Volumetric Error Model Research Articles

An analytical approach for crucial geometric errors identification of multi-axis machine tool based on global sensitivity analysis

Geometric errors directly affect the tool tip position, reduce machining accuracy, and are one of the most important errors of multi-axis machining tool. However, the geometric errors are intercoupling, and the measured values at different points vary and are stochastic. The identification of the most crucial geometric errors and the determination of a method to control them is a key problem to improve the machining accuracy of machine tool. To achieve this goal, a new analytical method, to identify crucial geometric errors for a multi-axis machine tool is proposed here based on multibody system (MBS) theory and global sensitivity analysis. The volumetric error modeling of multi-axis machine tool has been given by MBS theory, which describes the topological structure of multibody system simply and conveniently in a matrix. The stochastic characteristic of geometric errors is taken into consideration and Sobol global sensitivity analysis method is introduced to identify crucial geometric errors of machine tool. A vertical machining center is selected as an illustration example. The analysis results reveal that the analytical method presented in this paper can identify the crucial geometric errors and are helpful to improve the machining accuracy of multi-axis machine tool.

Geometric accuracy allocation for multi-axis CNC machine tools based on sensitivity analysis and reliability theory

Machining accuracy of a machine tool is influenced by geometric errors produced by each part and component. Different errors have varying influence on the machining accuracy of a tool. The aim of this study is to optimize errors to get a desired performance for a numerical control machine tool. Applying multi-body system theory, a volumetric error model was constructed to track and compensate effects of errors during operation of the machine, and to relate the functional specifications on volumetric accuracy to the permissible errors on the joints and links of the machine. Error sensitivity analysis was used to identify the influence of different errors (especially the errors which have large influences) on volumetric error. Based on First Order and Second Moment theory, an error allocation approach was developed to optimize allocation of manufacturing and assembly tolerances along with specifying the operating conditions to determine the optimal level of these errors so that the cost of controlling them and the cost of failure to meet the specifications is minimized. The approach developed was implemented in software and an example of the geometric errors budgeting for a five-axis machine was discussed. It is identified that the different optimal standard deviations reflect the cost-weighted influences of the respective parameters in the equations of the functional requirements. This study suggests that it is possible to determine the coupling relationships between these errors and optimize the allowable error budgeting between these sources.

Frequency domain error analysis in turning

In spite of the large body of work on error analysis in turning, there are very few references that directly address the relationship between the original frequency content of the different dynamic errors of the machine tool and of the machining process and the resulting spatial frequency content of the machined surface. In this paper, the dynamic errors of a machine tool are classified into two categories: (a) kinematics-induced and (b) vibration-induced dynamic errors. Through a theoretical analysis, it will be shown that the spatial frequency content of the turned surface is not directly influenced by the original frequency factors of the machine dynamic error components, but by the aliased frequency factors which will be explained in this paper. On the basis of the establishment of the deterministic mathematical relationship between the frequency contents of the machine dynamic errors in the volumetric error model and the spatial frequency content of the turned surface in radial directions, a method for obtaining the frequency spectrum of the machined surface error in radial directions is given. In addition, a method to influence the number of spatial frequency components of the surface error in radial directions and to predict and control their magnitude is put forward. A case study of a flat surface turning is presented to highlight the effectiveness of the theoretical analysis and of the proposed methods. This study has potential applications in predicting and controlling the spatial content of machined surfaces, in selecting proper machining conditions, as well as in designing machine tools for applications in which strict spatial frequency requirements are placed on the workpiece surface.

Research on Volumetric Error Measurement, Modeling and Compensation for NC Machine Tools

With the increasing requirements of the machining accuracy of CNC machine tools, the impact of thermal deformation is growing. Thermal error compensation technology can predict and compensate the thermal errors in real-time, and improve the machining accuracy of the machine tool. In this paper, the research objects of thermal error compensation is expanded to the volumetric error of the machine tool, the volumetric error modeling of a three-axis machine tool is fulfilled and a compensator is developed for the compensation experiment, which provides scientific basis for the improvement of the machining accuracy.

Development of Double-Axis Double-Rest CNC Machining Center

The design for a double-axis double-rest CNC machining center is introduced by describing its key machine elements and machine tool design procedures. Then based on the theory of the multi-body system, the modeling process of the volumetric error model for the CNC machining center is expatiated and the result of the modeling is given. It is verified that the error of the machine tool is from three line error and three angular errors between structural units as well as the vertical error between axes. Finally experiments are carried out to evaluate the machining performance of this designed machine tool.

초정밀 롤 금형 가공기의 기하학적 오차 측정 방법: 모의실험

In this study, a measurement method of double ball-bar is proposed to measure the geometric errors of an ultra-precision roll mold machine tool. A volumetric error model of the machine tool is established to investigate the effects of the geometric errors to a radius error and a cylindricity of the roll mold. A measurement path is suggested for the geometric errors, and a ball-bar equation is derived to represent the relation between the geometric errors and a measured data of the double ball-bar. Set-up errors, which are inevitable at the double ball-bar installation, also are analyzed and are removed mathematically for the measurement accuracy. In addition, standard uncertainty of the measured geometric errors is analyzed to determine the experimental condition. Finally, the proposed method is tested and verified through simulation.

Volumetric Error Model of Large CNC Machine Tool and Verification Based on Particle Swarm Optimization

Volumetric error has large effect on machine tool accuracy; improving CNC machine tool accuracy through error compensation has received significant attention recently. This paper intends to represent volumetric error measurement based on laser tracker. The volumetric error is modeled by homogenous transformation matrix with each coordinate corresponding to each motion axis. Based on parts of spatial points volumetric error, the geometric errors which affect volumetric positioning error are verified through particle swarm optimization with the L2 parameters as the target function. The chebyshev orthogonal polynomials are applied to approximate geometric errors.

Thermally induced volumetric error modeling based on thermal drift and its compensation in Z-axis

Traditional thermally induced volumetric error modeling requires 21 geometric error components at different temperatures. Taking thermal drift errors into account, 30 geometric errors are described to model volumetric error in this paper. The main sources of thermally induced volumetric error are positioning errors of each axis and thermal drift errors. An experiment on milling and boring machine is carried out, which shows that volumetric error in Z-axis is affected significantly. To compensate volumetric error of Z-axis, a model of positioning error is proposed based on nut temperature. A finite elements analysis of headstock thermal characteristic is carried out, and error chain is established, which shows the main source of thermal drift of Z-axis is ram expansion. Thermal drift compensation system of Z-axis is developed based on Invar metal and thermal error compensation module of Siemens CNC system. Therefore, the positioning error and thermal drift of Z-axis are compensated. The thermally induced volumetric error in Z-axis is reduced by 80 % after compensation.

Transmission system accuracy optimum allocation for multiaxis machine tools’ scheme design

Transmission components are the main mechanical elements in a machine system, the accuracy level of the transmission system is one of the major sources of the machining error of multiaxis machine tools. This article investigates motion error analysis, volumetric motion error model for transmission system and the accuracy allocation method for multiaxis machine tools during the early design stage. For this purpose, a transmission system volumetric motion error model, which is based on the motion error matrix and screw theory, is derived for mapping transmission components’ error parameters to the volumetric motion errors of machine tools. The volumetric motion error matrix combines motion errors along the machine tools’ kinematic chains. Subsequently, the volumetric motion error model is expressed as a volumetric motion error twist, which is formulated from the volumetric motion error matrix. Additionally, the transmission system volumetric motion error twist model is used as design criteria for accuracy optimum allocation, with constraints on the twist magnitude and design variable limits. Then, design optimization is performed by using a multiobjective nonlinear optimization technique to minimize the manufacturing cost and volumetric motion error twist pitch. To solve this multiple objective optimum problem, this study proposes an approach integrating Lagrange multiplier and gradient descent operator with non-dominated sorting genetic algorithm-II (NSGA-II). Modified non-dominated sorting genetic algorithm-II searches for an allocation scheme Pareto optimal front. Consequently, VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) determines the best compromise solution from the Pareto set. Finally, a numerical experiment for the optimal design of a numerical control machine tool is conducted, which highlights the advantages of the proposed methodology.

Volumetric error modeling and sensitivity analysis for designing a five-axis ultra-precision machine tool

The five-axis machine tools are increasingly popular for meeting the demand of machining the workpiece with growing geometric complexity and high accuracy. This paper studies the volumetric error modeling and its sensitivity analysis for the purpose of machine design. The volumetric error model of a five-axis machine tool with the configuration of RTTTR is established based on rigid body kinematics and homogeneous transformation matrix, in which 37 error components are involved. The sensitivity analysis of volumetric error regarding 37 error components is carried out respectively. The analysis results are successfully used for the accuracy design and manufacture of a five-axis ultra-precision machine tool. The preliminary experiment of machining sine grid surface testifies the high accuracy and effectiveness of the designed five-axis machine tool.

Volumetric Error Compensation for the MScMS-II

Large scale measuring systems, i.e. measuring systems characterized by a measurement volume from some meters up to some hundreds of meters, are gaining importance in industry to check large parts or track the position of automated vehicles. In contrast with classical monolithic measuring systems, modern large scale measuring systems are constituted by constellations of sensors able to track the position of objects by triangulation or trilateration. This new design allows a greater system flexibility, scalability, and portability, together with a general reduction of costs. The MScMS-II is a large scale measuring system based on infrared triangulation. It has been designed to guarantee the maximum flexibility and reconfigurability, so every set-up procedure has been reduced as much as possible, so that its deployment and calibration requires a short time. However, its accuracy could benefit of a more complete volumetric calibration through the definition of a model of the volumetric error to be compensated. In this paper a self-calibration procedure based on a simple one-dimensional uncalibrated artifact is proposed to define a volumetric error model of the MScMS-II. Self-calibration can be performed in short time and can improve system performance by reducing systematic errors. Experimental results complete the work.

Analysis and Modeling of Error Sources for Spiral Bevel Gear Honing Machine Based on Multi-Body System Theory

Analyzing some main errors of NC spiral bevel gear honing machine-tool, the elements of geometric error, thermal error and force error etc., which are constructed 39 error sources of the machine by stack method. Based on multi-body system theory, using homogeneous transfer matrix(HTM) method to present six feature matrixes that includes ideal-static matrix, ideal-kinematic matrix, ideal-static translation error matrix, ideal-static rotary error matrix, non-ideal rotary motion error matrix and non-ideal translation motion error matrix, which are built between of adjacent body. Finally, the synthetic volumetric error model of six-axis honing machine-tool is established.

Error Modeling of a Parallel Wedge Precision Positioning Stage

The parallel wedge precision positioning stage (PW-PPS) presents a novel configuration of a parallel mechanism for precision positioning applications. Based on its specific parallel configuration, the corresponding inverse and forward kinematic models were developed and used to formulate the volumetric error model of the mechanism. The error model that considers the influence of manufacturing errors is built in two steps. In the first, the structural parameter-induced errors associated with the PW-PPS's structural parameters and input variables were considered, while in the second, the joint clearance-induced errors produced by joint clearances were taken into account. The structural parameter-induced errors were modeled based on complete differential-coefficient theory, while the joint clearance-induced errors due to joint clearances were modeled based on the virtual work and deterministic method. In the latter case, the kinetostatic model and joint error contact modes were analyzed to build a joint clearance-induced error model. The relationship between the different error sources and the output pose error of the mechanism's moving platform was obtained. Finally, considering practical values for the mechanism's parameters and errors, the error distribution in the PW-PPS's workspace was evaluated to determine the distributive rules of the various error components.

Volumetric error modeling and compensation considering thermal effect on five-axis machine tools

This article intends to provide an error compensation system for five-axis machine tools. A volumetric error model is established with homogeneous transformation matrix method, from which compensation values of both orientation and position errors can be obtained. Thirty-seven errors on a five-axis machine tool are classified into three categories – functional, random, and negligible errors, among which the effect of the first one on volumetric accuracy is considered as great enough to be included in this model. Some typical modeling methods are discussed on positioning and straightness errors, considering both geometric and thermal effects. Then, we propose a compensation implementation technique based on the function of external machine zero point shift and Ethernet data communication protocol for machine tools. Finally, laser diagonal measurements have been conducted to validate the effectiveness of the proposed volumetric error compensation system.

Research on volumetric error compensation for NC machine tool based on laser tracker measurement

Error compensation is an effective method to improve the accuracy of NC machine tool. The compensation results are greatly affected by the error modeling and error measurement, so how to establish an accurate error model and accurately detect the geometric errors of machine tool are particularly important. In the paper, the volumetric error model of a multi-axis NC machine tool is established based on the multi-body system theory. The relative position deviations between the rotary axis and linear axis of the machine tool are considered in the modeling. To achieve quick and accurate detection, a laser tracker is based on the multi-station and time-sharing measurement principle to detect the geometric errors of machine tool, and each error of linear axis and rotary axis can be identified by this method. With the error model, error compensation can be carried out by modifying the machining process (G code), and the machining accuracy can be improved with the new G code. Experiment results show that the motion errors of a milling machine are significantly reduced after compensation, which verifies the effectiveness of compensation method.

Application of Ant Colony Algorithm to Volumetric Thermal Error Modeling and Compensation of a CNC Machine Tool

Volumetric errors are the major contributor to the dimensional errors of a workpiece in precision machining. Error compensation technique is a cost-effective way to reduce volumetric errors. Accurate modeling of volumetric errors is a prerequisite of error compensation. In this paper, a volumetric error model was proposed by using neural networks based on ant colony algorithm. Finally, a volumetric error compensation system was developed based on the proposed model, and which has been applied to a CNC machine tool in daily production. The results show that the volumetric errors are reduced and the machining accuracy of the machine tool is improved.

Geometric error compensation of spherical surface grinding system

Kinematics theory for a multi-body system is used to analyse translational joint error, rotational joint error, and quadrature error in a spherical grinding system. A virtual grinding point method is proposed that is based on process features, and the feasibility as well as effectiveness of this method is demonstrated. A volumetric error model of the grinding system is created and the compensation method is coded into a control computer program. A laser interferometer is used to experimentally measure the error both with and without the proposed error compensation scheme. The experimental results validate the proposed approach in that they show that the spherical surface grinding precision is significantly improved.

Tolerance Modeling and Optimization of XY-Table for LED Die Bonder Based on Multi-Body Systems

High performance XY-table is commonly used in packaging equipments which needs rational tolerance to ensure its high performance requirements and low manufacturing costs. The related studies mainly focus on high speed motion control algorithms and high precision structure design. The proper tolerance is essential in the development process of new products. In this paper, a new method for tolerance optimization based on Multi-body systems is presented. The volumetric error model for XY-table is established based on Multi-body systems. And then, by identifying the basic geometric error components, the relationships between the final output precision of the XY-table and the geometry error sources are established. The tolerance optimization model of XY-table using the above relationships is presented. In this model, objective function is the total manufacturing costs and the constraints are the above relationships. By solving the optimization model, the optimal tolerances are obtained. Finally, a tolerance design example of LED die bonder is given to illustrate the proposed method.

Research on Geometric Errors Model and Identification of 5-Axis Machining Center for Processing Turbo Molecular Pump Rotor

This paper investigates the accuracy evaluative factors of 5-axis turbo molecular pump rotor machining center.Using rigid body kinematics techniques and homogenous transformation matrices, the systemic geometric volumetric error model are established for error synthesis. Novel volumetric accuracy model can be verified effectiveness better estimation of machine performance, by means of physical simulation and measurement. The effect of the individual axis geometric errors can become increasingly significant as the chain of dependent axis is extended. The effect of the rotary axis and their errors cannot be ignored. Calculating volumetric accuracy as the maximum difference between the error vector at any two positions can be computationally intensive.

Volumetric Error Modelling, Measurement, and Compensation for an Integrated Measurement-Processing Machine Tool

The volumetric error of a measurement-processing integrated machine tool was studied by using a complicated surface workpiece grinding machine as a special example. The model of volumetric error was established by using homogeneous transformation matrices, and the effect of volumetric error on coordinate transformation between the measurement and the processing work station was analysed. Various error components of the machine tool were measured with a laser interferometer and an electronic level, and the volumetric error was compensated by external software. With a ball bar system and grinding experiments, the volumetric position accuracy was tested after compensation. The experiment results illustrated that both the volumetric position accuracy and machining precision were improved dramatically after compensation.