A Method of General Stiffness Modeling for Multi-axis Machine Tool

Yan, Rong; Peng, Fangyu; Li, Bin

doi:10.1007/978-3-540-88518-4_108

Cited by 8 publications

(1 citation statement)

References 6 publications

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“…Therefore, determining the stiffness model matrix and investigating its stiffness characteristics over its workspace are necessary and can help programmers direct tool motion planning. Some studies 7–16 have examined the modelling methods and stiffness characteristics of parallel mechanisms. Bi 10 applied the kinetostatic method to develop a stiffness model.…”

Section: Introductionmentioning

confidence: 99%

Stiffness modelling and comparison of the 5-UPS/PRPU parallel machine tool with its non-redundant counterpart

Zhou

Yao

et al. 2016

Proceedings of the Institution of Mechanical Engineers, Part B:

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This article presents a derivation of the stiffness matrix of a general redundantly actuated parallel mechanism based on the overall Jacobian. The Jacobian of the constraints and actuations is derived using reciprocal screw theory. Based on the mapping relationship between constraint, actuated and external forces combined with the principle of virtual work, a compatibility equation for the deformation of all of the limbs is achieved, and the stiffness model of the general redundantly actuated parallel mechanism is derived. The 5-UPS/PRPU redundantly actuated parallel machine tool is used to illustrate this method. The parallel machine tool comprehensively reveals the effect of the elastic deformation of activepassive joints and some basic transmission parts. The stiffness model is further validated by experimental data. Moreover, the global stiffness matrix of the general redundantly actuated parallel mechanism can be separated into two parts via matrix decomposition. The first part is the stiffness matrix of the corresponding non-redundant parallel mechanism, and the second part is the stiffness matrix of the redundantly actuated limbs (actuators). The redundantly actuated 5-UPS/PRPU parallel machine tool is also investigated for further analysis. The different stiffness characteristics of the machine tool and its corresponding non-redundant 5-UPS/PRPU parallel machine tool are compared. Actuation redundancy is found to improve the stiffness performance of the machine tool efficiently.

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