Tolerance analysis for setup planning: A graph theoretical approach

Setup planning is the act of preparing detailed work instructions for setting up a part. The purpose of setting up a part is to ensure its stability during machining and, more importantly, the precision of the machining processes. Therefore, tolerance control can be achieved proactively via setup planning. This fact was somewhat overlooked in the computer-aided process planning (CAPP) research community. While many researchers focused their attention on tolerance chart analysis, the issue of tolerance analysis for setup planning was relatively unexplored. To systematically solve the setup planning problem, a graph theoretical approach is proposed. The design specification of a part is represented as a graph. The problem of identifying the optimal setup plan is transformed into a graph search problem. A setup planning algorithm for rotational parts was then developed. The algorithm was evaluated and found to be both efficient and effective.     

Setup adjustment for discrete-part manufacturing processes with asymmetric cost functions

This paper presents a feedback adjustment rule for discrete-part manufacturing processes that experience errors at the setup operation which are not directly observable due to part-to-part variability and measurement error. In contrast to previous work on setup adjustment, the off-target cost function of the process is not symmetric around its target. Two asymmetric cost functions—constant and quadratic functions—are considered in this paper. By introducing a bias term in the feedback adjustment rule, the process quality characteristic converges to the optimal steady-state target from the lower cost side of the cost function. This minimizes the off-target loss incurred during the transient phase of adjustment. A machining application is used to illustrate the proposed adjustment procedure and to demonstrate the savings generated by the proposed feedback adjustment rule compared to an adjustment rule due to Grubbs and to an integral controller. It is shown that the advantage of the proposed rule is significant when the cost of the items is high, items are produced in small lot sizes and the asymmetry of the cost function is large.     

Capability index of a complex-product machining process

A complex product often requires a high machining precision. This is often achieved by a close-loop machining process to be carried out in several stages, and the measurements, fixture adjustments, and feedback or feed-forward control are inserted after each of these stages. The Complex Product Machining Process (CPMP) Capability Index (CPMPCI) is affected by the control and adjustments in a CPMP, and hence the calculation results of CPMPCI can be used as references to select a proper CPMP. In this paper, we present a novel calculation method of CPMPCI as quality control and improvement technology in a CPMP. A linear model is proposed for describing the variation propagation effect throughout all stages in a CPMP, and an observation model with the pre-specified control and adjustment strategy is employed to calculate the process mean and variation during a CPMP. Finally, through application of Taguchi's quality loss function, the CPMPCI calculation method is derived. The feasibility and effectiveness of this method are validated by a case study on a three-stage CPMP.     

Machining error compensation using radial basis function network based on CAD/CAM/CAI integration concept

This paper presents a machining error compensation methodology using an Artificial Neural Network (ANN) model trained by an inspection database of the On-Machine-Measurement (OMM) system. This is an application of the CAD/CAM/CAI integration concept. First, to improve machining and inspection accuracies, the geometric errors of a three-axis CNC machining centre and the probing errors are compensated using a closed-loop configuration. Then, a workpiece is machined using the machining centre, and the error distributions of the machined surface are inspected using OMM. In order to analyse efficiently the machining errors, two characteristic error parameters, W err and D err , are defined. Subsequently, these parameters are modelled using a Radial Basis Function (RBF) network approach as an ANN model. Based on the RBF network model, the tool path is corrected to effectively reduce the errors using an iterative algorithm. In the iterative algorithm, the changes of the cutting conditions can be identified according to the corrected tool path. In order to validate the approaches proposed in this paper, an experimental machining process is performed, and the results are evaluated. As a result, about 90% of machining error reduction can be achieved through the proposed approaches.     

Optimal Adjustment in the Presence of Deterministic Process Drift and Random Adjustment Error

A state-space process-control model involving adjustment error and deterministic drift of the process mean is presented. The optimal adjustment policy is developed by dynamic programming. This policy calls for a particular adjustment when a Kalman-filter estimator is outside a deadband defined by upper and lower action limits. The effects of adjustment cost, adjustment variance, and drift rate on the optimal policy are discussed. The optimal adjustment policy is computed for a real machining process, and a simulation study is presented that compares the optimal policy to two sensible suboptimal policies.     

Graph-based set-up planning and tolerance decomposition for computer-aided fixture design

Set-up planning plays an important role in integrating design with process planning and fixture design. Its main task is to determine the number and sequence of set-ups, and select locating datum, machining features and operations in each setup. Computer-based set-up planning may be used to generate automatically a setup plan based on tolerance analysis for minimizing locating error, calculating machining error stack-up and improving CAD/CAPP/CAFD (Computer-aided Fixture Design) integration efficiency. Most of the current set-up planning systems were based on empirical methods (such as rule and knowledge base) and their applications background was plus/minus a dimensioning and tolerancing (GD&T) scheme. Today, more and more industries are using a true positioning Geometric Dimensioning and Tolerancing (GD&T) scheme in design and manufacturing. To support this requirement, this paper presents an analytical set-up planning approach with three techniques, (1) an extended graph to describe a Feature and Tolerance Relationship Graph (FTG) and a Datum and Machining Feature Relationship Graph (DMG), which could be transferred to an analytical computer model; (2) seven set-up planning principles to minimize machining error stack-up under a true positioning GD&T scheme; and (3) tolerance decomposition models to partition a tolerance into interoperable machining errors, which could be used for locating error analysis or for feedback to design stage for design improvement. These techniques are implemented in a computer system and it is integrated with a commercial CAD/CAM system to support an automobile manufacturing enterprise in fixture design and production planning.     

基于多元半参数回归建模的机械加工过程误差分析

机械加工过程的误差分析对于消减误差源、提升工序质量具有重要的实际指导意义．研究者们尝试了多种误差分析方法用于获得误差源对加工质量的作用规律,然而由于加工误差的复杂性,各有局限性．本文则根据工程经验和数学推导建立了用于一般机械加工过程误差分析的多元半参数回归模型,基于测量数据详细讨论了所建立模型的参数估计和非参数规律辨识问题．仿真实例证明,与现有方法相比,本文所提方法能够准确估计上游工序传递误差,有效辨识当前工序系统误差的作用规律,研究成果为一般机械加工过程的误差分析奠定了基础．     

工业CT探测尺寸误差的校准及误差分析

针对工业CT探测尺寸误差的校准需求,提出一套基于标准球的校准工业CT探测尺寸误差的方法,并对引起探测尺寸误差的各种因素进行了详细分析。首先使用中国计量科学研究院标准测长机对标准球的直径进行校准,再使用标定后的标准球校准工业CT探测尺寸误差。实验结果表明球标准器能够满足工业CT探测尺寸误差校准的需求,既能被精密校准,又可在工业CT中获得低伪像的高质量图像,从而实现对工业CT探测尺寸误差的校准。通过对影响工业CT探测尺寸误差因素的分析,讨论了工业CT成像过程中各环节的误差源,对于建立工业CT测量系统全面的校准方法和溯源具有重要意义。     

Optimal fixture parameters considering locator errors

A machining fixture consists of elements such as locators, clamps and supports. Fixture design aims at ensuring workpiece quality by restraining the workpiece in the desired position throughout machining thereby minimising the overall machining error. Workpiece elastic deformation and geometric error of locators are major components of the overall machining error. The effect of geometric error is considerable in certain cases and hence cannot be ignored. For a given error in locators, the geometry related machining error is manifest in the locator layout whereas the workpiece deformation depends on both the layout and the external forces such as clamping and machining forces. Layout of fixturing elements and the applied clamping forces are collectively called fixture parameters. The objective of minimising the total machining error can be achieved by optimising either one or both of these parameters. In this research work both of these parameters are simultaneously optimised using a genetic algorithm (GA). A finite element model of the workpiece fixture system is developed and analysed using commercial finite element software ANSYS®. Elastic deformation of workpiece under machining loads is obtained from the finite element model. MATLAB® based GA is interfaced with ANSYS® for the determination of total machining error and subsequent optimisation with the objective of complying with tolerance requirements on the critical machining feature. Results indicate that the error sources can contribute to the final machining error in varying degrees. The results also underscore the need to consider the entire machining path for optimisation of the fixture parameters.     

Modelling and compensation of fixture locators’ error in CNC milling

Fixture errors are one of the error sources in machining operations. The fixture errors consist of positioning inaccuracies and errors due to workpiece and fixture deformations. Fixture locators’ height error causes incorrect positioning of the workpiece in the fixture and inaccuracy in machined surfaces which can be much more than the locators’ height error. For machining precise workpieces, it is necessary to eliminate these errors. This paper presents a method for modelling and compensating the fixture locators’ height error effect on workpiece machined surfaces. In this method, the planes of workpiece actual coordinate system (ACS) are mathematically modelled in the workpiece theoretical coordinate system (TCS). Using the model, required homogenous transformation matrix for coinciding ACS with TCS and modifying machining toolpath for compensating the errors is generated. The presented model is used to develop a post-processing fixture locator error compensation module, which can modify CNC machining codes to eliminate the effect of fixture locators’ height error on the workpiece machined surfaces. For verifying the presented method, machining simulations and cutting experiments have been performed in this work. The results show that the method can eliminate the effect of fixture locators’ height error on the workpiece machined surfaces considerably.     

A quality control method for complex product selective assembly processes

Selective assembly is an important step during the manufacturing process for a complex product to meet precision requirements. The high precision requirement of complex product often results in producing a large number of surplus components in selective assembly process current practices. In this paper, we develop a comprehensive model which permits the integration of machining process parameters design, variation analysis and fault diagnosis, process adjustment and control strategy, process capability index calculation and matchable degree calculation. The model can be applied to evaluate and improve product, process and system design at early development stages, or support the improvement of matchable degree for a complex production selective assembly process. In this model, we have introduced a navel concept of general matchable degree for a multiple components selective assembly process. The implementation procedure and functional modules of the proposed model are given in details with an industrial case presented to illustrate the implementation of the proposed method.     

Part dimension deviation control in batch manufacturing process for monitoring error sources

In a batch manufacturing process a cross-correlation exists among dimension deviations of different parts. The modelling and control of these deviations are essential to improve product dimension quality. Traditional dimension deviation statistical control methods have been focused on retrospectively analysing part dimension feature, while based on the spatial relationship between part dimensional features and error sources showed in part dimension error propagation model, this paper presents a method to control part dimension deviation in batch manufacturing that focuses on error sources. At each operation, total part deviation is separated into three components corresponding to three error sources. Therefore, a multivariate exponentially weighted moving average (MEWMA) chart for error sources is proposed to control part dimension deviations with identified error sources attribute to part dimension deviation. Efficiency and reliability of this model were verified by simulation analysis in common error source abnormal patterns, and the model is proved to be effective for detecting small deviations in a batch manufacturing process.     

Setup planning for machining the features of prismatic parts

This paper focus on the development of a formalized procedure for automatic generation of feasible setups and then to select an optimal setup plan for machining the features of a given prismatic part. The proposed work simultaneously considers the basic concepts of setup planning from both machining and fixturing viewpoints in order to formulate feasible setup plans. The tasks that are performed are: (a) identifying groups of features that can be machined in a single setup, (b) determining a suitable work piece orientation, i.e. the suitable datum planes for each setup, (c) determining all the feasible setup plans to machine the given set of features of prismatic parts, and (d) evaluating the feasible setup plans on the basis of technological (available tolerance) and economical conditions (total setup time). For the proposed work the authors have introduced four new concepts namely, ‘surface fit for location’, ‘primary group’ ‘secondary group’, and ‘eligible group’. The first concept plays an important role in the identification of suitable faces of the part for positioning, clamping and supporting. The other three help in clustering of features, which can be converted in to candidate setups.     

超精密加工振动误差源诊断实验研究

超精密车床结构及加工过程的复杂性使得对加工精度的影响因素不能完全确定，尤其是随机性因素的影响更难确定。为此本文首先系统分析了超精密车床中影响加工精度的各项误差源，然后通过实验辨识了主要振动误差源对加工精度的影响，为减少和补偿由这些误差源引起的误差提供了依据和指导。     

Engineering model-based Bayesian monitoring of ramp-up phase of multistage manufacturing process

Process monitoring of full mass production phase of multistage manufacturing processes (MMPs) has been successfully implemented in many applications; however, monitoring of ramp-up phase of MMPs is often more difficult to conduct due to the limited information to establish valid process control parameters (such as mean and variance). This paper focuses on the estimation of the process control parameters used for monitoring scheme design of ramp-up phase of MMPs. An engineering model of variation propagation of an MMP is developed and reconstructed to a linear model, establishing a relationship between the error sources and the variation of product characteristics. Based on the developed linear model, a two-step Bayesian method is proposed to estimate the process control parameters. The performance of the proposed Bayesian method is validated with simulation data and real-world data, and the results demonstrate that the proposed method can effectively estimate process parameters during ramp-up phase of MMP.     

非球面非零位横向剪切干涉检测与波前重建

本文分析了非球面非零位检测中3种典型的非球面度及其变化率、调整误差、回程误差以及干涉仪系统误差,提出了非球面度变化率是影响检测误差的主要因素,并给出了非球面非零位检测面形加工误差的确定方法.对基于Zernike多项式拟合的最小二乘法和系数转换法进行了对比研究,分析了剪切量和多项式拟合阶数对波前重建精度的影响,并给出了数值模拟结果.为了验证以上方法的可行性及检测精度,针对一单点金刚石车削的抛物面反射镜,利用顶点球作为测试波前进行非零位横向剪切干涉检测,并用最小二乘法进行波前重建.实验结果表明,在非球面度变化率最大的反射镜边缘处面形误差最大,达到0.203μm,研究结果为横向剪切干涉仪用于非球面加工过程中在位检测提供了技术支撑.     

Identifying and visualizing nonlinear variation patterns in multivariate manufacturing data

In modern manufacturing processes, it is not uncommon to have hundreds, or even thousands, of different process variables that are measured and recorded in databases. The large quantities of multivariate measurement data usually contain valuable information on the major sources of variation that contribute to the final product or process variability. The focus of this work is on variation sources that result in complex, nonlinear variation patterns in the data. We propose a model for representing nonlinear variation patterns and a method for blindly identifying the patterns, based on a sample of measurement data, with no prior knowledge of the nature of the patterns. The identification method is based on principal curve estimation, in conjunction with a data preprocessing step that makes it suitable for high dimensional data. We also discuss an approach for interactively visualizing the nature of the identified variation patterns, to aid in identifying and eliminating the major root causes of manufacturing variation.     

Integrating GD&T into dimensional variation models for multistage machining processes

Recently, the modelling of variation propagation in multistage machining processes has drawn significant attention. In most of the recently developed variation propagation models, the dimensional variation is determined through kinematic analysis of the relationships among error sources and dimensional quality of the product, represented by homogeneous transformations of the actual location of a product's features from their nominal locations. In design and manufacturing, however, the dimensional quality is often evaluated using Geometric Dimensioning and Tolerancing (GD&T) standards. The method developed in this paper translates the GD&T characteristic of the features into a homogeneous transformation representation that can be integrated in existing variation propagation models for machining processes. A mathematical representation using homogeneous transformation matrices is developed for position, orientation and form characteristics as defined in ANSI Y14.5; further, a numerical case study is conducted to validate the developed methods.     

A new active error compensatory method of machinery accuracy†

A new active error compensatory method for on-line cutting control has been developed for reduction of the form errors in machining. This approach is a combination of in-process gauging and model active compensatory control. In this approach, there are two features of substantial importance: stochastic modelling and optimum forecasting. Through stochastic modelling, the cutting tool error motions can be represented by a simple model without the necessity of obtaining the complex cause-and-effect relationships between various errors and error sources, and more importantly, it is possible to account for both repeatable and non-repeatable parts of errors. Optimum forecasting is an important prerequisite for a rational control strategy, considering the inevitable time delay associate with sensing, computation and actuation. The proposed control method was implemented for the control of cylindricity in boring operations. Through the controller simulation based on experimental measurements, the improvement in cylindricity accuracy confirms the effectiveness of this proposed strategy