Geometric model of a rolling process for multi-wave tubes

2001 ◽  
Vol 215 (5) ◽  
pp. 533-545
Author(s):  
S-C Yang ◽  
C-K Chen
Keyword(s):  
Coordinate Transformation ◽  
Analytical Procedure ◽  
Geometric Model ◽  
Rolling Process ◽  
Numerical Examples ◽  
Cross Rolling ◽  
Potential Applications ◽  
Conjugate Surfaces ◽  
Set Of Points ◽  
Envelope Theory

From a geometric viewpoint, this work considers the process of wavy tubes cross-rolling at the precision rolling section as meshing of a pair of conjugate surfaces. This work applies coordinate transformation and envelope theory to determine the spatial set of points for contacting surfaces that define the roller. The proposed method can be used to derive the roller surfaces for cross-rolling and parallel rolling of wavy tube manufacture. The envelope theory and the analytical procedure for the proposed method are presented. Numerical examples are presented to demonstrate the application of the method developed in this paper. The advantages, limitations and potential applications of cross-rolling are briefly reported.

Edges of Regression and Limit Normal Point of Conjugate Surfaces1

1998 ◽  
Vol 122 (4) ◽  
pp. 419-425 ◽  
Author(s):  
Ningxin Chen
Keyword(s):  
Differential Geometry ◽  
Contact Boundary ◽  
Boundary Line ◽  
Tangent Point ◽  
Common Tangent ◽  
Numerical Examples ◽  
Envelope Surface ◽  
The Common ◽  
Conjugate Surfaces ◽  
Definition Of

The presented paper utilizes the basic theory of the envelope surface in differential geometry to investigate the undercutting line, the contact boundary line and the limit normal point of conjugate surfaces in gearing. It is proved that (1) the edges of regression of the envelope surfaces are the undercutting line and the contact boundary line in theory of gearing respectively, and (2) the limit normal point is the common tangent point of the two edges of regression of the conjugate surfaces. New equations for the undercutting line, the contact boundary line and the limit normal point of the conjugate surfaces are developed based on the definition of the edges of regression. Numerical examples are taken for illustration of the above-mentioned concepts and equations. [S1050-0472(00)00104-5]

Coupled Thermo-Mechanical FEA of Three-Roll Cross Rolling Process for Rings with Small-Hole and Deep Groove

2012 ◽  
Vol 560-561 ◽  
pp. 846-852 ◽  
Author(s):  
Qi Ma ◽  
Lin Hua ◽  
Dong Sheng Qian
Keyword(s):  
Rolling Process ◽  
Small Hole ◽  
Fe Model ◽  
Forming Process ◽  
Software Environment ◽  
Cross Rolling ◽  
Design And Optimization ◽  
Forming Technology ◽  
Deep Groove ◽  
Plastic Forming

Ring parts with small-hole and deep groove such as duplicate gear and double-side flange, are widely used in various engineering machineries. Three-roll cross rolling (TRCR) is a new advanced plastic forming technology for the processing of rings with small-hole and deep groove. In this paper, a 3D coupled thermo-mechanical FE model for TRCR of ring with small-hole and deep groove is established under ABAQUS software environment. By simulation and analysis, the evolution and distribution laws of strain and temperature in the forming process are revealed, and the effects of the key process parameters on the deformation uniformity are explored. The results provide valuable guideline for the technological parameter design and optimization.

Geometric design of a pinion with two circularly arrayed conical teeth for roller drives

2006 ◽  
Vol 220 (9) ◽  
pp. 1405-1412 ◽  
Author(s):  
T-S Lai
Keyword(s):  
Mathematical Model ◽  
Coordinate Transformation ◽  
Geometric Design ◽  
Solid Modelling ◽  
Design Algorithm ◽  
Circular Arrays ◽  
Roller Drive ◽  
New Type ◽  
Design Case ◽  
Envelope Theory

This article presents a mathematical model and geometric design algorithm for a new type of roller drive. The pinion has conical teeth in two circular arrays instead of one. This work is based on coordinate transformation and envelope theory, from which the equation of meshing of the cycloid drive is derived. The pinion profiles are the equidistant curves of the epicycloid profiles except the contour of the pinion conical tooth holes. Although there are twice as many pinion teeth as conventional rollers, their speed ratios are identical. This approach can design roller drives in which the pinion has two circular arrays of conical and cylindrical rollers. On the basis of these results, the corresponding solid modelling is constructed by CAD. Four examples are presented to demonstrate the feasibility of this approach. These examples can be a useful reference as a design case for other tooth profiles.

A Study on Shape Optimization Using Affine Transformation

2001 ◽  
Author(s):  
Satoshi Kitayama ◽  
Hiroshi Yamakawa
Keyword(s):  
Shape Optimization ◽  
Cantilever Beam ◽  
Coordinate Transformation ◽  
Affine Transformation ◽  
Sufficient Conditions ◽  
Optimal Shape ◽  
Design Domain ◽  
Shape Transformation ◽  
Numerical Examples ◽  
Inclined Beam

Abstract This paper presents a new method to determine an optimal shape using affine transformation which is used in the field of Computer Aided Design (CAD), linear programming, and etc. We use affine transformation as coordinate transformation. Affine transformation is a linear transformation, so that shapes transformed must be linearly. Shape optimization of a inclined beam for example, we can deal with in the following manner. We define a simple cantilever beam first in initial design domain, and calculate an optimal shape. Then we use affine transformation remaining with optimal shape calculated in simple design domain and get to an optimal shape of the inclined beam. To compare with an optimal shape obtained by our proposed method, we calculate an optimal shape directly by conventional method in the same design domain after coordinate transformation. We show that affine transformation plays a role as scaling to structural optimization by finite element method and that necessary and sufficient conditions between design variables and shape transformation matrix may exist to get an exact optimal shape. We treat some numerical examples by our proposed method. In numerical examples, we consider shape optimization of inclined cantilever beam for simplicity. We show that some stepwise linear optimal shapes could be expressed from an optimal shape of a simple cantilever beam by using affine transformation. Optimal shape calculated by our method can obtain easily and speedy. Through some numerical examples, we could examine effectiveness of our proposed method.

STUDY OF A SINGLE SCREW COMPRESSOR WITH A CONICAL TEETH GATE ROTOR

2008 ◽  
Vol 32 (3-4) ◽  
pp. 333-352
Author(s):  
Yang Shyue-Cheng ◽  
Tsang-Lang Liang
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Software Package ◽  
Analytical Procedure ◽  
Conjugate Problem ◽  
Screw Compressor ◽  
Main Rotor ◽  
Conjugate Pair ◽  
Single Screw ◽  
Envelope Theory

From a geometric viewpoint, a mathematical model of a single screw compressor with a conjugate pair of meshing conical teeth gate rotor is a conjugate problem. Coordinate transformation and envelope theory are applied to determine the sets of spatial points of the contacting surfaces that define the main rotor of a single screw compressor. Envelope theory and analytical procedure are used to derive mathematical models of a gate rotor and a main rotor. Stress analysis for the single screw compressor mechanism is performed. PowerMILL software package is used to simulate the manufacture of a main rotor. A numerical example with a compressor ratio of 11:6 is presented to demonstrate the application of the mathematical models developed in this paper.

Effect of the Rolling Process on Microstructures and Mechanical Properties of the Extruded LA91 Alloy Sheet

2011 ◽  
Vol 686 ◽  
pp. 90-95 ◽  
Author(s):  
Bin Jiang ◽  
Qing Shan Yang ◽  
Liang Gao ◽  
Fu Sheng Pan
Keyword(s):  
Mechanical Properties ◽  
Microstructure Evolution ◽  
Hot Rolling ◽  
Rolling Process ◽  
Alloy Sheet ◽  
Rolling Reduction ◽  
Thermal Compression ◽  
Cross Rolling ◽  
The Cross ◽  
Rolling Route

The microstructure evolution of the extruded Mg-9Li-1Al (LA91) during rolling was investigated taking account of effects of different routes including hot rolling, and cross rolling. The rolling parameters were suggested by thermal compression testing. As a result, the suggested rolling parameters were 250°C and 1.0s-1. Transverse hot rolling would bring a finer microstructure to the as-rolled LA91 sheet. With the enhancement of the rolling reduction during unidirectional hot rolling the α-Mg phase became granular or short rod-like from long strip-like. Transverse + longitudinal hot rolling would improve the microstructure and was a better cross rolling route by which the strength and the elongation of the cross rolled LA91 sheet reached 243MPa and 20% respectively. The over-aging existed in the cross rolled LA91 sheets.

Finite element simulation of a cross rolling process

2016 ◽  
Vol 24 ◽  
pp. 283-292 ◽  
Author(s):  
Matruprasad Rout ◽  
Surjya K. Pal ◽  
Shiv B. Singh
Keyword(s):  
Finite Element ◽  
Finite Element Simulation ◽  
Rolling Process ◽  
Cross Rolling ◽  
Element Simulation

APPLYING TWO-PARAMETER ENVELOPE THEORY TO DETERMINING SPHERICAL CAM PROFILE WITH CYLINDERICAL FOLLOWERS

2000 ◽  
Vol 24 (2) ◽  
pp. 415-435 ◽  
Author(s):  
Shyue-Cheng Yang ◽  
Cha’o-Kuang Chen
Keyword(s):  
Geometric Model ◽  
Geometric Characteristic ◽  
Parameter Family ◽  
Geometric Models ◽  
Numerical Example ◽  
Pressure Angle ◽  
Cam Profile ◽  
Cutting Path ◽  
Two Parameter ◽  
Envelope Theory

Using the envelope theory of two-parameter family of ball surfaces, two geometric models of spherical cam can be easily obtained when the follower-motion program has been given. The results of the envelope theory are used to determine an optimal spherical cam profile with an oscillating cylindrical follower. Some investigations of geometric characteristic, such as pressure angle and cutting path, are determined using the obtained geometric model. The principle curvatures are analyzed to avoid undercutting. Finally, a numerical example is given to illustrate the application of the procedure.

Motion Representation: Different Conventional Forms, Duplex Mapping and Conjugation Form

1992 ◽  
Author(s):  
Chih-Hsin Chen ◽  
Hong-Jian Chen
Keyword(s):  
Fundamental Equation ◽  
Body Motion ◽  
Surface Generation ◽  
Mobility Analysis ◽  
Vector Form ◽  
Motion Representation ◽  
Orientation Change ◽  
The Matrix ◽  
Potential Applications ◽  
Conjugate Surfaces

Abstract Four fundamental forms for representing rigid body motion, i.e. the rotation-of-vector form, the matrix form, the quaternion form and the screw form, all based on the conventional concept that motion is specified by the movement of a reference point together with an orientation change, are expounded. The inter-relationships among these forms are elucidated. The geometric images of these representation-forms, i.e. the motion mappings, are explained, and an innovative duplex-mapping, a powerful tool for mobility analysis of multi-loop mechanisms and robots, is introduced. An exotic motion representation, based on a concept totally different from the conventional concept, is described. This is a purely geometric representation, a representation by a pair of conjugate curves on respective conjugate surfaces, and is called the conjugation form of motion representation. The conversion from the conjugation form to the rotation-of-vector form and the inverse conversion are described. These conversions, which constitute the essential and featured contents of the Theory of Conjugate Surfaces, have great potential applications in motion design for numerically controlled manufacturing and in surface generation by numerically controlled manufacturing. The basis equations for the conversions, i.e. the three relationship-equations, are deduced. The fundamental equation conjugation, the four conjugato-kinematic entities and the five differential formulas for the inverse conversion are derived.

Development of a Rational Basis for Design of Advanced Brushing Tools

1994 ◽  
Vol 116 (3) ◽  
pp. 308-315 ◽  
Author(s):  
R. J. Stango ◽  
Chih-Yuan Shia ◽  
J. A. Henderson
Keyword(s):  
Service Life ◽  
Product Development ◽  
Iterative Procedure ◽  
General Framework ◽  
Analytical Procedure ◽  
Design Strategy ◽  
Rational Basis ◽  
Numerical Examples ◽  
Performance Requirements ◽  
Mechanics Analysis

In this paper, issues that are relevant to the design of brushing tool systems are examined and discussed. First, a general framework for brush design is presented that can provide a basis for the synthesis of advanced brushing tools, that is, brushes having predetermined performance characteristics and service life. The proposed general design strategy utilizes an iterative procedure that is based upon applicative considerations, performance requirements, and geometric/materials issues that are peculiar to a specific brush system. Next, an analytical procedure is developed that can facilitate the design of brush stiffness and brush compliance properties. This aspect of the design problem is formulated on the basis of nondimensional parameters that are associated with a quasi-static, large-displacement mechanics analysis for brush/workpart interaction. Numerical examples are presented illustrating the use of this approach for the design of brushing tools that possess unique stiffness/compliance functions. Implications that this design capability can have on the development of advanced brushing processes, as well as product development and brush manufacture, are briefly discussed.

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