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.     

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.     

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.     

On-machine measurement of location errors on five-axis machine tools by machining tests and a laser displacement sensor

This paper proposes an on-machine measurement (OMM) of all location errors on five-axis machine tools. Five machining patterns are successively performed on a cubic workpiece. The basic idea is to use a set of large rotations of rotary axes to prolong the moving distance of linear axes when squareness errors of linear axes are identified. Then, a set of small rotations of rotary axes are used to decouple the squareness errors of linear and rotary axes. Based on this, the long and deep slots in previous machining tests are improved to be a set of short and shallow ones. These miniaturized slots reduce the material removal and minimize the influence of cutting force and thermal deformation on the measuring results. Then the cutting tool is substituted by a laser displacement sensor (LDS) to measure the mismatch between the finished surfaces of the corresponding slots. All the measured surfaces are located on the bottom of the slots to fit the LDS characteristic of one dimensional measurement. Three gestures of the rotary table and tilting head are used to implement the single-setup OMM and the influence of location errors on the measuring results is compensated. Validation of the identified values is also provided by a set of simple tests using different measuring instruments. The efficiency and accuracy of location errors measurement method on five-axis machine tools are improved.     

Accuracy enhancement of five-axis machine tool based on differential motion matrix: Geometric error modeling,identification and compensation

This paper presents the precision enhancement of five-axis machine tools according to differential motion matrix, including geometric error modeling, identification and compensation. Differential motion matrix describes the relationship between transforming differential changes of coordinate frames. Firstly, differential motion matrix of each axis relative to tool is established based on homogenous transformation matrix of tool relative to each axis. Secondly, the influences of errors of each axis on accuracy of tool are calculated with error vector of each axis. The sum of these influences is integration of error components of machine tool in coordinate system of tool. It endows the error modeling clear physical meaning. Moreover, integrated error components are transformed to coordinate frame of working table for integrated error transformation matrix of machine tools. Thirdly, constructed Jacobian is established using differential motion matrix of each axis without extra calculation to compensate the integrated error components of tool. It makes compensation easy and convenient with reuse of intermediate. Fourthly, six-circle method of ballbar is developed based on differential motion matrix to identify all ten error components of each rotary axis. Finally, the experiments are carried out on SmartCNC500 five-axis machine tool to testify the effectiveness of proposed accuracy enhancement with differential motion matrix.     

Development of an on-machine profile measurement system in ELID grinding for machining aspheric surface with software compensation

Efficient manufacture of dimensionally accurate optical surface on hard and brittle materials is a major concern for optoelectronic industry. Electrolytic in process dressing (ELID) grinding is proved as a reliable process to achieve this optical quality nano-surface finish on hard and brittle materials. Besides surface finish it is important to ensure dimensional accuracy by improving profile and form accuracy of the ground aspheric surface. Kinematic factors are commonly considered the reasons for the dimensional inaccuracy in a machined part. Software compensation is a direct and economical method to overcome several kinematic factors and improve the dimensional accuracy. Last, but most important, is the monitoring of achieved surface profile to ensure more accurate profile radius in the finished part. So an on-machine profile measurement system based on coordinate measuring machine (CMM) principle has been developed to check the profile radius of the ground surface. In this study software compensation was applied in ELID grinding of an aspheric surface in order to compensate the wheel wear until the measured surface profile machined on BK7 glass reaches within tolerable limit.     

Kinematic and geometric error compensation of a coordinate measuring machine

In this paper, kinematic modelling of a Coordinate Measuring Machine (CMM) is carried out and the methodology followed in modelling is explained in detail. The model is simplified by certain assumptions which may result in over-simplification of the model. Consequently, the model is investigated and enhanced by adding the relevant and suitable geometric error terms. Different approaches are employed to evaluate the model coefficients. In the first approach, a commercial ring gauge is measured in a structured lattice in the work volume of the CMM. Resulting errors in these measurements are used in conjunction with some statistical methods to arrive at sets of model coefficients values. The second approach is based on measurement of the individual 21 error terms in the CMM by means of laser interferometry. These measurements are used to evaluate another set of model coefficients. A compensation strategy is proposed and tested using the model and the sets of coefficients obtained. Volumetric Performance of the CMM is evaluated according to ASME standards, before and after compensation. Improvement in the CMM volumetric performance is demonstrated and compared.     

Derivation of machine tool error models and error compensation procedure for three axes vertical machining center using rigid body kinematics

Volumetric positional accuracy constitutes a large portion of the total machine tool error during machining. In order to improve machine tool accuracy cost-effectively, machine tool geometric errors as well as thermally induced errors have to be characterized and predicted for error compensation. This paper presents the development of kinematic error models accounting for geometric and thermal errors in the Vertical Machining Center (VMC). The machine tool investigated is a Cincinnati Milacron Sabre 750 3 axes CNC Vertical Machining Center with open architecture controller. Using Rigid Body Kinematics and small angle approximation of the errors, each slide of the three axes vertical machining center is modeled using homogeneous coordinate transformation. By synthesizing the machine's parametric errors such as linear positioning errors, roll, pitch and yaw etc., an expression for the volumetric errors in the multi-axis machine tool is developed. The developed mathematical model is used to calculate and predict the resultant error vector at the tool–workpiece interface for error compensation.     

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.     

Geometric and quasi-static thermal error compensation for a laser digitizer equipped coordinate measuring machine

An emerging trend in dimensional inspection of manufactured parts is the use of coordinate measuring machines (CMMs) equipped with non-contact laser digitizers instead of traditional contact probes. Error mapping is generally proprietary to the CMM controller, and the accuracy of such a combined system is limited by the lack of integrated CMM/laser digitizer error compensation. This paper reports progress towards achieving such a system.Geometric error compensation measurements are made on a test machine at 20, 25 and 30 °C. Performance of the system was tested by measuring a special optically coated sphere ballbar artifact. The scan coordinates, the CMM axis scale positions and temperature were recorded simultaneously in real time. The CMM error compensation data was then used to post process the laser digitizer coordinates to obtain improved global part coordinates.Inclusion of the error compensation terms is shown to reduce the dispersion of results by 65 to 80%.     

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.     

Development of a hybrid rapid prototyping system using low-cost fused deposition modeling and five-axis machining

Currently, two major processes are being used to produce prototypes, namely machining and rapid prototyping. Machining is generally more accurate and precise, but it is difficult to produce objects with certain complicated features. In contrast, rapid prototyping can produce objects with complicated features, which allows materials to be used more efficiently. However, due to the uneven shrinkage and residual stresses within rapid prototyping products, their accuracy is usually uncertain. This study attempts to integrate these two manufacturing processes and develop a hybrid rapid prototyping system in order to overcome the disadvantages associated with each process and to develop new applications. Fused deposition modeling (FDM) was used as the rapid prototyping process in this work. A spindle and a low-cost FDM extruder were designed to be placed on each end of a rotary axis in a five-axis machine tool. The proposed design allows the rotation of the axis on the five-axis machine to switch between machining and FDM, thus achieving the advantage of reducing costs for extra actuators without sacrificing working space. The case studies demonstrated that the proposed hybrid system can build FDM objects without using support materials and produce FDM parts with metal embedded to increase the stiffness. The system can also conduct five-axis machining on a completed FDM part or trim the freeform surface fabricated by FDM to achieve more accurate dimensions or better surface finish.     

Accuracy improvement of miniaturized machine tool: Geometric error modeling and compensation

A novel capacitance–sensor based multi-degree-of-freedom (DOF) measurement system has been developed for measuring geometric errors of a miniaturized machine tool (mMT) overcoming the size limitations. In the present work five geometric error components of a three-axis mMT are measured simultaneously along each axis and the squareness errors are determined by the slopes of straightness error profiles. Least-squares fitting method is used to represent the analytical models of geometric errors. A kinematic chain consisting of various structural members of mMT is introduced to establish the positional relationships among its coordinate frames. Based on this kinematic chain a general volumetric error model has been developed to synthesize all geometric error components of a miniaturized machine tool. Then, a recursive compensation method is proposed to achieve error compensation efficiently. Test results show that the positioning accuracy of miniaturized machine tool has been improved with compensation.     

Thermal error mode analysis and robust modeling for error compensation on a CNC turning center

In this paper a novel concept of thermal error mode analysis is proposed in order to develop a better understanding of the thermal deformation on a turning center. The thermal error of the machine can be treated as the superposition of a series of thermal error modes with corresponding mode shapes and time constants. The selection of sensor location can then be improved based on the thermal error mode analysis. A robust modeling approach is also proposed to minimize the errors due to temperature measuring noise and the adverse effect of environmental changes. Through the use of thermal error mode analysis and the robust modeling approach, the number of thermal sensors has been reduced from 16 to four. The thermal error compensation system has been applied to a turning center in daily production for more than two years and it has kept year-round accuracy. The thermal drift in workpiece diameter on the turning center has been reduced from 35 μm to 6 μm from its center of tolerance.     

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.     

Real-time generation and control of cutter path for 5-axis CNC machining

This paper presents a new approach to real-time generation and control of the cutter path for 5-axis machining applications. The cutter path generation method comprises real-time algorithms for cutter-contact path interpolation, cutter offsetting, and coordinate conversion. In addition, a global feedback loop is closed by the CNC interpolator so as to augment the controlled accuracy in practical cutter path generation. An error compensation algorithm and a feedrate adaptation algorithm for the control loop are developed, respectively.