Mover Positions Research Articles

Model-based flux control of an electropermanent magnet for adaptive zero power gravity compensation

This paper presents a model-based flux control for a variable reluctance actuator with an electropermanent magnet, used for adaptive zero power gravity compensation in magnetic levitation systems. With the hysteresis of the electropermanent magnet being identified and approximated, tailored current pulses are applied by the model-based flux control to tune the magnetization of the electropermanent magnet. In this way, the resulting stationary reluctance force compensates the gravitational force of the levitated mover mass. Based on the identified hysteresis, a non-linear control law is derived, which is extended by an integrator term to compensate modelling uncertainties. In comparison to the state of the art model-free control, the model-based control increases the force tuning rate by a factor of 14 to 19 N/s and improves the robustness of the experimental system in variable mover positions.

Performance and design comparison of moving-magnet linear oscillating actuators based on their mover positions

PurposeThis study aims to investigate and compare the characteristics of three topologies of moving-magnet linear oscillating actuator (LOA) based on their mover position. Positive aspects and consequences of every topology are demonstrated. Three topologies of axially magnetized moving-magnet LOA; outer mover, inner mover (IM) and dual stator (DS) are designed and examined. Due to its characteristically high thrust density and more mechanical strength, axially magnetized tubular permanent magnets (PMs) are used in these topologies.Design/methodology/approachLOAs are designed and optimized using parametric sweep, in term of design parameters and output parameters like thrust force, stroke and operating resonance frequency of the LOA. All the pros and cons of each topology are investigated and compared. Output parameters of the LOAs are compared using same size of the investigated LOAs. Mover mass, which plays a vital role in resonant operation, is analyzed for IM and DS designs. Investigated LOAs are compared with conventional designs of LOA for compressor in refrigeration system with regards of motor constant, stroke and thrust per PM mass.FindingsThis paper analyzes three topologies of moving-magnet LOAs. The basic difference between investigated LOAs is the radius of tubular-shaped mover from its central axis. All the design parameters are compared and concluded that thrust per PM mass of IMLOA is maximum. OMLOA provides maximum motor constant of value 180 N/A. DSLOA provides thrust force with motor constant 120 N/A and required intermediate materials of PMs. All the three designs give the best results in terms of motor constant and thrust per PM mass, compared to conventional designs of LOA.Originality/valueThis paper determines the impact of mover position from its central axis in a tubular-shaped moving-magnet LOA. This work is carried out in correspondence of latest papers of LOA.

Design and Analysis of a Novel Linear Oscillating Actuator with Dual Stator Rectangular Geometry

This paper proposes a new design of a linear oscillating actuator (LOA) with rectangular topology of stator and mover. The shape of a permanent magnet (PM) has a major impact on cost, mechanical strength and generation of magnetic flux density. This design uses rectangular PMs that are relatively cheaper than tubular PMs. Proposed LOA operates on single phase AC loading source. All the design parameters are optimized by using parametric sweep and the response of the LOA in terms of thrust force is compared. The Electromagnetic (EM) force received by the mover is investigated at various mover positions as well as at different values of the current. Motor constant is examined toward both directions of the force. Resonance phenomena is analyzed using input and output power of the LOA, which is the unique advantage of the LOA. Compared to the conventional LOA designs, the output parameters of the LOA, such as EM force, stroke, operating frequency and power, show great improvement with regards of volume of the proposed LOA. This topology shows significant development in terms of thrust force, motor constant, easy manufacturing and cost. Moreover, range of the stroke of proposed LOA is feasible for linear refrigeration system.

Design Optimization of Linear-Rotary Motion Permanent Magnet Generator With E-Shaped Stator

A linear-rotary motion permanent magnet (PM) generator is investigated with six axial modular E-shaped stator sections arranged circumferentially, which can meet the requirement of wave and tidal energies generation. The PM pole is magnetized in radial direction, and the adjacent PM poles with opposite magnetized directions are interlaced by half mover pole pitch both in circumferential and axial directions, which are located on the mover surface. The rotational and rectilinear motions are achieved by one magnetic circuit structure according to the transverse flux principle and electromagnetic induction principle. The optimization design and electromagnetic properties of the proposed motor are calculated by 3-D finite element simulation. Then the optimal structural parameters are obtained. The back electromotive force (back EMF) and harmonics, the amplitudes of the cogging torque and detent force are decreased than those of the initial topology. Since three phases of the nine phase windings generate same initial phase angle of back EMF whether it works in rotational or rectilinear motion, the traditional three phase energy storage system can be used to realize the energy storage of the nine phase windings, which reduces the difficulty of electrical energy storage. The variation of the amplitude of back EMF is hardly affected with different mover positions, which is conducive to improve the efficiency of marine energy power generation.

Contour Tracking Control of a Linear Motors-Driven X-Y-Y Stage Using Auto-Tuning Cross-Coupled 2DOF PID Control Approach

Linear motors (LMs) are widely used in numerous industry automation where precise and fast motions are required to convert electric energy into linear actuation without the need of any switching mechanism. This study aims to develop a control strategy of auto-tuning cross-coupled two-degree-of-freedom proportional-integral-derivative (ACC2PID) to achieve extremely high-precision contour control of a LMs-driven X-Y-Y stage. Three 2PID controllers are developed to control the mover positions in individual axes while two compensators are designed to eliminate the contour errors in biaxial motions. Furthermore, an improved artificial bee colony algorithm is employed as a powerful optimization technique so that all the control parameters can be concurrently evaluated and optimized online while ensuring the non-fragility of the proposed controller. In this way, the tracking error in each axis and contour errors of the biaxial motions can be concurrently minimized, and further, satisfactory positioning accuracy and synchronization performance can be achieved. Finally, the experimental comparison results confirm the validity of the proposed ACC2PID control system regarding the multi-axis contour tracking control of the highly uncertain and nonlinear LMs-driven X-Y-Y stage.

Design and Analysis of a Self-Holding Three-Position Electric Tubular Actuator

A self-holding three-position electric tubular actuator (SHTPETA) is described in the article. The proposed linear actuator can be applied in a clutch system, where it is necessary to change certain mover positions over time. Other potential applications of such actuators can be shift of gears, coupling (decoupling) of various moving (rotating) mechanisms, or electromagnetic valves. The self-holding force of the proposed SHTPETA is achieved by the reluctance force between the armature and mover cores, where a magnetic flux is excited by a permanent magnet located in the armature and an excitation current is not needed, whereas the moving force is determined by the dc voltage (current) applied to two coils located in the stationary part of the SHTPETA. The article proposes a relatively fast and simple approach for the SHTPETA design process based on the required forces and moved distance.

Flux Characteristics Analysis of a Single-Phase Tubular Switched Reluctance Linear Launcher

This paper analyzed the flux characteristics of a single-phase tubular switched reluctance linear motor (TSRLM) based on magnetic equivalent circuit (MEC) method. The single-phase TSRLM is divided into five different parts, which are the teeth of the stator, the yoke of the stator, air gap, the teeth of the mover, and the yoke of the mover. The reluctance of every part is expressed in analytical formulas at five special mover positions. The flux linkages at five special mover positions are calculated by magnet tube method and Gauss–Seidel iteration method which takes the saturation into consideration. A high-order Fourier series method is used to map the nonlinear relationship between flux linkage, current, and mover position with the flux linkage data calculated by the MEC method. The calculated flux linkage is consistent with 3-D finite-element method and experimental results. The dynamic and static performance of the simulation utilized with MEC method is consistent with those in experiments, which verifies the accuracy of the MEC method proposed in this paper.

Flux Characteristics Analysis of a Single-Phase Tubular Switched Reluctance Linear Launcher Based on 3-D Magnetic Equivalent Circuit

This paper calculates the flux characteristic of a single-phase tubular switched reluctance linear launcher (TSRLL) with 3-D magnetic equivalent circuit (MEC) method. First, the 3-D finite element (FE) model of the single-phase TSRLL is established in FLUX, which is the foundation of the 3-D MEC model. The single-phase TSRLL is divided into different parts, including the teeth of the stator, the yoke of the stator, air gap, the teeth of the mover, and the yoke of the mover. The flux linkage at different mover positions and different currents is calculated with the proposed 3-D MEC model. Compared with the 3-D finite-element analysis (FEA) results, 3-D MEC model can obtain the flux characteristics of the single-phase TSRLL in a shorter time. The result of the 3-D MEC of the single-phase TSRLL is consistent with the 3-D FEM results and the experimental results, which validates the correctness of the proposed 3-D MEC model.

Flux Characteristics Analysis of a Double-Sided Switched Reluctance Linear Machine Under the Asymmetric Air Gap

This paper analyzes the flux characteristics and normal force of the double-sided switched reluctance linear machine (SRLM) under the asymmetric air gap. The magnetic equivalent circuit (MEC) of the machine and the details of the flux paths configuration at six distinct mover positions under the asymmetric air gap are included. Then, six special mover position magnetization curves are calculated by solving the MEC with the method of Gauss–Seidel. The magnetic flux-linkage model and thrust model based on six distinct mover positions are established by analytical polynomial. Three-dimensional (3-D) finite-element method (FEM) simulation and the experimental study with the prototype hardware are carried out to validate the accuracy of the MEC model calculated for the flux linkage and normal force. The six distinct mover positions flux linkage and normal force calculated by the MEC are consistent with the 3-D FEM calculated data and experimental data. It indicates that the proposed method to calculate the flux linkage and the normal force is feasible and effective. The dynamic analysis is also conducted. The simulated phase current waveforms are also consistent with the experimental results. It indicates that the presented method can be used to simulate the phase current under the asymmetry air gap effectively. The normal force under different asymmetry rates is analyzed, which provides the theoretical basis for reducing the unbalanced force of the double-sided SRLM.

Flux Characteristics Analysis of Single-Phase Tubular Permanent Magnet Linear Motor

The flux characteristics of a single-phase tubular permanent magnet linear motor (TPMLM) are analyzed with a magnetic equivalent circuit (MEC) method in this paper. First of all, the single-phase TPMLM is mainly divided into five parts, including stator sleeve, stator yoke, air gap, the permanent magnetic part of mover, and the ferromagnetic part of mover. In consideration of saturation, the flux linkage of the single-phase TPMLM at four special mover positions can be calculated with the help of the magnetic tube method and Gauss–Seidel iteration. The nonlinear relationship between flux linkage, mover position, and current can be mapped utilizing a high-order Fourier series with the flux linkage data obtained from the MEC method. It is consistent with a three-dimensional finite element method and experimental data. What is more, the simulated dynamic and static performance of the TPMLM are also consistent with experimental data, which verifies the effectiveness of the proposed MEC method.

Parametric Design Analysis of Magnetic Sensor Based on Model Order Reduction and Reliability-Based Design Optimization

This paper presents a novel parametric design analysis of the magnetic sensor module used to find mover positions in linear motors. The proposed framework utilizes a computationally inexpensive proper orthogonal decomposition-dynamic mode decomposition-based model order reduction (MOR), coupled with a multiparameter moment matching method. The model is then utilized by a moment-based probabilistic design optimization method that considers the manufacturing uncertainties to find the optimal sensor design. A magnetic sensor module is designed for employing the proposed framework, and the results show that: 1) the proposed MOR technique is accurate; 2) the reliability analysis performed during the probabilistic design optimization can help to reduce the excessive non-compliance costs for the manufacturers; and 3) the combined framework is able to significantly expedite the optimal design search.

Electromagnetic Analysis of Flux Characteristics of Double-Sided Switched Reluctance Linear Machine

This paper analyzed the flux characteristics of the double-sided switched reluctance linear machine. The magnetic equivalent circuit is given. The magnetization curves at six special mover positions are respectively calculated by the flux tube method, the magnetic flux paths distribution of air gap segments are presented, and the details of the magnetic reluctance component of each path are described. The calculated magnetization curves at six special mover positions is used as the switches for training the magnetic flux linkage model based on the BP neural networks with a GA algorithm. The mathematical mapping relationship between the mover position and the phase current to the magnetic flux linkage is established, and the magnetic flux linkage at certain mover position and certain phase current is calculated by the mathematical mapping relationship. Simulation and the experimental study with the prototype hardware are carried out on the magnetization curves at six special mover positions and three velocities of the mover. It is shown that the magnetization curves at six special mover positions calculated by magnetic equivalent circuit are consistent with the 3-D FEM calculated data and the experimental data, and the simulated phase current waveforms are also consistent with the experimental results. The magnetic equivalent circuit, the analytical calculation of the magnetization curves at six special mover positions, and the BP neural networks magnetic flux linkage model with GA algorithm are validated.

Characteristic analysis of planar motor using the volume integral equation method

The characteristics of a three-phase synchronous permanent magnet planar motor (SPMPM) are analyzed numerically using a volume integral equation method (VIEM). The mover dimensions are optimized to minimize the detent force. The back-EMF waveform is calculated and the coil dimensions are optimized to set the back-EMF constant to a constant value regardless of mover positions. All simulation results are verified by a comparison with experimental results.

Sequential Product Positioning Under Differential Costs

This paper examines the product positioning decisions of firms that enter a market sequentially and that have potentially different cost structures. It shows that if the first mover knows the second mover to have a lower production cost, it positions away from the most attractive location in the market; further, the larger the second-mover's cost advantage, the farther away the first mover positions from the most attractive location. The paper also models uncertainty in the first-mover's mind about the later-entrant's cost structure, and shows that an increase in this uncertainty (in the sense of mean-preserving spread) also makes the first mover position farther from the most attractive location in the market. Overall, this paper suggests that unless the first entrant in a market is certain that the later entrant will not have a superior cost structure, it may be better off leaving the best position in the market vacant and having a niche or fringe product.