A generalized on-line estimation and control of five-axis contouring errors of CNC machine tools

Nonlinear and configuration-dependent five-axis kinematics make contouring errors difficult to estimate and control in real time. This paper proposes a generalized method for the on-line estimation and control of five-axis contouring errors. First, a generalized Jacobian function is derived based on screw theory in order to synchronize the motions of linear and rotary drives. The contouring error components contributed by all active drives are estimated through interpolated position commands and the generalized Jacobian function. The estimated axis components of contouring errors are fed back to the position commands of each closed loop servo drive with a proportional gain. The proposed contouring error estimation and control methods are general, and applicable to arbitrary five-axis tool paths and any kinematically admissible five-axis machine tools. The proposed algorithms are verified experimentally on a five-axis machine controlled by a modular research CNC system built in-house. The contouring errors are shown to be reduced by half with the proposed method, which is simple to implement in existing CNC systems.     

Modeling and improvement of dynamic contour errors for five-axis machine tools under synchronous measuring paths

In this paper, a contour error model of the tool center point (TCP) for a five-axis machine tool is proposed to estimate dynamic contour errors on three types of measuring paths. A servo tuning approach to achieve five-axis dynamic matching is utilized to improve contouring performance of the cutting trajectory. The TCP control function is developed to generate measuring trajectories where five axes are controlled simultaneously to keep the TCP at a fixed point. The interpolation method of the rotary axes with S-shape acceleration/deceleration (ACC/DEC) is applied to plan smooth five-axis velocity profiles. The contour error model for five axes is derived by substituting five-axis motion commands into servo dynamics models. The steady state contour error (SSCE) model is demonstrated to illustrate three particular dynamic behaviors: the single-circle with amplitude modulation, double-circle effect and offset behavior. Furthermore, the model is also utilized to investigate the behaviors of dynamic contour errors change in 3D space. The factors that affect dynamic contour errors, including the initial setup position, feedrate and five-axis servo gains, are analyzed. With the developed servo tuning process under the measuring paths (CK1, CK2 and CK4), the contour errors caused by servo mismatch are reduced remarkably. Finally, experiments are conducted on a desktop five-axis engraving machine to verify the proposed methodology can improve dynamic contouring accuracy of the TCP significantly.     

Modeling and analysis of servo dynamics errors on measuring paths of five-axis machine tools

Dynamic error is one of the major error sources for five-axis machine tools in achieving high-speed machining. It can be estimated and compensated by means of servo dynamics modeling and servo control method. This paper presents a contour error model on five-axis measuring paths where the dynamics and contour errors of the tool center point (TCP) can be estimated accurately during five-axis synchronized motions. The forward and inverse kinematics equations are derived according to the kinematic configuration of a C-type five-axis machine. To generate smooth measuring paths, the S-shape acceleration/deceleration (ACC/DEC) method is applied on planning the motion trajectory. The contour error model of the TCP is derived by substituting the commands of the measuring trajectory into the servo dynamics models. To investigate how the contour charts of the TCP are affected by the dynamic gains of five-axis servo loops, twelve combinations under different gains are studied. It is shown that, for the CK2 path, the steady-state contour error consists of an offset and a double-circular trajectory which is quite different from that of two-axis contour path. By tuning the gains of the servo loops, the dynamics mismatch among five axes can be eliminated and the contour error of the TCP (CETCP) can be reduced. To validate the contour error equations, simulations and experiments are performed to demonstrate that the proposed method improves the contouring performance of the TCP significantly when performing five-axis synchronized motions.     

Multibody dynamic modeling of five-axis machine tool vibrations and controller

A computationally efficient, reduced-order multibody dynamic model of a five-axis machine tool is presented. The machine tool is modeled by substructures assembled via flexible springs and damping elements at interfaces which affect the machining performance. NC tool path commands are processed by the linear acceleration-based motion trajectory filters and fed to the axis servo controllers through an inverse kinematic model of the machine. The computed motor torque commands are applied to the structural dynamic model of the machine at the motor connections. The experimentally validated model predicts the performance of the five-axis CNC machine's controller along the tool path.     

Smooth trajectory generation for five-axis machine tools

This paper presents a smooth spline interpolation technique for five-axis machining of sculptured surfaces. The tool tip and orientation locations generated by the CAM system are first fitted to quintic splines independently to achieve geometric jerk continuity while decoupling the relative changes in position and orientation of the cutter along the curved path. The non-linear relationship between spline parameters and displacements along the path is approximated with ninth order and seventh order feed correction splines for position and orientation, respectively. The high order feed correction splines allow minimum deviation from the reference axis commands while preserving continuous jerk on three translational and two rotary drives. The proposed method has been experimentally demonstrated to show improvements in reducing the excitation of inertial vibrations while improving tracking accuracy in five-axis machining of curved paths found in dies, molds and aerospace parts.     

Pre-compensation of servo contour errors using a model predictive control framework

Methods for pre-compensating contour errors in servo systems by adding components of the predicted contour error to the reference position command have recently been proposed in the literature. Such methods are very effective when the curvatures of the desired path are small but their performance degrades at locations of sharp curvature because they lack look-ahead capabilities. This paper presents an improved method for pre-compensating contour errors in servo systems by modifying reference position commands using a model predictive control framework. The pre-compensation value at any given location along the desired path is defined as a weighted average of contour errors within a prediction horizon, and the weights are selected to minimize the sum of squares of the estimated contour errors over the chosen prediction horizon. Constraint enforcement functionalities are also built into the proposed method to ensure that the pre-compensated reference commands stay within specified velocity and acceleration limits. Simulations and experiments are used to compare the performance of the proposed method to a recently proposed pre-compensation approach which lacks look-ahead and constraint enforcement capabilities. Significant improvements in contouring accuracy over the existing method are demonstrated.     

Contour error control of CNC machine tools with vibration avoidance

A vibration avoidance and contouring error compensation algorithm for feed drives is presented. The residual vibrations are avoided by applying input shaping filters on the reference axis commands. The input shaping filter avoids the excitation of the structural modes but at the expense of increasing tracking and contouring errors. The tracking errors are estimated from the closed loop transfer function of drives, and used to predict the contouring errors which are mapped to the each axis for pre-compensation. The integrated vibration avoidance and contouring error compensation is experimentally demonstrated to improve the damping and contouring accuracy on a two-axis table.     

数控机床闭环进给伺服系统运动误差的研究

机床数控系统根据插补结果发出位置控制指令对各坐标轴进行独立的位置闭环控制,驱动相应的机械传动机构,最终实现精确的轮廓进给运动.本文研究了各轴位置闭环控制特性对轮廓误差的影响,分析了两坐标轴进给运动控制系统圆弧运动时因伺服系统有限带宽引起的半径误差和运动轴性能不匹配引起的椭圆误差,并进行了仿真验证.     

Feed optimization for five-axis CNC machine tools with drive constraints

Real time control of five-axis machine tools requires smooth generation of feed, acceleration and jerk in CNC systems without violating the physical limits of the drives. This paper presents a feed scheduling algorithm for CNC systems to minimize the machining time for five-axis contour machining of sculptured surfaces. The variation of the feed along the five-axis tool-path is expressed in a cubic B-spline form. The velocity, acceleration and jerk limits of the five axes are considered in finding the most optimal feed along the tool-path in order to ensure smooth and linear operation of the servo drives with minimal tracking error. The time optimal feed motion is obtained by iteratively modulating the feed control points of the B-spline to maximize the feed along the tool-path without violating the programmed feed and the drives’ physical limits. Long tool-paths are handled efficiently by applying a moving window technique. The improvement in the productivity and linear operation of the five drives is demonstrated with five-axis simulations and experiments on a CNC machine tool.     

A method of testing position independent geometric errors in rotary axes of a five-axis machine tool using a double ball bar

Ensuring that a five-axis machine tool is operating within tolerance is critical. However, there are few simple and fast methods to identify whether the machine is in a “usable” condition. This paper investigates the use of the double ball bar (DBB) to identify and characterise the position independent geometric errors (PIGEs) in rotary axes of a five-axis machine tool by establishing new testing paths. The proposed method consists of four tests for two rotary axes; the A-axis tests with and without an extension bar and the C-axis tests with and without an extension bar. For the tests without an extension bar, position errors embedded in the A- and C-axes are measured first. Then these position errors can be used in the tests with an extension bar, to obtain the orientation errors in the A- and C-axes based on the given geometric model. All tests are performed with only one axis moving, thus simplifying the error analysis. The proposed method is implemented on a Hermle C600U five-axis machine tool to validate the approach. The results of the DBB tests show that the new method is a good approach to obtaining the geometric errors in rotary axes, thus can be applied to practical use in assembling processes, maintenance and regular checking of multi-axis CNC machine tools.     

Virtual prediction and constraint of contour errors induced by cutting force disturbances on multi-axis CNC machine tools

This paper presents a strategy to virtually predict and constrain the contouring errors contributed by cutting force disturbances on feed drives. The tracking errors on each feed drive are predicted as a linear function of tangential feed by evaluating the product of estimated power spectrum of cutting forces and disturbance frequency response function along the tool path in virtual CAM environment. The corresponding tool tip contouring and tool axis orientation errors are estimated and constrained by scaling the feed along the tool path. The algorithm is experimentally illustrated to improve the machining accuracy on a 5 Axis CNC machine tool.     

Machining accuracy improvement in five-axis flank milling of ruled surfaces

The aim of this study is to develop a new adjustment method for improving machining accuracy of tool path in five-axis flank milling of ruled surfaces. This method considers interpolation sampling time of the five-axis machine tools controller in NC tool path planning. The actual interpolation position and orientation between G01 commands are estimated with the first differential approximation of Taylor expansion. The tool swept volume is modeled using the envelope surface and compared with the design surface to determine the deviation, which corresponds to the machining error induced by the linear interpolation. We propose a feedrate adjustment rule that automatically controls the tool motion at feedrate-sensitive corners based on a bisection method, thus limiting the maximum machining errors and improving the machining accuracy. Experimental cuts are conducted on different ruled surfaces to verify the effectiveness of the proposed method. The result shows that it can enhance the machining quality in five-axis flank milling in both simulation and practical operation.     

五轴数控机床转动轴与平动轴联动的轮廓误差仿真分析

以主轴头两摆的五轴联动数控机床为研究对象,对转动轴与平动轴联动加工不同空间位置圆弧时的轮廓误差进行了分析。采用D-H(Denavit-Hartenberg)法对按不同圆弧路径加工时各轴的进给指令计算公式进行了推导,并将指令输入到动态仿真工具Simulink构建的进给系统仿真模型中,比较刀具理想位置与实际位置的偏差,从而得到轮廓误差曲线。通过仿真曲线分析了轮廓误差的分布特性,得到了各参数对轮廓误差影响的对应关系,利用这种关系检测机床,达到提高机床性能的目的,同时为机床的调整与维修提供一种便捷手段。     

Rapid identification technique for virtual CNC drives

This paper presents a technique for rapid identification of machine tool drives by conducting a short G-code test. The proposed strategy uses commanded and measured axis profiles and requires minimal intervention to the servo control loop. The drive system is identified as a whole, including the feed mechanism, motor, amplifier, and the control law. The methodology is fairly general and applicable to linear or ball screw drives, controlled with commonly used controllers like P, PI, PID, P–PI Cascade or Adaptive Sliding Mode Control; with or without feedforward dynamic or friction compensation. In order to guarantee the stability of identified dynamics, bounds are imposed on the pole locations. The identified models can be used in a Virtual CNC system for predicting the contouring and tracking errors to different part programs. Simulation and experimental case studies are presented, where tracking and contour errors are successfully predicted using drive models identified with the proposed strategy.     

Measurement and verification of position-independent geometric errors of a five-axis machine tool using a double ball-bar

In this study, position-independent geometric errors, including offset errors and squareness errors of rotary axes of a five-axis machine tool are measured using a double ball-bar and are verified through compensation. In addition, standard uncertainties of measurement results are calculated to establish their confidence intervals. This requires two measurement paths for each rotary axis, which are involving control of single rotary axis during measurement. So, the measurement paths simplify the measurement process, and reduce measurement cost including less operator effort and measurement time. Set-up errors, which are inevitable during the installation of the balls, are modeled as constants. Their effects on the measurement results are investigated to improve the accuracy of the measurement result. A novel fixture consisting of flexure hinges and two pairs of bolts is used to minimize set-up error by adjusting the ball's position located at the tool nose. Simulation is performed to check the validation of measurement and to analyze the standard uncertainties of the measurement results. Finally, the position-independent geometric errors of the five-axis machine tool (involving a rotary axis and a trunnion axis) are measured using proposed method.     

Total ballbar dynamic tests for five-axis CNC machine tools

The linear and rotary axes of a five-axis machine tool are driven simultaneously to generate a specified tool position and orientation in workpiece coordinates. It is crucial that these servo-controlled axes are of balanced dynamics to achieve high tracking accuracy. In this paper, ballbar circular tests for all possible combinations of linear and rotary axes of a five-axis machine tool are investigated and total ballbar dynamic tests are proposed. Through the relational arrangement of the test sequence, the total ballbar dynamic tests can be employed to identify dynamic differences between linear and rotary axes. More importantly, the velocity gains of the position control loops of all servo-controlled linear and rotary axes can be tuned synchronously to eliminate gain mismatch errors. Experimental results have proved the effectiveness of the new methods.     

Five-axis tool orientation smoothing using quaternion interpolation algorithm

In five-axis machining, abrupt changes of tool axes may deteriorate the part surface, hence smoothing of tool orientations becomes an important issue. In the present tool path generation procedure, the tool orientation smoothing method (TOS method) is coupled with the cutting error improvement method (CEI method). TOS method is used to smooth tool orientations in order to reduce cutting errors and increase the machining efficiency. CEI method modifies existing cutter location data (CL data) so that final cutting errors are kept within the required tolerance. Experimental results show that the tool paths generated by the present procedure have better machining efficiency, better surface quality, and no interferences between the tool and part surfaces.     

A new compensation method for geometry errors of five-axis machine tools

The present study aims to establish a new compensation method for geometry errors of five-axis machine tools. In the kinematic coordinate translation of five-axis machine tools, the tool orientation is determined by the motion position of machine rotation axes, whereas the tool tip position is determined by both machine linear axes and rotation axes together. Furthermore, as a nonlinear relationship exists between the workpiece coordinates and the machine axes coordinates, errors in the workpiece coordinate system are not directly related to those of the machine axes coordinate system. Consequently, the present study develops a new compensation method, the decouple method, for geometry errors of five-axis machine tools. The method proposed is based on a model that considers the tool orientation error only related to motion of machine rotation axes, and it further calculates the error compensations for rotation axes and linear axes separately, in contrast to the conventional method of calculating them simultaneously, i.e. determines the compensation of machine rotation axes first, and then calculates the compensation associated with the machine linear axes. Finally, the compensation mechanism is applied in the postprocessor of a CAM system and the effectiveness of error compensation is evaluated in real machine cutting using compensated NC code. In comparison with previous methods, the present compensation method has attributes of being simple, straightforward and without any singularity point in the model. The results indicate that the accuracy of positioning was improved by a factor of 8–10. Hence, the new compensation mechanism proposed in this study can effectively compensate geometry errors of five-axis machine tools.     

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

Although error modeling and compensation have given significant results for three-axis CNC machine tools, a few barriers have prevented this promising technique from being applied in five-axis CNC machine tools. One crucial barrier is the difficulty of measuring or identifying link errors in the rotary block of five-axis CNC machine tools. The error model is thus not fully known. To overcome this, the 3D probe-ball and spherical test method are successfully developed to measure and estimate these unknown link errors. Based on the identified error model, real-time error compensation methods for the five-axis CNC machine tool are investigated. The proposed model-based error compensation method is simple enough to implement in real time. Problems associated with the error compensation in singular position of the five-axis machine tool are also discussed. Experimental results show that the overall position accuracy of the five-axis CNC machine tool can be improved dramatically.     

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

To improve the accuracy of CNC machine tools, error sources and its effects on the overall position and orientation errors must be known. Most motional errors in the error model of five-axis machine tool can be measured with modern laser interferometer devices, but there are still some not measurable geometric errors. These not measurable errors include constant, inaccurate link errors of components such as rotary axes block, main spindle block and tool holder. After setting all measured errors in the error model, a reduced error model is defined, which describes the influence of each unknown and not measurable link error on the overall position errors of the five-axis machine tool. On the other hand, the newly developed probe-ball device can measure the overall position errors of five-axis machine tools directly. Based on the reduced model and the overall position errors, the link errors can be estimated very accurately with the least square estimation method. The error model is then fully known and can be used for advanced purposes such as error prediction and compensation.