Volumetric Error Compensation Research Articles

Inclusion of Bidirectional Angular Positioning Deviations in the Kinematic Model of a Six-DOF Articulated Robot for Static Volumetric Error Compensation

To improve a robot’s absolute positioning accuracy, researchers have extensively studied the robot kinematic model containing position and orientation errors of rotary axis average lines, widely known as Denavit–Hartenberg (D-H) parameters. To further improve the absolute positioning accuracy of industrial robots, this article proposes a novel kinematic model and its identification scheme. The proposed kinematic model for a serial-linked industrial robot contains the bidirectional angular positioning deviations of each rotary axis, represented in a lookup table, in addition to its D-H parameters. The angular positioning deviations of the rotary axes are modeled as a function of angular command positions, along with the direction of rotation to model the influence of backlash. This article also proposes a novel approach to identify the proposed kinematic model with the bidirectional angular positioning deviations using a laser tracker with indexing each rotary axis at specified angular positions (“circle point method”). Moreover, the model-based compensation technique is being experimentally investigated to validate the prediction accuracy of the proposed model. The findings of the experiment show that the proposed model enhances the robot’s absolute positioning accuracy significantly over the entire workspace.

Novel Compensation Method of Volumetric Errors for Micro-Coordinate Measuring Machines Using Abbe and Bryan Principles

To improve the accuracy of micro-coordinate measuring machines (CMMs) to nanometer scale, numerous hardware improvements have been studied and carried out in recent years, albeit with high costs and application limitations. Error compensation technology through software has also been applied because of its high precision, high efficiency and low cost. A global volumetric error compensation model on the basis of the Abbe and Bryan principles for micro-CMMs is proposed in this study. The volumetric errors of the general CMMs were also analyzed, and the transmission relationship between the volumetric and geometric errors was established in the proposed model. The parameters in the model, including 21 geometric errors and Abbe/Bryan offsets were measured and used to compensate for the volumetric errors. A zero-class gauge block was tested using a micro-CMM based on ISO 10360-2. With the volumetric error compensation, the standard deviations of the length measurements in the different diagonal directions were reduced by more than 65 %. Thus, the effectiveness of the proposed method was established. This study provides a general modeling method and compensation techniques of volumetric errors for people involved in accuracy improvement for CMMs and machine tools.

Modeling and compensation of volumetric errors for a six-axis automated fiber placement machine based on screw theory

This paper presents a novel modeling and compensation method for the volumetric errors of a six-axis gantry automated fiber placement (AFP) machine. Based on the screw theory, the forward and inverse kinematics models of the AFP machine are established. In order to improve the accuracy of the inverse kinematics solution, the Paden-Kahan sub-problem method is used to perform the inverse kinematics solution for the simplified topology of the rotary axes. Using error motion twist to establish a volumetric error transfer model for 54 geometric errors. According to the measurement data of a laser tracker and the Levenberg-Marquardt method to identify the geometric error parameters. The explicit formula of the inverse kinematics solution is used to obtain the error compensation of each motion axis, and the G code of the laying path is modified by the iterative method to realize the compensation of the volumetric errors. By comparing the positions of the tool center point before and after the error compensation, the practicability of the volumetric error modeling and iterative compensation methods are verified, and the geometric accuracy of the AFP machine can be effectively improved.

An integrated methodology of volumetric error modeling, validation, and compensation for horizontal machining centers

It is crucial to perform volumetric error forward analyses of horizontal machining centers, including modeling, validation, and compensation, so that workpiece machining accuracies can be improved. Aiming at solving three major problems so far emerged in the machine tool volumetric error forward analyses, an integrated methodology is proposed in this paper. Firstly, in order to formulate a kinematic model without uncertainties and inconsistencies, a principle to determine the correct product relations of nominal motions to motion errors is systematically developed. Secondly, a novel validation approach based on the concept of volumetric vector Euclidean norm is demonstrated in this paper, assuring that the constructed volumetric error model can be quantitatively assessed without engaging any compensation processes. Thirdly, an optimal compensation technology is also presented to achieve the objective that the compensation residual errors, which are likely generated from the existing inverse superposition compensation strategies, can be diminished or even eliminated. A commercial horizontal machining center is selected to apply and verify the proposed integrated methodology.

A Kinematic Error Controller for Real-Time Kinematic Error Correction of Industrial Robots

Industrial robots are being used more and more for manufacturing applications that require accuracy beyond what can be obtained from joint measurement. While offline calibration techniques such as volumetric error compensation can be used to correct robot kinematic error, these methods are unable to compensate for robot deformations caused by changing tool loads during the manufacturing operation. This paper explores the use of a real-time robot kinematic error compensation technique where an external high-precision feedback sensor (in this case a laser tracker) directly measures the robot kinematic error and corrections are implemented during processing. A robot kinematic error model is constructed to describe the difference between the programmed trajectory of the robot’s last link and the actual trajectory based on the laser tracker measurement of the 6DoF sensor attached to the last link of the robot. The compensation scheme developed in this paper requires the synchronization of the robot encoder and laser tracker sensor measurements, which is accomplished in the Robot Operating System (ROS). The previously developed kinematic error observer is briefly discussed and a kinematic error compensation that adjusts the robot’s reference path in real time is created in this paper. A discussion of the system (i.e., Yaskawa/Motoman MH180 industrial robot and Automated Precision Inc. laser tracker) hardware components and the software architecture utilized in the experiments conducted in this paper are provided. Initial experimental studies are conducted to determine delays in the feedback measurement, which was 30 ms, explore the effects of controller gain on the system performance, and characterize the noise in the feedback measurement. The controller had an overdamped response with a settling time of 8.758 s. Subsequent experiments investigated the effect of robot velocity on tracking and the ability of the controller to reject a constant force disturbance. It was found that the kinematic error increased linearly as the robot velocity increased, and the controller was able to reject a constant force disturbance of 45 lb within the designed settling time.

Novel six-axis robot kinematic model with axis-to-axis crosstalk

Conventionally, the volumetric error compensation of six-axis robots is mostly based on a kinematic model with position and orientation errors of the rotary axis average lines, known as Denavit–Hartenberg (D–H) parameters. This study proposes a novel kinematic model with angular positioning deviation of each rotary axis, modeled as a function of the command angle and rotation direction. The error motions of one rotary axis can be dependent on the angular position of other axes owing to changes in the moment of inertia or center of gravity. The prediction accuracy of the proposed model was experimentally evaluated. Compensation experiments showed a significant reduction in the static volumetric error over the entire workspace.

Assessment of non-rigid body, direction- andvelocity-dependent error motions and their cross-talk by two-dimensional digital scale measurements at multiple positions

The conventional volumetric error compensation for a machine tool is based on the machine's kinematic model, which formulates the tool center point (TCP) position based on the assumption of rigid-body motion of each axis. Particularly in large-sized machine tools, error motions that do not satisfy this assumption may have a significant impact on the machine's overall volumetric accuracy. In addition to position-dependent quasi-static error motions included in the conventional kinematic model, this paper proposes a scheme to assess quasi-static cross-talk between axes and direction- and velocity-dependent error motions. This paper proposes test procedures to measure two dimensional (2D) contour error trajectories by using a 2D digital scale (cross grid encoder). Unlike many previous works, this paper proposes to perform the tests at multiple positions over the machine tool's entire workspace, and the error motions are assessed by comparing contour error profiles. An experimental case study on a large-sized bridge-type vertical machine tool shows that such influences can be significant error contributors. The proposed tests can assess error motions only at discrete points where a 2D digital scale is installed. It can be applied as accuracy inspection to ‘‘roughly’’ assess the machine's volumetric accuracy by using a 2D digital scale only, but it is generally not for the compensation.

Volumetric error compensation of machine tool using laser tracer and machining verification

Volumetric error is a primary factor that affects the accuracy of machining tools. The ability to ascertain volumetric error in a rapid and simple manner is of significant importance, and this can remarkably reduce the probability of temperature variation during the experiment. This study proposes a strategy for volumetric error measurement and compensation based on laser tracer for the 3-axis numerical control (NC) machining tool, and verifies the machining accuracy of a concave semi-spheroid test piece. In this study, the calibration methods employed by the laser tracer and the error separation algorithm of the machining tool are initially investigated. Following this, the accuracy of the geometric error measurement is verified using the laser interferometer. The cubic spline interpolation method is then employed to establish the tool path volumetric error model in the 3-axis NC machining tool, and the G-code modification is conducted for volumetric error compensation. Experiment results show that when the error compensation is performed, the improvement in the accuracy as compared with the initial state exceeds 50% not involving machining. To evaluate the accuracy and effectiveness of the proposed method, two machining tests to obtain a concave semi-spheroid test piece with and without volumetric error compensation strategy are studied, and the corresponding accuracies are measured by a high precision coordinate–measuring machine. It is found that the machining accuracy after having performed the error compensation is approximately 43% higher than that obtained on the pre-volumetric error compensation.

A novel modeling of volumetric errors of three-axis machine tools based on Abbe and Bryan principles

The modelling of volumetric errors of machine tools has been widely used by the method of Homogeneous Transformation Matrix (HTM) based on rigid body kinematics analysis for a long time. Without spindle induced errors and thermal errors, to establish a closed-loop HTM for a three-axis machine tool, the total of 21 geometric errors are the primary elements to be known. It is well known that the measured points of translational errors are directly related to the volumetric error at the tool cutting point through rigid body kinematics. In the generalized HTM method, however, this relationship is missing. This report, therefore, proposes a new comprehensive approach to formulate the volumetric errors based on the famous Abbe principle in order to derive the error term in the motion direction, and Bryan principle to derive the error terms in orthogonal to the motion direction. The proposed methodology is simple in concept, rational in physical meaning and easy in implementation. Experimental results, including faster multi-degree-of-freedom error measurements, volumetric error analysis and compensation on a testbed of small machine tool, validate the correctness and effectiveness of this method.

Volumetric error measurement and compensation of three-axis machine tools based on laser bidirectional sequential step diagonal measuring method

This paper proposes an approach to the measurement, modeling, and compensation of the volumetric errors for three-axis machine tools, using laser bidirectional sequential step diagonal measurement. Disparate measuring tracks are specially arranged for forward and backward paths, and the conforming error decoupling method is demonstrated. By decoupling, all the geometric errors which can result in volumetric errors are distinguished simultaneously, including translational and angular errors. In comparison with the traditional unidirectional measuring method, the proposed bidirectional method distinguishes more geometric errors (the angular errors) by measuring the same four body diagonals. Uncertainty analysis based on the Monte Carlo simulation was conducted, followed by experimental validation on a vertical machining center. The result of the experiment indicates that the diagonal systematic deviation of positioning is reduced by 90% after volumetric compensation.

An improved machine tool volumetric error compensation method based on linear and squareness error correction method

Error compensation is one of effective and economical means to improve the machining accuracy of machine tools. The measurement accuracy of kinematic errors has great impact on the accuracy of machine tool error modeling. Some measurement errors are inevitably generated due to the distortion of the slide table and the limit of local measuring stroke. To solve these problems, an improved machine tool volumetric error compensation method is proposed in this paper, based on linear and squareness error correction method. The linear errors, including position errors and straightness errors, are corrected by considering the distance effect between optical mirror groups and the surface of worktable. The squareness errors are corrected through modifying local squareness errors measured with double ball bar to global squareness errors, with the aid of straightness errors measured with multi-laser calibrator. Then volumetric errors are obtained based on multi-body system theory, and volumetric diagonal errors are measured with laser interferometer. It is illustrated that the bidirectional systematic deviation of positioning of four volumetric diagonals reduced about 81.3%, 35.2%, 29.2%, and 4.5% respectively by using this improved machine tool volumetric error compensation method, and it is of obvious advantages in contrast with traditional compensation method with direct measurement data. The improved error compensation method proposed in this paper has universal applicability and has great significance on machine tool accuracy improvement.

Volumetric Error Modelling and Compensation for Batch of Vertical Machining Centers Based on Sensitivity Analysis

Volumetric Error Modelling and Compensation for Batch of Vertical Machining Centers Based on Sensitivity Analysis

Measurement method for volumetric error of five-axis machine tool considering measurement point distribution and adaptive identification process

To improve the machine tool accuracy, geometric error identification is required for volumetric error compensation. This paper presents a method for the geometric error identification of a five-axis machine tool that considers the optimised distribution of measurement points and accurate description of geometric errors. The measurement is performed using a laser tracker that permits rapid error data collection over a large measurement range. In the volumetric error modelling, the geometric errors are described as position-dependent Chebyshev polynomials. Hence, the identification of geometric errors is converted into the identification of polynomial coefficients. In the identification process, a distribution method for measurement points is proposed to improve the identification accuracy by minimising the influence of measurement error on the identification result. At the same time, an adaptive approach is introduced to accurately define the polynomial orders of geometric errors to improve the identification accuracy. Simulations and experiments are conducted to verify the geometric error identification method. In addition, the proposed method is compared with other methods. Based on the identification result of geometric errors and the volumetric error model, the volumetric error of any position in a workspace can be predicted and further compensated.

An Optimal Method for Improving Volumetric Error Compensation in Machine Tools Based on Squareness Error Identification

This paper proposes a new method to identify the squareness errors of machine tools and gives an optimal method to improve the volumetric compensation accuracy based on the identified squareness errors. The volumetric error model based on screw theory is proposed and the effects of the squareness errors on the volumetric errors have been analyzed to clarify the possibility of improving volumetric error compensation by proper and accurate squareness errors. Then the identification method of the squareness errors is deduced in theory considering a 3-axis horizontal machine tool. With the identified squareness errors, an optimal method to improve volumetric error compensation in machine tools has been proposed. Experiments have verified that the 3 identified squareness errors are in accordance with the measured squareness errors within the accuracy range. Moreover, compared with the traditional measurement of squareness errors not considering the PDGEs, the proposed method is more effective and shows error compensation improvement in the volumetric error compensation process.

A volumetric positioning error compensation method for five-axis machine tools

Volumetric positioning error is an important index that influences the machining accuracy of five-axis machine tools. Although the available compensation methods, including hardware and software compensation, provide approaches to improve the volumetric positioning accuracy of five-axis machine tools, the cost-effect ratio of these methods is usually not acceptable for most users. Based on the volumetric error model of a five-axis machine tool and the sag error compensation function together with the table multiplication function in Siemens 840D system, a novel volumetric positioning error compensation method is proposed in this paper. The experiments show that the proposed compensation method can effectively improve the machining accuracy of the machine tool with really low cost, which shows good perspective in manufacturing industry.

Volumetric error compensation model for five-axis machine tools considering effects of rotation tool center point

Conventional volumetric error compensation strategies for five-axis machines directly generate compensation values without considering the RTCP (rotation tool center point) effects, which causes additional movements of translational axes with the movement of rotary axes, so the compensation values for three linear axes need to be recalculated. In this paper, a volumetric error compensation model considering RTCP is proposed. In the model, the compensation values for translational axes totally consist of three parts, i.e., position errors caused by the volumetric error, position variations caused by the compensation of rotary axes, and caused by RTCP. Firstly, the compensation values for rotary axes are obtained based on the volumetric error model and the inverse kinematics. Then, the compensation values for three linear axes are calculated in detail based on the compensation values of rotary axes and RTCP effects. Finally, ballbar tests of a cone-frustum toolpath are selected to verify the proposed compensation model.

Using the Segmented Iterative Learning Control Method to Generate Volumetric Error-Compensated Part Programs for Three-Axis CNC Milling Machine Tools

This study proposes using the iterative learning control method to adjust the volumetric error-compensated tool path, where the working volume motion accuracy of three-axis computerized numerical control (CNC) milling machine tools is increased by segmented modification of the part program. As the three-axis CNC milling machine tools generally have volumetric error of working volume, this study refers to the measured and established table of volumetric errors and uses the method of the modifying part program for volumetric error compensation of machine tools. This study proposes using part-program single-block positioning segmented for volumetric error compensation, as the generated compensated part program with multiple compensated blocks can effectively compensate the volumetric error of working volume in the tool moving process. In terms of the compensated tool path computing method, this study uses the iterative learning control (ILC) method and refers to compensated tool path and volumetric errors along the compensated tool path for iterative computation. Finally, a part program with multiple blocks is modified by the converged optimal compensated tool path, in order that the modified part program has higher-precision volumetric error compensation effect. The simulation result shows that the rate of improvement of error of the volumetric error compensation method proposed in this study is 70%. The result of cutting tests shows that the average rate of improvement of the straightness error of the test workpiece is 60%, while the average rate of improvement of height error is 80%. Therefore, the results of simulation and cutting tests can prove the feasibility of using the ILC method for segmented modification of the volumetric error-compensated part programs proposed in this study.

Volumetric error modeling, identification and compensation based on screw theory for a large multi-axis propeller-measuring machine

Large multi-axis propeller-measuring machines have two types of geometric error, position-independent geometric errors (PIGEs) and position-dependent geometric errors (PDGEs), which both have significant effects on the volumetric error of the measuring tool relative to the worktable. This paper focuses on modeling, identifying and compensating for the volumetric error of the measuring machine. A volumetric error model in the base coordinate system is established based on screw theory considering all the geometric errors. In order to fully identify all the geometric error parameters, a new method for systematic measurement and identification is proposed. All the PIGEs of adjacent axes and the six PDGEs of the linear axes are identified with a laser tracker using the proposed model. Finally, a volumetric error compensation strategy is presented and an inverse kinematic solution for compensation is proposed. The final measuring and compensation experiments have further verified the efficiency and effectiveness of the measuring and identification method, indicating that the method can be used in volumetric error compensation for large machine tools.

Thermally induced volumetric error compensation by means of integral deformation sensors

A common approach to describe errors in machine tools is the volumetric error modeling. For three-axis machine tools, this includes a structural loop model of 21 geometric/kinematic error components. The dislocation at the tool tip is then the result of the kinematic decomposition of these error components and can be derived with simple mathematical techniques. The concept behind this modeling approach is that geometric/kinematic errors include a time-invariant, deterministic term and a time-variant, load-dependent, stochastic term. Thermal effects cause the most detrimental time-variant term. In order to include them in volumetric error models, the variation of the error components with respect to the thermal loading on the machine tool structure has to be measured. The most of the research has focused until now on measuring the variation of the most significant error components with temperature. Collecting these data is however difficult and time-consuming and the resulting models are too cumbersome for the industrial use. This paper proposes a new method for calculating thermally induced volumetric error based on the direct measurement of the structural deformations. This measurement has a higher content of information than common temperature sensor methods, since the structural deformations are the outcome of all thermal sources combined. To demonstrate the effectiveness of the proposed model, several thermal loads were applied on a three-axis milling machine, while the dislocation at the tool tip was measured with an R-test based procedure.

Geometric error analysis and compensation for multi-axis spiral bevel gears milling machine

This article proposes a method to analyze and compensate geometric errors of six-axis CNC grinding machines for spiral bevel gears. Volumetric error prediction and compensation models are realized by the forward and inverse kinematics modeling via the screw theory. Key geometric error items of motion axes and their influences on gear tooth performance are modeled and analyzed. Advantages of the proposed compensation method for geometric errors over the machine settings modification method are demonstrated. The compensation strategy has been verified on a six-axis grinding machine controlled by a Siemens CNC. The pitch error and tooth form error of machined gears before and after compensation are compared to validate the effectivity of the proposed compensation method.