and Ahn
, H.-J.
, 2017
, “Hysteresis Curve Analysis of a Cycloid Reducer Using Non-Linear Spring With a Dead Zone
,” Int. J. Precis. Eng. Manuf.
, 18
(3
), pp. 375
–380
. 53.
Semjon
, J.
, Hajduk
, M.
, Jáno
, R.
, and Tuleja
, P.
, 2012
, “Procedure Selection Bearing Reducer TwinSpin for Robotic Arm
,” Appl. Mech. Mater.
, 245
(1
), pp. 261
–266
. www.scientific.net/AMM.245.26154.
Chen
, B.
, Zhong
, H.
, Liu
, J.
, Li
, C.
, and Fang
, T.
, 2012
, “Generation and Investigation of a New Cycloid Drive With Double Contact
,��� Mech. Mach. Theory
, 49
(1
), pp. 270
–283
. 55.
Sun
, X.
, Han
, L.
, and Wang
, J.
, 2019
, “Tooth Modification and Loaded Tooth Contact Analysis of China Bearing Reducer
,” Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci.
, 233
(17
), pp. 6240
–6261
. 56.
Ishida
, T.
, Wang
, H.
, Hidaka
, T.
, and Hashimoto
, M.
, 1994
, “Rotational Transmission Error of K-H-V-Type Planetary Gears With Cycloid Gears: 2nd Report, Effects of Manufacturing and Assembly Errors on Rotational Transmission Error
,” Trans. Jpn. Soc. Mech. Eng. Ser. C
, 60
(578
), pp. 3510
–3517
. 57.
Yue
, H.
, Wu
, X.
, Shi
, Z.
, Zhang
, Y.
, Ye
, Y.
, Zhang
, L.
, and Fu
, Y.
, 2022
, “A Comprehensive Cycloid Pin-Wheel Precision Reducer Test Platform Integrated With a New Dynamic Measurement Method of Lost Motion
,” Metrol. Meas. Syst.
, 29
(1
), pp. 207
–229
.58.
Wang
, S.
, Tan
, J.
, Gu
, J.
, and Huang
, D.
, 2020
, “Study on Torsional Vibration of RV Reducer Based on Time-Varying Stiffness
,” J. Vib. Eng. Technol.
, 9
(1
), pp. 73
–84
. 59.
Zhang
, C.
, Dong
, H.
, Dong
, B.
, and Wang
, D.
, 2022
, “A Bi-Directional Drive Model for Lost Motion Behavior of Planetary Gear Train
,” Mech. Mach. Theory
, 174
(1
), p. 104885
. 60.
Li
, T.
, Tian
, M.
, Xu
, H.
, Deng
, X.
, An
, X.
, and Su
, J.
, 2020
, “Meshing Contact Analysis of Cycloidal-Pin Gear in RV Reducer Considering the Influence of Manufacturing Error
,” J. Braz. Soc. Mech. Sci. Eng.
, 42
(3
), p. 133
. 61.
Kreith
, F.
, and Goswami
, Y.
, 2004
, The CRC Handbook of Mechanical Engineering
, CRC Press
, Boca Raton, FL
.62.
Yi
, J.
, Jin
, T.
, Zhou
, W.
, and Deng
, Z.
, 2020
, “Theoretical and Experimental Analysis of Temperature Distribution During Full Tooth Groove Form Grinding
,” J. Manuf. Process.
, 58
(1
), pp. 101
–115
. 63.
Deng
, H.
, and Xu
, Z.
, 2019
, “Dressing Methods of Superabrasive Grinding Wheels: A Review
,” J. Manuf. Process.
, 45
(1
), pp. 46
–69
. 64.
Jain
, N. K.
, and Petare
, A. C.
, 2017
, “1.4 Review of Gear Finishing Processes,” Comprehensive Materials Finishing
, M. S. J.
Hashmi
, ed., Elsevier
, Oxford
, pp. 93
–120
.65.
Xia
, C.
, Wang
, S.
, Wang
, S.
, Ma
, C.
, and Xu
, K.
, 2021
, “Geometric Error Identification and Compensation for Rotary Worktable of Gear Profile Grinding Machines Based on Single-Axis Motion Measurement and Actual Inverse Kinematic Model
,” Mech. Mach. Theory
, 155
(1
), p. 104042
. 66.
Su
, J. X.
, Zhang
, Y. Z.
, and Deng
, X. Z.
, 2020
, “Analysis and Experimental Study of Cycloid Gear Form Grinding Temperature Field
,” Int. J. Adv. Manuf. Technol.
, 110
(3–4
), pp. 1
–17
.67.
Wu
, Y.
, Zheng
, J.
, Chen
, T.
, and Li
, L.
, 1999
, “The Analysis Research of the Geometric Lost Motion of High Accurate RV Reducer Used in Robot
,” J. Dalian Rail. Inst.
, 20
(2
), pp. 24
–27
.68.
Sun
, Y.
, Zhao
, X.
, Jiang
, F.
, Zhao
, L.
, Liu
, D.
, and Yu
, G.
, 2014
, “Backlash Analysis of RV Reducer Based on Error Factor Sensitivity and Monte-Carlo Simulation
,” Int. J. Hybrid Inf. Technol.
, 7
(2
), pp. 283
–292
. 69.
Li
, X.
, Chen
, B.-k.
, Wang
, Y.-w.
, and Lim
, T. C.
, 2018
, “Mesh Stiffness Calculation of Cycloid-Pin Gear Pair With Tooth Profile Modification and Eccentricity Error
,” J. Cent. South Univ.
, 25
(7
), pp. 1717
–1731
. 70.
Hu
, C.
, Geng
, G.
, and Spanos
, P. D.
, 2021
, “Stochastic Dynamic Load-Sharing Analysis of the Closed Differential Planetary Transmission Gear System by the Monte Carlo Method
,” Mech. Mach. Theory
, 165
(1
), p. 104420
. 71.
Krajnik
, P.
, Hashimoto
, F.
, Karpuschewski
, B.
, da Silva
, E. J.
, and Axinte
, D.
, 2021
, “Grinding and Fine Finishing of Future Automotive Powertrain Components
,” CIRP Ann.
, 70
(2
), pp. 589
–610
. 72.
Olsson
, A.
, Sandberg
, G.
, and Dahlblom
, O.
, 2003
, “On Latin Hypercube Sampling for Structural Reliability Analysis
,” Struct. Saf.
, 25
(1
), pp. 47
–68
. 73.
Bock
, J.
, and Hettenhausen
, J.
, 2012
, “Discrete Particle Swarm Optimisation for Ontology Alignment
,” Inf. Sci.
, 192
(6
), pp. 152
–173
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