Nonlinear Model Analysis and “Switching Model” of AC–DC Three-Degree-of-Freedom Hybrid Magnetic Bearing

Abstract

The most widely studied linear models of the suspension forces in AC-DC three-degree of freedom hybrid magnetic bearings (AC-DC 3-DOF HMB) may not be practical for application to the precision control of bearings with larger air-gaps for larger suspension forces. In addition, the simplified linear and the real nonlinear models in linear zone of current and displacements have not been compared before. In the present study, the two most commonly used nonlinear models are analyzed comprehensively to address the lack of nonlinear model analysis in previous research and to seek the most appropriate model for both nonlinear and linear zones (full zone). The results show that no single model completely approximates the test results over the entire zone. A composite model, such as the "switching model", is more accurate. To illustrate the applicability of the results to both nonlinear model analysis and the proposed "switching model," nonlinear stiffness and performance test experiments were conducted. It is concluded that the model analysis and the proposed "switching model" can provide a control system with the most suitable mathematical models of the suspension force.

Experimental Analysis and Full Prediction Model of a 5-DOF Motorized Spindle

“…In [16], a "switching model" was proposed for the AC-DC 3-DOF HMB that involved a wide range of displacements and currents for the rotor. The concept of a "switching model" can then be applied to a 5-DOF HMB to form a full operation-domain model; this will make the mathematical model of suspension forces for the 5-DOF motorized spindle more complete and accurate.…”

“…The concept of a "switching model" can then be applied to a 5-DOF HMB to form a full operation-domain model; this will make the mathematical model of suspension forces for the 5-DOF motorized spindle more complete and accurate. Referring to the existing analysis result of "switching model" for the AC-DC 3-DOF HMB in [16], the "full switching model" of the 5-DOF AC HMB-supported motorized spindle selection table can be derived, as shown in Table 1. There are still four submodels in the composite "full switching model", which are called Model (1), Model (2), Model (3) and Model (4).…”

“…Although the "switching model" has been proven accurate in an AC-DC 3-DOF HMB system in [16], whether the "full switching model" is useful in 5-DOF HMBs is unproven and the real-time performance should be emphatically investigated. Therefore, the related experimental data must be selected to determine a more effective modeling method.…”

“…This study investigates a five-degrees-of-freedom (5-DOF) motorized spindle supported with AC HMBs [16]. The magnetic bearings used to support the 5-DOF motorized spindle are the AC 2-DOF HMB and the AC-DC 3-DOF HMB, both of which have perfect structures, accurate models and mature classical control technologies [17].…”

“…As for the full operating area of the motorized spindle, the most comprehensive and practical model is the "switching model". However, compared to the 3-DOF magnetic bearing system in [16], a "switching model" applied to a 5-DOF motorized spindle may adversely affect the real-time performance of the control system due to the large amount of data processing for displacement and current. Therefore, if a model based on a different operating state can be set in advance, the model will be more efficient and achieve better real-time performance in practice.…”