טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentRotman Noam
SubjectThe Influences of Preload on Rotating Circular Planetary
Beam and Helical Spring Dynamics
DepartmentDepartment of Mechanical Engineering
Supervisor Dr. Itzhak Porat
Full Thesis text - in Hebrew Full thesis text - Hebrew Version


Abstract

The thesis studies the dynamics of springs and curved beams loaded by external forces/torques and rotating in constant speed. Both analytical developments and Ansys finite elements models are being used to examine the influences of preloads on the dynamics the rotating structures. Unique test system was built to measure the natural frequencies of preloaded rotating or stationary springs and measurements were compared with the analytical models. Comparison between measurements and models showed excellent match.

 Initially, the research develops the equations of motion of a planar curved beam. This model is a degeneration of the three dimensional model developed by Levy [1] inspired by Love's [2] curved beam equations generated by Kirchhoff theory.  Some assumptions are being used during the development and were tested during solution to obtain its qualification: Second order quantities were neglected. Cross section inertia was neglected. Using those assumptions we obtain three equations but four parameters to solve: Tangential force N1, Normal force N3 and displacements u and w. Solution was possible using a third assumption: Inextensible assumption, meaning, that by loading the beam the curvature changes but not the overall length. This leads us to a supplemental equation defining a differential ratio between the displacements.

The boundary conditions used in solving the models were elementary end forces/displacements and more practical cases of Coupling feature. In this case, we presented a beam that connects a rotating load to a motor.

During this work we tested the execution of finite elements modal solutions of rotating beams and helixes using ANSYS. Only in the 10th revision and further ANSYS contains modules that make it possible to take the Coriolis acceleration into its modal solutions consideration. By default ANSYS modal studies is not influenced by external loads. Though loaded models can be determined by a Pre stressed modal analysis. Analytic and finite elements solutions were tested by empiric measurements. Comparison between measurements and models showed excellent match.

One purpose of this work was to verify an analytical rotating spring dynamic model published in Levy [1]. The verification was made using finite elements ANSYS models and an experimental set that measured the vibrations of static and rotating springs. Analysis of the measured springs and analytical/finite elements models gives us good understanding about the dynamic properties of rotating springs, natural frequencies, radial and axial modes, combined modes and critical rotating speeds. Comparing measurements with the various models (analytical and finite elements) showed excellent match.