Gain-Scheduled Control of Asymmetric Thrust Magnetic Bearing

The thrust position of the magnetic levitation rotor can be changed, bringing convenience to the practical application of cold compressors. This paper derives the mathematical model of asymmetric thrust magnetic bearings for a cold compressor and analyzes the changes in the system characteristics with the equilibrium position. By constructing PID controllers associated with the structural parameters of the magnetic bearing, the adaptive adjustment of the control parameters under different balanced position commands is realized. The simulation and experimental results prove that the gain-scheduled control method proposed in this paper can achieve a robust stability of the rotor in the range of 50 to 350 μm, and not at the cost of the response speed, adjustment time, and overshoot. The research results have reference significance for the structure design of asymmetric thrust magnetic bearings and play an important role in the commissioning and performance improvement of cold compressors.

Control Performance, Stability Conditions, and Bifurcation Analysis of the Twelve-Pole Active Magnetic Bearings System

The active magnetic bearings system plays a vital role in high-speed rotors technology, where many research articles have discussed the nonlinear dynamics of different categories of this system such as the four-pole, six-pole, eight-pole, and sixteen-pole systems. Although the twelve-pole system has many advantages over the eight-pole one (such as a negligible cross-coupling effect, low power consumption, better suspension behaviors, and high dynamic stiffness), the twelve-pole system oscillatory behaviors have not been studied before. Therefore, this article is assigned to explore the effect of the magneto-electro-mechanical nonlinearities on the oscillatory motion of the twelve-pole system controlled via a proportional derivative controller for the first time. The normalized equations of motion that govern the system vibrations are established by means of classical mechanics. Then, the averaging equations are extracted utilizing the asymptotic analysis. The influence of all system parameters on the steady-state oscillation amplitudes is explored. Stability charts in a two-dimensional space are constructed. The stable margin of both the system and control parameters is determined. The obtained investigations reveal that proportional gain plays a dominant role in reshaping the dynamics and motion bifurcation of the twelve-pole systems. In addition, it is found that stability charts of the system can be controlled by simply utilizing both the proportional and derivative gains. Moreover, the numerical simulations showed that the twelve-poles system can exhibit both quasiperiodic and chaotic oscillations besides the periodic motion depending on the control parameters’ magnitude.

On the Performance of a Nonlinear Position-Velocity Controller to Stabilize Rotor-Active Magnetic-Bearings System

The performance of a nonlinear position-velocity controller in stabilising the lateral vibrations of a rotor-active magnetic-bearings system (RAMBS) is investigated. Cubic nonlinear position-velocity and linear position-velocity controllers are introduced to stabilise RAMBS lateral oscillations. According to the proposed control law, the nonlinear system model is established and then investigated with perturbation analysis. Nonlinear algebraic equations that govern the steady-state oscillation amplitudes and the corresponding phases are derived. Depending on the obtained algebraic equations, the different frequency response curves and bifurcation diagrams are plotted for the studied model. Sensitivity analysis for the linear and nonlinear controllers’ gains is explored. Obtained analytical results demonstrated that the studied model had symmetric bifurcation behaviours in both the horizontal and vertical directions. In addition, the integration of the cubic position controller made the control algorithm more flexible to reshape system dynamical behaviours from the hardening spring characteristic to the softening spring characteristic (or vice versa) to avoid resonance conditions. Moreover, the optimal design of the cubic position gain and/or cubic velocity gain could stabilise the unstable motion and eliminate the nonlinear effects of the system even at large disc eccentricities. Lastly, numerical validations for all acquired results are performed, where the presented simulations show accurate correspondence between numerical and analytical investigations.

Technological assurance of reliability of centrifugal pumps for pumping biomass processing products based on adaptive dampers

In almost every mechanical system, moving mechanisms slide over stationary parts, creating friction and, as a result, unwanted energy losses. In engineering, sliding or rolling bearings are most often used as supports. However, any system can benefit from a greater reduction in friction between components. As will be shown in this article, the stability problem can be solved by blocking vibrations in the radial direction. The latest technological advances in the field of manufacturing magnetic materials make it possible to integrate magnetic bearings with permanent magnetization (hereinafter - MBPM) into a larger number of mechanical systems. This blocking of radial movement is carried out without the use of a mechanical sliding bearing, chosen for its simplicity and ease of integration. To facilitate the integration of the MBPM into the overall system of the device, it is important to know the mechanical properties of magnetic bearings, namely stiffness and damping, as well as the performance characteristics and limits of their operation. This article examines the possibility of using an adaptive damper in centrifugal pumps to ensure the technological reliability of the equipment. Alternating permanent magnets in the direction of their movement is the most optimal option, leading to large and smooth hysteresis loops of force - displacement. The proposed arrangement of magnets ensures the adaptability of the device with the determination of its optimal size, and also takes into account the edge and surface effects in the design of the damper. In addition, the article discusses theoretical and technical issues of levitation - free floating of bodies. Magnetic suspension can be used to study only those processes where mechanical connections are undesirable. The use of magnetic suspension for balancing centrifugal pumps during transportation of biomass processing products, supports of mixing devices in reactors in biomass processing reactors and other machine components opens up wide opportunities.