Investigation of Gyroscopic Effect on the Stability of High Speed Micromilling via Bifurcation Analysis

Catastrophic tool failure due to the low flexural stiffness of the micro-tool is a major concern for micromanufacturing industries. This issue can be addressed using high rotational speed, but the gyroscopic couple becomes prominent at high rotational speeds for micro-tools affecting the dynamic stability of the process. This study uses the multiple degrees of freedom (MDOF) model of the cutting tool to investigate the gyroscopic effect in machining. Hopf bifurcation theory is used to understand the long-term dynamic behavior of the system. A numerical scheme based on the linear multistep method is used to solve the time-periodic delay differential equations. The stability limits have been predicted as a function of the spindle speed. Higher tool deflections occur at higher spindle speeds. Stability lobe diagram shows the conservative limits at high rotational speeds for the MDOF model. The predicted stability limits show good agreement with the experimental limits, especially at high rotational speeds.

Mechanics of the gyroscopic precession and calculation of the Galactic mass

A spinning gyroscope precesses about the vertical due to a torque acting upon the wheel. The torque is generated by the shift of moment of force by gravity and it points to the vertical instead of the tangential direction of precession. This intuition offers an alternative and straightforward view of precession dynamics in comparison with the literature. It also presumes a dynamic balance of momentum between circular motions of the wheel spin and precession. Accordingly, the gyroscopic dynamics is then applied to the study of galactic motion of the solar system in space and the Galactic mass is calculated with the inclusion of gyroscopic effect of the solar planets. Results indicate that the gyroscopic effect of Mercury orbiting around the Sun can increase the calculated Galactic mass by 23% in comparison with the result obtained by the classic approach.

Modelling and Stability Analysis for a Magnetically Levitated Slice Motor (MLSM) with Gyroscopic Effect and Non-Collocated Structure Based on the Extended Inverse Nyquist Stability Criterion

Stability of the rotor motion is the precondition for the reliable operation of magnetically levitated slice motors (MLSMs). However, with gyroscopic effect and non-collocated structure existing simultaneously, its stability analysis faces a tremendous challenge, because the torsional motions couple with the radial translational ones, making MLSM a multiple-input and multiple-output (MIMO) system with high order. Therefore, in this paper, we first establish a novel MIMO rotor dynamics closed-loop model and further convert it into an equivalent single-input and single-out (SISO) feedback control system by constructing complex variables, meanwhile reducing the system order by half. Beneficial from the equivalence between the MIMO and SISO systems, the sufficient and necessary conditions of the absolute stability of MLSM are derived by the extended inverse Nyquist stability criterion in the complex domain. Additionally, the effectiveness of the proposed modelling and stability analysis method is evaluated by simulation and experimental results. Thus, apart from PID parameters, this paper demonstrates that the stability of MLSM is also affected by the coupling of gyroscopic effect and non-collocated structure, which should serve as an essential guideline for system regulation of MLSM.

On the Analysis of Damped Gyroscopic Systems Using Lyapunov Direct Method

In this work, the stability properties of damped gyroscopic systems have been studied using Lyapunov direct method. These systems are generally stable because of the presence of gyroscopic effect. Conditions for determining the stability of the damped gyroscopic systems have been developed. Solution bounds of amplitude and velocity have been obtained for both homogeneous and inhomogeneous cases. An example is given to show how the stability conditions are applied to systems to determine its stability status.

The Mathematical Model for the Tippe Top Inversion

The dynamics of rotating objects is an area of classical mechanics that has many unsolved problems. Among these problems are the gyroscopic effects manifested by the spinning objects of different forms. One of them is the Tippe top designed as the truncated sphere which is fitted with a short, cylindrical rod for rotation. The unexplainable gyroscopic effect of the Tippe top is manifested by its inversion towards the support surface. Researchers tried to describe this gyroscopic effect for two centuries, but all modelings were on the level of assumptions. It is natural because the Tippe top has a more complex design than the simple spinning disc, which gyroscopic effects did not have an analytical solution until recent time. The latest research, in the area of gyroscopic effects, reveals the action of the system of several interrelated inertial torques on any spinning object. The gyroscopic inertial torques are generated by their rotating mass. These inertial torques and the variable ratio of the angular velocities of the spinning object around axes of rotations constitute the fundamental principles of gyroscope theory. These physical principles of dynamics of rotating objects enable to description and compute of any gyroscopic effects and also the Tippe top inversion.