Consistent Derivations of Spring Rates for Helical Springs

2009 ◽  
Vol 131 (7) ◽  
Author(s):  
Clive L. Dym
Keyword(s):  
Potential Energy ◽  
Total Potential Energy ◽  
Helical Spring ◽  
Helical Springs ◽  
Total Potential ◽  
Coiled Spring ◽  
Displacement Based ◽  
Minimum Total Potential Energy ◽  
First Time ◽  
Consistent Application

The spring rates of a coiled helical spring under an axial force and an axially directed torque are derived by a consistent application of Castigliano’s second theorem, and it is shown that the coupling between the two loads may not always be neglected. The spring rate of an extensional spring is derived for the first time through the use of the displacement based principle of minimum total potential energy. The present results are also compared with available derivations of and expressions for the stiffness of a coiled spring.

scholarly journals Three-Point Bending of Seven Layer Beams – Theoretical and Experimental Studies

2016 ◽  
Vol 62 (2) ◽  
pp. 115-133 ◽  
Author(s):  
E. Magnucka-Blandzi ◽  
P. Paczos ◽  
P. Wasilewicz ◽  
A. Wypych
Keyword(s):  
Potential Energy ◽  
Experimental Studies ◽  
Middle Surface ◽  
Total Potential Energy ◽  
Three Point Bending ◽  
Simply Supported ◽  
Total Potential ◽  
The Subject ◽  
Minimum Total Potential Energy

Abstract The subject of the analytical and experimental studies therein is of two metal seven-layer beam - plate bands. The first beam - plate band is composed of a lengthwise trapezoidally corrugated main core and two crosswise trapezoidally corrugated cores of faces. The second beam - plate band is composed of a crosswise trapezoidally corrugated main core and two lengthwise trapezoidally corrugated cores of faces. The hypotheses of deformation of a normal to the middle surface of the beams after bending are formulated. Equations of equilibrium are derived based on the theorem of minimum total potential energy. Three-point bending of the simply supported beams is theoretically and experimentally studied. The deflections of the two beams are determined with two methods, compared and presented.

A simplified formulation of adhesion problems with elastic plates

2009 ◽  
Vol 465 (2107) ◽  
pp. 2217-2230 ◽  
Author(s):  
Carmel Majidi ◽  
George G. Adams
Keyword(s):  
Potential Energy ◽  
Contact Area ◽  
Contact Region ◽  
Bending Moment ◽  
Total Potential Energy ◽  
Work Of Adhesion ◽  
Contact Radius ◽  
Algebraic Complexity ◽  
Elastic Plates ◽  
Total Potential

The solution of adhesion problems with elastic plates generally involves solving a boundary-value problem with an assumed contact area. The contact region is then found by minimizing the total potential energy with respect to the contact area (i.e. the contact radius for the axisymmetric case). Such a procedure can be extremely long and tedious. Here, we show that the inclusion of adhesion is equivalent to specifying a discontinuous internal bending moment at the contact region boundary. The magnitude of this moment discontinuity is related to the work of adhesion and flexural rigidity of the plate. Such a formulation can greatly reduce the algebraic complexity of solving these problems. It is noted that the related plate contact problems without adhesion can also be solved by minimizing the total potential energy. However, it has long been recognized that it is mathematically more efficient to find the contact area by specifying a continuous internal bending moment at the boundary of the contact region. Thus, our moment discontinuity method can be considered to be a generalization of that procedure which is applicable for problems with adhesion.

An Optimization Method for the Static Balancing of Manipulators Using Springs

2020 ◽  
Author(s):  
Jieyu Wang ◽  
Xianwen Kong
Keyword(s):  
Potential Energy ◽  
Objective Function ◽  
Multiple Solutions ◽  
Optimization Method ◽  
Total Potential Energy ◽  
Static Balancing ◽  
Attachment Point ◽  
Total Potential

Abstract This paper discusses a novel optimization method to design statically balanced manipulators. Only springs are used to balance the manipulators composed of revolute (R) joints. Since the total potential energy of the system is constant when statically balanced, the sum of squared differences between the two potential energy when giving different random values of joint variables is set as the objective function. Then the optimization tool of MATLAB is used to obtain the spring attachment points. The results show that for a 1-link manipulator mounted on an R joint, in addition to attaching the spring right above the R joint, the attachment point can have offset. It also indicates that an arbitrary spatial manipulator with n link, whose weight cannot be neglected, can be balanced using n springs. Using this method, the static balancing can be readily achieved, with multiple solutions.

Automatic Refinement of FE Shell Models Based on a Local Energy Function

2013 ◽  
Author(s):  
Antonio Carminelli ◽  
Giuseppe Catania
Keyword(s):  
Potential Energy ◽  
Local Density ◽  
Free Vibration Analysis ◽  
Element Model ◽  
Companion Paper ◽  
Total Potential Energy ◽  
Shape Functions ◽  
Total Potential ◽  
Error Functional ◽  
Local Patch

This paper deals with an adaptive refinement technique of a B-spline degenerate shell finite element model, for the free vibration analysis of curved thin and moderately thick-walled structures. The automatic refinement of the solution is based on an error functional related to the density of the total potential energy. The model refinement is generated by locally increasing, in a sub-domain R of a local patch domain, the number of shape functions while maintaining constant the functions polynomial order. The local refinement strategy is described in a companion paper, written by the same authors of this paper and presented in this Conference. A two-step iterative procedure is proposed. In the first step, one or more sub domains to be refined are identified by means of a point-wise error functional based on the system total potential energy local density. In the second step, the number of shape functions to be added is iteratively increased until the difference of the total potential energy, calculated on the sub domain between two iteration, is below a user defined tolerance. A numerical example is presented in order to test the proposed approach. Strengths and limits of the approach are critically discussed.

First-Principles Study on Crystal Configuration and Many-Body Cohesive Energy of Solid Argon

2019 ◽  
Vol 807 ◽  
pp. 135-140
Author(s):  
Xi Jin Fu
Keyword(s):  
Potential Energy ◽  
Interaction Energy ◽  
First Principles ◽  
Total Potential Energy ◽  
Basis Set ◽  
Many Body ◽  
Body Interaction ◽  
Total Potential ◽  
Geometric Configurations ◽  
Solid Argon

Based on the first-principles, using CCSD(T) ab initio calculation method, many-body potential energy of solid argon are accurately calculated with the atomic distance R from 2.0Å to 3.6Å at T=300K, and firstly establish and discuss the face-centered cubic (fcc) atomic crystal configurations of two-, three-, and four-body terms by geometry optimization. The results shows that the total number of (Ar)2 clusters is 903, which belongs to 12 different geometric configurations, the total number of (Ar)3 clusters is 861, which belongs to 25 different geometric configurations, and the total number of (Ar)4 clusters of is 816 which belongs to 27 different geometric configurations. We find that the CCSD(T) with the aug-cc-pVQZ basis set is most accurate and practical by comprehensive consideration. The total potential energy Un reachs saturation at R>2.0Å when the only two-and three-body interaction energy are considered. When R≤2.0Å, the total potential energy Un must consider four-and higher-body interaction energy to achieve saturation. Many-body expansion potential of fcc solid argon is an exchange convergent series.

Energy-free adjustment of gravity equilibrators by adjusting the spring stiffness

2008 ◽  
Vol 222 (9) ◽  
pp. 1839-1846 ◽  
Author(s):  
W D van Dorsser ◽  
R Barents ◽  
B M Wisse ◽  
M Schenk ◽  
J L Herder
Keyword(s):  
Potential Energy ◽  
Total Potential Energy ◽  
Spring Stiffness ◽  
External Energy ◽  
Static Balancing ◽  
Concept Model ◽  
Total Potential ◽  
Novel Variant ◽  
Energy Conserving

Static balancing is a useful concept to reduce the operating effort of mechanisms. Spring mechanisms are used to achieve a constant total potential energy, thus eliminating any preferred position. Quasi-statically, the mechanism, once statically balanced, can be moved virtually without the operating energy. In some cases, it is desirable to adjust the characteristic of the balancer, for instance, due to a change in the payload in a gravity balanced mechanism. The adjustment of current static balancers requires significant operating energy. This paper will present a novel variant to adjust the spring- and linkage-based static balancers without the need for external energy. The variant makes use of the possibility to adjust the spring stiffness in an energy-conserving way by adjusting the number of active coils. The conditions under which it functions properly will be given, and a proof of the concept model will be shown.

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