Dynamic Analysis and Design of Steel-Ball Grinding Machines Based on No-Slip Cases
Based on no-slip cases between steel balls and lapping discs while a horizontal grinding machine is working, the motion equations of the ball lapping are established and the law of motion is revealed by the MATLAB software. This paper shows that the difference of the trace spacing is reduced by increasing the disc diameter, which can make the trace distribution of the steel ball surface more uniform. In order that balls do not slip when rotary disc drives them to rotate, the ranges of the lapping pressure and lapping disc speed is deduced by using the dynamics analysis considering from the vertical trench surface and along the groove surface, respectively. Finally, this paper takes the selected material as an example to analyze the process parameters that affect the lapping curves, and explains the selection principles of alpha and beta when the trench has some bias, which can provide a reference to improve the quality of the steel balls surface.
VIBRATIONS OF HYBRID CERAMIC BALL BEARINGS
Hybrid ceramic ball bearings with silicone nitride balls and steel rings were tested, and the vibration characteristics were compared with those of conventional steel ball bearings. In this study, two types of hybrid ceramic ball bearings and two types of conventional steel ball bearings were used as test bearings. The test bearings were operated under several rotational speeds and axial loads. The radial and the axial vibrations on the outer ring of each test bearing were detected by an accelerometer. The vibrations were examined by using an FFT analyzer. From the experimental results, analysis and discussion, the vibration characteristics of hybrid ceramic ball bearings, compared with those of conventional steel ball bearings, are explained.
STABILITY AND BIFURCATION OF ROTOR MOTION IN A MAGNETIC BEARING
Abstract The equations of motion of a two-degrees-of-freedom mass in a magnetic bearing are non-linear in displacement, with geometric coupling of the magnetic bearing coupling the horizontal and vertical components of rotor motion. The non-linear forced response is studied in two ways: (1) using imbalance force; (2) using non-imbalance harmonic force. In the forced response, only periodic motion is investigated here. Stable periodic motion is obtained by numerical integration and by the approximate method of trigonometric collocation. Where unstable motion coexists with stable motion after a bifurcation of periodic motion, the unstable motion is obtained by the collocation method. The periodic motions' local stability and bifurcation behavior are obtained by Floquet theory. The parameters i.e., rotor speed, imbalance eccentricity, forcing amplitude, rotor weight, and geometric coupling are investigated to find regimes of non-linear behavior such as jumps and subharmonic motion.