This paper presents an algorithm for identifying particular deviations such as angular deviations around linear axes relating to rotary axes in 5-axis machining centers. In this study, three kinds of simultaneous three-axis control motions are designed for each rotary axis to identify the deviations. In the measurement, two translational axes and one rotary axis are simultaneously controlled keeping the distance between a tool and a worktable constant. Telescoping ball bar is an effective instrument for measuring the relative displacement to the reference length in the work volume because its attitude is freely changed. In these three-axis control motions, the sensitive direction of the ball bar is kept constant. In order to determine the deviations, we derive eight equations from the relationship between the eccentricities obtained from the measured circular trajectories and the approximations derived from the mathematical model based on the simulation. In the simulation, a mathematical model considering the particular deviations is developed and then the characteristic diagrams are prepared for every deviation and every three-axis control motion. Based on the results, we propose a procedure for identifying the particular deviations in 5-axis machining centers and its procedure has been applied to identify the deviations actually. From both the simulation and the experiment, it has been confirmed that the proposed method gives precision results and is able to apply to the measurement of 5-axis machining center which is a tilting rotary table type.

Identification and compensation of systematic deviations particular to 5-axis machining centers

This thesis is written to advance the reader's knowledge of precision-engineering principles and their application to designing machines that achieve both sufficient precision and minimum cost. It provides the concepts and tools necessary for the engineer to create new precision machine designs. Four case studies demonstrate the principles and showcase approaches and solutions to specific problems that generally have wider applications. These come from projects at the Lawrence Livermore National Laboratory in which the author participated: the Large Optics Diamond Turning Machine, Accuracy Enhancement of High- Productivity Machine Tools, the National Ignition Facility, and Extreme Ultraviolet Lithography. Although broad in scope, the topics go into sufficient depth to be useful to practicing precision engineers and often fulfill more academic ambitions. The thesis begins with a chapter that presents significant principles and fundamental knowledge from the Precision Engineering literature. Following this is a chapter that presents engineering design techniques that are general and not specific to precision machines. All subsequent chapters cover specific aspects of precision machine design. The first of these is Structural Design, guidelines and analysis techniques for achieving independently stiff machine structures. The next chapter addresses dynamic stiffness by presenting several techniques for Deterministic Damping, damping designs that can be analyzed and optimized with predictive results. Several chapters present a main thrust of the thesis, Exact-Constraint Design. A main contribution is a generalized modeling approach developed through the course of creating several unique designs. The final chapter is the primary case study of the thesis, the Conceptual Design of a Horizontal Machining Center.

Principles and Techniques for Designing Precision Machines

The volumetric accuracy of machine tools is represented by a map of position and orientation error vectors of the tool over the volume concerned. Numerical compensation for volumetric error is possible in many latest commercial CNCs for machine tools. This paper reviews indirect measurement schemes for machine tool kinematics, in which the tool center position is measured as the superposition of error motions of linear or rotary axes. Each error motion can be separately identified by best-fitting a set of measured tool center positions to the kinematic model of machine tools. Indirect measurement schemes for the kinematics of three orthogonal linear axes, as well as the fiveaxis kinematics with two rotary axes, will be reviewed.

Indirect Measurement of Volumetric Accuracy for Three-Axis and Five-Axis Machine Tools: A Review

The position invariant geometric inaccuracies of a machine tool are the first to influence the quality of machined parts. A systematic approach is presented to identify some of these errors on a five-axis machine tool. The methodology is applied to the link error parameters such as joint misalignments, angular offset and rotary axis separation distance. A method based on the mathematical analysis of singularities of linear systems is used to assist in selecting a minimal but sufficient set of link error parameters for the calibration of a machine tool. A number of criteria are proposed in order to verify that the identified parameters accurately predict the positioning errors of the true machine. Finally, the numerical effectiveness of this method is shown through simulations.

Theory and simulation for the identification of the link geometric errors for a five-axis machine tool using a telescoping magnetic ball-bar

The total volumetric error within the workspace of a machine tool is induced by the propagation of both scalar and position dependent geometrical errors, as well as time-variant thermal errors. This paper presents a compact volumetric error model which can be used as a basis for a practical compensation scheme. The broad objective is to increase the achievable accuracy of an industrial five-axis CNC machine tool. In place of using Denavit-Hartenberg (D-H) transformations, the method used here directly considers the shape and joint transformations for inaccurate links and joints using small angle approximations and then finds the total volumetric error in the workspace as a function of all the possible errors. The development of the model shows that angular deviations are independent of translational errors. However, the tool point deviations are dependent on both translational and rotational errors. The model has been used for the design and testing of a compensation strategy. The simulation studies indicate that CNC compensation for errors in X , Y and Z axes is possible. However, the capability of the CNC compensation for pitch, roll and yaw errors is dependent on the positioning of the rotary axes on the machine tool. This is shown by an example using the compensation scheme developed.

Modelling geometric and thermal errors in a five-axis cnc machine tool

Fixe-axis capabilities on machine tools are becoming increasingly common. However, the problem of modeling the propagation of errors of individual axes through the kinematic chain, and their effect on the position and orientation errors of the cutting tool in the machine's work space has not been addressed. To increase the accuracy capabilities of such machines it is crucial to be able to study this propagation and develop approaches to minimize their effects on the errors at the tool tip. This paper discusses an approach to model the effects of the positioning errors of a machine's axes on the accuracy (positioning and orientation) of the cutting tool in its work space. Computer programs are developed for implementing the models and generating error contours or maps showing the variation of the different components of a machine's volumetric errors in its work space. This is a useful tool that can be used in machine tool design for the budgeting of errors and for optimization of a machine's accuracy.

Mapping the effects of positioning errors on the volumetric accuracy of five-axis CNC machine tools

Quasistatic error sources, which include thermal, mechanical loading and geometric error sources, are responsible for a very large proportion (typically, 70%) of the volumetric errors of a numerically controlled machine-tool This paper, the first in a set of three, discusses the development of a very general model for the effects of geometric errors of the components of the kinematic chain (structural members and axes) of a machine on the volumetric errors in the work space The effects of the other two sources are modeled as changes in the geometric error The generality of the model arises from the fact that the errors along an axis of the machine can be characterized by any polynomial functions and the model is recursive in the order of these polynomials This model can be used as the basis of a compensation scheme as well as in budgeting of errors on a machine-tool

Kinematic modeling of quasistatic errors of three-axis machining centers

Optimal budgeting of quasistatic machine tool errors

This paper is the second in a series of three papers addressing the problem of modeling and compensation of quasistatic machine-tool errors. In the first paper of this set, a general nth order model for the geometric errors of a machine was developed. The use of such a model as the basis of an on-line compensation scheme for a machine-tool requires that its parameters be known and changes in their magnitudes (due to mechanical and thermal changes) tracked during its operation. This paper presents a parameter estimation approach which requires observation of components of the volumetric error of the machine at certain points in the machine's work space. What is the minimal number of observations required? and What are the best locations for these observation points in a machine's work space? are questions answered in this paper. The estimation procedure is discussed for a first order model; however, it generalizes to any order error model. Experimental evidence of the effectiveness of the first order model error model in adequately representing the quasistatic errors of a machine-tool is presented. The effectiveness of the parameter estimation approach is also demonstrated. Finally, the use of the model and parameter estimation procedure as the basis of a compensation scheme that is practicable in a production environment is discussed.

Parameter estimation and model verification of first order quasistatic error model for three-axis machining centers

This paper, the last in a series of three papers dealing with modeling and compensation of quasistatic machine-tool errors, discusses strategies for introducing compensations for quasistatic errors. It is assumed, based on the work presented in the previous papers in this set, that an adequate and accurate model is available for characterizing the volumetric errors in the work space of a machine due to quasistatic effects. Such models indicate that quasistatic errors result in a nonlinear distortion of the work volume. Consequently, the compensations become position dependent and simple strategies such as using constant offsets will not work. Under the assumption of the availability of an error model, strategies are developed for obtaining compensations when locating the cutting tool at a point in the work space or moving it along a straight line or circular trajectory. The motivation behind this analysis is its use in “preprocessing” NC programs so that compensated NC programs can be developed, based on an updated (current) model of the machine's error, and given to the machine for execution. The strategies developed are tested using experimentally obtained error models for a three-axis machine. The computational tests indicate that a high level of compensation accuracy is possible.

V.S.B. Kiridena

Papers

Mapping the effects of positioning errors on the volumetric accuracy of five-axis CNC machine tools

Kinematic modeling of quasistatic errors of three-axis machining centers

Optimal budgeting of quasistatic machine tool errors

Parameter estimation and model verification of first order quasistatic error model for three-axis machining centers

Computational approaches to compensating quasistatic errors of three-axis machining centers