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We propose a novel combined five-degrees-of-freedom (5-DOFs) hybrid magnetic bearing (HMB) with only one permanent magnet ring (PMR) used for turboexpanders. It has two radial magnetic bearing (RMB) units; each has four poles and one thrust magnetic bearing (TMB) to control 5-DOFs. Based on one PMR, the bias flux of the two radial magnetic bearing units and the one thrust magnetic bearing unit is constructed. As a result, ultra-high-speed, lower power loss, small size, and low cost can be achieved. Furthermore, the equivalent magnetic circuit method and 3D finite element method (FEM) are used to model and analyze the combined 5-DOFs HMB. The force-current, force-position, torque-coil currents, the torque-angle position, and the stiffness models of the combined 5-DOFs HMB are given. Moreover, its coupling problems between the RMB units and the AMB unit are also proposed in this paper. An example is given to clarify the mathematical models and the coupling problems, and the linearized models are proposed for the follow-up controller design.

Magnetic bearing can provide many advantages for turbomachinery such as high-speed, long-life, higher efficiency, lower maintenance, and higher reliability. However, the greatest benefit for turboexpanders is realized by the ability of the magnetic bearings to run in the process gas, which in turn eliminates the lube oil and dry gas seals. As a result, there is no lube oil to contaminate the process. Elimination of the lubrication system also provides significant size and mass savings for off-shore applications. The turboexpanders in S2M, GE, SKF, and so forth have been equipped with the magnetic bearings [^{3} turbo-oxygen gas expander is tested by Xiping et al. [

The configuration of turboexpander supported by the active magnetic bearings in 5 DOFs. 1: expander wheel; 2: displacement sensor; 3: radial magnetic bearing; 4: thrust magnetic bearing; 5: shaft; 6: touchdown bearing; 7: compressor wheel.

In order to reduce the power consumption, cost, and size, it is important to reduce the number of the units by means of combining the RMB and AMB. Integrated axial magnetic bearing and radial magnetic bearing with the conical rotor are designed and analyzed [

In this paper, a novel combined 5-DOFs HMB with only one PMR is proposed to be used for turboexpanders in this paper. The combined 5-DOFs HMB consists of two RMB units each with four poles and one AMB unit. The bias flux of the two RMB units and AMB unit is supplied by only one PMR. The low power consumption, compact structure, and small size can be gained due to the combined 5-DOFs HMB, the permanent magnetic bias HMB, and the reduction in the number of the poles of the RMB units. The low cost is gained due to the one PMR used. Moreover, ultra-high-speed is also gained due to the small outside diameter of the rotor thrust disk. The equivalent magnetic circuit method and 3D finite element method (FEM) are used to model and analyze the combined 5-DOFs HMB. The force-current, force-position, torque-current, the torque-angular position, and the stiffness models of the integral 5-DOFs HMB are given. Moreover, its coupling problems between the RMB units and the AMB unit are also proposed. An example is given to clarify the mathematical models and the coupling problems, and the linearized models are proposed for the follow-up controller design.

This paper is organized as follows. First, in Section

A simplified configuration of turboexpander supported by the combined 5-DOFs HMB is shown in Figure

The configuration of turboexpander supported by the combined 5-DOFs HMB. 1: expander wheel; 2: displacement sensor; 3: the combined 5-DOFs HMB; 4: shaft; 5: touchdown bearing; 6: compressor wheel.

The configuration and magnetic circuit of the combined 5-DOFs HMB. (a) The section view of the RMB unit

The force and moment produced by the combined 5-DOFs HMB.

According to construction of the combined 5-DOFs HMB, the magnetic resistance of the iron path and flux leakage is neglected, the permeability of the iron is assumed to be infinite, and their equivalent bias and control magnetic circuits can be gained and are shown in Figure

Equivalent bias circuit and control circuits of the combined 5-DOFs HMB. (a) The equivalent bias circuit. (b) The equivalent control circuit of RMB unit

Figure

According to the structure of the combined 5-DOFs HMB (Figure ^{−7} H/m;

The bias flux in Figure

As shown in Figures

The reluctances of radial air gap are written by

The reluctances of axial air gap are written by

The control flux in the radial air gaps of

The control flux in the radial air gaps,

Substituting (

Since the net force is zero at the center position in radial and axial directions, (

According to the structure of the combined 5-DOFs HMB (Figure

Substituting (

Since the net force is zero at the center, (

The RMB units

The change in radial air gap is

Using the Taylor series expansion for small values of

The current stiffness

From Figure

The alternation of the radial air gap will affect the current stiffness and the displacement stiffness of the AMB unit and will be calculated by

The combined 5-DOFs HMB parameters are given in Table

Design parameters of the combined 5-DOFs HMB.

Parameters | Value |
---|---|

Inner diameter of the RMB unit rotor stacks (mm) | 46 |

Outer diameter of the RMB unit rotor stacks (mm) | 68 |

Length of the RMB unit rotor stacks (mm) | 20 |

Inner diameter of the RMB unit stator (mm) | 69 |

Outer diameter of the RMB unit stator (mm) | 113 |

Length of the RMB unit stator (mm) | 20 |

Radial pole shoe area (mm^{2}) |
734 |

The number of winding turns in coil of RMB unit | 220 |

Inner diameter of the axial pole shoe (mm) | 76 |

Outer diameter of the axial pole shoe (mm) | 90 |

The number of winding turns in coil of AMB unit | 250 |

The radial and axial air gap (mm) | 0.5 |

Relative permeability of the permanent magnet ring | 1.082 |

Outer diameter of the permanent magnet ring (mm) | 126 |

Inner diameter of the permanent magnet ring (mm) | 113 |

Length of the permanent magnet ring (mm) | 5 |

The linearized model is given by

The finite element model using Ansoft Maxwell V13 is built and shown in Figure

The 3D finite element model and mesh of the 5-DOFs HMB except the air. (a) The 3D finite element model. (b) The 3D finite element mesh. (c) Section view of the 3D finite element mesh.

When the control currents in radial coil currents and axial coil current are 0 A, and the rotor position changes from −0.4 mm to 0.4 mm in

Curves of the force-rotor position and displacement stiffness in

When the rotor locates at radial and axial center and the coil current in

Curves of the force-coil current in

When the rotor in

Curves of the force-coil current and rotor position in

Curves of the displacement stiffness-rotor position-coil current and rotor position in

Curves of the current stiffness-coil current and rotor position in

When the control currents in radial coil currents and axial coil current all are 0 A, and the rotor position changes from −0.4 mm to 0.4 mm in

The force-rotor position in

When the rotor locates at radial and axial center and the coil current in

The force-coil current in

When the rotor locates its center position in

The force-coil current and rotor position in

The curves of the stiffness versus rotor position in

The torque can be produced by the RMB units

Curves of the torque-angular position of the combined 5-DOFs HMB and its tilting displacement stiffness (using linearized method, nonlinear method, and FEM). (a) Curves of the torque-angular position of the combined 5-DOFs HMB. (b) The tilting displacement stiffness.

When the rotor locates at radial and axial center and the coil currents of the RMB units

Curves of the torque-coil current in RMB units

When the rotor locates its center position in

Curves of the torque-coil current and angular position around

Curves of the tilting displacement stiffness and the tilting current stiffness versus angular position around

Equation (

The displacement stiffness and the current stiffness of the RMB units

The effect of the coil current of the AMB unit on the displacement stiffness and current stiffness of the RMB units

The displacement and current stiffness of the RMB units

The 3D curves of the displacement stiffness and current stiffness of the RMB units

The displacement stiffness and the current stiffness of the RMB units

Figure

The displacement and the current stiffness of the AMB unit affected by the rotor position of the RMB unit in

The tilting displacement stiffness and tilting current stiffness of the RMB units

Curves of the tilting displacement stiffness and tilting current stiffness of the RMB units

Curves of the tilting displacement stiffness and tilting current stiffness of the RMB units

A novel combined 5-DOFs HMB with only one PMR is proposed, used for turboexpander, in this paper. The combined 5-DOFs HMB consists of two RMB units and one AMB unit. The bias flux of the two RMB units and AMB unit is supplied by only one PMR. The low power consumption, compact structure, and small size can be gained due to the combined 5-DOFs HMB, the permanent magnetic bias HMB, and the reduction in the number of the poles of the RMB. The low cost is gained due to the one PMR used. Moreover, ultra-high-speed is also gained due to the small outside diameter of the rotor thrust disk. The equivalent magnetic circuit method and 3D finite element method (FEM) are used to model and analyze the integral 5-DOFs HMB. The force-current, force-position, torque-coil currents, torque-angular position, and the stiffness models of the integral 5-DOFs HMB are given. Moreover, its coupling problems between the RMB units and the AMB unit are also proposed. An example is given to clarify the mathematical models and the coupling problems, and the linearized models are proposed for the follow-up controller design.

The authors declare no conflict of interests.

This work was supported by the Aviation Science Fund of China under Grant 2012ZB51019 and by the Cultivation and Development Project of Science and Technology Innovation Base of Beijing under Grant Z131104002813105.

^{3}turbo oxygen gas expander