Volumetric error analysis of a multi-axis machine tool machining a sculptured surface workpiece

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.

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

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%.

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.

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 geometrical error modeling of the numerically controlled (NC) lathe is the key technique to kinematics design, precision analysis and error compensation. The study gives out the modeling process of the generally geometrical error model based on the multi-body system theory for the multi-axis NC machine tools. By the multi-system theory, using the low series body arrays to describe the complex mechanical system, the article has finished the geometrical error modeling of the numerically controlled lathe, analyzed the influence on the model of error of perpendicularity between the linear axes. The modeling method is highly-efficient and can not be affected by the structure of the NC machine tools. The error compensation and command correction can be implemented by the geometric errors model.

Four-axis machine tools with two rotary axes are widely used in the machining of complex parts. However, due to an irregular kinematic relationship and non-linear kinematic function with geometric error, it is difficult to analyze the influence the geometry error of each axis has and to compensate for such a geometry error. In this study, an influence analysis method of geometric error based on the homogeneous coordinate transformation matrix and a compensation method was developed, using the Newton iterative method. Geometric errors are characterized by a homogeneous coordinate transformation matrix in the proposed method, and an error matrix is integrated into the kinematic model of the four-axis machine tool as a means of studying the influence the geometric error of each axis has on the tool path. Based on the kinematic model of the four-axis machine tool considering the geometric error, a comprehensive geometric error compensation calculation model based on the Newton iteration was then constructed for calculating the tool path as a means of compensating for the geometric error. Ultimately, the four-axis machine tool with a curve tool path for an off-axis optical lens was chosen for verification of the proposed method. The results showed that the proposed method can significantly improve the machining accuracy.

Multi-axis machining of a complex surface is not only efficient but also reduces workpiece set-up errors. However, engineers usually rely on experience when determining set-up orientation and often cannot finish complex surfaces in one set-up. In this paper, a rational evaluation method for workpiece orientation and configuration of machine tool before tool path planning is proposed to increase the efficiency and reliability of process planning. By incorporating the visibility cone into workspace analysis, a software module is constructed in this research for optimum workpiece orientation and configuration of machine tool. First, the configurations of three-, four- and five-axis machine tools were synthesised, and the workspace was then analysed using form-shaping function. Both position vector and normal vector of each point along the u and v directions in the machining surface were employed to calculate the visibility range as the point of the visibility cone. In 3-axis machining, all normal vectors of the surface were projected on a unit sphere. All normal vectors were ensured to be within the visibility range of the ball-mill cutter as the workpiece set-up orientation changed. In 4-axis machining, the intersection between the visibility cone of each point and the workspace was obtained by changing the set-up orientation. In 5-axis machining, according to different workspaces of 5-axis machine tools, the visibility range of the machining surface was determined to yield the intersection between the visibility cone and the workspace by changing the workpiece orientation. The proposed method for evaluating manufacturability has been demonstrated to generate optimum workpiece set-up orientation and the suitable configuration of machine tools. Tool interference with workpiece surface can be avoided, which can help improve the planning of tool path.

Cutting force is the major factor which causes machine tool geometric error, for the sake of finding the relationship between cutting force and the machine tool geometric error, this paper established a model to simulate and analysis, Mastered the situation of stress distribution of various points on the machine and the regularity of internal stress and strain distribution; designed experiments for the precise measurement, and obtained the actual data of machine geometric error. the data matches the results of the simulative analysis. the results has a certain referential value to optimize the design of machine tool, the geometric error modeling and make the realization of software compensation, etc.

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.

Test cutting used to verify cutting conditions and machining accuracy after a numeric control (NC) program is written for end milling the mold and die indispensable to manufacturing is generally effective, because it is based on trial and error. The virtual machining simulator we designed to verify machining accuracy uses an accuracy-prediction model and an error prediction expression for workpieces, integrating machine-tool deformation and geometric error models. We also propose calculation for copying errors to a workpiece.

Enhanced virtual machining for sculptured surfaces by integrating machine tool error models into NC machining simulation

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.