Generation Geometrical Product Specification Research Articles

Tolerance analysis method considering multifactor coupling based on the Jacobian–torsor model

Assembly quality affects the performance of mechanical products and reasonable tolerance designs are central to assembly quality. Unreasonable tolerance design leads to the mechanical equipment performance degradation under complex operating conditions. This study developed a novel tolerance analysis method that considers the influence of temperature, load, and other environmental factors based on the Jacobian–torsor and skin models. First, the deformation caused by multifactor coupling was analyzed using the finite element method, and the feature surface of deformation is extracted. Second, the deformation extraction and tolerance conversion based on the new generation geometrical product specification theory was used to convert the deformation of the feature into the dimension, orientation, and form tolerance. Third, the modified Jacobian–torsor model considering multifactor coupling was constructed by superimposing the converted tolerance with the design tolerances. Finally, the abrasion problem of the airborne actuator was considered as an example to verify the effectiveness and accuracy of the novel method. Through the accurate calculation of tolerances, it accurately analyzes the assembly state of the product under the influence of environmental factors, and provides more accurate guidance for the design and optimization of product tolerance in complex working conditions.

Uncertainty evaluation of straightness in coordinate measuring machines based on error ellipse theory integrated with Monte Carlo method

According to the new generation geometrical product specification, it is necessary to provide measurement uncertainty together with measurement results in order to determine the reliability of results. The traditional methods used for the uncertainty evaluation of straightness are laborious and time-consuming owing to a large quantity of repeated measurements or a complicated computational process. Based on the error ellipse theory and the Monte Carlo method, a novel method for uncertainty evaluation is proposed. Through the error ellipse theory, in the measuring space of coordinate measuring machines, the positional uncertainty of sampling points can be more accurately considered to be represented by an ellipse. By integrating the Monte Carlo method, only with limited sets of real measured data in small experimental trials, the uncertainty propagation from a single sampling point to the whole straight line can be demonstrated clearly in the simulation without requiring large amounts of time and labour. The detailed procedures of uncertainty evaluation are given. The straightness uncertainty can then be obtained by statistical analysis of the simulation results. Real straightness measurement experiments were carried out and compared with the results from the proposed method. The difference was no more than 5%, which verified the validity of the method.

Optimisation estimation of uncertainty integrated with production information based on Bayesian fusion method

The new generation Geometrical Product Specifications require consideration of the effects of measurement uncertainty in the product inspection. This study estimated the measurement results and the uncertainty by integrating the statistical production information into the product detection results to rationally and fairly narrow the uncertainty area of qualification determination. Based on the Bayesian information fusion and statistical inference principle, the model of uncertainty evaluation is established. The Bayesian information fusion model integrated measuring information with manufacturing information was built, with which the uncertainty of product inspection was reappraised based on posteriori distribution function. The validity of the proposed method and theory was demonstrated by the example analysis.

Uncertainty Estimation of Robot Geometric Parameters and End-Effecter Position Based on New Generation GPS

The robot end-effecter positioning accuracy can be improved by the calibration of robot geometric parameters errors. According to the requirements of new generation geometrical product specification (GPS), the calibration uncertainty should be given when the calibration results are given. In this paper, the modified Denavit-Hartenberg method (MDH) of six-joint series robot is established and the joint movement trajectory method is applied to calibrate the robot geometric parameters. The uncertainty contributors significant are analyzed and the calibration uncertainty of robot geometric parameters is estimated based on the guide to the expression of uncertainty in measurement (GUM). In order to overcome the limitations of GUM for highly nonlinear model and reduce computational cost based on Monte Carlo Simulation (MCS) error estimation, an adaptive MCS (AMCS) is proposed to estimate the uncertainty distribution of robot end-effector position. Simulation and practical example are illustrated and the experiments results confirm that not only can the proposed method evaluate the calibration uncertainty of geometric parameters, but also the uncertainty distribution of end-effecter positions in the whole robot workspace can be estimated by AMCS in which the number of MCS trials can be selected adaptively and the quality of the numerical results can be controlled directly. The proposed method not only can evaluate the uncertainty of six-joint series robot geometric parameters and end-effecter position rapidly and accurately, but also can be popularized to the estimation of calibration uncertainty of other kinds of robot geometric parameters.

Application of New Generation Geometrical Product Specifications in the practice in Small and Medium Sized enterprises

The increasing development of modern methods of product manufacturing implies an improvement and a new approach to the modern drawing specification in design documentation for design requirements of different parts and assemblies. The ISO Technical Committee 213 has published 148 standards and 48 otherstandards are under development. These standards set out requirements for the accuracy of geometrical characteristics of products. They define requirements for the linear sizes, dimensions different than linear sizes as well as geometric deviations such as form, orientation, location deviations and run-out, and surface roughness and waviness. Ways of indication of these requirements in the drawings are discussed. Many standards are dedicated to the requirements for measuring these characteristics, to measuring instruments for linear sizes and geometrical characteristics. This report reviews the general concept of geometrical product specifications (GPSs), the GPS model, and new terminology by tolerancing linear sizes, geometrical specifications that facilitate communication between design manufacturing and verification and prevent ambiguous interpretation of requirements. Based on the metrological expertise of the drawings in a number of small and mediumsized enterprises, the degree of implementation of the new generation GPS standards and the problems related to it have been analysed.

The Difference Between GUM and ISO/TC 15530-3 Method to Evaluate the Measurement Uncertainty of Flatness by a CMM

Uncertainty estimation in coordinate measuring machine (CMM) measurements is one of the highest priority tasks in modern industrial world due to its importance in the manufacturing metrology, especially if we take into account the fact that workpieces, according to a new generation of geometrical product specifications, can be accepted/rejected only on the basis of the total measurement results. Evaluation of measurement uncertainty of a CMM is a complex task, especially in the verification of errors of forms. Among several standard methods that can be used to estimate measurement uncertainty, we performed a comparison between two of these for the case of flatness measurement. Optical flat was used in order to exclude a number of essential factors in the case study. The results showed that the expanded measurement uncertainty assessed by GUM is greater than the value of the expanded measurement uncertainty obtained using the ISO 15530 method. However, both methodologies have shown that the maximum permissible error of a CMM has the greatest impact on uncertainty and also, that the total result evaluated by both approaches is close to the maximum permissible error of a CMM.

Study of 3D Tolerance Modeling Method for Complex Feature Geometric Variations

The aim of this paper is to present a 3D tolerance mathematical model for complex feature geometric variations oriented the new generation Geometrical Product Specifications (GPS). According to the definition of geometric feature and taxonomy of geometric variations in the new generation GPS system, the proposed model is based on the small displacements torsor (SDT) concept, and the geometric deviations treated as relative location or rotation variations between the nominal geometry feature and the associated feature are expressed by the SDT parameters. Moreover, the tolerance models for several kinds of complex feature geometric variations are constructed and discussed. Finally, a numerical example is given to illustrate the application of the proposed tolerance model, and the results indicate that the proposed model is capable in dimensional and geometrical tolerances modeling. The model completely based on the mathematics foundation is in compliance with the current GPS standards system.

New Generation Geometrical Product Specification (GPS) Backed Flatness Error Estimation and Uncertainty Analysis

Measurement and verification are one of the prime stages in the entire course of geometrical products in new generation of geometrical product specifications (GPS) standard. Like other kinds of form tolerances, flatness error is one of the important characteristics affecting the functionality and quality of machined components; sufficient efforts have long been made to determine the flatness error close to the true value based on the minimum zone method (MZM) and still needs continual improvement. This paper presents real coded genetic algorithms referred as Efficient Genetic Algorithms (EGA) for flatness error based on minimum zone method having good precision, repeatability and fast convergence rate. This paper also presents evaluation procedure for measurement uncertainty in flatness error based on new generation geometrical product specifications (GPS). Uncertainty in flatness error has been determined and evaluation procedure is provided to prove the conformance or non-conformance by taking into account the uncertainty in measurement. The contributing factors in measurement uncertainties have been identified and then quantified. The flatness error and evaluation theory in this paper are in the framework of new generation GPS standard. Two practical examples have been presented to show the effectiveness of EGA and shed some light on the uncertainty evaluation theory based on new generation GPS standard.

Evaluation of Compliance Uncertainty in Product Inspection Based on the New Generation Geometrical Product Specifications

Evaluation of Compliance Uncertainty in Product Inspection Based on the New Generation Geometrical Product Specifications

Measurement uncertainty evaluation of conicity error inspected on CMM

The cone is widely used in mechanical design for rotation, centering and fixing. Whether the conicity error can be measured and evaluated accurately will directly influence its assembly accuracy and working performance. According to the new generation geometrical product specification(GPS), the error and its measurement uncertainty should be evaluated together. The mathematical model of the minimum zone conicity error is established and an improved immune evolutionary algorithm(IIEA) is proposed to search for the conicity error. In the IIEA, initial antibodies are firstly generated by using quasi-random sequences and two kinds of affinities are calculated. Then, each antibody clone is generated and they are self-adaptively mutated so as to maintain diversity. Similar antibody is suppressed and new random antibody is generated. Because the mathematical model of conicity error is strongly nonlinear and the input quantities are not independent, it is difficult to use Guide to the expression of uncertainty in the measurement(GUM) method to evaluate measurement uncertainty. Adaptive Monte Carlo method(AMCM) is proposed to estimate measurement uncertainty in which the number of Monte Carlo trials is selected adaptively and the quality of the numerical results is directly controlled. The cone parts was machined on lathe CK6140 and measured on Miracle NC 454 Coordinate Measuring Machine(CMM). The experiment results confirm that the proposed method not only can search for the approximate solution of the minimum zone conicity error(MZCE) rapidly and precisely, but also can evaluate measurement uncertainty and give control variables with an expected numerical tolerance. The conicity errors computed by the proposed method are 20%-40% less than those computed by NC454 CMM software and the evaluation accuracy improves significantly.

Research on the Intelligent Annotation Technology of Geometrical Tolerance Based on Geometrical Product Specification (GPS)

To solve the problem of geometrical tolerance annotation in CAD software is not in conformity with the requirement of the new generation Geometrical Product Specification (GPS), an intelligent annotation module of geometrical tolerance which is integrated seamlessly with Creo software is developed. In the developed module, the new annotation requirements of geometrical tolerance, such as intersection plane, orientation plane, and collection plane, are provided, and their application rules are given. The design rules of geometrical characteristics are put forward based on invariance class provided by the new generation GPS, and the relationship between geometrical tolerance zone and the additional symbols is established. By using of building standard symbols library, inquiring of geometrical tolerance value automatically, and simplifying user interface, the intelligent and convenience geometrical tolerance annotation is realized. The case study indicates that using the developed module make the geometrical tolerance annotation in CAD software easier and more convenient.

Line to Plane Parallelism Error Evaluation of the New Generation GPS Based on DCWPSO

Currently Least Squares Method (LSM) is commonly applied in the error evaluation, but it is adaptive to the condition of low accuracy requirement. Besides, the error value obtained by LSM is not the minimum. In order to accurately evaluate parallelism error, the minimum zone mathematical model of the parallelism is given based on the new generation geometrical product specification and verifications (GPS). According to the characteristics of parallelism error evaluation, a new adaptive Particle Swarm Optimization algorithm with dynamical inertia weight (DCWPSO) is proposed to solve target optimization problems of the error evaluation. Finally we use the measurement of a line to plane parallelism error evaluation as an example to validate the proposed method. The experiment results show the feasibility and availability of the method．

An Approach for the Evaluation of Sphericity Error and Its Uncertainty

The verification uncertainty theory in new generation geometrical product specification (GPS) has been applied in the whole process of geometrical product specification and verification. According to the uncertainty theory, a novel method for the uncertainty evaluation of sphericity errors was proposed. The association operator in new generation GPS was applied. The mathematical model of the sphericity error and the optimal objective function were developed under the condition of minimum zone. Particle swarm optimization (PSO) algorithm was used to search for the optimal solution of sphericity error. The coefficients of the correlation element and propagation of uncertainty were calculated so that the sphericity error and the uncertainty of the result can be obtained. The evaluation results are accurate and consistent with requirements of a new generation GPS standard. It also indicates that this method can improve the integrity and veracity of verification.

Standardized Design and Evaluation of Coordinate Measurement Based on the New Generation of GPS

Currently coordinate measurement has been the most important methods of geometric measurement. The measuring principle is completely different with traditional instrument such as gauges, caliper etc. Instrument accuracy assessment, traceability methods and the evaluation of the measurement results have been the research focus. This paper presents a method for specification design and evaluation of coordinate measurement combined with the new generation of GPS (Geometrical product specifications), which are verified by measuring concentricity using laser tracker.

Monte carlo method for the uncertainty evaluation of spatial straightness error based on new generation geometrical product specification

Straightness error is an important parameter in measuring high-precision shafts. New generation geometrical product specification(GPS) requires the measurement uncertainty characterizing the reliability of the results should be given together when the measurement result is given. Nowadays most researches on straightness focus on error calculation and only several research projects evaluate the measurement uncertainty based on “The Guide to the Expression of Uncertainty in Measurement(GUM)”. In order to compute spatial straightness error(SSE) accurately and rapidly and overcome the limitations of GUM, a quasi particle swarm optimization(QPSO) is proposed to solve the minimum zone SSE and Monte Carlo Method(MCM) is developed to estimate the measurement uncertainty. The mathematical model of minimum zone SSE is formulated. In QPSO quasi-random sequences are applied to the generation of the initial position and velocity of particles and their velocities are modified by the constriction factor approach. The flow of measurement uncertainty evaluation based on MCM is proposed, where the heart is repeatedly sampling from the probability density function(PDF) for every input quantity and evaluating the model in each case. The minimum zone SSE of a shaft measured on a Coordinate Measuring Machine(CMM) is calculated by QPSO and the measurement uncertainty is evaluated by MCM on the basis of analyzing the uncertainty contributors. The results show that the uncertainty directly influences the product judgment result. Therefore it is scientific and reasonable to consider the influence of the uncertainty in judging whether the parts are accepted or rejected, especially for those located in the uncertainty zone. The proposed method is especially suitable when the PDF of the measurand cannot adequately be approximated by a Gaussian distribution or a scaled and shifted t-distribution and the measurement model is non-linear.

Uncertainty Management of Flatness According to PUMA

Next generation of Geometrical Product Specifications (GPS) is the foundation of the technology standards and metrology specifications of mechanical and electric products. GPS estimation of uncertainty can make the results of verification of products reliable and can be compared globally. Flatness is an important geometrical feature of a product and has great influence to the product performance and assembly quality. The uncertainty in flatness three-dimensional measurements must be estimated according to GPS standards to assure the related functions of a product. According to t ISO/TS 14253-2, a calculation method of the uncertainty in flatness three-dimensional measurement by certain fitting method is proposed. The method was evaluated and improved according to Procedure for Uncertainty Management, which is given by next generation of GPS. The measurement process which can meet the target uncertainty was obtained at last.

On Generation of the Specification Model for Concentricity Based on Mathematical Modeling

Feature specifications are important composite parts in the new generation of geometrical product specifications and verification (GPS). According to the theories of specification model of shaft parts, this paper presents a method to generation of specification model of concentricity. Firstly, the mathematical model of concentricity is established in terms of nominal geometrical features of product for the parts the functional requirement are satisfied. Secondly, the simulation points of the model are generated by using the methods of axial stratification and circumferential multi-angles. The concentricity specification model could be generated after these operations of association and collection. Finally, an example is applied to illustrate the new method. The experiment results show the effectiveness of the proposed method.

Flatness error evaluation and verification based on new generation geometrical product specification (GPS)

New generation geometrical product specification (GPS) links the whole course of a geometrical product from the research, development, design, manufacturing and verification to its release, utilization, and maintenance. Measurement process is one of the most important part of verification/inspection in the new generation GPS. With the knowledge-intensive and globalization trend of the economy, unifying the evaluation and verification of form errors will play a vital role in international trade and technical communication. Considering the plane feature is one of the most basic geometric primitives which contribute significantly to fundamental mechanical products such as guide way of machine tool to achieve intended functionalities, the mathematical model of flatness error minimum zone solution is formulated and an improved genetic algorithm (IGA) is proposed to implement flatness error minimum zone evaluation. Then, two evaluation methods of flatness error uncertainty are proposed, which are based on the Guide to the Expression of Uncertainty in Measurement (GUM) and a Monte Carlo Method (MCM). The calculating formula and the propagation coefficients of each element and correlation coefficients based on GUM and the procedures based on MCM are developed. Finally, two examples are listed to prove the effectiveness of the proposed method. An investigation into the source and effects of different uncertainty contributors for practical measurement on CMM is carried out and the uncertainty contributors significant are analyzed for flatness error verification. Compared with conventional methods, the proposed method not only has the advantages of simple algorithm, good flexibility, more efficiency and accuracy, but also guarantees the minimum zone solution specified in the ISO/1101 standard. Furthermore, it accords with the requirement of the new generation GPS standard which the measurement uncertainty characterizing the reliability of the results is given together. And it is also extended to other form errors evaluation and verification.

Application of Monte Carlo Method in the Measurement Uncertainty Estimation Technology in next Generation of GPS

Next generation of Geometrical Product Specifications (GPS) is the foundation of the technology standards and metrology specifications of mechanical and electric products. GPS estimation of measurement uncertainty can improve the reliability of the verification result. In the indirect measurement, the transfer characteristic is very complex. So, it is very difficult to estimate the uncertainty in the indirect measurements according to the transfer formula given by GUM. For the indirect measuring of an inside cone angle, the mathematical relation between the measurand and measurement results is established firstly. Then Monte Carlo method was adopted to conduct the sampling and synthesis of measurement uncertainty contributors. At last, the measurement method was evaluated and improved according to Procedure for Uncertainty Management. Experimental result shows that Monte Carlo Simulation method has a good application foreground in the uncertainty estimation and measurement program design.

Study on tolerance modeling of complex surface

The aim of this paper was to present a tolerance modeling method of complex features. Geometric deviation of a characteristic/feature is divided into intrinsic deviation and situation deviation based on the new generation geometrical product specification in the paper. On the basis of vector parametric representation of theoretical surface, intrinsic deviation between substitute surface and ideal surface is described by vector function. Based on 3D rigid body kinematics, homogeneous transformation matrix-based method is used to describe the situation deviation of the substitute surface relative to the reference feature in Euclidean space. An example was given using the proposed modeling method.