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dc.contributor.authorForrester, Merville Kennethen_US
dc.date.accessioned2014-03-14T20:35:15Z
dc.date.available2014-03-14T20:35:15Z
dc.date.issued1998-04-30en_US
dc.identifier.otheretd-05062002-004428en_US
dc.identifier.urihttp://hdl.handle.net/10919/32249
dc.description.abstractThe objective of this research is to determine the three-dimensional stiffness matrix of a rectangular cross-section helical coil compression spring. The stiffnesses of the spring are derived using strain energy methods and Castiglianoâ s second theorem. A theoretical model is developed and presented in order to describe the various steps undertaken to calculate the springâ s stiffnesses. The resulting stiffnesses take into account the bending moments, the twisting moments, and the transverse shear forces. In addition, the springâ s geometric form which includes the effects of pitch, curvature of wire and distortion due to normal and transverse forces are taken into consideration. Similar methods utilizing Castiglianoâ s second theorem and strain energy expressions were also used to derive equations for a circular cross-section spring. Their results are compared to the existing solutions and used to validate the equations derived for the rectangular cross-section helical coil compression spring. A finite element model was generated using IDEAS (Integrated Design Engineering Analysis Software) and the stiffness matrix evaluated by applying a unit load along the springâ s axis, then calculating the corresponding changes in deformation. The linear stiffness matrix is then obtained by solving the linear system of equations in changes of load and deformation. This stiffness matrix is a six by six matrix relating the load (three forces and three moments) to the deformations (three translations and three rotations). The natural frequencies and mode shapes of a mechanical system consisting of an Additional mass and the spring are also determined. Finally, a comparison of the stiffnesses derived using the analytical methods and those obtained from the finite element analysis was made and the results presented.en_US
dc.publisherVirginia Techen_US
dc.relation.haspartEtd.pdfen_US
dc.rightsI hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to Virginia Tech or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report.en_US
dc.subjectrectangular cross-sectionen_US
dc.subjectlateral stiffnessen_US
dc.subjectaxial stiffnessen_US
dc.subjectmoment stiffnessen_US
dc.subjectHelical Springen_US
dc.subjectfinite element analysisen_US
dc.titleStiffness Model of a Die Springen_US
dc.typeThesisen_US
dc.contributor.departmentMechanical Engineeringen_US
dc.description.degreeMaster of Scienceen_US
thesis.degree.nameMaster of Scienceen_US
thesis.degree.levelmastersen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineMechanical Engineeringen_US
dc.contributor.committeechairMitchiner, Reginald G.en_US
dc.contributor.committeememberWicks, Alfred L.en_US
dc.contributor.committeememberKnight, Charles Eugeneen_US
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-05062002-004428/en_US
dc.date.sdate2002-05-06en_US
dc.date.rdate2003-05-17
dc.date.adate2002-05-17en_US


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