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Dynamics of double pin caterpillar platform using a generalized cylindrical contact model

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Abstract

Compared with the single pin crawler, a double pin caterpillar platform has lower vibration and noise, which is widely used in tracked vehicles. However, its dynamical model is more complex due to its high degrees of freedom and laborious contact detection involved. It is significant to develop an accurate and efficient contact algorithm between tracks and wheels. In this paper, the profiles of the track connector and the tooth groove are discretized into several arc surfaces. The contact between them is characterized as convex and concave. Accordingly, a general mathematical description of the tooth profile is established to describe the real tooth groove geometry. Then a generalized cylindrical contact model is developed to evaluate forces. In the contact detection process, the local frames of the sprocket and tooth groove are employed, resulting in the vector quantities and coordinate transformations describing the contact arc surfaces constantly. This approach can facilitate programming and effectively improve calculation efficiency. Subsequently, a field test was performed to verify the correctness of the dynamical model. To reduce the wear of the sprocket, different cases are simulated, and a reasonable radius of the rubber ring is proposed.

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Data Availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

References

  1. Zhao, Z., Liu, H., Chen, H., Hu, J., Guo, H.: Kinematics-aware model predictive control for autonomous high-speed tracked vehicles under the off-road conditions. Mech. Syst. Signal Process. 123, 333–350 (2019)

    Article  ADS  Google Scholar 

  2. Wang, P., Yu, H., Rui, X., Zhang, J., Gu, J.: Transversal vibration analysis of the upper span of nonlinear closed-loop track systems. Appl. Math. Model. 78, 249–267 (2020)

    Article  MathSciNet  Google Scholar 

  3. Wallin, M., Aboubakr, A.K., Jayakumar, P., Letherwood, M.D., Gorsich, D.J., Hamed, A., Shabana, A.A.: A comparative study of joint formulations: application to multibody system tracked vehicles. Nonlinear Dyn. 74(3), 783–800 (2013)

    Article  Google Scholar 

  4. Wang, P., Wang, G., Rui, X., Yu, H., Zhang, S.: Contact dynamics analysis of the single-pin meshing pair of a tracked vehicle. Nonlinear Dyn. 104(2), 1139–1155 (2021)

    Article  Google Scholar 

  5. Scholar, C., Perkins, N.C.: Efficient vibration modelling of elastic vehicle track systems. J. Sound Vib. 228(5), 1057–1078 (1999)

    Article  ADS  Google Scholar 

  6. Huh, K., Hong, D.: Track tension estimation in tacked vehicles under various maneuvering tasks. J. Dyn. Syst. Meas. Control 123(2), 179–185 (2001)

    Article  Google Scholar 

  7. Sandu, C., Freeman, J.S.: Military tracked vehicle model, part I: multibody dynamics formulation. Int. J. Veh. Syst. Model. Test. 1(1), 48–67 (2005)

    Google Scholar 

  8. Sandu, C., Freeman, J.S.: Military tracked vehicle model. Part II: case study. Int. J. Veh. Syst. Model. Test. 1(1), 216–231 (2005)

    Google Scholar 

  9. Ma, Z., Perkins, N.C.: A super-element of track-wheel-terrain interaction for dynamic simulation of tracked vehicles. Multibody Syst. Dyn. 15(4), 347–368 (2006)

    Article  Google Scholar 

  10. Lee, J.H., Choi, J.H., Shabana, A.A.: Spatial dynamics of multibody tracked vehicles part II: contact forces and simulation results. Veh. Syst. Dyn. 29(2), 113–137 (1998)

    Article  Google Scholar 

  11. Nakanishi, T., Shabana, A.A.: Contact forces in the non-linear dynamic analysis of tracked vehicles. Int. J. Numer. Methods Eng. 37(8), 1251–1275 (1994)

    Article  Google Scholar 

  12. Gat, G., Franco, Y., Shmulevich, I.: Fast dynamic modeling for off-road track vehicles. J. Terramech. 92, 1–12 (2020)

    Article  Google Scholar 

  13. American, N.: Standards Institute, Precision Power Transmission Roller Chains, Attachments, and Sprockets (1975). ANSI Standard B29.1-1975, New York

  14. Ambrósio, J., Pombo, J.: A unified formulation for mechanical joints with and without clearances/bushings and/or stops in the framework of multibody systems. Multibody Syst. Dyn. 42(3), 317–345 (2018)

    Article  MathSciNet  Google Scholar 

  15. Ambrosio, J., Malça, C., Ramalho, A., Ramalho, A.: Planar roller chain drive dynamics using a cylindrical contact force model. Mech. Based Des. Struct. Mach. 44(1–2), 109–122 (2016)

    Article  Google Scholar 

  16. Pereira, C., Ambrósio, J., Ramalho, A.: Dynamics of chain drives using a generalized revolute clearance joint formulation. Mech. Mach. Theory 92, 64–85 (2015)

    Article  Google Scholar 

  17. Pereira, C.M., Ramalho, A.L., Ambrósio, J.A.: A critical overview of internal and external cylinder contact force models. Nonlinear Dyn. 63(4), 681–697 (2011)

    Article  Google Scholar 

  18. Tian, Q., Flores, P., Lankarani, H.M.: A comprehensive survey of the analytical, numerical and experimental methodologies for dynamics of multibody mechanical systems with clearance or imperfect joints. Mech. Mach. Theory 122, 1–57 (2018)

    Article  Google Scholar 

  19. Rui, X., Wang, X., Zhou, Q., Zhang, J.: Transfer matrix method for multibody systems (Rui method) and its applications. Sci. China, Technol. Sci. 62(5), 712–720 (2019)

    Article  ADS  Google Scholar 

  20. Wang, P., Rui, X., Yu, H.: Study on dynamic track tension control for high-speed tracked vehicles. Mech. Syst. Signal Process. 132, 277–292 (2019)

    Article  ADS  Google Scholar 

  21. Rui, X., Bestle, D.: Reduced multibody system transfer matrix method using decoupled hinge equations. Int. J. Mech. Syst. Dyn. 1(2), 182–193 (2021)

    Article  Google Scholar 

  22. Rui, X., Zhang, J., Zhou, Q.: Automatic deduction theorem of overall transfer equation of multibody system. Adv. Mech. Eng. 6, 1–12 (2015)

    Google Scholar 

  23. Rui, X., Zhang, J., Wang, X., Rong, B., He, B., Jin, Z.: Multibody system transfer matrix method: the past, the present, and the future. Int. J. Mech. Syst. Dyn. 2(1), 3–26 (2022)

    Article  Google Scholar 

  24. Corral, E., Meneses, J., Castejón, C., García-Prada, J.C.: Forward and inverse dynamics of the biped PASIBOT. Int. J. Adv. Robot. Syst. 11(7), 109 (2014)

    Article  Google Scholar 

  25. Wang, G., Liu, C.: Further investigation on improved viscoelastic contact force model extended based on Hertz’s law in multibody system. Mech. Mach. Theory 153, 103986 (2020)

    Article  ADS  Google Scholar 

  26. Liu, C., Zhang, K., Yang, R.: The FEM analysis and approximate model for cylindrical joints with clearances. Mech. Mach. Theory 42(2), 183–197 (2007)

    Article  Google Scholar 

  27. Rodrigues Da Silva, M., Marques, F., Tavares Da Silva, M., Flores, P.: A compendium of contact force models inspired by Hunt and Crossley’s cornerstone work. Mech. Mach. Theory 167, 104501 (2022)

    Article  Google Scholar 

  28. Corral, E., Moreno, R.G., García, M.J.G., Castejón, C.: Nonlinear phenomena of contact in multibody systems dynamics: a review. Nonlinear Dyn. 104(2), 1269–1295 (2021)

    Article  Google Scholar 

  29. Bai, Z., Xu, F., Zhao, J.: Numerical and experimental study on dynamics of the planar mechanical system considering two revolute clearance joints. Int. J. Mech. Syst. Dyn. 1(2), 256–266 (2021)

    Article  Google Scholar 

  30. Liu, J., Zhao, F., Xiao, Z., Wang, Y., Liu, Z., Zheng, H.: The establishment of the normal contact force model for a one-dimensional sphere chain subjected to impact load. Int. J. Mech. Syst. Dyn. 2(1), 131–142 (2022)

    Article  ADS  Google Scholar 

  31. Corral, E., Gismeros Moreno, R., Meneses, J., García, M.J.G., Castejón, C.: Spatial algorithms for geometric contact detection in multibody system dynamics. Mathematics 9(12), 1359 (2021)

    Article  Google Scholar 

  32. Marques, F., Flores, P., Claro, J.C.P., Lankarani, H.M.: Modeling and analysis of friction including rolling effects in multibody dynamics: a review. Multibody Syst. Dyn. 45(2), 223–244 (2019)

    Article  MathSciNet  Google Scholar 

  33. Pennestrì, E., Rossi, V., Salvini, P., Valentini, P.P.: Review and comparison of dry friction force models. Nonlinear Dyn. 83(4), 1785–1801 (2016)

    Article  Google Scholar 

  34. Brown, P., McPhee, J.: A continuous velocity-based friction model for dynamics and control with physically meaningful parameters. J. Comput. Nonlinear Dyn. 11(5), 54502 (2016)

    Article  Google Scholar 

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Funding

This work was supported by the Natural Science Foundation of Jiangsu Province (No. BK20210321), the National Natural Science Foundation of China (No. 11972193), and the National Natural Science Foundation of China (No. 12202196).

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Authors and Affiliations

  1. Nanjing University of Science and Technology, Nanjing, China

    Pingxin Wang, Xiaoting Rui, Guoping Wang, Hailong Yu, Bin He & Junjie Gu

Authors
  1. Pingxin Wang
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  2. Xiaoting Rui
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  3. Guoping Wang
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  4. Hailong Yu
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  5. Bin He
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  6. Junjie Gu
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Contributions

Assoc. Prof. Pingxin Wang wrote the main manuscript text and provided the funding acquisition. Prof. Xiaoting Rui and Prof. Guoping Wang contributed to the conception of the study. Prof. Hailong Yu and Prof. Bin He helped perform the analysis with constructive discussions. Assoc. Prof. Junjie Gu provided the funding acquisition.

Corresponding author

Correspondence to Junjie Gu.

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Wang, P., Rui, X., Wang, G. et al. Dynamics of double pin caterpillar platform using a generalized cylindrical contact model. Multibody Syst Dyn 60, 317–345 (2024). https://doi.org/10.1007/s11044-023-09900-0

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  • DOI: https://doi.org/10.1007/s11044-023-09900-0

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