טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentLevy Yuval
SubjectVibrations of a Rotating Helical Spring
DepartmentDepartment of Mechanical Engineering
Supervisor Dr. Itzhak Porat


Abstract

This thesis deals with coupled vibrations (longitudinal and lateral) of a helical spring rotating at constant speed, with arbitrary pitch angle.
A lot has been published about vibrations of non-rotating helical springs during the last 100 years, but none about a rotating one. The present thesis is the first study that presents a complete dynamical model of a rotating helical spring.
A set of differential equations of motion for the rotating spring was developed, based on the known equations for a non-rotating vibrating spring.
We consider a model in which the wire diameter is small compared to the diameter of the spring, hence the spring is considered to be a bent rod, subjected to forces and moments at its cross section, that vibrates with a small amplitude about its steady state position, while ignoring products of the displacements and their derivatives. The wire is not extensible and its element inertia and external forces are negligible
Appropriate expressions for the acceleration of the wire element, for the relations between moments at the cross section, motion of the section and the radii of curvature, and for the basic geometry of the helical wire, yield  a set of non-linear differential equations, simulating the spring’s dynamics.
Small perturbations from its stable rotational state, yield a system of linear and homogeneous differential equations. Solving these equations results in the vibration modes of the rotating spring.
The vibration modes of the rotating spring are waves moving at variable velocity and amplitute. Critical rotation velocities exist for the lateral vibration modes.
Comparison of the results for a null rotation speed to computational and experimental data from the literature, results in precisely the same modes.