Contouring Control of a Five-Axis Machine Tool with Equivalent Errors

Feedrate blending method for five-axis linear tool path under geometric and kinematic constraints

Local corner smoothing method is commonly adopted to smooth linear (G01) tool path segments in computer numerical control (CNC) machining to realize continuous motion at transition corners. However, because of the highly non-linear relation between the arc-length and the spline parameter, and the challenge to synchronize the tool tip position and tool orientation, real-time and high-order continuous five-axis tool path smoothing and interpolation algorithms have not been well studied. This paper proposes a real-time C3 continuous corner smoothing and interpolation algorithm for five-axis machine tools. The transition corners of the tool tip position and tool orientation are analytically smoothed in the workpiece coordinate system (WCS) and the machine coordinate system (MCS) by C3 continuous PH splines, respectively. The maximum deviation errors of the smoothed tool tip position and the tool orientation are both constrained in the WCS. An analytical synchronization algorithm is developed to guarantee the motion variance of the smoothed tool orientation related to the tool tip displacement is also C3 continuous. The corresponding real-time interpolation method is developed with a continuous and peak-constrained jerk. Simulation results verify that the maximum deviation errors caused by the tool path smoothing algorithm are constrained, and continuous acceleration and jerk of each axis are achieved along the entire tool path. Comparisons demonstrate that the proposed algorithms achieve lower amplitude and variance of acceleration and jerk when compared with existing methods. Experiments show that the proposed five-axis corner smoothing and interpolation algorithms are serially executed in real-time with 0.5-ms cycle.

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 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

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.

The kinematical behavior of 5-axis machine tool introduced by toolpath calculation has a close relation with processing efficiency and quality of parts. For the category of sculptured surface parts with abrupt curvature, such as turbine blade and fixed guide vane, the most commonly utilized spiral contouring toolpath modes usually encounter some trouble during actual machining, the reason lies in the difficult tool orientation control near the edge of such parts. However, the global optimization for the spiral toolpath means increased computation burden, and so it is time consuming. In this paper, an efficient 5-axis toolpath optimization algorithm is presented, and the objective is to smooth the rotary axes’ motion caused by drastically changed tool orientation on spiral toolpath for abrupt curvature parts machining. To reduce the computation burden, only path segments on the spiral trajectory-owned weak kinematic performance are selected for further optimizing. To obtain smoother motion for rotary axes, the specific optimization computation for the selected path segments is conducted in the Machine Coordinate System (MCS) instead of the Part Coordinate System (PCS). The optimization model is constructed and a related solution method is presented to ensure the high-performance optimization. The complete optimization algorithm is demonstrated on a spiral 5-axis toolpath for the turbine blade finish machining, and the result shows that only 25.9% optimization computation is needed compared with global optimization algorithm. And then, the actual machining experiments are carried out by using paraffin as cut material, and the machining time with optimized toolpath is decreased by 19.7% compared with initial toolpath. In addition, the surface quality of parts is significantly improved after conducting the optimization. This study proves that the proposed algorithm can significantly improve the processing efficiency and surface quality of parts with abrupt curvature and provides an efficient method to optimize the spiral 5-axis toolpath used for finish machining parts with abrupt curvature.

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.

Machine tool geometric inaccuracies are frequently corrected through the use of compensation tables available in machine tool controllers. Each compensation table contains a set of values that determine the incremental change in the commanded position of an axis given the current positions of the axes. While a five-axis machine tool, for example, can have at most 25 compensation tables, most machine tool controllers limit the number of compensation tables that can be implemented and provide constraints on the combinations of compensation tables that can be utilized. This work presents an artificial intelligence-based methodology to select and populate the optimal set of machine tool compensation tables when these limitations and constraints exist. Using data from an industrial five-axis machine tool to construct a kinematic error model, simulation results for the proposed methodology and a heuristic based on the impact of individual compensation tables when selecting six compensation tables are compared, and the proposed methodology is found to outperform the heuristic. The proposed methodology and a solution based on a full set of compensation tables are experimentally implemented on the machine tool and the mean volumetric error resulting from the proposed methodology is found to be only 25 μm less than the volumetric error resulting from the full set of tables. The proposed methodology is then implemented in two more simulation studies where constraints are imposed on which combination of compensation tables could be used and which type of compensation tables could not be utilized. The resulting mean volumetric error was 7.0 and 28.3 μm greater, respectively, than the unconstrained solution.

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.

The accuracy of high speed five-axis machine tool is mainly determined by the contour accuracy of machine tools. The contour accuracy evaluation and improvement of 5-axis machine tools have always been concerned. In order to simplify the calculation of five-axis contour error considering the synchronization between tool tip position and tool orientation, a novel five-axis contour evaluation index TCCE(Two-point Cutter location Contour Error) is proposed in this paper, which is based on the tool axis trajectory surface. The calculating method of the proposed index by NC servo encoder input from 5-axis machine tools is introduced. Finally, the experiment is performed to evaluate the trajectory accuracy and servo matching performance of the machine tool with the proposed contour error evaluation index and the calculating method.

Selecting noncoplanar beam directions in a patient coordinate system for radiotherapy planning

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.

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

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.