Measurement and Compensation of Pivot Point Positional Error on Five-Axis 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.

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

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.

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.

To enhance the accuracy, an efficient methodology was developed and described for systematic geometric error correction and their compensation in five-axis machine tools. The methodology is capable of compensating the overall effect of all position-dependent and position-independent errors which contribute to volumetric workspace. It was implemented on a five-axis grinding machine for error compensation and for the check of its effectiveness. Error compensation algorithm was designed, and a routine was written in Matlab software. The developed technique and software are based on an error table which interprets the function of axis through cubic spline technique and synthesis modeling of a machine tool. Recursive compensation methodology was used to remove the machine errors from the actual tool path and inverse technique was implemented to find the corrected positions of prismatic and rotary joints. Moreover, it can convert the corrected tool paths into practical compensated NC codes. The generated, corrected and modified NC codes directly fed to the controller of a five-axis machine tool. Validation of the technique was preceded by repeated experimentation of measurement and through machining of typical standard workpieces with some additional specific features. Experimental results exhibit effective compensation and remarkable improvement in the parametric and volumetric-workspace accuracy of the five-axis machine tool.

In the manufacturing industry, computer numerical control (CNC) machine tool has been applied widely due to their high adaptability and precision in the machining of diversity shape, especially five-axis CNC machine tools. However, more error terms related to rotary axes, in which location errors are always considered as one of the most fundamental error sources, affect directly to machine tool performance. Thus, ensuring that a five-axis machine tool is machining within tolerance is a crucial demand in the market. This study investigates an efficient strategy using a specific 3D artifact to identify and characterize the location errors in rotary axes of a five-axis machine tool. The intended 3D artifact consists of a base plate, 2 standards ball with high roundness embedded on the top surface of the base. A Touch Trigger Probe will be utilized as the calibration instrument to capture the coordinate of 6 arbitrary contact points of the balls, then an optimization algorithm is applied to calculate the coordinate of the centers of the balls. By comparisons the relative position of the imaginary circles made of those centers with the ideal ones, all location errors will be measured individually.

High accuracy contour error estimation and direct contour error control are two major approaches to reduce the contour error. However, two key factors make them complex for five-axis machine tools: the nonlinear kinematics and the coupling between the tool position and orientation. In this study, by finding the reference point nearest to the current actual position, and interpolating the point with two neighboring reference points and using the distance ratio, a new contour error estimation method for five-axis machine tools is proposed, which guarantees high accuracy while depending on only the reference points. By adding a weighted contour error on the tracking error in the workpiece coordinate system, and specifying a desired second-order error dynamics based on the error variable, an effective contouring control method is proposed, which can alleviate the problem: when the contour error components are introduced into the controller, the contour errors increase instead in some regions of the tracking trajectory. A series of experiments are performed on a tilting-rotary-table (TRT) type five-axis machine tool. The results reveal that the proposed estimation method has high accuracy, and compared with the case without contour error control, the proposed control approach can reduce the contour error along the whole trajectory.

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.

A neural network based compensation strategy for five-axis machine tool error correction has been developed. It is capable of significantly reducing geometric, kinematic and thermal errors between the tool tip and the workpiece. The error prediction ability of the neural network is demonstrated using a simulation of the compensation strategy. A two-stage training procedure for learning the weights of the neural network is proposed. The first stage uses a simulation model to train the dominant relationships between the errors and the sensors. The second stage of training would use actual measurements made on a five-axis machine tool to learn the remaining subtle relationships between the errors and the sensors. The simulation of the machine is based on Homogeneous Transformation Matrices (HTM). They model the position and orientation errors in each structural component. These error matrices are multiplied together to find the error between the tool and the workpiece. The coefficients required by the HTM model were selected so that the simulation model closely matched the measured performance of the five-axis machine tool. Thermocouples were used to measure temperature, and a laser interferometer, with the appropriate optics, was used for position and orientation error measurement. Preliminary simulation results based on an analysis of the spindle support arm and the Z column are available for the first stage of training. They indicate that a reduction in error from 100μm to 5μm is possible using a neural network model.

The application of traditional three-axis milling machine center is very popular and the related application technology is also much matured resulting in mechanical components to be machined with good quality. Machine tool has therefore become an inevitable facility in precision manufacturing. Furthermore, the pursuit of higher precision machining has thus demanding five-axis machine tool to be adopted owing to its flexibility and capability in machining more precise mechanical components in shorter time. However, one of the key factors for the popularity in smooth introduction of five-axis machine tool would be based on a very user friendly learning and teaching environment. This is partly because two more rotational axes in a five-axis machine tool could generate very complex toolpath movement that is out of the imagination of a general operator. Furthermore, the price of an industrial five-axis machine tool is not normally affordable by an educational institute; to the worse, the maintenance cost is also very high. There is very high risk for a novice to collide during the learning process and this will generally cause big worry of a teacher. This paper aims for the development of a virtual machining center simulation system with switchable modular components to ease the learning process in getting acquainted with a five-axis machine tool. A five-axis machine tool consists generally of two modules: (1) CNC controller and Operation panel, and (2) machine tool hardware. The developed system will provide the novice with four CNC controller with operation human machine interface (HMI), and three typical types of five-axis machine tool, Head-Head (HH), Head-Table (HT), and Table-Table (TT), are also supported. The developed modularized and switchable machining center simulation system has been successfully developed and is very helpful to both learner and teacher

Accuracy test of five-axis CNC machine tool with 3D probe-ball. Part II: errors estimation

In the integrally shaping process from a simple material shape to an objective shape, it is necessary to reduce the time required for the machining process in order to improve cost savings and the effectiveness of mass production. For the purpose of achieving high efficiency in the integral shaping from simplicity materials, we have focused on a rough cutting process that requires the most time in the manufacturing process. The purpose of this research is to propose a method for realizing high-speed rough machining using five-axis machine tools with a voxel model, and confirm the high efficiency of the rough cutting. In this research, we use five-axis controlled machine tools for material machining, and suggest two machining methods for the rough cutting process using the voxel model. The first method derives the tool posture where the cutting removal quantity becomes the maximum; this method also carries out a rough cutting process via 3+2 axis controlled machining. The other method carries a complete convex shape that includes the required shape, and simultaneously machines via five-axis machining based on the complete convex shape. This paper demonstrates the 3+2 axis control machining method that uses the voxel model to perform the rough machining process with high efficiency, and the simultaneous five-axis control machining method that uses a complete convex shape model for rough machining. We confirm the results with a computer simulation and actual machining experiments.

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.

The CNC machine tool is the passive executor of machining code. It cannot predict the machining accuracy during machining. If the error is found to be out of tolerance after processing, it will not only scrap the parts, but also greatly affect the processing efficiency. This phenomenon is very prominent when machining sculptured surface parts with five-axis machine tools. Therefore, this paper proposes a Digital Twin (DT) modeling method of five-axis machine tools for predicting Continuous Trajectory Contour Error (CTCE) caused by tracking errors and geometric errors. The DT consists of three parts: the Setpoints Trajectory (ST) model, the Actual Trajectory (AT) model considering tracking errors and geometric errors and the CTCE model. For a specific machine tool, according to the basic geometric information of the machine tool (tool length, kinematic chain information, etc.) and 41 geometric errors, the DT can be established. Inputting the Setpoints Positions (SPs) and the Linear Encoder Detection Positions (LEDPs), the DT can be used to predict the Tool-Tip Position Trajectory (TTPT) contour error and the Tool Orientation Trajectory (TOT) contour error. In order to verify the proposed method experimentally, the KMC400S U five-axis machine tool is selected to establish its DT by which the contour error of the S-shaped trajectory are predicted offline. Then, the DMU50 five-axis machine tool is selected to establish its DT to predict the contour error of the circular trajectory in real time. Combined with the deep motion mechanism, this paper proposes a DT modeling method for the vertical application scene of parts machining accuracy prediction, which is of great significance to developing the DT application theory and ensuring the machining accuracy of parts.

Inevitable machine motion errors change the cutting tool trajectory and degrade the machined surface quality. Compared to the mature error measurement technologies developed for traditional precision CNC machine tools, the increasing use of ultra-precision machine tools (UPMTs) has shown some distinctive characteristics in error modelling, measurement, and compensation. This paper attempts to summarise state-of-the-art research in the calibration of geometric errors of UPMTs. A general routine for a UPMT error calibration is proposed in this literature review. Various error modelling methods, instruments, and measurement methods applicable to the geometric error measurement of both the linear and rotary axes are discussed using typical case studies. With respect to these achievements, there is a real concern regarding the reproducibility of measurement sensors used for the calibration of UPMTs and it remains challenging to decompose the volumetric motion error of UPMTs. Owing to the high flexibility in practice, trial cutting and a sensitivity analysis-based error measurement and compensation provide a promising solution to achieve a fast UPMT calibration.