An inspection advisor for form error in cylindrical features

Due to inherent variability in even the so-called “high-precision” machines, the need for accurate, quick and economical inspection of tolerances of machined features has become very important. Coordinate measuring machines (CMMs) are very popular in industry for inspection of components. In addition to hardware capabilities, some of the critical factors that affect the accuracy and precision of inspection using CMMs have been identified as sample size, sampling technique and form evaluation method. Selecting an optimal inspection plan for the CMM is vital to improve the quality of measurements while simultaneously minimizing inspection costs and time. The motivation behind this paper is to provide the user flexibility and control in choosing an optimal inspection plan for evaluation of form error in cylindrical features according to his/her specific needs in a practical manufacturing scenario. In view of this objective, a two-way relationship between the inspection strategy used and inspection performance metrics achieved has been established using multiple regression. The forward model is a plan evaluator that computes numerical estimates of the expected accuracy and precision for different inspection plans. The reverse model is a strategy designer that recommends the most economical inspection plan that can meet the acceptable quality criteria considering the user’s constraints and available resources. Both the models have been incorporated into a user-friendly inspection advisor with a graphical interface.     

Investigation on sampling size optimisation in gear tooth surface measurement using a CMM

Coordinate measuring machines (CMMs) are widely used in the gear manufacturing industry. One of the main issues for contact inspection using a CMM is the sampling technique. In this paper the gear tooth surfaces are expressed by series of parameters and inspection error compensation and initial value optimisation method are presented. The minimum number of measurement points for 3D tooth surfaces are derived. If high precision is required, more points need to be inspected. The sampling size optimisation is obtained from the criterion equation. The surface form deviation and initial values are optimised using the minimum zone method and genetic algorithms. A feature-based inspection system for spur/helical gears is developed and trials and simulations demonstrate that the method developed is suitable and very effective. This revised version was published online in October 2004 with a correction to the issue number.     

Designing small samples for form error estimation with coordinate measuring machines

We propose a method for designing inspection plans of small size for use in form error evaluation of parts from batch or mass production using coordinate measuring machines. The method exploits a priori information coming from large sample inspection of one or a few parts of the lot. It is based on a regression model fitted to the large sample. The model is used twice. First, it provides the dominant pattern of the surface. Then, the deviations from the model that are relevant to form error are captured by weighting the points of the convex-hull of the large sample with the regression residuals. Based on two case studies, we show that the method provides a good accuracy in the estimation of straightness and flatness with very few measurement points. Comparative results also indicate that the method outperforms both the typical sampling schemes used in industry (random sampling, latin hypercube sampling), which do not exploit a priori information, and a recently proposed method using the same kind of a priori information.     

Batch circular form error characterization and evaluation

In practice, it is necessary to understand the general quality status of a batch of circular features machined under the same or similar conditions. In particular, it is necessary to understand the possible worst case among such a batch of circular features. To this end, a brand-new concept called “batch circular form error” is presented in this paper. Detailed definitions of batch circular form error including batch circular form error with ideal conditions and batch circular form error with realistic conditions are provided. Accordingly, the evaluation algorithms of batch circular form error are developed. The algorithms include the characterization of the deterministic profile of circular features and the evaluation of batch circular form error based on a given profile confidence level. Case studies with simulation and experimental data are used for demonstration. The results show that the batch circular form error can be estimated with the data measured from any circular feature in the batch, as long as the sample size is large enough and random ratio is not too large.     

Enhance performance of inspection process on Coordinate Measuring Machine

Coordinate Measuring Machine (CMM) has been an important inspection tool in quality control for several years owing to its high accuracy and precision. Effectiveness of inspection plan generated by CMM greatly depends on measurement cycle time. Lesser the inspection time taken by CMM to measure a given part better will be the performance of inspection process. Therefore, it has been critical to reduce measurement time for efficient performance of inspection process. In this paper, methodologies to generate most suitable measurement path resulting into minimum inspection time has been introduced. These methodologies are based on different algorithms to reduce measurement cycle time for CMM. The different algorithms have successfully been explored and compared to show their effectiveness in minimizing inspection time for stationary CMM equipped with touch trigger probe. The proposed methodologies have also been implemented and tested on real-world mechanical part with certain number of features to demonstrate their applicability.     

Research on the uncertainties from different form error evaluation methods by CMM sampling

As a part of the new measurement uncertainty system proposed in the new generation of Geometrical Product Specifications and Verification, the evaluation methods of uncertainties to form errors have been researched in mechanical engineering, which are calculated based on the error propagation principle and statistical concept under certain conditions. In this paper, the evaluation datum is obtained by using both the least squares method and the genetic optimization algorithm. Their computation uncertainties to flatness and roundness were compared with each other using the sample data from a coordinate measurement machine (CMM). The results show that the uncertainties obtained from the genetic algorithm-based method are similar to those from the least squares method according to their evaluation parameters. The evaluation uncertainties from different methods become a little smaller with more sample points. A more significant conclusion is that the evaluation uncertainties from two methods are so small that they almost do not affect the measurement uncertainties to form error, which, in fact, mainly comes from the CMM sampling. Therefore, for the efficiency and simplification of calculation, especially for the cylintricity with more parameters, the uncertainties from evaluation methods can be neglected where the precision is not so strict.     

工件圆度误差测量不确定度评定

为了实现工件圆度误差的不确定度评定,对基于三坐标测量机的工件圆度轮廓数据的采样策略、圆度评定方法及不确定度评定方法进行研究。首先,根据工件圆度轮廓特征进行实验测量,获取不同工件的多个样本。接着,基于最小二乘法和微分进化优化算法对样本的圆度误差进行了误差评定。然后,在分析比较误差大小的基础上,说明了采用的采样策略和微分进化评定算法。最后,基于圆度误差评定结果运用了测量不确定度表示指南(GUM)和蒙特卡洛方法(MCM)进行不确定度评定。实验结果表明:微分进化算法与最小二乘法相比均值差最大达到1.1μm, MCM方法比GUM方法得到的标准不确定度均值小0.02μm。合理的采样点数、微分进化算法及MCM不确定度评定方法可以得到更稳定可靠、精度高的评定结果。     

Accurate evaluation of free-form surface profile error based on quasi particle swarm optimization algorithm and surface subdivision

Although significant progress has been made in precision machining of free-form surfaces recently, inspection of such surfaces remains a difficult problem. In order to solve the problem that no specific standards for the verification of free-form surface profile are available, the profile parameters of free-form surface are proposed by referring to ISO standards regarding form tolerances and considering its complexity and non-rotational symmetry. Non-uniform rational basis spline(NURBS) for describing free-form surface is formulated. Crucial issues in surface inspection and profile error verification are localization between the design coordinate system(DCS) and measurement coordinate system(MCS) for searching the closest points on the design model corresponding to measured points. A quasi particle swarm optimization(QPSO) is proposed to search the transformation parameters to implement localization between DCS and MCS. Surface subdivide method which does the searching in a recursively reduced range of the parameters u and v of the NURBS design model is developed to find the closest points. In order to verify the effectiveness of the proposed methods, the design model is generated by NURBS and the measurement data of simulation example are generated by transforming the design model to arbitrary position and orientation, and the parts are machined based on the design model and are measured on CMM. The profile errors of simulation example and actual parts are calculated by the proposed method. The results verify that the evaluation precision of freeform surface profile error by the proposed method is higher 10%-22% than that by CMM software. The proposed method deals with the hard problem that it has a lower precision in profile error evaluation of free-form surface.     

Automated dimensional inspection planning using the combination of laser scanner and tactile probe

Combining multiple sensors on CMMs (Coordinate Measuring Machines) is useful to fulfil the increasing requirements on both complexity and accuracy in dimensional metrology. Yet, the methodology to plan measurement strategies for systems combining different types of sensors is still a major challenge. Such planning is commonly done in an interactive way. This paper presents a methodology which can create inspection plans automatically for CMM inspection combining a touch trigger probe and a laser scanner. The inspection features are specified based on the extracted geometry features and the associated PMI (Product and Manufacturing Information) items from a CAD model. A knowledge based sensor selection method is applied to choose the suited sensor for each inspection feature. For touch trigger measurements, the sampling strategy considers the measurement uncertainty calculated by simulation. A geometry-guide method is developed for collision-free probing path generation. For laser scan measurements, the required view angles and positions of the laser scanner are determined iteratively, based on which the scan path is generated automatically. The proposed methodology is tested for several cases and validated by measurement experiments. The methodology provides suited planning results and can be used for automated dimensional inspection, i.e. Computer Aided Quality Control (CAQC).     

复杂系统小子样可靠性综合检验方法

一次计数抽样检验方法是一种基于经典统计理论的试验分析方法,由于它具有较强的通用性,被广泛应用于工程实践中.但该方法由于忽略其他信息的作用,需要较大的试验样本量,不适用于小子样产品的检验问题.为解决上述问题,考虑到子系统的性能在一定程度上能决定全系统的性能,提出适用于串联系统的一次计数抽样综合检验方法.该方法充分利用子系统试验数据,可将子系统试验与全系统试验进行折合,从根本上减少系统的样本量.通过实例仿真分析结果表明,所提出的综合检验方法是合理可行的,较传统计数抽样检验方法所需样本量大大减少,从而满足小子样抽样的要求.     

Adaptive sampling method for inspection planning on CMM for free-form surfaces

Coordinate measurement machines (CMMs) have been widely used in inspecting mechanical parts with higher accuracy. Both the distribution and the number of the sampled points on measurand have an important effect on the efficiency and quality of the measurement of CMMs. In this paper, an adaptive sampling method is proposed for inspection planning on CMM for free-form surface. The points are iteratively sampled from a form error model, which is constructed by superimposing appropriate form errors on the nominal data. Moreover, a modified algorithm is introduced to determine the deviation of two point sets for the improvement of the inspecting accuracy, and the inspection uncertainty is also analyzed. A comparison is performed between the proposed method and the two well-known sampling methods, which are the equi-parametric method and the patch mean Gaussian curvature-based method, both simulated and experiment results show the effectiveness and robustness of this method.     

Rectifying inspection for acceptable quality loss limit based on variable repetitive group sampling plan

It is usually assumed that a quality characteristic in an item obeys a normal distribution in the case that the quality of items is evaluated based on the variable property. Then, the concept of Taguchi’s quality loss has been accepted as the evaluation measure of quality instead of the traditional attribute property such as the proportion of nonconforming items. From this viewpoint, some variable sampling plans indexed by the quality loss have been investigated before now. As a study earliest among them, the variable single sampling plan based on operating characteristics (OC) indexed by the quality loss was considered. On the other hand, the attribute repetitive group sampling plan on OC was proposed for reducing the sampling number in the inspection. Recently, the variable repetitive group sampling (VRGS) plan on OC indexed by the quality loss has been considered. By the way, the rectifying inspection is known as one of the schemes of acceptance sampling inspection. Then, Dodge-Romig single sampling plans are known as the traditional rectifying inspection based on attribute sampling plans. Dodge-Romig rectifying attribute sampling plans provide the lot tolerance percent defective (LTPD) scheme on each lot and the average outgoing quality limit (AOQL) scheme for many lots. Furthermore, the rectifying variable single sampling (RVSS) plan indexed by the quality loss was investigated. In conformity with the traditional rectifying attribute sampling plans for the LTPD and AOQL schemes, the acceptance quality loss limit (AQLL) and specified permissible average outgoing surplus quality loss limit (PAOSQLL) schemes are respectively proposed in the RVSS plans indexed by the quality loss. In this article, we suppose that the quality characteristic in an item obeys a normal distribution. Under this condition, the rectifying variable repetitive group sampling (RVRGS) plan for AQLL is considered for the purpose of reducing the average total inspection (ATI). Specifically, the design procedure for finding out the required sample size and inspection criteria for satisfying the constraint of the quality assurance is derived. Lastly, it is shown that ATI of the RVRGS plan is reduced in comparison with that of the RVSS plan under the same condition.     

基于正交距离回归齿面的齿轮误差评定

为了通过测量齿面拓扑轮廓来获取特征线误差,提出了一种基于正交距离回归齿面的误差计算方法。对该方法涉及的实际齿面与理论齿面匹配算法、拓扑轮廓误差的计算与分解及齿面特征线误差的评定算法进行了研究。首先,通过坐标测量方法获取的齿面拓扑数据,建立包含回归齿面参数的非线性方程。然后,求解非线性方程得到回归齿面参数的最优近似解,从而得到与实际齿面匹配的理论齿面,拓扑测量点相对理论齿面的正交距离即为齿面拓扑误差。最后,基于齿轮误差多自由度理论,对实际齿面进行局部自由度及全局自由度回归,进一步分解出齿面的齿廓误差和螺旋线误差。以一标准圆柱直齿轮的齿面拓扑测量点数据为例进行了误差计算,结果显示:计算的结果与直接进行特征线测量的结果差值小于0.5μm,表明提出的基于正交距离回归齿面进行齿轮误差评定的方法是有效的,可以应用于坐标类仪器检测齿轮误差。     

Adaptive sampling point planning for free-form surface inspection under multi-geometric constraints

Free-form surfaces have been widely used in aerospace, automotive and other fields. Due to its complex geometry, free-form surface inspection is generally conducted by touch-trigger or measuring probe-based Coordinate Measurement Machines or On-machine Measurement. Sampling strategy plays a decisive role in improving both measurement accuracy and efficiency, which is determined by sample size and distribution of sample points. However, it is difficult to simultaneously take the surface curvature, sampling density and approximation error into account, considering the complexity of surface geometry. In this paper, triangle mesh simplification is innovatively adopted in sampling planning to achieve multi-geometric constraints. As triangle mesh has outstanding advantages in representing the surface features, strong stability and is easy to modify its structure, free-form surface is converted to a dense triangle mesh. Triangle mesh simplification is implemented by iteratively contracting triangle edges. An improved quadric error metric is established to decide contraction order and optimal target vertices under discrete curvature constraint. Sampling density is controlled by limiting the triangle edge length. Detailed adaptive sampling algorithm under multi-geometric constraints is then developed. Both simulation and experiment are conducted to validate feasibility and robustness of the proposed method. The results are compared with uniform sampling and existing adaptive sampling strategy to show that the proposed method can prominently reduce sampling error when sample size is small.     

An Object Oriented Planner for Inspection of Prismatic Parts – OOPIPP

Coordinate measuring machines (CMMs) have been widely accepted and are increasingly used for carrying out inspections. With the increase in complex designs and tighter tolerances, the inspection process involving a CMM has become critical and there is a need to plan it effectively. In the present work, an object oriented planner for the inspection of prismatic parts (OOPIPP) has been developed. It incorporates interactive feature recognition and carries out all the essential steps of inspection planning, that is, selection of the most stable part orientation, arriving at number and distribution of inspection points, feature accessibility analysis, sequencing of probe orientations, removal of duplicate faces, and, finally, sequencing of faces. Various relationships between different entities of the system and distinct features of OOM have been used to develop the algorithms of different modules. Fuzzy logic for decision making has also been applied and a suitable method of combining fuzzy sets has been used for the selection of part orientation and for sequencing probe orientations.     

Automated visual inspection of geometric tolerance in circular components

In the manufacture of engineering products circular features are widely used. Roundness is one of the basic form errors encountered in circular features. The analysis of roundness error becomes crucial in the case of automated inspection. This paper presents mathematical models and algorithms to determine the roundness error in circular features using digital vision systems. Different approaches for determining out-of-roundness error are investigated and a proper approach is suggested. A methodology is proposed to determine the out-of-roundness error and number of lobes present in circular components. The proposed algorithm has been implemented and its reliability is reported in the paper     

基于形状特征的自由曲面采样算法的研究

测点采样是自由曲面零件检测的关键步骤.基于零件的两个形状特征因子:曲率因子、局部曲面片大小因子,提出一种面向不同类型曲面的采样算法,推导出曲率因子、局部曲面片大小因子的计算公式,进而优选合理的采样方案.该采样算法具有适应性广、无需繁琐的迭代过程等特点.用NURBS表达曲面,根据零件的梯度信息模拟制造误差并考虑测量误差,对采样过程进行了仿真分析,仿真结果验证了该采样策略的有效性.     

Variable sampling inspection plans with screening for assuring average outgoing surplus quality loss limit indexed by Taguchi’s loss

Taguchi has proposed a variable-quality evaluation called “Taguchi’s quality loss” instead of the attribute quality evaluation such as the proportion of nonconforming items. Arizono et al. have proposed a single acceptance sampling plan based on operating characteristics from the viewpoint of assuring Taguchi’s quality loss. This sampling plan is designed to guarantee the constraints of the prescribed acceptance probabilities for respective lots with the allowable quality loss limit and the unallowable quality loss limit. However, in the acceptance sampling plan based on operating characteristics, the corrective action for rejected lot is not prescribed. On the other hand, the sampling inspection plan with screening is well known as the sampling scheme with the corrective action for rejected lots. Then, there is the attribute sampling inspection scheme with screening in order to guarantee the expectation of the proportion of nonconforming items in the shipping lot. However, the variable sampling inspection scheme with screening has not yet been prescribed. Then, in this article, we propose a variable sampling scheme with screening procedure for the purpose of assuring the upper limit of the maximum expected surplus loss indexed by Taguchi’s loss.     

Least squares evaluations for form and profile errors of ellipse using coordinate data

To improve the measurement and evaluation of form error of an elliptic section, an evaluation method based on least squares fitting is investigated to analyze the form and profile errors of an ellipse using coordinate data. Two error indicators for defining ellipticity are discussed, namely the form error and the profile error, and the difference between both is considered as the main parameter for evaluating machining quality of surface and profile. Because the form error and the profile error rely on different evaluation benchmarks, the major axis and the foci rather than the centre of an ellipse are used as the evaluation benchmarks and can accurately evaluate a tolerance range with the separated form error and profile error of workpiece. Additionally, an evaluation program based on the LS model is developed to extract the form error and the profile error of the elliptic section, which is well suited for separating the two errors by a standard program. Finally, the evaluation method about the form and profile errors of the ellipse is applied to the measurement of skirt line of the piston, and results indicate the effectiveness of the evaluation. This approach provides the new evaluation indicators for the measurement of form and profile errors of ellipse, which is found to have better accuracy and can thus be used to solve the difficult of the measurement and evaluation of the piston in industrial production.     

A neural network approach to determining optimal inspection sampling size for CMM

This paper reports a neural network approach to determining the optimal inspection sampling size of ‘hole’ features using the Coordinate Measuring Machine (CMM). Factors which could affect sample size due to design, manufacturing, and measurement related factors, i.e. size, dimensional and geometrical tolerances, machining processes, and confidence levels, have been studied. Machining process type, size, and tolerance band have been identified as the known factors which may affect the sample size required. Experiments have been carried out to collect sampling size data versus the variation of these factors for different ‘hole’ features. The implicit correlation between the sample size and these factors, has been achieved by training a back-propagation neural network using the collected data. The neural network architecture is described, and the test of the trained neural network on a few new ‘hole’ features is presented to highlight the applicability of this approach.