M.Sc Student | Levy Yuval |
---|---|

Subject | Vibrations of a Rotating Helical Spring |

Department | Department of Mechanical Engineering |

Supervisor | Dr. Itzhak Porat |

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.