Novel method for position-independent geometric error compensation of five-axis orthogonal machine tool based on error motion

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.

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.

Identification and compensation of position independent geometric errors of dual rotary axes for hybrid-type five-axis machine tool based on unit dual quaternions

Accuracy enhancement of five-axis CNC machines through real-time error compensation

Geometric errors are one of the primary potential sources of error in a five-axis machine tool. There are two types of geometric errors: position-dependent geometric errors and position-independent geometric errors. A method is proposed to identify and measure the position-independent geometric errors of a five-axis machine tool with a tilting head by means of simultaneous multi-axis controlled movements using a double-ball bar (DBB). Techniques for identifying position-independent geometric errors have been proposed by other researchers. However, most of these are based on the assumption that position-dependent geometric errors (such as linear displacement, straightness, and angular errors) are eliminated by compensation, once the position-independent geometric errors have been identified. The approach suggested in this paper takes into account the effect of position-dependent geometric errors. The position-dependent geometric errors are first defined. Path generation for circle tests with two or three simultaneous control movements is then carried out to measure the position-independent geometric errors. Finally, simulations and experiments are conducted to confirm the validity of the proposed method. The simulation results show that the proposed method is sufficient to accurately identify position-independent geometric errors. The experimental results indicate that the technique can be used to identify the position-independent errors of a five-axis machine tool with a tilting head.

To solve the five-axis machining accuracy problems that caused by assembly precision and direction error of rotary axes of inclinable head in high precision five axis machine tool. By selecting the five axis machine tool with inclinable head AB, GMC1230u, as the research object and analyzing the causes of the inclinable head error, the kinematics relationship of the rotation center position error and axis tilt error is established. By that, the direction vectors of each rotation axis and the position vector of rotation center are calculated based on the regression analysis of on-line measurement of the tool center point position and the calibration of five-axis RTCP function parameters is also accomplished. Finally, the compensation for inclinable head error in five-axis machine tools is fulfilled efficiently and remarkable improvement of RTCP machining accuracy is achieved.

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.

In this paper, a method is proposed for identification of 11 position-independent geometric errors (PIGEs) of five-axis machine tools with a tilting/rotary table via single-ball measurements and three-dimensional (3D) geometric sensitivity analysis. Eleven PIGEs were identified, including three squareness errors between three linear axes, two offset errors, and two squareness errors for the tilting/rotary axis. The approach uses a set-up of a ball and three circular measurements involving simultaneous control of two linear axes and a tilting/rotary axis. A 3D geometric sensitivity analysis is carried out to investigate the effects of the 11 PIGEs on each of the measurement’s paths and between the measurement paths. The particular measurement paths used allow the radius of the circular path at the first measurement, and the distance between the circular paths of the second and third measurements, to be increased for accurate identification of the 11 PIGEs. The proposed method was also used to derive root-sum-square values of sensitivity coefficients, and then applied to a commercial five-axis machine tool for experimental verification. It calculates the peak-to-valley values of the positional deviations in the x-, y-, and z-directions along the test paths as 152.1, 118.2, and 47.1 μm, respectively, without compensation for the identified PIGEs, and as 17.6, 15.0, and 11.4 μm, respectively, with compensation. The results confirm the validity of our proposed method.

Five-axis machine tools with two additional rotational degrees of freedom provide more flexibility in tilting the tool axis to various orientations than conventional three-axis machine tools do, subsequently increasing the cutting efficiency and avoiding tool collision against a workpiece. Also, the risk of programming error can be avoided by simulating the five-axis Numerical Control (NC) code before real machining. This work presents a five-axis machine tool cutting simulation system with a nonorthogonal linear axis configuration. A window-based cutting system written by Borland C++ Builder and OpenGL is also developed based on the kinematics model of the proposed machine tool. Furthermore, implementing and verifying the five-axis NC code demonstrates the effectiveness of the proposed scheme.

Error analysis and compensation method of displacement measurements based on reflection projection imaging

The five-axis machine tools are increasingly popular for meeting the demand of machining the workpiece with growing geometric complexity and high accuracy. This paper studies the volumetric error modeling and its sensitivity analysis for the purpose of machine design. The volumetric error model of a five-axis machine tool with the configuration of RTTTR is established based on rigid body kinematics and homogeneous transformation matrix, in which 37 error components are involved. The sensitivity analysis of volumetric error regarding 37 error components is carried out respectively. The analysis results are successfully used for the accuracy design and manufacture of a five-axis ultra-precision machine tool. The preliminary experiment of machining sine grid surface testifies the high accuracy and effectiveness of the designed five-axis machine tool.

Based on the established serial 6-DOF robot calibration experiment platform, this paper aims to analyze and compare the effects of four error compensation methods, which are pseudotarget iteration-based error compensation method with three different forms and the Newton–Raphson-based error compensation method. Firstly, the pose error model of the serial robot is established based on the M-DH model in this paper. The calibration results show that the accuracy of the Staubli TX60 robot has been greatly improved. The average comprehensive position accuracy is increased by 88.7%, and the average comprehensive attitude accuracy is increased by 56.6%. Secondly, the principles of the four error compensation methods are discussed, and the effectiveness of the four error compensation methods are compared through experiments. The results show that the four error compensation methods can achieve error compensation well. The compensation accuracy is consistent with the identification accuracy of the kinematic model. The pseudotarget iteration with differential form has the best performance by the comprehensive consideration of accuracy and computational efficiency. Error compensation determines whether the accuracy of the identified model can be achieved. This paper presents a systematic experimental validation research on the effectiveness of four error compensation methods, which provides a reliable reference for the kinematic error compensation of industrial robots.

Research on Intelligent Glue-coating Robot Based on Visual Servo

The simultaneous measurement and identification of position-independent geometric errors (PIGEs) and position-dependent geometric errors (PDGEs) of dual rotary axes in five-axis machine tools remain a significant challenge in precision machining. To address this issue, this study develops a geometric error measurement system for the dual rotary axes of a five-axis machine tool by integrating a scanning probe, a block, and a calibration sphere. Unlike conventional touch-trigger probes, the scanning probe acquires continuous measurement signals along the surfaces of the block and the calibration sphere, enabling the extraction of richer geometric features and providing sufficient data for the simultaneous analysis of multiple geometric error components. The proposed measurement system is implemented on a five-axis machine tool, Uni5X-400, manufactured by FALCON Machine Tools Co., Ltd., to measure the geometric information of the calibration sphere and the block and thereby identify 20 PIGEs and PDGEs associated with the dual rotary axes. A kinematic model of the measurement system is established using homogeneous coordinate transformation matrices. By applying forward and inverse kinematics, the spatial positions of the calibration sphere and block are derived, forming an explicit relationship between volumetric errors and geometric errors. The resulting error identification equations are solved using the least squares method. Experimental results demonstrate that the proposed approach can efficiently and accurately identify the geometric errors of the dual rotary axes and maintain robust reliability under real-world operating conditions, making it suitable for practical calibration and accuracy improvement of five-axis machine tools.

Enhancing the accuracy of machine tool is a key goal of machine tool manufactures and users. To characterize the Quasi-static errors and then use software compensation is an important step for accuracy enhancement. The effectiveness of an error compensation scheme relies heavily on the error model. The model must be concise and roust which can be applied to any machine tool. The total Quasi-static errors within the workspace of a five-axis gantry machine tool is composed of geometric error, kinematic error, thermal error. This paper presents an error model which can be used for practical compensation scheme. Homogeneous transformation matrix, rigid body kinematic and small angle approximations are used in this paper for error modeling.