Kinematic modelling of a 3-axis NC machine tool in linear and circular interpolation

  • Xavier Pessoles
  • Yann Landon
  • Walter Rubio


Machining time is a major performance criterion when it comes to high-speed machining. CAM software can help in estimating that time for a given strategy. But in practice, CAM-programmed feed rates are rarely achieved, especially where complex surface finishing is concerned. This means that machining time forecasts are often more than one step removed from reality. The reason behind this is that CAM routines do not take either the dynamic performances of the machines or their specific machining tolerances into account. The present article seeks to improve simulation of high-speed NC machine dynamic behaviour and machining time prediction, offering two models. The first contributes through enhanced simulation of three-axis paths in linear and circular interpolation, taking high-speed machine accelerations and jerks into account. The second model allows transition passages between blocks to be integrated in the simulation by adding in a polynomial transition path that caters for the true machining environment tolerances. Models are based on respect for path monitoring. Experimental validation shows the contribution of polynomial modelling of the transition passage due to the absence of a leap in acceleration. Simulation error on the machining time prediction remains below 1%.


High-speed machining Linear interpolation Circular interpolation Polynomial transition 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Tapie L, Mawussi K, Anselmetti B (2007) Circular tests for HSM machine tools: bore machining application. Int J Mach Tools Manuf 47(5):805–819CrossRefGoogle Scholar
  2. 2.
    Flores V, Ortega C, Alberti M, Rodriguez CA, de Ciurana J, Elias A (2007) Evaluation and modeling of productivity and dynamic capability in high-speed machining centers. Int J Adv Manuf Technol 33(3):403–411CrossRefGoogle Scholar
  3. 3.
    Korkut I, Donertas M (2007) The influence of feed rate and cutting speed on the cutting forces, surface roughness and tool-chip contact length during face milling. Mater Des 28(1):308–312Google Scholar
  4. 4.
    Tsai MC, Cheng CW, Cheng MY (2003) A real-time NURBS surface interpolator for precision three-axis CNC machining. Int J Mach Tools Manuf 43(12):1217–1227CrossRefGoogle Scholar
  5. 5.
    Liu X et al (2005) Adaptive interpolation scheme for NURBS curves with the integration of machining dynamics. Int J Mach Tools Manuf 45(4–5):433–444CrossRefGoogle Scholar
  6. 6.
    Xu RZ, Xie L, Li CX, Du DS (2008) Adaptive parametric interpolation scheme with limited acceleration and jerk values for NC machining. Int J Adv Manuf Technol 36(3):343–354CrossRefGoogle Scholar
  7. 7.
    Sencer B, Altintas Y (2008) Feed optimization for five-axis CNC machine tools with drive constraints. Int J Mach Tools Manuf 48(7–8):733–745CrossRefGoogle Scholar
  8. 8.
    Siemens (2008) DOConWEB. Available documentation.
  9. 9.
    Erkorkmaz K, Altintas Y (2001) High speed CNC system design. Part I: jerk limited trajectory generation and quintic spline interpolation. Int J Mach Tools Manuf 41(9):1323–1345CrossRefGoogle Scholar
  10. 10.
    Aguilar IH (2006) Commande des bras manipulateurs et retour visuel pour des applications à la robotique de service. Ph.D. thesis, Université de Toulouse IIIGoogle Scholar
  11. 11.
    Nam S, Yang M (2004) A study on a generalized parametric interpolator with real-time jerk-limited acceleration. Comput Aided Des 36(1):27–36CrossRefGoogle Scholar
  12. 12.
    Lavernhe S, Tournier C, Lartigue C (2008) Kinematical performance prediction in multi-axis machining for process planning optimization. Int J Adv Manuf Technol 37(5):534–544CrossRefGoogle Scholar
  13. 13.
    Tounsi N, Bailey T, Elbestawi MA (2003) Identification of acceleration deceleration profile of feed drive systems in CNC machines. Int J Mach Tools Manuf 43(5):441–451CrossRefGoogle Scholar
  14. 14.
    Monreal M, Rodriguez CA (2003) Influence of tool path strategy on the cycle time of high-speed milling. Comput Aided Des 35(4):395–401CrossRefGoogle Scholar
  15. 15.
    Pateloup V, Duc E, Ray P (2004) Corner optimization for pocket machining. Int J Mach Tools Manuf 44(12–13):1343–1353CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2009

Authors and Affiliations

  1. 1.INSA, UPS, Mines Albi, ISAE; ICA (Institut Clément Ader)Université de ToulouseToulouseFrance

Personalised recommendations