Edward P. Morse

A gap-based approach to capture fitting conditions for mechanical assembly

Abstract An approach, called the GapSpace model, is proposed to find the sufficient and necessary conditions—we call these the ‘fitting conditions’ (FC)—for non-interfering mechanical assemblies. When different parts are assembled, some features will be in contact while other features may not be able to touch one another or they may interfere. We refer to the ‘gap size’ relating two features as zero, positive or negative. In the GapSpace approach, the linear sum of some gaps forms the FCs that are determined by the dimensions and tolerances. After all FCs are identified, tolerance analyses can be easily performed. The model can be integrated with commercial CAD products (such as Pro/E) for tolerance analysis.

On the Enduring Appeal of Least-Squares Fitting in Computational Coordinate Metrology

The vast majority of points collected with coordinate measuring machines are not used in isolation; rather, collections of these points are associated with geometric features through fitting routines. In manufacturing applications, there are two fundamental questions that persist about the efficacy of this fitting—first, do the points collected adequately represent the surface under inspection; and second, does the association of substitute (fitted) geometry with the points meet criteria consistent with the standardized geometric specification of the product. This paper addresses the second question for least-squares fitting both as a historical survey of past and current practices, and as a harbinger of the influence of new specification criteria under consideration for international standardization. It also touches upon a set of new issues posed by the international standardization on the first question as related to sampling and least-squares fitting.

Interoperability: Linking Design and Tolerancing with Metrology

On October 30, 2014 the American National Standards Institute (ANSI) approved QIF v 2.0 (Quality Information Framework, version 2.0) as an American National Standard. Subsequently in early 2016 QIF version 2.1 was approved. This paper describes how the QIF standard models the information necessary for quality workflow across the full metrology enterprise. After a brief description of the XML ‘language’ used in the standard, the paper reports on how the standard enables information exchange among four major activities in the metrology enterprise (product definition; measurement planning; measurement execution; and the analysis and reporting of the quality data).

Size tolerancing revisited: A basic notion and its evolution in standards:

Size is a fundamental descriptor of objects—it allows us to quantify “how big” objects are and to compare and classify objects based on this notion. In the world of International Organization for Standardization Geometrical Product Specification and Verification, size is defined much more narrowly: it is restricted to features of size, and the methods of inducing size values from an actual workpiece are strictly controlled. The release of ISO 14405-1:2010 has introduced a rich new set of size specification modifiers, which includes two-point and spherical local sizes, least squares, maximum inscribed and minimum circumscribed associations, as well as calculated diameters (inferred from the circumference, area, or volume of the feature of interest). Further modifiers allow the specification of statistics of local size measurements, such as maximum, minimum, range, average, and others. This article will present “size” as a fundamental engineering notion from several viewpoints and trace its evolution in engineering drawings. It will then discuss the implications of the use of the recently standardized size modifiers in engineering design and investigate the issues that may arise in the application and interpretation of these extensions to size.

Statistical Tolerance Analysis Using GapSpace

This paper describes a new method for statistical tolerance analysis using the GapSpace model. We show how, after modeling the distribution of manufactured dimensions with a joint probability density function, assembly analysis is performed by integrating the density function over a tolerance region or assembly region described in GapSpace. Through an example, this paper addresses how statistical tolerance analysis should mimic the “manufacturing scheme” of the parts and how the GapSpace model can be used to identify optimal results.

Positioning sensor by combining photogrammetry, optical projection and a virtual camera model

A novel, low cost, non-contact measurement technique is proposed to realize an optical positioning sensor that enables real-time measurement of a small lightweight modules location. The technique is based on a combination of photogrammetry, optical projection and a virtual camera model. The module generates an optical pattern that is observable on the surrounding walls, photogrammetry is used to track the motion of the projected optical pattern, and this indirectly allows the motion of the module to be tracked. This is done by treating the module as a virtual pinhole camera, generating a virtual image that carries the angular characteristics of the optical pattern. Images of the projected optical pattern on the walls taken by cameras around the room, together with the virtual image, are then processed through a photogrammetry-based bundle adjustment. This results in a position and orientation estimate of all cameras, including the virtual pinhole camera. The position and orientation of the virtual camera is therefore also the position and orientation of the module. Both experiment and optical ray-trace simulations are performed to validate the proposed technique. Experimental agreement of 3 parts in 104?was obtained by translating the module over 0.9?m. The incorporation of the virtual camera model is innovative, leads to a simple solution, and is more robust than the previously published approach.

On the Complexity of Mechanical Assemblies

There is no doubt that today’s mechanical systems are complex. Mechanical systems tend towards greater complexity as each component interacts with a larger number of neighboring components. This structure of interaction permits function-sharing of the components — one of the hallmarks of creative design. Function-sharing is one of the interesting ways in which mechanical design differs from, for example, solid state circuit design. Assembly models that require fixed contact between components at specified locations to determine their relative positions will also have gaps that provide clearance between the components. The complexity of these assembly models is linear in the number of gaps, as the clearance at each gap is dependent on a single set of dimensions. However, if the assembly model is defined in terms of potential (vs. required) contacts between components, the complexity of the analysis increases dramatically. In this paper we describe the complexity of assemblies analyzed in a single direction (i.e. one-dimensional analyses) and propose a means of characterizing different types of assemblies.Copyright

Using Optical Projection in Close-range Photogrammetry for 6DOF Sensor Positioning

A novel, low cost, non-contact, six degrees of freedom (DOF) measurement technique is proposed that enables real-time measurement of a small lightweight module’s location. Straight forward applications of the proposed technique include robot calibration by installing the module to the end effector of a robot arm, and head-tracking in a typical virtual reality environment by attaching the module to a human head. The technique is based on a combination of photogrammetry and optical pattern projection. The module generates an optical pattern that is observable on the surrounding walls, and photogrammetry is used to measure the absolute coordinates of features in the projected optical pattern with respect to a defined global coordinate system. By combining these absolute coordinates with the known angular information of the optical projection beams, a minimization algorithm can be used to extract the absolute coordinates and angular orientation of the module itself. Experimental agreement of 1 to 5 parts in 103 was obtained by translating the module over 0.9 m and by rotating it through 60°. Numerical simulations were conducted to demonstrate that optimum design of the projected pattern gives a lower associated measurement uncertainty than is possible by direct photogrammetric measurement with traditional tie points. This paper documents the proof of principle and describes how the measurement can be further improved.

Assembly Analysis of Interference Fits in Elastic Materials

The objective of this work is to provide fast approximations of force/work/energy calculations for designers of assemblies in which interference is required. In this paper, the subjects of interest are assemblies in which there are several sets of features that can influence the final location of the parts, once assembled. The analysis includes a systematic approach in developing an analytical model involving basic laws of equilibrium and more advanced finite element based models to estimate the work required for assembly and the total strain energy in the components after assembly is complete. In this approach, an ideal press-fit type interference assembly is considered initially and solution methodology is developed. A non-symmetric hinge assembly with multiple interferences is analyzed later with the developed approach and the results are compared with the experimental observations. The suitability of the GapSpace assembly analysis method [1] for assemblies in which there is interference between the components is also investigated.

Statistical Analysis of Assemblies Having Dependent Fitting Conditions

Analysis of the propagation of geometric variability through assemblies is used to estimate the probability that randomly selected components will, in fact, assemble. This process is known as Statistical Tolerance Analysis. One-dimensional analyses utilize a direct root-sum-square composition of the contributing part dimensions (the dimension stack) to estimate the probability that appropriate clearances will be maintained in the assembled configuration. Higher dimensional analyses frequently use the sensitivities of the clearances to dimensional changes based on the kinematics of the assembly. However, commercial tolerance analysis software does not support the analysis of assemblies where more than one dependent variable (a clearance) appears in each dimension stack. This paper describes the extension of a novel modeling method to accommodate statistical variability in assemblies. Assemblies are modeled in terms of their clearance conditions between mating surfaces, and parts are allowed to “float” with respect to one another, rather than being required to have all degrees of freedom removed in the final assembly. Variability in part dimensions is transformed to variation in the clearances, allowing inter-dependent dimension stacks sharing multiple, dependent clearances. The differences in predicted yield — will the parts fit together as designed? — for assemblies whose components can float with respect to one another is compared to similar assemblies where relative motion is fixed by a specified condition of contact or alignment.Copyright