Quadratic Sensitivity Analysis of Fixtures and Locating Schemes for Rigid Parts

Abstract

The main purpose of locating schemes are to position parts. The locating scheme utilizes tooling elements, referred to as locators, to introduce geometric constraints. A rigid part is uniquely positioned when it is brought into contact with the locators. By using kinematic analysis we derive a quadratic sensitivity equation that relates position error in locators with the resulting displacement of the part held by the locating scheme. The sensitivity equation which depends on the locator positions and the workpiece geometry around the contact points can be used for locating scheme evaluation, robust fixture design, tolerancing and diagnosis. The quadratic sensitivity equation derived in this paper is novel by adequate dealing with locator contact at nonprismatic surfaces, nonsmall errors, locator error interaction effects and locator errors in arbitrary directions. Theory for comparing the relative gain in precision by using the quadratic sensitivity equation instead of the linear is developed. The practical relevance of the quadratic sensitivity equation is tested through numerical experiments.

On the Error Elimination for Multi-Axis CNC Machining

“…In other words, a feature on a workpiece can be machined without error if the desired adjustments of locators can be determined by using Eq. (17) so that the displacements of the workpiece are consistent with the kinematic chain errors in the multi-axis CNC machine.…”

“…In the past several years, most research has been focused on fixture design [1][2][3][4][10][11][12][13][14][15][16][17] and machine tool error modeling [5][6][7][8][9]. The kinematic modeling, analysis, and characteristics of fixture configuration are discussed [1][2][10][11][12][13][14].…”

Method for automating digital fixture-setups that are optimal for machining castings to minimize scrap

“…Rong [1] called it Computer Aided Fixture Design and, with Bai and Wu [2,3], produced fixture schemas and planning modular fixtures. Carlson describes the sensitivity of errors in fixture schema [4]. Wang [5] presents a fixture kinematic analysis based on the full kinematics of contact between the workpiece and the fixture which includes not only the arbitrary locator location errors but also the surface properties at non-prismatic contacts.…”

Analysis of Variations Control Model for Vehicle Manufacture

“…After that, Sayeed and Demeter [25] developed a software that can automatically determine the geometric parameters of the point, so that the positioning can satisfy both the deterministic and the complete constraints. Carlson [26] and Wang [27] use the surface contact model to study the problem of deterministic positioning, complete constraint and positioning accuracy. As a continuation of the research, the theoretical basis of the deterministic positioning and complete constraints is the kinematics, the main method are as follows: Helix theory and coordinate transformation.…”