Theoretical analysis of transmission error in rack and pinion systems

  1. Ulacia, Ibai 1
  2. Sánchez, Miryam B. 2
  3. Iñurritegui, Aurea 1
  4. Arana, Aitor 1
  5. Larrañaga, Jon 1
  6. Pedrero, José I. 2
  1. 1 Mondragon Unibertsitatea, Faculty of Engineering, Loramendi 4, 20500 Mondragon, Spain
  2. 2 UNED, Departamento de Mecánica, Juan del Rosal 12, 28040 Madrid, Spain
Actas:
MATEC Web of Conferences

ISSN: 2261-236X

Año de publicación: 2023

Volumen: 387

Páginas: 01001

Tipo: Aportación congreso

DOI: 10.1051/MATECCONF/202338701001 GOOGLE SCHOLAR lock_openAcceso abierto editor

Resumen

Rack and pinion drive systems are widely used in machine tools with long travel distances because the stiffness is independent of the travelled distance, in contrast to other drive systems such as ballscrews. Although the inherent backlash problem of gear systems has been solved by means of utilizing two pinions independently preloaded, the time-varying mesh stiffness causes periodic position differences between the motor encoder and table position, which is known as transmission error, and may lead to vibrations and dynamic load. Few experimental works have analyzed such transmission error, but there are no theoretical approaches in the scientific literature. Therefore, this work aims to first extend previous analytical and approximate equations for mesh stiffness of gearing to rack and pinion systems and validate them with finite element methods. Finally, the effect of geometry variations, such as pressure angle and tooth thickness tolerance, on transmission error is discussed.

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Información de financiación

The authors express their gratitude to the Spanish Council for Scientific and Technological Research for the support of the project PID2019-110996RB-I00, and UNED for the support of the action 2023-ETSII-UNED-04. I. Ulacia is also grateful to the Basque Government´s Department of Education for the support of the project ref. MV_2023_1_0033.

Referencias bibliográficas

  • Uriarte L., Zatarain M., Axinte D., Yagüe-Fabra J., Ihlenfeldt S., Eguia J., Olarra A., CIRP Ann. 62 (2013)
  • Verl A., Engelberth T., CIRP Ann. 67 (2008)
  • Engelbert T., Apprich S., Friedrich J., Coupek D., Lechler A., Prod. Eng. Res. Devel. 9 (2015)
  • Franco O., Beudaert X., Erkorkmaz K., J. Manuf. Mater. Process. 4 (2020)
  • Sánchez M.B., Pleguezuelos M., Pedrero J.I., Mech. Mach. Theory 109 (2017)
  • Weber C., Banaschek K., Vieweg Verlag, Braunschweig, Germany (1955)
  • Sainsot P., Velex P., Duverger O., J. Mech. Des. 126 (2004)
  • Pleguezuelos M., Sánchez M.B., Pedrero J.I., MATEC web of Conferences 317 (2020)
  • Marafona J., Marques P., Martins R., Seabra J., Mech. Mach. Theory 166 (2021)
  • Steinle L., Lechler A., Neubauer M., Verl A., Production Engineering 16 (2022)
  • Chen Z., Zeng M., Fuentes-Aznar A., J. Mech. Des. 142 (2020)
  • Duchemin M., Collee V., SAE Int J Engines 9 (2016)
  • Marano D, Piantoni A, Tabaglio L, Lucchi M, Barbieri M., Pellicano F. First World congress on condition monitoring (2017)
  • Zhou C., Dong X., Wang H., Liu Z., J. Brazilian Soc. Mech. Sci. & Eng. 44 (2022)
  • Larrañaga J., Ulacia I., Iñurritegui A., Arana A., German J., Elizegi J., AGMA FTM (2018)
  • Litvin F.L., Fuentes A., Gonzalez-Perez I., Carvenali L., Kawasaki K., Handschuh R.F., Comp. Meth. in App. Mech. and Eng. 192 (2003)
  • Dumitrache P., Mechanical Engineering 17 (2012)
  • Abaqus theory manual.
  • Iñurritegui A., Arana A., Hernandez M., Elizegi J., Ulacia I., Larrañaga J., XXII CNIM. (2018)
  • Sánchez M.B., Pleguezuelos M., Pedrero J.I., Mech. Mach. Theory 139 (2019)
  • Sánchez M.B., Pleguezuelos M., Pedrero J.I., Mech. Mach. Theory 133 (2019)
  • Sánchez M.B., Pleguezuelos M., Pedrero J.I., Meccanica 48 (2013)