Tolerance Analysis Considering form Errors in Planar Datum Features

The paper investigates the role of planar datum features in tolerance analysis problems. Mating relations between datum planes are shown to involve translational and rotational errors, which are related to form tolerances and are usually neglected in tolerance analysis. To evaluate these errors, the contact between datum planes was simulated by a stochastic model, where two surface profiles are randomly generated and then registered to reproduce a mating condition. Concepts of fractal geometry were exploited to make the generation consistent with the autocorrelation properties of actual surfaces resulting from manufacturing processes. A simulation plan allowed to predict the amount of contact errors as a function of size, tolerance and process-related assumptions on the two features. An example of 3D tolerance chain is presented to demonstrate the relevance of form errors in the variation of assembly requirements

A static analogy for 2D tolerance analysis

Purpose - This paper aims to present a method for the tolerance analysis of mechanical assemblies that is suitable to nonlinear problems where explicit functional equations are difficult or even impossible to write down. Such cases are usually modelled by linearised tolerance chains, whose coefficients (or sensitivities) are calculated from assembly data. Design/methodology/approach - The method is based on the free-body diagrams of force analysis, which are shown to be related to the sensitivities of linearised functional equations. Such an analogy allows the conversion of a tolerance chain into a corresponding static problem, which can be solved by common algebraic or graphical procedures. Findings - The static analogy leads to a correct treatment of tolerance chains, as the analysis of several examples has confirmed by comparison to alternative methods. Research limitations/implications - Currently, the method has only been tested on two-dimensional chains of linear dimensions for assemblies with nonredundant kinematic constraints among parts. Practical implications - The proposed method lends itself to ready application by using simple operations with minimal software assistance. This could make it complementary to current methods for calculating sensitivities, which are mathematically complex and require software implementation for deployment in industrial practice. Originality/value - Analogy with force analysis, which has not been previously highlighted in the literature, is a potentially interesting concept that could be extended to a wider range of tolerancing problems

Implementation of dimensional management methodology and optimisation algorithms for pre-drilled hinge line interfaces of critical aero assemblies - A case study

A dimensional management procedure is developed and implemented in this work to deal with the identification of the optimum hole diameter that needs to be pre-drilled in order to successfully join two subassemblies in a common hinge line interface when most of the degrees of freedom of each subassembly have already been constrained. Therefore, an appropriate measure is suggested that considers the assembly process and permits the application of optimisation algorithms for the identification of the optimum hole diameter. The complexity of the mechanical subassemblies requires advanced 3D tolerance analysis techniques to be implemented and the matrix method was adopted. The methodology was demonstrated for an industrial, aerospace engineering problem, i.e. the assembly of the joined wing configuration of the RACER compound rotorcraft of AIRBUS Helicopter and the necessary tooling needed to build the assembly. The results indicated that hinge line interfaces can be pre-opened at a sufficiently large size and thus, accelerate the assembly process whilst the suggested methodology can be used as a decision making tool at the design stage of this type of mechanical assembly

A framework for tolerance modeling based on parametric space envelope

Geometric dimensioning and tolerancing (GD&T) tolerance standards are widely used in industries across the world. A mathematical model to formulate tolerance specifications to enable comprehensive tolerance analysis is highly desirable but difficult to build. Existing methods have limited success on this with form and profile tolerance modeling as a known challenge. In this paper, we propose a novel tolerance modeling framework and methodology based upon parametric space envelope, a purposely built variation tool constructed from base parametric curve. Under proposal, geometric variation (deviation as well as deformation) is modeled and linked to envelope boundary control points’ movement. This indirect tolerance modeling brings various benefits. It is versatile and can handle full set of tolerances specified under GD&T standards including form, profile, and runout tolerance. The proposal can deal with complex manufacturing part and is capable of providing modeling accuracy required by many applications. The proposed approach has added advantage of facilitating integration of various computer-aided systems to meet emerging industry demands on tolerancing in a new era of digital manufacturing. The proposed methodology is illustrated and verified with an industrial case example on a two-part assembly

The dimensional variation analysis of complex mechanical systems

Dimensional variation analysis (DVA) is a computer based simulation process used to identify potential assembly process issues due the effects of component part and assembly variation during manufacture. The sponsoring company has over a number of years developed a DVA process to simulate the variation behaviour of a wide range of static mechanical systems. This project considers whether the current DVA process used by the sponsoring company is suitable for the simulation of complex kinematic systems. The project, which consists of three case studies, identifies several issues that became apparent with the current DVA process when applied to three types of complex kinematic systems. The project goes on to develop solutions to the issues raised in the case studies in the form of new or enhanced methods of information acquisition, simulation modelling and the interpretation and presentation of the simulation output Development of these methods has enabled the sponsoring company to expand the range of system types that can be successfully simulated and significantly enhances the information flow between the DVA process and the wider product development process

Tolerancing: Managing uncertainty from conceptual design to final product

Variability is unavoidable in the realization of products. While design must specify ideal geometry, it shall also describe limits of variability (tolerances) that must be met in order to maintain proper product function. Although tolerancing is a mature field, new manufacturing processes and design methodologies are creating new avenues of research, and modelling standards must also evolve to support these processes. In addition, the study of uncertainty has produced widely-accepted methods of quantifying variability, and modern tolerancing tools should support these methods. The challenges introduced by new processes and design methodologies continue to make tolerancing research a fertile and productive area

Modelling and controlling variation propagation in mechanical assembly of high speed rotating machines

Assembly plays a vital role in the quality of a final product and has a great impact on the manufacturing cost. The mechanical assemblies consist of parts that inevitably have variations from their ideal dimensions. These variations propagate and accumulate as parts are assembled together. Excessive amount of variations in an assembly may cause improper functionality of the product being assembled. Improving assembly quality and reducing the assembly time and cost are the main objectives of this thesis. The quality of an assembly is determined in terms of variations in critical assembly dimensions, also known as Key Characteristics (KCs). Key Characteristics are designated to indicate where excess variation will affect product quality and what product features and tolerances require special attention. In order to improve assembly quality and reduce assembly time and cost, it is necessary to: (1) model non-ideal parts based on tolerances defined in design standards or current industrial practice of component inspection, (2) model assemblies and their associated assembly processes to analyse tolerance stack-up in the assembly, (3) develop probabilistic model to predict assembly variation after product assembly, and (4) implement control strategies for minimising assembly variation propagations to find optimum configuration of the assembly. Two assembly models have been developed, a linear model and a fully non-linear model for calculating assembly variation propagations. The assembly models presented in this thesis also allows for inclusion of geometric feature variation of each assembly component. Methods of incorporating geometric feature variations into an assembly variation model are described and analysis techniques are explained. The assembly variation model and the geometric variation models have been developed for 20 and 3D assemblies. Modelling techniques for incorporating process and measurement noise are also developed and described for the nonlinear assembly model and results are given to demonstrate the calculation of assembly variations while considering part, process and measurement errors. Two assembly case studies originating in sub-assemblies of aero-engines have been studied: Case Study 1, representing the rotating part (rotor) of an aero-engine, and Case Study 2, representing non-rotating part (stator) of an aero-engine. A probabilistic method based on the linear model is presented as a general analytical method for analysis of 3D mechanical assemblies. Probability density functions are derived for assembly position errors to analyse a general mechanical assembly, and separate probability functions are derived for the Key Characteristics (KCs) for assembly in Case Studies 1 and 2. The derived probability functions are validated by using the Monte Carlo simulation method based on the exact (full non-linear) model. Results showed that the proposed probabilistic method of estimating tolerance accumulation in mechanical assemblies is very efficient and accurate when compared to the Monte Carlo simulation method, particularly if large variations at the tails of the distributions are considered. Separate control strategies have been implemented for each case study. Four methods are proposed to minimise assembly variations for Case Study 1, and one error minimisation method is suggested for assemblies of Case Study 2. Based on the developed methods to optimise assembly quality, the two case studies were investigated, and it was found that the proposed optimisation methods can significantly improve assembly quality. The developed optimisation methods do not require any special tooling (such as fixtures) and can easily be implemented in practice