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The Denavit and Hartenberg approach applied to evaluate the consequences in the tool tip position of geometrical errors in five-axis milling centres

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Abstract

In this work, a methodology for the estimation of the geometrical accuracy of five-axis milling centres is developed by using the well-known formulation proposed by Denavit and Hartenberg. Five-axis milling centres are kinematically much more complex than three-axis centres and, therefore, the consequences of parallelism and squareness errors between elements and joints are not as easily calculated. In the method presented here, assembly errors are introduced as additional geometric parameters in the element transformation matrices, resulting in the real transformation matrix for a real and, therefore, imperfect five-axis milling machine. This matrix defines the real position of the tool in the absolute reference system. Three types of machine structures have been studied, which are the most commonly built, assembled and sold: gantry with a two-rotary-axes head, transverse column with a two-rotary-axes tilting table and, finally, a machine with a swivelling spindle and rotating plate. Each of the elemental errors is described and the way to introduce them into the Denavit and Hartenberg matrices is proposed. Some of the errors can be measured using the ISO standard procedures but others must be measured using special experiments, which are described in Sect. 4 of this paper. Finally, a real application of the proposed methodology to improve the precision of a multi-axis drilling operation is explained.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of the Basque Country, ETSII, C/Alameda de Urquijo s/n, 48013, Bilbao, Spain

    A. Lamikiz, L. N. López de Lacalle, O. Ocerin & D. Díez

  2. Fundación Fatronik, Paseo Mikeletegi, 7 Parque Tecnológico, 20009, San Sebastián, Spain

    E. Maidagan

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  1. A. Lamikiz
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  2. L. N. López de Lacalle
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  3. O. Ocerin
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  4. D. Díez
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  5. E. Maidagan
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Correspondence to L. N. López de Lacalle.

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Lamikiz, A., López de Lacalle, L.N., Ocerin, O. et al. The Denavit and Hartenberg approach applied to evaluate the consequences in the tool tip position of geometrical errors in five-axis milling centres. Int J Adv Manuf Technol 37, 122–139 (2008). https://doi.org/10.1007/s00170-007-0956-5

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  • DOI: https://doi.org/10.1007/s00170-007-0956-5

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