Sensitivity Analysis for Optimal Design of Multibody Systems with Clearance Joint
محورهای موضوعی : Mechanical EngineeringSaeed Ebrahimi 1 , Esmaeil Salahshoor 2 , Saeed Nouri 3
1 - Department of Mechanical Engineering,
Yazd University, Iran
2 - Department of Mechanical Engineering,
Yazd University, Iran
3 - Department of Mechanical Engineering,
Yazd University, Iran
کلید واژه: Direct Differentiation, Clearance Joint, Optimization, Momentum Exchange Approach, Sensitivity analysis,
چکیده مقاله :
This paper deals with the sensitivity analysis and optimization of system parameters for a classical slider-crank mechanism as a multibody system which includes a clearance between the joints of coupler and slider. Due to the nonlinearity involved in the dynamics of clearance joints, the base reaction force, exerted on the base from the crank, changes roughly and does not vary as smooth as the case of the mechanism with ideal joint. Variation of the base reaction force can be a measure of the undesired vibrations induced due to the effect of clearance joint. After deriving the equations of motion and modeling the clearance, the direct differentiation method is used to conduct a local sensitivity analysis to assess the sensitivity measure of the base reaction force on some kinematic and contact parameters. The results show that the reaction force is more sensitive to the variation of link lengths and link masses compared to the variation of contact surface characteristics such as Young’s modulus, restitution coefficient and contact generalized stiffness in most parts of the motion cycle. On the other hand, the sensitivity of the base reaction force to the clearance size is very higher than its sensitivity to the above-mentioned kinematic and contact properties. Finally, based on the results of the sensitivity analysis, an optimization procedure is used to reduce the amount of the maximum base reaction force by choosing the optimized link lengths.
[1] Flores, P., Ambrósio, J., Pimenta Claro, J. C., and Lankarani, H. M., Kinematics and Dynamics of Multibody Systems with Imperfect Joints, Lecture Notes in Applied and Computational Mechanics, Vol. 34, Springer-Verlag, Berlin, Germany, 2008.
[2] Ebrahimi, S., A Contribution to Computational Contact Procedures in Flexible Multibody Systems, Ph.D. Dissertation, Reihe: Schriften aus dem Institut für Technische und Numerische Mechanik der Universität Stuttgart, Band 8, Shaker Verlag, Germany, 2007.
[3] Ebrahimi, S., Eberhard, P., Contact of Planar Flexible Multibody Systems Using a Linear Complementarity Formulation, PAMM Proceedings in Applied Mathematics and Mechanics, Vol. 5, 2005, pp. 197-198.
[4] Zhang, X., Zhang, X., and Chen, Z., Dynamic Analysis of a 3-RRR Parallel Mechanism with Multiple Clearance Joints, Mechanism and Machine Theory, Vol. 78, 2014, pp. 105-115.
[5] Erkaya, S., Analysis of Joint Clearance Effects on Dynamics of Six DOF Robot Manipulators, Mechanisms and Machine Science, Vol. 24, 2015, pp. 307-314.
[6] Li, Y., Quan, Q., Li, H., Tang, D., Li, Z., Fan, W., and Deng, Z., Air Rudder Mechanism Dynamics Considering Two Elements: Joint Clearance and Link Flexibility, Journal of Mechanical Science and Technology, Vol. 31, No. 7, 2017, pp. 3189–3197.
[7] Ben Abdallah, M. A., Khemili, I., and Aifaoui, N., Numerical Investigation of a Flexible Slider–crank Mechanism with Multijoints with Clearance, Multibody System Dynamics, Vol. 38, No. 2, 2016, pp. 173–199.
[8] Wang, X., Liu, G., Modeling and Simulation of Revolute Joint with Clearance in Planar Multibody Systems, Journal of Mechanical Science and Technology, Vol. 29, No. 10, 2015, pp. 4113–4120.
[9] Salahshoor, E., Ebrahimi, S., and Maasoomi, M., Nonlinear Vibration Analysis of Mechanical Systems with Multiple Joint Clearances using the Method of Multiple Scales, Mechanism and Machine Theory, Vol. 105, 2016, pp. 495–509.
[10] Li, P., Chen, W., Li, D., Yu, R., A Novel Transition Model for Lubricated Revolute Joints in Planar Multibody Systems, Multibody System Dynamics, Vol. 36, No. 3, 2016, pp. 279–294.
[11] Ebrahimi, S., Salahshoor, E., and Maasoomi, M., Application of the Method of Multiple Scales for Nonlinear Vibration Analysis of Mechanical Systems with Dry and Lubricated Clearance Joints, Journal of Theoretical and Applied Vibration and Acoustics, Vol. 3, No. 1, 2017, pp. 42-61.
[12] Mukras, S., Kim, N. H., Mauntler, N. A., Schmitz, T. L., and Sawyer, W. G., Analysis of Planar Multibody Systems with Revolute Joint Wear, Wear, Vol. 268, 2010, pp. 643–652.
[13] Su, Y., Chen, W., Tong, Y., and Xie, Y., Wear Prediction of Clearance Joint by Integrating Multibody Kinematics with Finite Element Method, Proc. ImechE part J: Journal of Engineering Tribology, Vol. 224, 2010, pp. 815-823.
[14] Feng, B. Z., Yang, Z., and Gui, W. X., Wear Analysis of Revolute Joints with Clearance in Multibody Systems, Science China Physics, Mechanics and Astronomy, Vol. 56, 2013, pp. 1581–1590.
[15] Pei, L., Wei, C., and Bin, Z. A., An Improved Practical Model for Wear Prediction of Revolute Clearance Joints in Crank Slider Mechanisms, Science China Technological Sciences, Vol. 56, No. 2, 2013, pp. 2953-2963.
[16] Zhao, B., Zhang, Z. N., and Dai, X. D., Modeling and Prediction of Wear at Revolute Clearance Joints in Flexible Multibody Systems, Proc. ImechE part C: Journal of Mechanical Engineering Science, Vol. 228, No. 2, 2014, pp. 317-329.
[17] Zhao, B., Dai, X. D., Zhang, Z. N., Wu, S. H., and Xie, Y. B., Numerical Study of Parametric Effects on Joint Wear in the Flexible Multibody Systems with Different Flexibilities and Clearance Sizes, Proc. ImechE part J: Journal of Engineering Tribology, Vol. 228, No. 8, 2014, pp. 819-835.
[18] Flores, P., A Parametric Study on the Dynamic Response of Planar Multibody Systems with Multiple Clearance Joints, Nonlinear Dynamics, Vol. 61, 2010, pp. 633–653.
[19] Wang, X., Liu, G., Ma, S., and Tong, R., Effects of Restitution Coefficient and Material Characteristics on Dynamic Response of Planar Multibody Systems with Revolute Clearance Joint, Journal of Mechanical Science and Technology, Vol. 31, No. 2, 2017, pp. 587-597.
[20] Zhang, Z., Xu, L., Tay, Y. Y., Flores, P., and Lankarani, H., Multi-Objective Optimization of Mechanisms with Clearances in Revolute Joints, Mechanisms and Machine Science, Vol. 24, 2015, pp. 423-433.
[21] Erkaya, S., Uzmay, I., Optimization of Transmission Angle for Slider-Crank Mechanism with Joint Clearances, Structural and Multidisciplinary Optimization, Vol. 37, 2009, pp. 493–508.
[22] Erkaya, S., Uzmay, I., Investigation on Effect of Joint Clearance on Dynamics of Four-bar Mechanism, Nonlinear Dynamics, Vol. 58, 2009, pp. 179–198.
[23] Sardashti, A., Daniali, H. M., and Varedi, S. M., Optimal Free-Defect Synthesis of Four-bar Linkage with Joint Clearance using PSO Algorithm, Meccanica, Vol. 48, 2013, pp. 1681–1693.
[24] Daniali, H. M., Varedi, S. M., Dardel, M., and Fathi, A., A Novel Algorithm for Kinematic and Dynamic Optimal Synthesis of Planar Four-Bar Mechanisms with Joint Clearance, Journal of Mechanical Science and Technology, Vol. 29, No. 5, 2015, pp. 2059–2065.
[25] Rahmanian, S., Ghazavi, M. R., Bifurcation in Planar Slider–Crank Mechanism with Revolute Clearance Joint, Mechanism and Machine Theory, Vol. 91, 2015, pp. 86–101.
[26] Farahan, S. B., Ghazavi, M. R., and Rahmanian, S., Bifurcation in a Planar Four-bar Mechanism with Revolute Clearance Joint, Nonlinear Dynamics, Vol. 87, No. 2, 2017, pp. 955–973.
[27] Vaidya, A. M., Padole, P. M., A Performance Evaluation of Four-Bar Mechanism Considering Flexibility of Links and Joints Stiffness, The Open Mechanical Engineering Journal, Vol. 4, 2010, pp. 16-28.
[28] Erkaya, S., Prediction of Vibration Characteristics of a Planar Mechanism Having Imperfect Joints using Neural Network, Journal of Mechanical Science and Technology, Vol. 26, 2012, pp. 1419-1430.
[29] Ebrahimi, S., Salahhoor, E., and Moradi, S., Vibration Performance Evaluation of Planar Flexible Multibody Systems with Joint Clearance, Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 39, No. 12, 2017, pp. 4895-4909.
[30] Salahhoor, E., Ebrahimi, S., and Zhang, Y., Frequency Analysis of a Typical Planar Flexible Multibody System with Joint Clearances, Mechanism and Machine Theory, Vol. 126, 2018, pp. 429-456.
[31] Ebrahimi, S., Vahdatazad, N., Multiobjective Optimization and Sensitivity Analysis of Honeycomb Sandwich Cylindrical Columns under Axial Crushing Loads, Thin-Walled Structures, Vol. 88, 2015, pp. 90–104.
[32] Innocenti, C., Kinematic Clearance Sensitivity Analysis of Spatial Structures with Revolute Joints, Journal of Mechanical Design, Vol. 124, No. 1, 1999, pp. 52-57.
[33] Tsai, M. J., Lai, T. H., Kinematic Sensitivity Analysis of Linkage with Joint Clearance based on Transmission Quality, Mechanism and Machine Theory, Vol. 39, No. 11, 2004, pp. 1189-1206.
[34] Deng, Y., Kinematic Sensitivity Analysis of Two Degrees of Freedom Translational Parallel Manipulators, Master Thesis, Research Institute in Communications and Cybernetic of Nantes, University of Genova, 2012.
[35] Dai, Y., Fu, Y., Li, B., Wang, X., Yu, T., and Wang, W., Clearance Effected Accuracy and Error Sensitivity Analysis: A New Nonlinear Equivalent Method for Spatial Parallel Robot, Journal of Mechanical Science and Technology, Vol. 31, No. 11, 2017, pp. 5493–5504.
[36] Flores, P., Ambrosio, J., On the Contact Detection for Contact-impact Analysis in Multibody Systems, Multibody System Dynamics, Vol. 24, No. 1, 2010, pp. 103-122.
[37] Anderson, K. S., Hsu, Y. H., Analytical Fully Recursive Sensitivity Analysis for Multibody Dynamic Chain Systems, Multibody System Dynamics, Vol. 8, 2002, pp. 1–27.
[38] Ebrahimi, S., Haghi, A., Characterization of the Contribution of Inertial Parameters to the Dynamics of Multibody Systems, Multibody System Dynamics, Vol. 30, No. 4, 2010, pp. 449-460.
[39] Chang, C. O., Nikravesh P. E., Optimal Design of Mechanical Systems with Constraint Violation Stabilization Method, Journal of Mechanisms, Transmissions, and Automation in Design, Vol. 107, 1985, pp. 493-498.
[40] Eberhard, P., Schiehlen, W., and Sierts, J., Sensitivity Analysis of Inertia Parameters in Multibody Dynamics Simulations, 12th IFToMM World Congress, Besancon, June 18-21, 2007.
[41] Ebrahimi, S., Hajizadeh, I., and Payvandy, P., Multiobjective Constrained Optimization of a Newly Developed Needle Driving Mechanism in Sewing Machine for Performance Improvement, International Journal of Advanced Design and Manufacturing Technology, Vol. 7, No. 3, 2014, pp. 9-18.
[42] Erkaya, S., Uzmay, I., A Neural–Genetic (NN–GA) Approach for Optimizing Mechanisms Having Joints with Clearance, Multibody System Dynamics, Vol. 20, No. 1, 2008, pp. 69- 83.
