Finite Element Analysis and Experiment Research on Machine Tool Cutting Force Error

This paper proposes a recognition methodology for key geometric errors using the feature extraction method and accuracy retentivity analysis and presents the approach of optimization compensation of the geometric error of a multiaxis machine tool. The universal kinematics relations of the multiaxis machine tool are first modelled mathematically based on screw theory. Then, the retentivity of geometric accuracy with respect to the geometric error is defined based on the mapping between the constitutive geometric errors and the time domain. The results show that the variation in the spatial error vector is nonlinear while considering the operation time of the machine tool and the position of the motion axes. Based on this aspect, key factors are extracted that simultaneously consider the correlation, similarity, and sensitivity of the geometric error terms, and the results reveal that the effect of the position‐independent geometric errors (PIGEs) on the error vectors of the position and orientation is greater than that of the position‐dependent geometric errors (PDGEs) of the linear and rotary axes. Then, the fruit fly optimization algorithm (FOA) is adopted to determine the compensation values through multiobjective tradeoffs between accuracy retentivity and fluctuation in the geometric errors. Finally, an experiment on a four‐axis horizontal boring machine tool is used to validate the effectiveness of the proposed approach. The experimental results show that the variations in the precision of each test piece are lower than 25.0%, and the maximum variance in the detection indexes between the finished test pieces is 0.002 mm when the optimized parameters are used for error compensation. This method not only recognizes the key geometric errors but also compensates for the geometric error of the machine tool based on the accuracy retentivity analysis results. The results show that the proposed methodology can effectively enhance the machining accuracy.

Kinematic accuracy is a key reason which influence workpiece's geometric error precision on traditional working process of precisely CNC（Computerized Numerical Control）P3G（polygon profile with 3 lobes） grinding machine. A systematic geometric error model has been presented for CNC P3G grinding machine， proposed multi-body system theory integrate with the structure of CNC P3G grinding machine tools, researched on the machine's space geometric errors. By means of separate geometric errors from the machine tools, build geometric mathematical error model. Then, identify 21 error parameters through method of 9 lines, analysis and calculate the total space geometric errors of the workpiece and wheel. Finally, formed a parameter-list and applied software error compensational technique ， achieved real-time control to the motions of workpiece and wheel. Experimental results shown that the geometrical error modeling technique is accurate and efficient, and the precision of CNC P3G grinding machine is highly raised 70%.

Total differential methods based universal post processing algorithm considering geometric error for multi-axis NC machine tool

The influence of geometric errors on the accuracy of machine tools tends to attract more attention to the increasing demand for high-precision machining. In this paper, geometric error modeling and sensitivity analysis are employed to quantify the importance of geometric error for a new efficient and automatic 6-axis welding equipment. The geometric error model of the 6-axis welding equipment with 36 geometric error components is established based on Lie theory. Based on the geometric error model, the new sensitivity analysis method, in which the deviation of the welding torch pose is treated as a distance metric in SE(3), is proposed to evaluate the influences of geometric errors on the accuracy of the welding torch. And the sensitivity coefficient of each geometric error is derived by considering the basic value of geometric errors. Numerical simulations of a typical welding trajectory for intersecting pipes are conducted to analyze the sensitivity of geometric errors by the new method. The simulation results verified the validity of the sensitivity analysis method and the dominant geometric errors affecting the accuracy of the welding equipment were identified. Compared with the previous sensitivity analysis method, the proposed sensitivity analysis method considers the orientation error and position error of the welding torch simultaneously, which is more convenient and effective, and can also be applied in precision design and geometric error compensation of machine tools.

The relative position and orientation deviation between grinding wheel and workpiece caused by geometric errors affect the machining accuracy of five-axis CNC gear profile grinding machine tools directly. Therefore, geometric error modeling and compensation are presented according to homogeneous transformation and differential motion matrix based on the multi-body system theory for the accuracy enhancement of the machine tools. Firstly, the open kinematic chain and the ideal homogeneous transformation matrix from workpiece to grinding wheel are established according to the topological structure of the CFXZAY-type, five-axis gear profile grinding machine tools and the basic homogeneous transformation matrix between coordinate frames. Secondly, the homogenous transformation matrices of linear pairs and rotary pairs with geometric errors are calculated, and the relationships of the error propagation from workpiece to grinding wheel are acquired as well on the basis of 37 geometric error components analysis. The geometric error models including position and orientation errors of grinding wheel in workpiece coordinate system are obtained with matrix multiplication by using small-angle approximation and ignoring the second-order and high-order error terms. Then, the Jacobian is obtained by using transforming differential motion matrix of each motion axis to compensate the integrated error components of the grinding wheel, which can make the compensation effective and convenient with using the corresponding homogeneous transformation matrix. Finally, error measurement, error compensation, and machining experiments are carried out on a five-axis CNC gear profile grinding machine tool SKMC-1200W/10 to verify the applicability and effectiveness of the proposed error modeling, error compensation, and research approach.

Geometric error compensation is a widely used and effective approach for enhancing the accuracy of Coordinate Measuring Machines (CMMs) and Computer Numerical Control (CNC) machines. The research in this field primarily focuses on the challenging task of developing geometric error modelling techniques. Currently, there are several well-established methods for modelling geometric errors. However, there is scarce availability of methods that can validate the established geometric error models. Therefore, this article proposes an analytical validation method for geometric error models based on the error transformation equation. The principle of the method is elaborately explained, and its correctness is verified through specific model verification example. The method proposed in this article enables rapid and accurate model correction and iteration, effectively reducing the economic and time costs of model validation in the current geometric error compensation process. Therefore, the method provides guidance for standardising the modelling process and could be widely applied to various structural forms of measurement and machining systems.

The geometric error of a three-axis vertical machining center is a critical technical indicator for evaluating its machining accuracy, and the precision of error identification plays a decisive role in the engineering effectiveness of compensation strategies. Based on the multibody system topology theory and the Denavit-Hartenberg matrix theory, this study establishes a contribution transfer model to quantify the impact of multi-axis geometric error on the positional errors at the end-effector of the three-axis vertical machining center. Experiments were performed on a VMC650 three-axis vertical machining center platform, where 21 geometric error items were precisely measured using a Renishaw XM-60 laser interferometer. An error spatial distribution function was constructed through polynomial regression analysis, and the optimal fitting coefficients of polynomial basis function combinations were solved to provide an analytical mathematical description for error prediction at arbitrary spatial positions. Based on the geometric error model, this study innovatively combines Monte Carlo sampling with principal component analysis to perform sensitivity analysis on geometric error parameters and analyze the transmission of geometric error under small disturbances, thereby effectively identifying key sensitive geometric error parameters. The research results offer theoretical guidance for structural optimization design and compensation parameter calibration of three-axis vertical machining centers, significantly enhancing their comprehensive machining accuracy.

An approach for geometric error modeling of parallel manipulators (PMs) based on the visual representation and direct calculation of conformal geometric algebra is introduced in this paper. In this method, the finite motion of an open-loop chain is firstly formulated. Through linearization of the finite motion, error propagation of the open-loop chain is analyzed. Then the error sources are separated in terms of joint perturbations and geometric errors. Next, motions and constraints of PMs are analyzed visually by their reciprocal property. Finally geometric error model of PMs are formulated considering the actuations and constraints. The merits of this new approach are twofold: (1) complete and continuous geometric error modeling can be achieved since finite motions are considered, (2) visual and analytical computation of motions and constraints are applied for transferring geometric errors from the open-loop chain to the PM. A 2-DoF rotational PM is applied to demonstrate the geometric error modeling process. Comparisons between simulation and analytical models show that this approach is highly effective.

The spindle error and geometric error are the main sources of inaccuracy in CNC machining. With the rising of the machine tool parts' temperature, the spindle error and geometric error increase continually, and the error curves have a nonlinear distribution. To analyze the thermal effects on spindle error and geometric error, an experiment is carried out. To improve the machining accuracy of a CNC machine, an error model is proposed based on orthogonal polynomials. With the application of the orthogonal polynomials, the polynomial regression can be transformed into multiple linear regressions which are easier to calculate. In order to implement the real-time error compensation for the thermally induced spindle error and geometric error, an error compensation method is proposed based on the external coordinate offset. The thermally induced spindle and geometric error are compensated by 90 % compared with no compensation.

Deep tissue injury (DTI) is a severe type of pressure ulcers affecting the viability of muscle tissue under bony prominences first [1]. Most researchers agree that prolonged elevated muscle tissue strains and stresses cause the onset of DTI. We recently showed that internal strain and stress distributions in muscle tissue of individuals can be evaluated by integrating Open-MRI examinations with subject-specific finite element (FE) analyses [2]. However, sub-dermal soft tissue strain and stress data from paraplegic wheelchair users are missing in the literature. Our present goals were therefore (i) to determine the strain and stress distributions in the gluteus muscles and enveloping fat under the ischial tuberosities (IT) of paraplegic wheelchair users during sitting and lying in an Open-MRI, (ii) to compare the paraplegic data to those obtained previously from normal subjects [2], and (iii) to compare between results obtained from paraplegics in the sitting and lying postures, in order to quantify the effect of posture on sub-dermal tissue mechanical conditions, particularly intramuscular shear stress.

Geometric error measuring, modeling, and compensation for CNC machine tools: A review

A new geometric error modeling approach for multi-axis system based on stream of variation theory

The distributions of internal stress and strain in martensite-retained ferrite duplex structure have been calculated by the Finite Element Method. The calculating model was a two dimensional plate irhich was obtained by taking the representative area from the morphology of the duplex structure. The results indicated that very inhomogeneous stress and strain distributions existed in the structure. The effects of the retained ferrite on these inhomogeneities were discussed according to the calculation results.

The purpose of this study was to improve the accuracy of three-axis CNC Milling Vertical engines with a general approach by using mathematical modeling methods of machine tool geometric errors. The inaccuracy of CNC machines can be caused by geometric errors that are an important factor during the manufacturing process and during the assembly phase, and are factors for being able to build machines with high-accuracy. To improve the accuracy of the three-axis vertical milling machine, by knowing geometric errors and identifying the error position parameters in the machine tool by arranging the mathematical modeling. The geometric error in the machine tool consists of twenty-one error parameters consisting of nine linear error parameters, nine angle error parameters and three perpendicular error parameters. The mathematical modeling approach of geometric error with the calculated alignment error and angle error in the supporting components of the machine motion is linear guide way and linear motion. The purpose of using this mathematical modeling approach is the identification of geometric errors that can be helpful as reference during the design, assembly and maintenance stages to improve the accuracy of CNC machines. Mathematically modeling geometric errors in CNC machine tools can illustrate the relationship between alignment error, position and angle on a linear guide way of three-axis vertical milling machines.

The dual-driving feed worktable (DDFW) is increasingly used in feed systems with high precision and dynamic performance requirements, while its geometric error, caused by the factors such as manufacturing, assembly errors and the deformation, is the main factor affecting positioning accuracy. The research on geometric error compensation of DDFW is significant. In this paper, geometric error analysis and compensation of DDFW, equipped with the open CNC system of BECKHOFF, are conducted. Firstly, the geometric error model of DDFW is established, and the geometric errors are measured by using dual-frequency laser interferometer. Then the electronic cam combined with virtual axis compensation algorithm is designed. Finally, the compensation experiment is completed, and the results show that the positioning precision of DDFW improves a lot with the proposed compensation strategy.