Load Distribution of Parallel Springs With Random Length and Stiffness

1987 ◽  
Vol 109 (4) ◽  
pp. 402-406 ◽  
Author(s):  
Go¨ran Gerbert ◽  
Jacques de Mare´
Keyword(s):  
Uniform Distribution ◽  
Load Distribution ◽  
Simple Formula ◽  
Mechanical Design ◽  
Numerical Results ◽  
Maximal Length ◽  
Major Influence ◽  
Length Variation ◽  
Spring Stiffness ◽  
Failure Risk

There are many applications in mechanical design where load distribution is modelled with parallel springs. Here random variation in spring length and spring stiffness is considered. Length variation is assumed to be the major influence and the case with uniform distribution is analyzed in detail. Small variations in spring stiffness are included. Numerical results are given. A simple formula is presented which gives the maximal length deviation as a function of the number of springs. The formula is based on a 10 percent failure risk which is a common number in practical mechanical design.

The Approximate Calculation of Eigenvalues for Certain Second-Order Linear Differential Equations

1961 ◽  
Vol 65 (605) ◽  
pp. 360-360 ◽  
Author(s):  
W. J. Goodey
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Simple Formula ◽  
Approximate Calculation ◽  
Technical Note ◽  
Second Order ◽  
Numerical Results ◽  
Linear Differential Equations ◽  
Order Linear ◽  
Linear Differential

In a recent technical note, Squire discussed the approximate solution of certain second-order linear differential equations by the method attributed variously to Riccati, Madelung, Wentzel, Kramers and Brillouin (the W.K.B. method), and others. The problem of eigenvalues, frequently met with in this type of equation, does not, however, appear to have received much attention by this method, and in this note a simple formula is developed which appears to give excellent numerical results in many cases.

The Transition to Perfect Generalization in Perceptrons

1991 ◽  
Vol 3 (3) ◽  
pp. 386-401 ◽  
Author(s):  
Eric B. Baum ◽  
Yuh-Dauh Lyuu
Keyword(s):  
Uniform Distribution ◽  
Statistical Physics ◽  
Numerical Results ◽  
Rigorous Proof

Several recent papers (Gardner and Derrida 1989; Györgyi 1990; Sompolinsky et al. 1990) have found, using methods of statistical physics, that a transition to perfect generalization occurs in training a simple perceptron whose weights can only take values ±1. We give a rigorous proof of such a phenomena. That is, we show, for α = 2.0821, that if at least αn examples are drawn from the uniform distribution on {+1, −1}n and classified according to a target perceptron wt ∈ {+1, −1}n as positive or negative according to whether wt·x is nonnegative or negative, then the probability is 2−(√n) that there is any other such perceptron consistent with the examples. Numerical results indicate further that perfect generalization holds for α as low as 1.5.

scholarly journals An analytical model to determine the impact force of drone strikes

2021 ◽  
Author(s):  
Florian Franke ◽  
Michael Schwab ◽  
Uli Burger ◽  
Christian Hühne
Keyword(s):  
Load Distribution ◽  
Impact Force ◽  
Analytical Calculation ◽  
Calculation Model ◽  
Material Behavior ◽  
Major Influence ◽  
Impact Model ◽  
Simulation Data ◽  
Input Parameters ◽  
The Impact

AbstractIn addition to the well-known threats of bird and hail strikes, small unmanned aerial vehicles (sUAV) pose a new threat to manned aviation. Determining the severity of collisions between sUAVs and aircraft structures is essential for the safe use and integration of drones in airspace. A generic analytical calculation model needs to be developed to supplement the existing test and simulation data. This paper presents an analytic model for drone collisions with perpendicular and inclined targets. The targets have a rigid or elastic material behavior. The aircraft impact model, which is used for the design of nuclear reactor structures, is transferred and adjusted for sUAV impacts to calculate the impact force. A mass- and a burst load distribution are needed as input parameters. Both distributions are determined for an sUAV design depending on the flight direction. Compared to previous calculations, the new approach is to consider a moving target structure, which produces more realistic results. We compare the calculation results with simulation data from sUAV collisions with a commercial airliner windshield from the literature. The calculations show plausible results and a good agreement with literature data. Subsequently, the influence of the input parameters on the impact force is investigated. We see that spring stiffness, target mass, burst load distribution and damping have minor influence on the overall impact force. The impact velocity, mass distribution and flight orientation on the other hand have a major influence on the impact force. Further tests are needed to validate the impact model.

Cross Orthogonality Between Eigenfunctions and Conjugate Eigenfunctions of a Class of Modified Helmholtz Operator for Pekeris Waveguide

2019 ◽  
Vol 27 (02) ◽  
pp. 1850048 ◽  
Author(s):  
Jianxin Zhu ◽  
Ying Zhang
Keyword(s):  
Bounded Domain ◽  
Simple Formula ◽  
Perfectly Matched Layer ◽  
Numerical Results ◽  
The Other ◽  
Helmholtz Operator ◽  
Other Hand ◽  
Pekeris Waveguide ◽  
The Cross ◽  
Local Base

The eigenfunctions of the modified Helmholtz operator have no orthogonality in a bounded domain with a perfectly matched layer (PML), which makes it difficult to calculate the coordinates under two different local bases when the marching algorithm is applied. In this paper, we derive the conjugate eigenfunctions of the operator and discuss the cross orthogonality between the eigenfunctions and their conjugate eigenfunctions. On the other hand, we derive a simple formula for calculating the coordinates under the local base. The numerical results indicate that this method is effective.

Novel Formulation of Bolt Elastic Interaction in Gasketed Joints

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
Sayed A. Nassar ◽  
Xianjie Yang
Keyword(s):  
Modulus Of Elasticity ◽  
Load Distribution ◽  
Test Procedure ◽  
Interaction Model ◽  
Elastic Interaction ◽  
Numerical Results ◽  
Experimental Results ◽  
Experimental Setup ◽  
Initial Assembly

Novel formulation was proposed for studying bolt elastic interaction during the tightening of a group of fasteners in flat faced gasketed joints. The model was used for developing tightening strategies that would achieve a more uniform clamp load in the flange at initial assembly. Clamp load distribution is investigated for various tightening sequences and values for the gasket modulus of elasticity, gasket thickness, and grip length. An experimental setup and test procedure were developed to verify the numerical results produced by the elastic interaction model. Analytical and experimental results were presented and discussed.

scholarly journals A Study of the Stress-Strain State of the Planetary Carrier Cheek

2019 ◽  
pp. 3-9
Author(s):  
F.I. Plekhanov ◽  
E.F. Vychuzhanina
Keyword(s):  
Bearing Capacity ◽  
Uniform Distribution ◽  
Load Distribution ◽  
Strain State ◽  
Load Capacity ◽  
Planetary Gear ◽  
Planetary Gears ◽  
Manufacturing Errors ◽  
Coupling Zone ◽  
Positive Effect

Planetary gears are commonly used in drive technology due to their high load capacity and good weight and size parameters. Among planetary gears, multi-satellite structures with a minimum number of excessive links are most widely used. They have a close to uniform distribution of the load in the engaged gears, which has a positive effect on the strength and bearing capacity of the drive. Such designs include planetary gears, the satellites of which are mounted on spherical bearings, and one of the main links (most often the sun gear) is self-aligning. This provides a theoretically uniform distribution of the load in the engaged gears when the mechanism has three satellites. However, high-loaded drives often use designs with a large number of satellites where the load is distributed unevenly due to gear manufacturing errors. The deformability of individual transmission elements has a significant positive effect on the distribution of the load in the gears, thus compensating for the manufacturing errors. In view of this, the authors propose a multi-satellite planetary gear with a carrier made with grooves in the cheeks, which reduces their rigidity and provides, with a rational choice of the parameters of the mechanism, an increase in the mechanism’s bearing capacity. When determining the carrier cheek’s compliance, two schemes of loading in the coupling zone with the axis of the satellite (uniform and nonuniform) are considered. The solution is obtained using Mohr’s integrals. A numerical analysis of the stressed-strain state of the carrier cheek performed using the finite element method in the SolidWorks environment showed that the results of the analysis were close to the theoretical ones. They corresponded to a uniform load distribution in the coupling zone of the satellite axis and the carrier cheek. The obtained dependences can be used in the design of a mechanical drive to determine the coefficients of the uneven load distribution over the planetary gear satellites and over the individual crowns of the satellite.

Propeller-Incidence Correction Due to Blade Thickness

1963 ◽  
Vol 7 (04) ◽  
pp. 1-6
Author(s):  
J. E. Kerwin ◽  
R. Leopold
Keyword(s):  
Load Distribution ◽  
Practical Importance ◽  
Numerical Results ◽  
Surface Theory ◽  
Lifting Surface ◽  
Blade Thickness

It is shown that the presence of finite blade thickness results in a disturbance velocity normal to the blades which is in addition to that predicted by lifting-surface theory. The results show that as blade thickness is increased, an incidence correction must be applied in order to maintain the same load distribution. Numerical results indicate that the correction is small at the tip and increases towards the root of the blades. Its magnitude is sufficient to be of practical importance in design.

A Survey of Optimization of Mechanical Design

1972 ◽  
Vol 94 (2) ◽  
pp. 495-499 ◽  
Author(s):  
A. Seireg
Keyword(s):  
Dynamic Systems ◽  
Load Distribution ◽  
Mechanical Design ◽  
Pressure Vessels ◽  
Optimization Techniques ◽  
Longitudinal Impact ◽  
Elastic Contact ◽  
Rotating Discs ◽  
Mechanical Elements

This paper presents a review of some illustrative examples of the use of optimization techniques in the design of mechanical elements and systems. The cases cited include gears, bearings, dynamic systems, rotating discs, pressure vessels, shafts under bending and torsion, beams subjected to longitudinal impact, and problems of elastic contact and load distribution.

scholarly journals Energetic Consequences of Series and Parallel Springs in Lower-Extremity Powered Prostheses

2019 ◽  
Author(s):  
Matt Carney ◽  
Hugh Herr
Keyword(s):  
Lower Extremity ◽  
Mechanical Design ◽  
Minimum Energy ◽  
Optimization Procedure ◽  
Spring Stiffness ◽  
Cost Of Transport ◽  
Stair Ascent ◽  
Trade Offs ◽  
Negative Effect ◽  
System Equations

We present electric energetic consequences for mechanical design trade-offs in lower-extremity powered prostheses. There are four main hardware components commonly implemented in these devices that can be tuned to achieve desired performance: motor, reduction ratio N, series spring stiffness Ks, and parallel spring stiffness Kp. The allowed joint range of motion is a fifth parameter that can also drastically change energy consumption. We apply a kinematically clamped analysis to the system equations to map the electric cost of transport (COT) for knee and ankle level-ground walking, in addition to ankle stair ascent and descent. We also utilize an optimization procedure to identify minimum energy hardware configurations. The energy map provides insight into consequences of variance from optimal parameters. Our results support the contribution of the series elastic element for improved power output. Parallel stiffness can provide up to 8% improvements in walking with minimal negative effect with varied terrain, and a varying ankle transmission ratio can similarly improve COT by 8% from level-ground to stair ascent. Limited dorsiflexion can further improve COT by 30%. These observations can provide the designer clarity to how design decisions modulate hardware performance.

Unmanned Ground Vehicle Energy Efficiency Validation in Territory Surveillance Mission

2016 ◽  
Vol 251 ◽  
pp. 164-170
Author(s):  
Eero Väljaots ◽  
Raivo Sell ◽  
Marius Rimasauskas
Keyword(s):  
Energy Efficiency ◽  
Mechanical Design ◽  
Major Influence ◽  
Vehicle Design ◽  
Test Case ◽  
Environment Interaction ◽  
Unmanned Ground Vehicle ◽  
Design Validation ◽  
Ground Vehicle ◽  
And Control

This paper describes test case of an energy efficiency validation method. Test case is selected as surveillance mission which is simple and common case for universal unmanned ground vehicle where environment dynamics has major influence. The prototype UGV platform is equipped with combined measurement system providing data about dynamic parameters of platform physical movement as well as real-time energy consumption. Platform energy efficiency is evaluated on several stages, enabling to evaluate both mechanical design and control system algorithms. In addition, environment interaction with the vehicle is measured also for analyzing the vehicle limitations and scope of use. Real-condition missions are used for vehicle design validation purposes.

Sign in / Sign up

Export Citation Format

Share Document