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TECHNICAL PAPERS

# Substitute Geometry of the Features of Size: Applications to Multidimensional Features

[+] Author and Article Information
V. Portman

Department of Mechanical Engineering, Ben-Gurion University of the Negev, POB 653, Beer-Sheva 84105, Israelportman@bgu.ac.il

V. Shuster

ENIMS, Moscow, Russia

Y. Rubenchik

Department of Mechanical Engineering, Ben-Gurion University of the Negev, POB 653, Beer-Sheva 84105, Israelyanina@bgu.ac.il

Y. Shneor

Center of Advanced Manufacturing Technology, ROTEM Ind., Ltd., Arava, Israelcamt@rotemi.co.il

J. Comput. Inf. Sci. Eng 7(1), 52-65 (Nov 14, 2006) (14 pages) doi:10.1115/1.2410021 History: Received September 13, 2005; Revised November 14, 2006

## Abstract

The problems of the substitute geometry for features of size are considered and an algorithm for synthesis of the substitute features (SF) is developed. Three and only three classes of surfaces are proved to have an incomplete set of position and orientation deviations within the SF equation: cylinders with any directrix, surfaces of revolution with any meridian, and helical surfaces with any profile. The form accuracy of multidimensional features relating to these classes is considered: ellipsoid of revolution, epitrochoidal cylinder, and Archimedean screw. The deterministic consideration is accompanied by evaluation of the uncertainty of the standard assessments of the geometric accuracy and capacity of the computing procedure.

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## Figures

Figure 1

Position vectors of the feature point in the coordinate system associated with the NF

Figure 8

Distributions of the points between two boundaries of the Min Z at eight cross sections and throughout the whole zone

Figure 2

Interrelationship between the NF and SF

Figure 3

Cylindrical surfaces: (a) general case; (b) circular cylinder; and (c) plane

Figure 4

Surfaces of revolution: (a) general case; (b) cylinder; (c) plane; and (d) sphere: (1) axis of revolution (2) meridian

Figure 5

Helical surfaces with straight (a) and nonstraight (b) profiles

Figure 6

Manufacturing process of the ellipsoid of revolution

Figure 7

Description of the ellipsoid of revolution: (a) the drawing; (b) the tolerance zone; (c) the cross and axial sections; and (d) the zone for the axis location

Figure 9

Comparison of form accuracy assessments of the ellipsoid obtained in 20 numerical experiments with and without regard to size deviations

Figure 10

The epitrochoidal cylinder

Figure 11

Parameterization of the epithrochoid

Figure 12

The Min Z-based assessment in one cross section of the epitrochoidal-type stator

Figure 13

Comparison of form accuracy assessments of the epitrochoidal cylinder with (the lower curve) and without (the upper curve) regard to size deviations

Figure 14

A trapezoidal profile of the Archimedean screw (h=H∕2)

Figure 15

Schema of evaluation of the accuracy of the screw

Figure 16

The Min Z-based assessments of the form accuracy of the screw along its length on a threaded length lm of the mating nut

Figure 17

The dispersion of the form accuracy assessments versus sample size N for three distribution functions

Figure 18

Capacity of the variational-method-based procedure versus sample size N and number p of the SPOD

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