Generalized Mechanical Equilibrium Condition for Multiphase Contact Lines and Multiphase Contact Points

Langmuir ◽  
2003 ◽  
Vol 19 (11) ◽  
pp. 4658-4665 ◽  
Author(s):  
Mohammad R. Shadnam ◽  
Alidad Amirfazli
Keyword(s):  
Equilibrium Condition ◽  
Mechanical Equilibrium ◽  
Contact Lines ◽  
Contact Points

A Numerical Contour Method for Simulating Spiral Groove Bottom Profiles

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Weifeng Wu ◽  
Shuo Sun ◽  
Quanke Feng
Keyword(s):  
Surface Profile ◽  
Contour Method ◽  
Contact Lines ◽  
Spiral Groove ◽  
Groove Surface ◽  
Contact Points ◽  
Envelope Method ◽  
Twin Screw ◽  
Rotor Profiles ◽  
Boundary Contact

The envelope method can be used to model the spiral groove surface profile in single screw compressors produced by cylindrical milling using the contact lines of the cutter surface and the groove. However, the envelope method cannot predict the groove bottom profile accurately because it does not account for the boundary contact lines on the end face of the cutter. A new numerical contour method is proposed to model the groove bottom profile by identifying the contact points on the end face of the cutter to a set position on the spiral groove. Results show that the new method can calculate accurately both the boundary and the inner contact line and thus simulate the groove bottom profile exactly. This method could also be used to simulate other profiles of machines, such as rotor profiles of twin screw compressors and screw pumps.

Analysis of Force Distribution in Grasps Using Augmentation

1996 ◽  
Vol 210 (1) ◽  
pp. 15-22 ◽  
Author(s):  
J S Dai ◽  
D R Kerr
Keyword(s):  
Rigid Body ◽  
Equilibrium Condition ◽  
Jacobian Matrix ◽  
Point Contact ◽  
Force Distribution ◽  
Mathematical Basis ◽  
New Approach ◽  
Contact Points ◽  
Geometric Compatibility ◽  
Force Equilibrium

A new approach to the analysis of statically indeterminate restraint of a rigid body with any arrangement of point contact is presented in this paper. The paper associates the elasticity at restraint contacts with geometric compatibility of the contact points and constructs elastic compatibility equations, which are complementary to the restraint equations. The equations so obtained are then used to augment the restraint equations and lead to an agumented Jacobian matrix. The new approach enables grasps to be analysed and synthesized in a constraint of combined elasticity and geometric compatibility, in addition to the force equilibrium condition. This gives a mathematical basis for the analysis of force distribution of the statically indeterminate restraint. Detailed reasoning and derivations are given followed by both planar and spatial examples.

scholarly journals A new equation for period vectors of crystals under external stress and temperature in statistical physics: mechanical equilibrium condition and equation of state

2021 ◽  
Vol 136 (1) ◽  
Author(s):  
Gang Liu
Keyword(s):  
Equation Of State ◽  
Equilibrium Condition ◽  
Statistical Physics ◽  
Structural Phase ◽  
External Pressure ◽  
External Stress ◽  
Mechanical Equilibrium ◽  
Dependent Form ◽  
New Equation ◽  
External Forces

AbstractStarting with the rigorous derivation of the work done on the center cell by external forces, a new equation is derived for the period vectors (cell edge vectors) in crystals under external stress and temperature. Since the equation is based on the principles of statistical physics, it applies to both classical and quantum systems. The existing theory for crystals under external pressure is covered as a special case. The new equation turns out to be the mechanical equilibrium condition and the equation of state for crystals under external stress and temperature. It may be used to predict crystal structures and to study structural phase transitions and crystal expansions. For linear elastic crystals, it takes the microscopic and temperature-dependent form of the generalized Hooke’s law, and may therefore be used to calculate the corresponding elastic constants. It should be helpful in studying piezoelectric and piezomagnetic materials, as the period vectors change with external stress. It is also consistent and can be combined with the previously derived corresponding one for Newtonian dynamics.

Tooth Contact and 3-D Stress Analysis of Involute Helical Gears

1992 ◽  
Author(s):  
M. A. Sahir Arikan ◽  
Mustafa Tamar
Keyword(s):  
Stress Analysis ◽  
Gear Tooth ◽  
Contact Point ◽  
Helical Gear ◽  
Contact Analysis ◽  
Contact Lines ◽  
Coordinate Systems ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Contact Points

Abstract An involute helical gear tooth is modelled by using helical gear geometry and a solid modelling package, and this model is used to determine the load distribution on contact lines of mating teeth, and to make the stress analysis by using three-dimensional tetrahedron finite elements with four nodes. Tooth contact analysis is made by using the theory of gearing. Geometry of the cutting tool is used to determine the surface equations of the pinion and the gear in their own coordinate systems, then these equations are transformed to a fixed coordinate system to make the tooth contact analysis and to find the coordinates of contact points. Found contact point coordinates are then transformed back to the original coordinate systems and contact lines on helical gear teeth are formed. Results of this analysis is used to determine the application points and directions of the forces acting on the tooth. Then the stiffnesses of meshing teeth and the load distributions on contact lines are found, which are then used for stress analysis.

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