This paper presents an innovative system determining machine tool quasi-static stiffness in machining space, so-called Stiffness Workspace System (SWS). The system allows for the assessment of the accuracy of a machine which has become a vital aspect over past years for machine tool manufacturers and users. Since machine tools static stiffness is one of the main criteria using to evaluate the machines' quality, it is crucial to highlight the relevance of experimental and analytical stiffness determination methods. Therefore, the proposed method is applied to estimate the spatial variation of static stiffness in the machine tool workspace. This paper describes the SWS system—its design, working principle, mounting conditions and signal processing. The major advantage of the system is the capability to apply forces of controlled magnitude and orientation as well as simultaneously measure the resulting displacements. The obtained results give possibility to estimate and evaluate static stiffness coefficients depending on the position and direction under loaded conditions. The results confirm the validity of the analyses of spatial stiffness distribution in the machine workspace.
In this paper, a method for estimation of cutting force model coefficients is proposed. The method makes use of regularized total least squares to identify the cutting forces from the measured acceleration signals and the frequency response function (FRF) matrix. An original regularization method is proposed which is based on the relationship between the harmonic components of the cutting forces. Numerical tests are performed to evaluate the effectiveness of the method. The method is compared with unregularized methods and common Tikhonov regularization combined with GCV and L-curve methods. It was found that the proposed method provides more accurate estimates of the cutting force coefficcients than the unregularized method and common regularization techniques. Furthermore the influence of acceleration measurement errors, FRF matrix errors and FRF matrix conditioning on the accuracy of the estimated coefficients is investigated. It was concluded that FRF matrix errors influence the most the accuracy of the results.
Designing machine tools for in situ machining is a challenging task due to their unique structures and restrictive functional requirements. Such a machine tool should be characterized by low mass, adequate machining accuracy and high machining stability. The paper presents the design of an ultra-light, axisymmetric, portable machine tool for in situ flange face milling. Due to a high compliance of the designed machine tool and a need of maintaining its low mass, structural modification aimed at stability increase were highly limited. Therefore, it was decided to select the spindle ensuring machining stability. The selection of the spindle was supported by finite element analysis. Based on numerical analyzes results a prototype with a proper spindle was build. Then, the accuracy of the finite element model and the predicted stability were experimentally verified, showing a good agreement with the real counterpart. Finally, two general conclusions were formulated: (i) in the case of machine tools characterized by high compliance and limited possibility of modifying their design a good choice may be the selection of a spindle that allows to obtain parameters that ensure stable machining, and (ii) it is possible to build low-dimensional, reliable finite element model without using substructuring or reduction methods, and a well-thought-out discretization and replacement elements of complex load bearing systems instead.
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