Effects of Belt Flexural Rigidity on the Transmission Error of a Carriage-driving System

2000 ◽  
Vol 122 (2) ◽  
pp. 213-218 ◽  
Author(s):  
Hung-Ming Tai ◽  
Cheng-Kuo Sung
Keyword(s):  
Boundary Conditions ◽  
Numerical Method ◽  
Experimental Technique ◽  
Moving Boundary ◽  
Flexural Rigidity ◽  
Three Dimensional ◽  
Transmission Error ◽  
Beam Model ◽  
Driving System ◽  
The Relationship

This paper investigates the effects of belt flexural rigidity and belt tension on transmission error of a carriage-driving system. The beam model associated with both the clamped and moving boundary conditions at two ends is utilized to derive the governing equation of the belt. The belt flexural rigidity is obtained and verified by an experimental technique. In addition, a numerical method is proposed to determine the belt profile, transmission error and transmission stiffness. Results show that transmission error of a carriage-driving system increases when the carriage moves away from the driving pulley due to finite belt flexural rigidity. According to the analyses, application of appropriate tension on the belt can significantly reduce the error. Furthermore, the transmission stiffness for representing the entire rigidity between the carriage and pulley is investigated based on the proposed beam model. A three-dimensional plot that indicates the relationship among the transmission stiffness, belt tension and the position of the carriage is obtained. [S1050-0472(00)01102-8]

Effects of Belt Flexural Rigidity on the Transmission Error of a Carriage-Driving System

2000 ◽  
Author(s):  
Hung-Ming Tai ◽  
Cheng-Kuo Sung
Keyword(s):  
Boundary Conditions ◽  
Numerical Method ◽  
Experimental Technique ◽  
Moving Boundary ◽  
Flexural Rigidity ◽  
Three Dimensional ◽  
Transmission Error ◽  
Beam Model ◽  
Driving System ◽  
The Relationship

Abstract This paper investigates the effects of belt flexural rigidity and belt tension on transmission error of a carriage-driving system. The beam model associated with both the clamped and moving boundary conditions at two ends is utilized to derive the governing equation of the belt. The belt flexural rigidity is obtained and verified by an experimental technique. In addition, a numerical method is proposed to determine the belt profile, transmission error and transmission stiffness. Results show that transmission error of a carriage-driving system increases when the carriage moves away from the driving pulley due to finite belt flexural rigidity. According to the analyses, application of appropriate tension on the belt can significantly reduce the error. Furthermore, the transmission stiffness for representing the entire rigidity between the carriage and pulley is investigated based on the proposed beam model. A three-dimensional plot that indicates the relationship among the transmission stiffness, belt tension and the position of the carriage is obtained.

On the Correlation Between Dynamic Transmission Error and Dynamic Tooth Loads in Three-Dimensional Gear Systems

2015 ◽  
Author(s):  
Nina Sainte-Marie ◽  
Philippe Velex ◽  
Guillaume Roulois ◽  
Franck Marrot
Keyword(s):  
Experimental Evidence ◽  
Three Dimensional ◽  
Transmission Error ◽  
Test Rig ◽  
Transmission Errors ◽  
Linear Dependency ◽  
Lumped Parameter ◽  
Dynamic Transmission Error ◽  
Time Variations ◽  
The Relationship

A three-dimensional dynamic model is presented to simulate the dynamic behavior of single stage gears by using a combination of classic shaft, lumped parameter and specific 2-node gear elements. The mesh excitation formulation is based on transmission errors whose mathematical grounding is briefly described. The validity of the proposed methodology is assessed by comparison with experimental evidence from a test rig. The model is then employed to analyze the relationship between dynamic transmission errors and dynamic tooth loads or root stresses. It is shown that a linear dependency can be observed between the time variations of dynamic transmission error and tooth loading as long as the system can be assimilated to a torsional system but that this linear relationship tends to disappear when the influence of bending cannot be neglected.

A Three-Dimensional Numerical Method for Turbomachinery Blading

1992 ◽  
Author(s):  
C. W. Gu ◽  
J. Z. Xu ◽  
J. Y. Du
Keyword(s):  
Boundary Conditions ◽  
Numerical Method ◽  
Stream Function ◽  
Three Dimensional ◽  
Computational Results ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Stream Functions ◽  
Derivatives Of ◽  
Convergent Solution

By inversing one of the stream functions and their principal equations in a three–dimensional flow the equations with the second–order partial derivatives of both the coordinate and another stream function are derived. The corresponding boundary conditions are easily specified. Based on these equations and the boundary conditions the convergent solution for turbomachinery blading is obtained. The computational results show that the method is simple and effective.

A Study on the Correlation Between Dynamic Transmission Error and Dynamic Tooth Loads in Spur and Helical Gears

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
N. Sainte-Marie ◽  
P. Velex ◽  
G. Roulois ◽  
J. Caillet
Keyword(s):  
Experimental Evidence ◽  
Three Dimensional ◽  
Transmission Error ◽  
System Behavior ◽  
Helical Gears ◽  
Transmission Errors ◽  
Linear Dependency ◽  
Lumped Parameter ◽  
Excitation Model ◽  
The Relationship

A three-dimensional (3D) dynamic gear model is presented which combines classic shaft, lumped parameter, and specific two-node gear elements. The mesh excitation model is based on transmission errors (TEs), and its mathematical grounding is briefly described. The validity of the proposed methodology is assessed for both spur and helical gears by comparison with experimental evidence. The model is then employed to analyze the relationship between dynamic transmission errors (DTE) and dynamic tooth loads (DF) or root stresses. It is shown that a linear dependency can be found as long as the system behavior is dominated by shaft torsion but that this linear relationship tends to disappear when bending cannot be neglected.

Self-similar elastic regime of filtration through moving boundary

2018 ◽  
Vol 13 (3) ◽  
pp. 64-72 ◽  
Author(s):  
S.V. Khabirov ◽  
S.S. Khabirov
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Boundary Problem ◽  
Moving Boundary ◽  
Dimensional Problem ◽  
One Dimensional ◽  
Elastic Regime ◽  
Self Similar ◽  
The One ◽  
The Relationship

The one-dimensional problem of elastic filtration of fluid through moving boundary is considered. The boundary conditions for invariant problem is introduced. The problem is reduced to overdetermine boundary problem for Veber equation. The exact solutions are obtained. For arbitrary invariant filtration law the relationship between overdetermine invariant boundary conditions is obtained.

Process Modeling: Lost-Foam Pattern Filling

2004 ◽  
Author(s):  
Peter J. Blaser ◽  
Dale M. Snider ◽  
Ken A. Williams ◽  
Alan E. Cook ◽  
Mark Hoover
Keyword(s):  
Boundary Conditions ◽  
Numerical Method ◽  
Phase Particle ◽  
Three Dimensional ◽  
Video Data ◽  
Particle In Cell ◽  
Polystyrene Beads ◽  
Multi Phase ◽  
Foam Pattern ◽  
Lost Foam

A transient, three-dimensional, multi-phase particle-in-cell approach is used to solve for the flow of polystyrene beads in complex three dimensional geometries which represent patterns used for lost-foam casting. The numerical method solves the gas conservation equations on an Eulerian grid and the motion of polystyrene beads is calculated in a Lagrangian frame of reference. The true particle size distribution is modeled, and the particle flow ranges from dilute to close-pack. Predicted fill behavior is compared to experimentally blown patterns using colored beads and to the measured transient filling of a pattern. The colored beads show a complex fill pattern which is calculated well by the numerical method. The transient calculation compares very well with measured video data, and the particle motion has unique particle behavior unlike a fluid. Because of uncertainties in boundary conditions in production lost-foam tooling, the sensitivity of lost-foam pattern filling to boundary conditions is examined.

scholarly journals Transonic Blade to Blade Calculations in an Axial, Radial or Mixed Flow Cascade Equipped With Splitter Blades

1985 ◽  
Author(s):  
Fernand Bertheau ◽  
Yves Ribaud ◽  
Valérie Millour
Keyword(s):  
Boundary Conditions ◽  
Numerical Method ◽  
Euler Equations ◽  
Three Dimensional ◽  
Computation Time ◽  
Leading Edge ◽  
Computer Code ◽  
Mixed Flow ◽  
Three Dimensional Flow ◽  
General Computer

A general computer code for pseudo-unsteady Euler equations integration in turbomachinery cascades has been developed. A quasi-three-dimensional flow hypothesis is assumed and only blade to blade calculation is considered here. Cascades may be axial, radial or mixed flow type. First the computerized quasi-orthogonal network is shown. This network takes into account splitters and is designed to reduce the computation time. Then, the numerical method is described and the major difficulties of this problem, which are boundary conditions, leading edge and trailing edge treatments, are presented. Finally, examples of calculations on turbines and compressors are given with emphasis on graphic representation.

scholarly journals A Numerical Procedure of Three-Dimensional Design Problem in Turbomachinery

1991 ◽  
Author(s):  
J. Z. Xu ◽  
C. W. Gu
Keyword(s):  
Mach Number ◽  
Boundary Conditions ◽  
Velocity Distribution ◽  
Numerical Method ◽  
Design Problem ◽  
Present Method ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Function Formulation ◽  
Mach Number Distribution

A numerical method for solving the three–dimensional aerothermodynamic design problem with some type of the Mach number distributions on the blade surfaces is presented. In the usual aerothermodynamic design of a turbomachinery the three–dimensional coordinates of the blade is attained through the stacking of the cascade profiles and may not ensure the desired velocity distribution. To avoid this problem the present method will give new coordinates of the blade according to the required Mach number distribution. The method is based on the pseudostream function formulation and the treatment of the boundary conditions in the design problem is given. The numerical results show that the method is simple and useful in design.

A Numerical Procedure of Three-Dimensional Design Problem in Turbomachinery

1992 ◽  
Vol 114 (3) ◽  
pp. 548-552 ◽  
Author(s):  
J. Z. Xu ◽  
C. W. Gu
Keyword(s):  
Mach Number ◽  
Boundary Conditions ◽  
Velocity Distribution ◽  
Numerical Method ◽  
Design Problem ◽  
Present Method ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Function Formulation ◽  
Mach Number Distribution

A numerical method for solving the three-dimensional aerothermodynamic design problem with some type of Mach number distributions on the blade surfaces is presented. In the usual aerothermodynamic design of a turbomachine, the three-dimensional coordinates of the blade are attained through stacking of the cascade profiles and may not ensure the desired velocity distribution. To avoid this problem, the present method will give new coordinates of the blade according to the required Mach number distribution. The method is based on the pseudostream function formulation and the treatment of the boundary conditions in the design problem is given. The numerical results show that the method is simple and useful in design.

scholarly journals Substructural Identification of Flexural Rigidity for Beam-Like Structures

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Ki-Young Koo ◽  
Jin-Hak Yi
Keyword(s):  
Boundary Conditions ◽  
Flexural Rigidity ◽  
Beam Theory ◽  
Beam Model ◽  
Single Variable ◽  
Euler Beam ◽  
Identification Method ◽  
Bridge Model ◽  
Euler Beam Theory ◽  
Girder Bridge

This study proposes a novel substructural identification method based on the Bernoulli-Euler beam theory with a single variable optimization scheme to estimate the flexural rigidity of a beam-like structure such as a bridge deck, which is one of the major structural integrity indices of a structure. In ordinary bridges, the boundary condition of a superstructure can be significantly altered by aging and environmental variations, and the actual boundary conditions are generally unknown or difficult to be estimated correctly. To efficiently bypass the problems related to boundary conditions, a substructural identification method is proposed to evaluate the flexural rigidity regardless of the actual boundary conditions by isolating an identification region within the internal substructure. The proposed method is very simple and effective as it utilizes the single variable optimization based on the transfer function formulated utilizing Bernoulli Euler beam theory for the inverse analysis to obtain the flexural rigidity. This novel method is also rigorously investigated by applying it for estimating the flexural rigidity of a simply supported beam model with different boundary conditions, a concrete plate-girder bridge model with different length of an internal substructure, a cantilever-type wind turbine tower structure with different type of excitation, and a steel box-girder bridge model with internal structural damages.

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