Twist Analisys of “Not Standard Sections”

August 15, 2009 by Luigi Giaccari · Leave a Comment
Filed under: FEM 
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Torsional Analisys
Purpose of this program is studying a not standard section subject to torsional stress. Not standard means the section is not included in engineering Handbooks. It can be studied with FEM analysis with commercial softwares, but sometimes this can become very rough.
Fortunatly Prandtl theory of membrane analogy comes to help, here a simple fem solution with linear triangular element is provided.Given a meshed geometry, it computes the shear stress distribution and stifness using Prandtl membrane analogy. As all fem programs, to give accurate
results, it needs a denser mesh were stress are supposed to have greater gradient and value.

This is a linear analysis effective for small displacements problems with homogeneous isotropic materials.
The tangential elastic modulus will be computed as G=E/(2*(1+poisson));
Note that there is no need of torque value, because of the linearity hipothesis, stresses,rotations and torque are univocally determined once only one of them is known.

Stiffnes modulus is calculeted in Nm/rad, this means is the rotation(rad) provoked by a 1Nm torque to a 1m length bar of the given section.

Inputs:

  • p : Nx2 array of nodes coordinates, [x1,y1; x2,y2; etc]
    IMPORTANT: computation have been made using millimeters!
  • t : Mx3 array of triangles as indices, [n11,n12,n13; n21,n22,n23; etc]
  • E : Elastic modulus of material
  • poisson : poisson ratio of material

Outputs: A grafical rapresentations of:

  • Shear stress
  • Membrane Analogy
  • Stres/torque relationship
  • Tau Flow

The call is:

TorsionFem(p,t,E,poisson)

so it is just necessary to have mesh and materials data.

For bugs, questions, suggestions just contact me at:

giaccariluigi@msn.com

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Basic Gear Design

August 13, 2009 by Luigi Giaccari · Leave a Comment
Filed under: CAD, Mechanics 
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Image Gear

Here you can find a simple tool to draw basic 3D spur gears feature. This tool is under development and collaboration is greatly appreciated. Several estention and improvements are possible. This can even be a basic brick for other graphical projects.

GearDesign returns the basic triangulated model of a 3D spur Gear. It requires in input a few standard parameter to insert in a structure. Here you can find the explanation of all parameters, for those who are not confident with mechanics but are curious to use this utility I suggest:

http://en.wikipedia.org/wiki/Gear

The INPUT parameters are:

  • The Gear structure
    Gear.m=1;%modulus
    Gear.z=20;%number of teeth
    Gear.Alpha=20;%Pressure angle degree
    Gear.Addendum=1;%addendum/modulus ratio
    Gear.Dedendum=1.25;%dedendum/modulus ratio
    Gear.FaceWidth=10;%Face width
    Gear.ShaftDiameter=4;%shaft diameter [mm]
    Gear.numpoint=10;%number of points to approximate the tooth profile
    Gear.t=[];%here will be stored the triangulation
    Gear.p=[];%here will be stored points data
  • plotflag: turn on a plot of the designed gear

The OUTPUT parameter is the Gear structure but with filled:

  • Gear.t (triangles)
  • Gear.p (points).

Here is a an example:

% BUILD THE GEAR STRUCTURE
Gear2.m=1;%modulus
Gear2.z=30;%number of teeth
Gear2.Alpha=20;%Pressure angle degree
Gear2.Addendum=1;%addendum/modulus ratio
Gear2.Dedendum=1.25;%dedendum/modulus ratio
Gear2.FaceWidth=4;%face width
Gear2.ShaftDiameter=8;%shaft diameter
Gear2.numpoint=10;%points to approximate the tooth profile
Gear2.t=[];%for the output
Gear2.p=[];%for the output

<p style="text-align: left;">% GEAR DESIGN
Gear2=GearDesign(Gear2,true);

A routine to experiment gears motion is provided.

GearMotion

For problems, questions, suggestions,:

giaccariluigi@msn.com

Created: 18/01/2009
Last Update: 18/01/2009
Author: Giaccari Luigi

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