Bayesian Reliability Modeling and Assessment Solution for NC Machine Tools under Small-sample Data

Although Markov chain Monte Carlo（MCMC） algorithms are accurate, many factors may cause instability when they are utilized in reliability analysis; such instability makes these algorithms unsuitable for widespread engineering applications. Thus, a reliability modeling and assessment solution aimed at small-sample data of numerical control（NC） machine tools is proposed on the basis of Bayes theories. An expert-judgment process of fusing multi-source prior information is developed to obtain the Weibull parameters＇ prior distributions and reduce the subjective bias of usual expert-judgment methods. The grid approximation method is applied to two-parameter Weibull distribution to derive the formulas for the parameters＇ posterior distributions and solve the calculation difficulty of high-dimensional integration. The method is then applied to the real data of a type of NC machine tool to implement a reliability assessment and obtain the mean time between failures（MTBF）. The relative error of the proposed method is 5.8020×10-4 compared with the MTBF obtained by the MCMC algorithm. This result indicates that the proposed method is as accurate as MCMC. The newly developed solution for reliability modeling and assessment of NC machine tools under small-sample data is easy, practical, and highly suitable for widespread application in the engineering field; in addition, the solution does not reduce accuracy.

Bayesian zero-failure reliability modeling and assessment method for multiple numerical control(NC) machine tools

A new problem that classical statistical methods are incapable of solving is reliability modeling and assessment when multiple numerical control machine tools(NCMTs) reveal zero failures after a reliability test. Thus, the zero-failure data form and corresponding Bayesian model are developed to solve the zero-failure problem of NCMTs, for which no previous suitable statistical model has been developed. An expert-judgment process that incorporates prior information is presented to solve the difficulty in obtaining reliable prior distributions of Weibull parameters. The equations for the posterior distribution of the parameter vector and the Markov chain Monte Carlo(MCMC) algorithm are derived to solve the difficulty of calculating high-dimensional integration and to obtain parameter estimators. The proposed method is applied to a real case; a corresponding programming code and trick are developed to implement an MCMC simulation in Win BUGS, and a mean time between failures(MTBF) of 1057.9 h is obtained. Given its ability to combine expert judgment, prior information, and data, the proposed reliability modeling and assessment method under the zero failure of NCMTs is validated.

STUDY ON NEW METHOD OF IDENTIFYING GEOMETRIC ERROR PARAMETERS FOR NC MACHINE TOOLS

The methods of identifying geometric error parameters for NC machine tools are introduced. According to analyzing and comparing the different methods, a new method-displacement method with 9 lines is developed based on the theories of the movement errors of multibody system (MBS). A lot of experiments are also made to obtain 21 terms geometric error parameters by using the error identification software based on the new method.

The Application of the GM(1,1) Metabolism Model to Error Data Processing of NC Machine Tools

This paper applied the gray system theory to error data processing of NCmachine tools according to the characteristic. It presented the gray metabolism model of error dataprocessing. The test method for the model needs less capacity. Practice proved that the method issimple, calculation is easy, and results are exact.

METHOD OF ENHANCING THE POSITIONING ACCURACY FOR NC MACHINE TOOLS

Based on the kinematics of the multi-body system , a general model for the positioning errors of NC machine tools by means of the lower numbered body array and the geometric constraint is presented. The parameters identification of geometric errors by an improved 22-line method is discussed. Moreover , an intelligent error compensation controller has been developed. All these are verified by a series of experiments on XH714 machining center. The results show that the prosition- ing errors with compensation have been reduced to ±7 μm from 50 μm.

Algorithm for Detecting Volumetric Geometric Accuracy of NC Machine Tool by Laser Tracker

Quick and accurate detecting the error of NC machine tool and performing the error compensation are important to improve the machining accuracy of NC machine tool. Currently, there are many methods for detecting the geometric accuracy of NC machine tool. However, these methods have deficiencies in detection efficiency and accuracy as well as in versatility. In the paper, a method with laser tracker based on the multi-station and time-sharing measurement principle is proposed, and this method can rapidly and accurately detect the geometric accuracy of NC machine tool. The machine tool is controlled to move in the preset path in a 3D space or 2D plane, and a laser tracker is used to measure the same motion trajectory of the machine tool successively at different base stations. The original algorithm for multi-station and time-sharing measurement is improved. The space coordinates of the measuring point obtained by the laser tracker are taken as parameter values, and the initial position of each base point can be determined. The redundant equation concerning the base point calibration can be established by the distance information of the laser tracker, and the position of each base point is further determined by solving the equation with least squares method, then the space coordinates of each measuring point can be calibrated. The singular matrix does not occur in calculation with the improved algorithm, which overcomes the limitations of the original algorithm, that the motion trajectory of machine tool is in a 3D space and there exits height difference between the base stations. Adopting the improved algorithm can expand the application of multi-station and time-sharing measurement, and can meet the quick and accurate detecting requirements for different types of NC machine tool.

Identification of the key thermal points on machine tools by grouping and optimizing variables

The grouping and optimization approach to identify the key thermal points on machine tools is studied.To solve the difficulty in grouping because of the high correlated variables from distinct groups,the variables grouping technique is improved.Temperature variables are sorted according to their relativities with the thermal errors.The representative temperature variables are determined by analyzing the variable correlation in sort order and removing the other variables in the same group.Considering the diverse effect of importing the different variables on thermal error model,the method of variable combination optimization is improved.Regression models made up of different combination of representative temperature variables are evaluated by the index of both the determined coefficient and the average residual squares to select the combination of the temperature variables.For the machine tools with complicated structures which need more initial temperature measuring points the improvement is demanded.The improved approach is applied to a precision horizontal machining center to identify the key thermal points.Experimental results show that the proposed approach is capable of avoiding the high correlation among the different groups' variables,effectively reducing the number of the key thermal points without depressing the prediction accuracy of the thermal error model for machine tools.

MODULE DEFINITION MODEL FOR MODULAR DESIGN AND MANUFACTU－RING OF HEAVY DUTY MACHINE TOOLS

The key techniques of modular design of heavy duty NC mathine tools are described. Amodule definition modelfor modular design and manufacturing of heavy duty NC machine tools isbulit and the essential composition of the module definition model (MDM) is discussed in detail. Itis composed of two models: the part definition model (PDM) and the module assembly model(MAM). The PDM and MAM are built and their structures are given. Using object-oriented know-ledge representation and based on these models, an intelligent support system of modular design forheavy duty NC machine tools is developed and implemented This system has been applied to thepractical use of Wuhan Heavy Duty Machine Tool Works

ESTIMATING THE CUTTER＇S MAXIMUM DIAMETER IN 5－AXIS NC FACE MILLING OF TURBINE BLADES

Based on the principles of differential geometry,the basic equations are derived for generating gouging free tool path in 5-axis NC face milling,the influence of surface's local geometry is discussed,and the conditions of using cutter with reasonable diameter are presented.

MOTION ERROR ESTIMATION OF 5-AXIS MACHINING CENTER USING DBB METHOD

In order to estimate the motion errors of 5-axis machine center, the double ball bar （DBB） method is adopted to realize the diagnosis procedure. The motion error sources of rotary axes in 5-axis machining center comprise of the alignment error of rotary axes and the angular error due to various factors, e.g. the inclination of rotary axes. From sensitive viewpoints, each motion error is possible to have a particular sensitive direction in which deviation of DBB error trace arises from only some specific error sources. The model of the DBB error trace is established according to the spatial geometry theory. Accordingly, the sensitive direction of each motion error source is made clear through numerical simulation, which is used as the reference patterns for rotational error estimation. The estimation method is proposed to easily estimate the motion error sources of rotary axes in quantitative manner. To verify the proposed DBB method for rotational error estimation, the experimental tests are carried out on a 5-axis machining center M-400 （MORISEIKI）. The effect of the mismatch of the DBB is also studied to guarantee the estimation accuracy. From the experimental data, it is noted that the proposed estimation method for 5-axis machining center is feasible and effective.

Dynamics Analysis of a Parallel Mill-turn Tool Spindle Head Driven by Dual-linear Motors Using Extended Transfer Matrix Method

The hybrid dynamics of multi-rigid-body and multi-flexible-body system becomes the mainstream of multi-body dynamics.Currently there lacks a compact approach to model the hybrid dynamics,especially in modern machine tool application,due to the difficulty of solving the hybrid equations or the limitation of current software when dealing with the hybrid dynamics.The extended transfer matrix method（E-TMM）,which extends elements in three-dimensional space with higher matrixes,is proposed to simplify the modeling process of the hybrid dynamics.The E-TMM modeling approaches of 3 basic elements including 3D vibrant rigid body,joint and flexible body are studied in details.A parallel mill-turn tool spindle head unit driven by dual-linear motors is chosen as a plant to demonstrate the E-TMM modeling process.By using E-TMM,the spindle head unit is simplified as a topological network consisting of the three types of element,i.e.,3D vibrant rigid body,joint and flexible body,including 11 rigid bodies,14 joints and 1 3D-Timoshenko beam.Then the dynamic model of the system can be easily obtained by deducing the element-network by means of state vector transformation.The dynamic characteristics of the spindle head,such as natural frequencies,dynamic flexibility,etc.can be predicted by solving the obtained model.Experiment verification indicates that the E-TMM is valid with enough accuracy in the dynamic analysis of the parallel mill-turn tool spindle head.The E-TMM is capable of modeling the dynamics of machine tool structure with no requirements of deducing and solving the sophisticated differential equations.Moreover,the E-TMM provides a simple and elegant tool for hybrid dynamic analysis in future dynamic design of machine tools.

Immune Clone Maximum Likelihood Estimation of Improved Non-homogeneous Poisson Process Model Parameters

Aiming at the solving problem of improved nonhomogeneous Poisson process( NHPP) model in engineering application,the immune clone maximum likelihood estimation( MLE)method for solving model parameters was proposed. The minimum negative log-likelihood function was used as the objective function to optimize instead of using iterative method to solve complex system of equations,and the problem of parameter estimation of improved NHPP model was solved by immune clone algorithm. And the interval estimation of reliability indices was given by using fisher information matrix method and delta method. An example of failure truncated data from multiple numerical control( NC) machine tools was taken to prove the method. and the results show that the algorithm has a higher convergence rate and computational accuracy, which demonstrates the feasibility of the method.