On the Exact Computation of the Swept Surface of a Cylindrical Surface Undergoing Two-Parameter Rational Bézier Motions

2000 ◽  
Author(s):  
J. Xia ◽  
Q. J. Ge
Keyword(s):  
Recent Work ◽  
Cylindrical Surface ◽  
Tool Path ◽  
Object Motion ◽  
Freeform Surfaces ◽  
New Approach ◽  
Volume Analysis ◽  
Swept Surface ◽  
Swept Volume ◽  
Two Parameter

Abstract This paper extends the recent work of Xia and Ge (1999) to develop methods for the exact analysis of the swept surface of a cylindrical surface undergoing two-parameter rational Bézier motions. Instead of the approach of analyzing the point trajectory of an object motion for swept volume analysis, this paper seeks to develop a new approach to swept volume analysis by studying the plane trajectory of a rational motion. It seeks to bring together recent work in swept volume analysis, plane representation of developable surfaces, as well as computer aided synthesis of freeform rational motions. The results have applications in design and approximation of freeform surfaces as well as tool path planning for 5-axis machining of freeform surfaces.

On the Exact Representation of the Boundary Surfaces of the Swept Volume of a Cylinder Undergoing Rational Bézier and B-Spline Motions

1999 ◽  
Author(s):  
J. Xia ◽  
Q. J. Ge
Keyword(s):  
Tool Path ◽  
Traditional Approach ◽  
Object Motion ◽  
Exact Representation ◽  
Tool Path Planning ◽  
New Approach ◽  
B Spline ◽  
Volume Analysis ◽  
Swept Volume ◽  
Boundary Surfaces

Abstract This paper develops methods for the exact analysis and representation of the swept volume of a circular cylinder undergoing rational Bézier and B-spline motions. Instead of following the traditional approach of analyzing the point trajectory of an object motion for swept volume analysis, this paper seeks to develop a new approach to swept volume analysis by studying the plane trajectory of a rational motion. It seeks to bring together recent work in swept volume analysis, plane representation of developable surfaces, as well as computer aided synthesis of freeform rational motions. The results have applications in design and approximation of freeforms surfaces as well as tool path planning for 5-axis machining of freeform surfaces.

On the Exact Representation of the Boundary Surfaces of the Swept Volume of a Cylinder Undergoing Rational Be´zier and B-Spline Motions

1999 ◽  
Vol 123 (2) ◽  
pp. 261-265 ◽  
Author(s):  
J. Xia ◽  
Q. J. Ge
Keyword(s):  
Tool Path ◽  
Traditional Approach ◽  
Object Motion ◽  
Exact Representation ◽  
Tool Path Planning ◽  
Freeform Surfaces ◽  
B Spline ◽  
Volume Analysis ◽  
Swept Volume ◽  
Boundary Surfaces

This paper develops methods for the exact analysis and representation of the swept volume of a circular cylinder undergoing rational Be´zier and B-spline motions. Instead of following the traditional approach of analyzing the point trajectory of an object motion for swept volume analysis, this paper develops a new method for swept volume analysis by studying the plane trajectory of a rational motion. It brings together recent work in swept volume analysis, plane representation of developable surfaces, as well as computer aided synthesis of freeform rational motions. The results have applications in design and approximation of freeform surfaces as well as tool path planning for 5-axis machining of freeform surfaces.

A Subdivision Scheme for Discrete Motion Generation and Swept Volume Analysis

2008 ◽  
Author(s):  
Carlos A. Trujillo ◽  
Qiaode Jeffrey Ge
Keyword(s):  
Discrete Model ◽  
Tool Path ◽  
Characteristic Curve ◽  
Boundary Surface ◽  
Subdivision Scheme ◽  
Computationally Efficient ◽  
Motion Generation ◽  
Nc Simulation ◽  
Swept Surface ◽  
Swept Volume

In this paper, the four-point interpolatory subdivision scheme for curve generation is adapted to the interpolation of a set of positions of a cylindrical tool represented by dual quaternions. The resulting discrete model of the tool path lends itself naturally to an algorithm for computing the characteristic curve belonging to the boundary surface of the swept volume of a cylinder at each of the discrete positions. This approach to compute the discrete model of the swept surface of a motion is numerically robust and computationally efficient since it is based only on linear combinations. The results have applications in NC simulation and verification, robot path planning, and computer graphics.

Near-constancy phenomena in branching processes

1991 ◽  
Vol 110 (3) ◽  
pp. 545-558 ◽  
Author(s):  
J. D. Biggins ◽  
N. H. Bingham
Keyword(s):  
Recent Work ◽  
Branching Processes ◽  
New Approach ◽  
Primary Motivation

The occurrence of certain ‘near-constancy phenomena’ in some aspects of the theory of (simple) branching processes forms the background for the work below. The problem arises out of work by Karlin and McGregor [8, 9]. A detailed study of the theoretical and numerical aspects of the Karlin–McGregor near-constancy phenomenon was given by Dubuc[7], and considered further by Bingham[4]. We give a new approach which simplifies and generalizes the results of these authors. The primary motivation for doing this was the recent work of Barlow and Perkins [3], who observed near-constancy in a framework not immediately covered by the results then known.

Kinematically Generated Dual Tensor-Product Surfaces

1998 ◽  
Author(s):  
Q. J. Ge ◽  
D. Kang ◽  
M. Sirchia
Keyword(s):  
Tensor Product ◽  
Geometric Design ◽  
Computer Aided Geometric Design ◽  
Freeform Surfaces ◽  
Computer Aided ◽  
Design And Manufacture ◽  
Two Parameter

Abstract This paper takes advantage of the duality between point and plane geometries and studies a class of tensor-product surfaces that can be generated kinematically as surfaces enveloped by a plane under two-parameter rational Bézier motions. The results of this cross-disciplinary work, between the field of Computer Aided Geometric Design and Kinematics, can be used as a basis for studying geometric and kinematic issues associated with the design and manufacture of freeform surfaces.

An Efficient, Accurate Approach to Representing Cutter-Swept Envelopes and Its Applications to Three-Axis Virtual Milling of Sculptured Surfaces

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Zezhong C. Chen ◽  
Wei Cai
Keyword(s):  
Tool Path ◽  
Basic Mechanism ◽  
Cnc Milling ◽  
Sculptured Surfaces ◽  
Machining Error ◽  
Tool Paths ◽  
Virtual Machining ◽  
Machining Errors ◽  
Computer Numerically Controlled ◽  
Swept Volume

To address a major technical challenge in simulating geometric models of machined sculptured surfaces in three-axis virtual machining, this paper presents an efficient, accurate approach to representing the 3D envelopes of a cutter sweeping sequentially through cutter locations; these envelopes embody the furrow patches of the machined surfaces. In our research, the basic mechanism of removing stock material in three-axis computer numerically controlled (CNC) milling of sculptured surfaces is investigated, and, consequently, an effective model is proposed to represent the 3D envelopes (or furrow patches). Our main contribution is that a new directrix (or swept profile) of the furrow patches (mathematically, ruled surfaces) is identified as a simple 2D envelope of cutting circles and is formulated with a closed-form equation. Therefore, the 3D cutter-swept envelopes can be represented more accurately and quickly than the existing swept-volume methods. With this innovative approach, a method of accurate prediction of the machining errors along tool paths in three-axis finish machining is provided, which is then applied to the optimization of tool-path discretization in two examples. Their results demonstrate the advantages of our approach and verify that the current machining-error-prediction methods can cause gouging in three-axis sculptured surface milling.

Pumping Loss of Shrouded Meshed Spur Gears

2020 ◽  
Vol 142 (11) ◽  
Author(s):  
Michael J. Hurrell ◽  
Jerzy T. Sawicki
Keyword(s):  
High Speed ◽  
Spur Gear ◽  
Test Facility ◽  
Spur Gears ◽  
Cfd Analysis ◽  
Total Load ◽  
New Approach ◽  
Computational Fluid Dynamics Cfd ◽  
Loss Component ◽  
Swept Volume

Abstract High speed rotorcraft transmissions are subject to load-independent power losses consisting of drag loss and pumping loss. Tightly conforming shrouds enclosing the transmission gears are often incorporated to reduce the drag component of the total load-independent losses. However, tightly conforming axial shrouds can result in an increase in the pumping loss component. Quantifying the pumping loss of shrouded gear transmissions has been the subject of many studies. This study presents a new approach for estimating pumping loss based on the concept of swept volume and examines the applicability of the approach to various shroud configurations. The drag loss and pumping loss of a shrouded spur gear pair have been determined through testing using the NASA Glenn Research Center (GRC) Gear Windage Test Facility. The results from this testing have been compared to theoretical results using the formulations presented in this study. In addition, computational fluid dynamics (CFD) analysis has been conducted for the various shroud configurations tested at NASA GRC. The results from the CFD analysis confirm the theoretical and empirical results and provide insight into the applicability of the swept volume approach for estimating pumping power loss of shrouded gear transmissions.

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