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.     

A tool-path control scheme for five-axis machine tools

This paper presents a new servo control method for five-axis machining applications. The proposed method conducts a direct elimination of the deviation error, the orientation error, and the tracking-lag error that are the main concerns for five-axis tool-path control. To achieve this purpose, the proposed five-axis control system is based on a real-time transformation between the drive-coordinate basis, in which the five drives are operated, and the workpiece-coordinate basis, in which the deviation error etc., are defined.     

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.     

Double ballbar test for the rotary axes of five-axis CNC machine tools

In this paper a new method that uses the double ballbar to inspect motion errors of the rotary axes of five-axis CNC machine tools is presented. The new method uses a particular circular test path that only causes the two rotary axes to move simultaneously and keeps the other three linear axes stationary. Therefore, only motion errors of the two rotary axes will be measured during the ballbar test. The theoretical trace patterns of various error origins, including servo mismatch and backlash, are established. Consequently, the error origins in the rotary block can be diagnosed by examining whether similar patterns appear in the motion error trace. The method developed was verified by practical tests, and the servo mismatch of the rotary axes was successfully detected.     

A smooth curve evolution approach to the feedrate planning on five-axis toolpath with geometric and kinematic constraints

Feedrate planning with geometric and kinematic constraints is crucial for sculptured surface machining. Due to the non-linear relationship between the Cartesian space and the joint space, the feedrate planning method for a given five-axis toolpath is very limited compared with that in three-axis machining. To achieve the exact control of the chord error and the kinematic characteristics of cutter and machine tool, this paper presents a new feedrate planning method for five-axis parametric path using a smooth curve evolution strategy. The constraints in feedrate planning are first classified as two types of neighbor-independent (NI) constraints and neighbor-dependent (ND) constraints. Then for constraint violated region, the detailed formulas of determining the update feedrates of violated sampling points are given using a decoupled manner. As a result, NI and ND constraints are satisfied respectively with one step and multi-step smooth curve evolution technique, which can smoothly deform the target feedrate profile to the desired update positions. Simulations and experiments are performed on the given tool path to validate the effectiveness of the proposed feed planning method. The results show that the proposed method is robust and effective in the exact control of constraints in the feedrate planning on complex five-axis toolpath.     

Ballbar dynamic tests for rotary axes of five-axis CNC machine tools

This paper proposes a new ball bar test method for the inspection of dynamic errors of rotary axes in five-axis CNC machine tools. The test circle is defined in a workpiece coordinate system and the ball bar test is performed by simultaneously driving of linear–rotary axis couple. The effects of the center position and the radius on the setting values, rotational range and measurement sensitivity of the rotary axis were investigated. The proposed ball bar test is performed in two steps: the circular positioning and the circular tracking with a continuous feed. Axial dynamic errors are obtained by subtracting the measured tracking errors from the positioning errors. A ball bar test system (BBTS) was developed to plan the tool path and the tool orientation, to communicate with the five-axis CNC controller and to process the measured data. Error patterns were simulated regarding the gain mismatch, backlash and tracking direction to help a fast diagnosis of the error sources. Simulations and experimental results prove the effectiveness of the new test method.     

Corner rounding of linear five-axis tool path by dual PH curves blending

The widespread linear five-axis tool path (G01 blocks) is usually described by two trajectories. One trajectory describes the position of the tool tip point, and the other one describes the position of the second point on the tool axis. The inherent disadvantages of linear tool path are tangential and curvature discontinuities at the corners in five-axis tool path, which will result in feedrate fluctuation and decrease due to the kinematic constraints of the machine tools. In this paper, by using a pair of quintic PH curves, a smoothing method is proposed to round the corners. There are two steps involved in our method. Firstly, according to the accuracy requirements of the tool tip contour and tool orientation tolerances, the corner is rounded with a pair of PH curves directly. Then, the control polygon lengths of PH curves are adjusted simply to guarantee the continuous variation of the tool orientation at the junctions between the transition curves and the remainder linear segments. Because the PH curves for corner rounding can be constructed without any iteration, and those two rounded trajectories are synchronized linearly in interpolation, which makes this smoothing method can be applied in a high efficiency way. Its high computational efficiency allows it to be implemented in real-time applications. This method has been integrated into a CNC system with an open architecture to implement on-line linear five-axis tool path smoothing. Simulations and experiments validate its practicability and reliability.     

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.     

Configuration analysis of five-axis machine tools using a generic kinematic model

Five-axis machine tools are designed in a large variety of kinematic configurations and structures. Regardless of the type of the intended analysis, a kinematic model of the machine tool has to be developed in order to determine the translational and rotational joint movements required to achieve a specified position and orientation of the cutting tool relative to the workpiece. A generic and unified model is developed in this study as a viable alternative to the particular solutions that are only applicable to individual machine configurations. This versatile model is then used to verify the feasibility of the two rotational joints within the kinematic chain of three main types of five-axis machine tools: the spindle rotating, rotary table, and hybrid type. A numerical measure of total translational joint movement is proposed to evaluate the kinematic performance of a five-axis machine tool. The corresponding kinematic analyses have confirmed the advantages of the popular machine design that employs intersecting rotational axes and the common industrial practice during setup that minimizes the characteristic rotating arm length of the cutting tool and/or workpiece.     

Pre-compensation of contour errors in five-axis CNC machine tools

This paper presents an analytical prediction and compensation of contouring errors in five-axis machining of splined tool paths. The position commands are first fitted to piecewise quintic splines while respecting velocity, acceleration and jerk continuity at the spline joints. The transfer function of each servo drive is kept linear by compensating the disturbance effect of friction with a feed-forward block. Using the analytically represented five-axis, splined tool path, splined tracking errors and kinematic model of the five-axis machine tool, contouring errors are predicted ahead of axis control loops. The contouring errors are decoupled into three linear and two rotary drives, and the position commands are modified before they are sent to servo drives for execution. The proposed method has been experimentally demonstrated to show significant improvement in the accuracy of contouring five-axis tool paths.     

Removing tool marks of blade surfaces by smoothing five-axis point milling cutter paths

Focused on the reverse movements of moving axes along five-axis tool paths, this study presents a procedure of removing a gouge phenomenon on impeller surfaces in five-axis machining. That is, when an impeller of a centrifugal compressor is being cut in finish milling, reverse movements and/or other linearization problems of moving axes along a five-axis interference-free tool path may make a cutter leave tool marks on the impeller surfaces. For generating interference-free cutter location (CL) data needed in rough, semi-finish and finish five-axis cutting processes, first, a simple yet useful approach is proposed. To identify the potential gouge area and to solve the problem for a tool path having reverse motion directions with its moving axes in finish milling, the CL data are further smoothed to remove the reverse movements about its rotating and tilting axes. The effectiveness of this procedure has been experimentally confirmed by successful five-axis finish milling of an impeller without leaving tool marks on its surfaces. In addition, with the spline tool paths, the machining time can be saved up to 23.57%.     

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.     

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 machining test to calibrate rotary axis error motions of five-axis machine tools and its application to thermal deformation test

This paper proposes a machining test to parameterize error motions, or position-dependent geometric errors, of rotary axes in a five-axis machine tool. At the given set of angular positions of rotary axes, a square-shaped step is machined by a straight end mill. By measuring geometric errors of the finished test piece, the position and the orientation of rotary axis average lines (location errors), as well as position-dependent geometric errors of rotary axes, can be numerically identified based on the machine׳s kinematic model. Furthermore, by consequently performing the proposed machining test, one can quantitatively observe how error motions of rotary axes change due to thermal deformation induced mainly by spindle rotation. Experimental demonstration is presented.     

虚拟轴机床数控系统手轮功能的开发

由于虚拟轴机床具有非线性映射的运动控制特点，手轮等功能的实现一直是虚拟轴机床数控系统开发中的难点之一，文章介绍了基于“PC＋PMAC”的硬件结构，结合PLC技术、中断技术以及实时多任务调度策略开发虚拟轴机床手轮功能的方法。该方法已成功应用于天津大学自主开发的虚拟轴机床数控系统，取得了良好效果。     

An accurate,efficient envelope approach to modeling the geometric deviation of the machined surface for a specific five-axis CNC machine tool

Geometric deviation, defined as the difference between the nominal surface and the simulation model of the machined surface, is the fundamental concern of five-axis tool path planning. Since the machined surface is part of the cutter envelope surface generated by the cutter motion, it is necessary to calculate the envelope surface in order to obtain the geometric deviation. In the stage of tool path planning, current approaches calculate the cutter envelope surface by using the cutter motion along the given tool path. However, the cutter motion of practical machining on a specific five-axis CNC machine tool is different from the given tool path. Moreover, the computation is very challenging when the accurate cutter motion of practical machining is applied to calculate the envelope surface. To overcome these two problems, a geometric envelope approach with two major distinctions is proposed in this paper. First, the envelope surface of the cutter undergoing a general motion is efficiently obtained as a closed-form vector expression. Second, the accurate cutter motion, which is determined by machine kinematic and interpolation scheme in practical machining, can be easily applied to calculate the accurate envelope surface. With the envelope surface, the geometric deviation is calculated to estimate the overcut or undercut in five-axis milling. An example is given to demonstrate the validity of the proposed method.     

Identification and compensation of geometric errors of rotary axes on five-axis machine by on-machine measurement

The geometric errors of rotary axes are the fundamental errors of a five-axis machine tool. They directly affect the machining accuracy, and require periodical measurement, identification and compensation. In this paper, a precise calibration and compensation method for the geometric errors of rotary axes on a five-axis machine tool is proposed. The automated measurement is realized by using an on-the-machine touch-trigger technology and an artifact. A calibration algorithm is proposed to calibrate geometric errors of rotary axes based on the relative displacement of the measured reference point. The geometric errors are individually separated and the coupling effect of the geometric errors of two rotary axes can be avoided. The geometry error of the artifact as well as its setup error has little influence on geometric error calibration results. Then a geometric error compensation algorithm is developed by modifying the numeric control (NC) source file. All the geometric errors of the rotary errors are compensated to improve the machining accuracy. The algorithm can be conveniently integrated into the post process. At last, an experiment on a five-axis machine tool with table A-axis and head B-axis structure validates the feasibility of the proposed method.     

Five-axis milling machine tool kinematic chain design and analysis

Five-axis CNC machining centers have become quite common today. The kinematics of most of the machines are based on a rectangular Cartesian coordinate system. This paper classifies the possible conceptual designs and actual existing implementations based on the theoretically possible combinations of the degrees of freedom. Some useful quantitative parameters, such as the workspace utilization factor, machine tool space efficiency, orientation space index and orientation angle index are defined. The advantages and disadvantages of each concept are analyzed. Criteria for selection and design of a machine configuration are given. New concepts based on the Stewart platform have been introduced recently in industry and are also briefly discussed.     

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.     

Accuracy test of five-axis CNC machine tool with 3D probe–ball. Part I: design and modeling

The error model of CNC machine tool describes the relationship between the individual error source and its effects on the overall position errors. A practical problem in applying this technique to five-axis machine tool is that the predicted position errors cannot be justified. This paper, the first in a set of two, presents a new measurement device, the probe–ball, which can be used to measure the overall position errors of five-axis machine tools directly. To perform the accuracy test, a three-degree-of-freedom (3D) measuring probe is installed in the main spindle and a base plate is fixed on the turntable. The kinematic chain of the five-axis machine tool is then closed through connecting the central ball on the base plate with the extension bar of the probe. To generate simultaneous axes motion under the condition of closed kinematic chain, the central ball is defined as origin of the workpiece coordinate frame and the probe is driven along a path on a spherical test surface with the central ball as center. The overall position errors are measured with the 3D measuring probe. A theoretical model is derived to explain the nature of the probe–ball error measurements.