Low Force Ripple Research Articles

Performance Investigation and Improvement of Linear Vernier Permanent Magnet Motor for Servo Application

With its high thrust density and low force ripple, the linear vernier permanent magnet motor (LVPMM) is regarded as a good competitor for linear servo applications. However, typical LVPMMs have shortcomings, such as phase imbalance, a long distributed-winding end, and low power factor. The goal of this work is to present a thorough analysis-based approach for performance enhancement that addresses all three flaws while enhancing the LVPMMs high thrust density advantage. Thanks to the proper slot/pole-pair combination, Halbach array PM, and a special three-modular structure, the proposed LVPMM improves thrust density by 28%, reduces force ripple to 1.2%, increases power factor by over 40%, and nearly eliminates three-phase imbalance when compared with those of a conventional LVPMM. Manufacturing and testing a 2.2 kW/2200 N prototype has confirmed the viability of the theoretical analysis and improvement process.

Multi-Objective Optimization Design of a Modular Linear Permanent-Magnet Vernier Machine by Combined Approximation Models and Differential Evolution

In this article, a modular linear permanent-magnet (PM) vernier machine is presented and optimized for high-precision and safety-critical direct-drive applications. The novelty of this article is to not only propose a multi-objective optimization method, but also present a modular linear PM vernier machine. The presented machine has the merit of desired fault-tolerant capability and improved force performances by mainly adopting the modular mover structure. And, the design principle of modular mover structure is introduced in detail in this article. To realize low detent force, high thrust force, low force ripple, and good fault tolerance, modular mover structure, PM array with flux-intensifying effect and six-phase structure are adopted in machine design. Furthermore, a new multi-objective optimization method is proposed to obtain a set of tradeoff solutions among multiple optimization objectives in machine optimization. First, to decompose the high dimension design space, the design variables are stratified into nonsensitive and sensitive levels by utilizing a comprehensive sensitivity analysis. Second, combined approximation models are implemented to decrease the large amount of computations. Then, to enhance the efficiencies of two multi-objective optimization processes, multi-objective differential evolution algorithm with ranking-based mutation operator is employed. After the optimization by the proposed multi-objective optimization method, the desired comprehensive performances with high optimization efficiency and accuracy can be obtained. Finally, to verify the results of theoretical analysis, a prototype machine is fabricated.

A New Asymmetric Planar V-Shaped Magnet Arrangement for A Linear PM Synchronous Motor

In this paper, a new asymmetric planar V-shaped magnet arrangement for a linear PM synchronous motor is proposed. Several magnet arrangements for the track of the proposed linear permanent magnet (PM) synchronous motor such as un-skewed magnets, conventional magnet skew, and V-shaped planar magnets have been investigated. The performance results of the linear motor with skewed magnets are compared to those of previously designed PM linear synchronous motor with conventional un-skewed rectangular-shaped (CuSRS) magnets. The forcer is kept the same for all track structures and a thorough comparison is provided for low detent force and low force ripple with the CuSRS and proposed planar V-shaped magnet skew approaches.

Optimisation of double‐sided linear switched reluctance motor for mass and force ripple minimisation

Linear switched reluctance motors (LSRMs) are attractive machines for industrial applications. Their structure is simple, robust, and low cost. Despite these advantages, LSRMs suffer from inherent high force ripples which induce noise and vibration problems. The force performance of these motors is largely influenced by their geometry. Therefore, the dimensions must be optimised to improve the force performance. The aim of the present work was to determine the optimum dimensions of a double-sided LSRM using non-dominated sorting genetic algorithm-II and multi-objective seeker optimisation algorithm along with a three-dimensional (3D) finite element analysis. The analysis and modelling results are presented, and a laboratory prototype is built. The results revealed that the optimised motor has a higher average force, lower force ripple, and lower total mass

Design Optimization and Performance Investigation of Linear Doubly Salient Slot Permanent Magnet Machines

Novel linear doubly salient slot permanent magnet machines (LDSSPMMs) are investigated in this paper. First, the machine topology and operation principle are introduced, and the choices of feasible slot/pole combinations and winding configurations for three armature phases are discussed. Then, the 12 slots and 10/11/13/14 poles LDSSPMMs with double-layer (DL)/single-layer windings are globally optimized using genetic algorithm. The electromagnetic performances including flux linkage, back electromotive force (back EMF), detent force, and static force-current characteristics are comparatively studied using two-dimensional (2-D) finite-element analysis (FEA). It shows that 12 slots/13 poles (12s/13p) and DL winding are the optimal choices to provide higher thrust force as well as lower force ripple. Moreover, the risk of local irreversible demagnetization of PMs is analyzed, which only occurs at very limited corners of the PMs and can be eliminated by PM shaping. Furthermore, the electromagnetic performances between linear variable flux reluctance machines (LVFRMs), linear hybrid-excited slot PM machines, linear primary yoke PM machines, and LDSSPMMs are comparatively studied. It shows that LDSSPMM can provide much higher thrust force than LVFRM at the same copper loss. With the increase of copper loss, LDSSPMM exhibits better thrust force capability than other machines. Finally, a prototype of 12s/13p DL-LDSSPMM is manufactured and tested to validate the 2-D FEA predicted results.

A HTS-Excitation Modular Flux-Switching Linear Machine With Static Seals

This paper proposes and analyzes a novel high-temperature superconducting (HTS) modular flux-switching linear machine for long-stator applications, which adopts the stator with a low-cost salient-pole iron core and accommodates both the armature windings and HTS-excitation windings on the short mover, thus facilitating static seals of cooling Dewar for the HTS windings. The key of the proposed machine is to employ a modular mover structure composed of separate phase modules to achieve a complementary pattern, such that the cogging force can be significantly offset to effectively reduce the force ripple while offering the advantages of very symmetrical back electromotive force (EMF) and high fault tolerance. The operation principle and optimization analysis of the proposed machine with concern on the HTS-excitation characteristics are carried out. Also, by using the two-dimensional finite element method, the electromagnetic performances of the proposed machine are investigated to verify its validity. The results show that it can offer symmetrical and sinusoidal back-EMF, high fault tolerance, and low force ripple.

Investigation of Novel Multi-Tooth Linear Variable Flux Reluctance Machines

Novel multi-tooth linear variable flux reluctance machines (LVFRMs) are proposed in this paper. First, the topologies and feasible primary-/secondary-pole combinations of singleand multi-tooth LVFRMs with six primary poles are introduced. Based on the analytical analysis of permeance model, the maximum average force can be obtained when the dc field and ac armature copper losses are equal. Moreover, four small teeth per primary pole (n = 4) LVFRM exhibits the largest average force. Furthermore, the electromagnetic performances of singleand four-tooth LVFRMs with N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> = nN <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> + 1 are comparatively studied using the 2-D finite-element analysis (FEA). It is shown that 6/25 primary-/secondary-pole four-tooth LVFRM can provide higher force capability and lower force ripple than that of 6/7 primary-/secondary-pole single-tooth LVFRM at relatively low copper loss. Similar to singletooth LVFRMs, four-tooth LVFRMs with N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> = nN <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> ± 1 exhibit more sinusoidal back electromotive force, larger thrust force and lower force ripple than those with N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> = nN <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> ± 2. Finally, the 3-D model of 6/25 primary-/secondary-pole four-tooth LVFRM is investigated to validate the 2-D FEA predicted results.

Quantitative Comparison of Novel Dual-PM Linear Motors for Ropeless Elevator System

Due to high land prices in the metropolitans, such as Hong Kong, Tokyo and New York, high-rise buildings are mushrooming one after another. The conventional vertical elevators in multi-level or low-rise building, which usually adopt rotational electric motors plus hoist cables with counterweights, are no longer applicable. The cable for hoisting elevators have the strength and stability problems as it gets longer and longer [1], [2]. For solving these problems, a ropeless elevator system with self-propelled cars is proposed and testified. This system adopts the linear motor to drive the elevator car and omits the counterweight and cable [3], [4]. Thus, the efficiency and operation performances are dramatically improved. Moreover, areas of the elevator hoistway can be reduced [5]. According to the requirements, linear motors for ropeless elevators need to satisfy the following features: high power density, high force density, high reliability, high ratio of payload to self-weight and low force ripple. To achieve the above features, dual permanent magnet (PM) linear motors with fault-tolerant teeth (FTT) are good candidates. When the elevator car size is fixed, one way to further increase the force density with the same current density is to adopt the dual-PM structure [6]. Thus, in this paper, four dual-PM linear motors are proposed and compared for the application of ropeless elevator system.

Analysis of double‐sided sandwiched linear flux‐switching permanent‐magnet machines with staggered stator teeth for urban rail transit

Linear flux-switching permanent-magnet (LFSPM) machines exhibit significant potential in many applications. A double-sided sandwiched LFSPM (DSSLFSPM) machine with high thrust force capability is investigated in this study. After being optimised for optimal thrust force using Maxwell 2D, this machine is found to deliver higher thrust force when compared with an optimised conventional 12/14 LFSPM machine. However, low thrust force ripple is also required in many applications. Thus, in order to reduce the thrust force ripple, the DSSLFSPM machine is improved by a staggered stator teeth structure and an end permanent-magnets method, then, two improved machines are obtained. The improved machines can reduce the thrust ripple to a very low level without thrust force density decrease. Further, the stator yoke thickness of the improved machines is optimised to reach optimal thrust force density. Finally, the performance of the DSSLFSPM-ST machines is analysed including the normal force, the efficiency and the power factor. It shows that the improved DSSLFSPM machines exhibit relatively low normal force and high thrust force density as well as low thrust ripples, indicating that they are suitable for long-stroke applications.

Fuzzy Predictive Force Control (FPFC) for Speed Sensorless Control of Single-side Linear Induction Motor

In this paper a model fuzzy predictive force control (FPFC) for the speed sensorless control of a single-side linear induction motor (SLIM) is proposed. The main purpose of of predictive control is minimizing the difference between the future output and reference values. This control method has a lower force ripple and a higher convergence speed in comparison to conventional predictive force control (CPFC). In this paper, CPFC and FPFC are applied to a linear induction motor and their results are compared. The results show that this control method has better performance in comparison to the conventional predictive control method.

Optimal design of a linear transverse‐flux machine with mutually coupled windings for force ripple reduction

This study presents a design method of a linear transverse-flux machine with mutually coupled windings aiming at the force ripple optimisation. Considering the three-dimensional (3D) magnetic flux in the proposed machine, a mathematic model based on Maxwell stress tensors is developed to facilitate the optimisation, so that the objectives depending on the selected design parameters can be analytically calculated. In order to reduce the optimisation time of the complex machine, mostly influential design parameters are evaluated by the Taguchi method first. Furthermore, the selected parameters are optimised with the human group optimisation algorithm. The main purpose of the algorithm is to attain the desired electromagnetic force with the minimum force ripple coefficient under the restriction of the overall volume. The proposed optimisation has been applied for a case study, and the final design is compared with that optimised by the genetic algorithm. The results show that the optimal machine design obtained by the proposed method has the lower force ripple coefficient, which is also verified by the 3D finite-element method and experiments.

Electromagnetic field analysis of novel low cogging force, linear switched reluctance motor, based on 2-D finite element method

This paper deals with electromagnetic design and 2-D (two-dimensional) magnetic field analysis of novel low force ripple linear switched reluctance (LSR) motor. The configuration that has been presented here has a higher number of rotor poles than stator poles, and the purpose of this configuration is to improve the force ripple, which is the weak point of LSRMs. In order to illustrate the conformity of the design parameter’s stage in this study, the calculated values of the magnetic field and cogging force characteristics are compared with that of their desired values. Also, the proposed configuration is compared to a 6-4 and 3-phase conventional LSRM with similar number of stator teethes, number of phases, and constraints in volume. From the numerical analysis of a proposed novel configuration, it has been observed that this machine produces higher force per unit volume and almost similar cogging force when compared to a conventional LSRM with identical number of stator teethes, number of phases, and constraints in volume. The obtained primary electric and magnetic characteristics for the proposed configuration are verified with the help of 2-D FE computations.

Novel linear switched-flux PM machine with 9/10 primary/secondary pole number combination

Purpose – Due to linear structure, linear switched flux permanent magnet machines (LSFPMMs) also may have odd pole primary, such as 9, 15, 21, etc., without unbalanced magnetic force in equivalent rotary machines. The paper aims to discuss these issues. Design/methodology/approach – In order to increase the thrust force density, the influence of some major design parameters, including split ratio, PM thickness, primary slot width and secondary pole width, are investigated by finite element analysis. For reducing the thrust force ripple under on-load condition, the end auxiliary teeth are adopted and their positions are also optimized. Findings – This novel 9/10 primary/secondary poles LSFPMM has high average thrust force and low thrust force ripple by optimization. The results demonstrate that the odd pole primary may be a good candidate for long-stroke linear direct drive application. Originality/value – A novel 9/10 primary/secondary poles linear switched flux permanent magnet machine is developed in this paper. The similar conclusions could be obtained for other LSFPMMs with odd pole primary.

Optimization and Analysis of a Yokeless Linear Flux-Switching Permanent Magnet Machine With High Thrust Density

This paper proposes a new yokeless linear flux-switching permanent magnet (LFSPM) machine topology with double magnets per mover module for maximizing thrust density. The optimization and analysis for the proposed yokeless LFSPM machine are carried out by the finite-element method. The comparison between the proposed yokeless LFSPM machine and the optimized conventional yokeless machine under the same constraints is conducted, showing that the proposed machine exhibits higher thrust density and low force ripple, while the product of power factor and efficiency of the new machine is marginally higher than that of the conventional yokeless machine.

Analysis and Optimization of a Novel Tubular Staggered-Tooth Transverse-Flux PM Linear Machine

A novel tubular staggered-tooth transverse-flux permanent magnet linear synchronous machine is proposed. The machine is characterized by simple structure and low flux leakage. First, the structure and the operational principle are introduced. Second, the 3-D equivalent magnetic circuit model of the machine is built, and the analytical expression of the electromagnetic force is derived. Last, the force density and the force ripple are optimized with respect to three key dimensional ratios by the 3-D finite-element method. An optimized scheme with the high force density of $2.697 \times 10^{5}$ N/ $\text{m}^{3}$ and the low force ripple of 2.78% is achieved. In addition, the characteristics of the proposed machine are compared with other topologies of linear machines.

Design Optimization of a Double-Sided Hybrid Excited Linear Flux Switching PM Motor With Low Force Ripple

This paper describes design techniques for a doublesided hybrid excited linear flux switching permanent magnet motor to achieve low force ripple while satisfying the required average thrust force. In this paper, we employ auxiliary poles fixed to both sides of the mover and determine the switching signal turn-on angle to reduce the force ripple in the initial design. Then, the sensitivity analysis of two split ratios is conducted to provide a feasible search direction for the optimization process. Finally, a finite-element-based optimization is utilized to minimize the force ripple and to satisfy the required average thrust force. Simulation results are validated by experimental measurement.

Optimal Design of a Double-Sided Permanent Magnet Linear Synchronous Motor for Ropeless Elevator System

The ropeless elevator driven by linear motor is expected to be a new solution to vertical transportation of skyscrapers and the deep underground mines. Due to high thrust force density, low force ripple and low cost etc., a double-sided permanent magnet linear synchronous motor (DPMLSM) with slotted iron core and multi-segment primary is proposed and designed. Based on the erected 2D finite element model, the structure is optimized in order to reduce the detent force. Moreover, the influence of manufacture error on force performance is also investigated. It is shown the proposed DPMLSM is suitable for the ropeless elevator.

Using Third Harmonic for Shape Optimization of Flux Density Distribution in Linear Permanent-Magnet Machine

This paper presents a sinusoidal permanent magnet (PM) shaping technique with third harmonic to improve the electromagnetic thrust force in linear slotless PM machines without sacrificing the thrust force ripple. Slotless PM linear machine possesses relatively low thrust force ripple due to the absence of cogging force, compared with slotted topology. However, thrust force ripple of the machine with rectangular PM shape still exists due to nonsinusoidal airgap flux density distribution produced by PMs. Sinusoidal shaping techniques can be used to reduce the thrust force ripple but the average thrust force is reduced as well. Therefore, a simple PM shaping technique with optimal 3rd harmonic is presented to improve the output thrust force but not to increase the thrust force ripple. The sinusoidal plus 3rd harmonic shaping technique is analytically demonstrated together conventional sinusoidal shaping method and verified with finite element method. The results show that the electromagnetic performance can be significantly improved.

Design and experimental validation of doubly salient permanent magnet linear synchronous motor for precision position control

A typical iron-core permanent magnet linear synchronous motor (PMSLM) suffers force ripple originated from detent force. Rare earth permanent magnets (PMs) in stationary part cause cost issue. This paper introduces a doubly salient PMLSM (DSPMLSM) which reduces force ripple and number of PMs in stationary part. A prototype DSPMLSM is made based on geometry optimization by response surface methodology (RSM) considering multiple responses combined with 2D finite element analysis (FEA). Analysis and experimental results show promising results that the proposed DSPMLSM displays low force ripple and good positionability.

A Linear Doubly Salient Permanent-Magnet Motor With Modular and Complementary Structure

A linear doubly salient permanent magnet (LDSPM) motor is particularly suitable for long stator applications due to its simple and low cost stator, which consists of only iron. This paper proposes a new LDSPM motor design with complementary and modular structure. The key of this structure is that the primary mover is composed of two modules whose positions are mutually four and one half of the stator pole pitch apart and there is a flux barrier between them. Hence, the back electromotive force (EMF) waveform and cogging force of the two modules have 180 electrical degree differences. This design results in the total cogging force being significantly reduced and the back-EMF of each phase becoming symmetrical because the even harmonics are canceled. For fair comparison, an existing linear LDSPM motor is designed based on the same electromagnetic parameters and compared by the means of finite element analysis (FEA). The results reveal that the proposed LDSPM motor can offer symmetrical back-EMF waveforms, smaller cogging force, lower force ripple, and higher magnet utilization factor than the existing one.