Low Thrust Ripple Research Articles

A Slotted Double-Primaries Permanent Magnet Synchronous Linear Motor With a Low Thrust Ripple

A Slotted Double-Primaries Permanent Magnet Synchronous Linear Motor With a Low Thrust Ripple

Electromagnetic analysis and detent force minimization of a linear vernier motor

This paper proposes a new dual-sided linear permanent magnet vernier motor (LPMVM). The advantages of high thrust density, low thrust ripple, positive force elimination and structural stability are introduced in detail. The double-sided structure and toroidal winding proved the novelty of the machine tool, which is suitable for high definition digital control machine tools. Firstly, the basic structure and working principle of the engine are introduced. Through theoretical analysis, the expressions of electromagnetic thrust and detent force are derived. Thirdly, basic characteristics of permanent magnetic magnet flux coupling, backless electromotive force, detent force and electromagnetic drive are analyzed by using a a simplified three-phase model with symmetric boundary in 3-D finite element analysis. Finally, the thrust density and the detent force of the designed motor are calculated and analyzed. The results show that the designed motor is superior to the linear permanent magnet synchronous motor.

Thrust Ripple Reduction of Dual-Side Toroidal-Winding Linear Permanent Magnet Vernier Machine by Unequal End-Teeth Width

The linear permanent magnet vernier machines have attracted more and more attention last several years due to its high thrust density at low speed, which is very suitable for the direct-drive applications. A dual-side toroidal-winding linear permanent magnet vernier machine (DSTWLPMVM) with the unequal end-teeth width is proposed in this paper to reduce the detent force and thrust ripple. The low detent force in DSTWLPMVM is achieved by combination of two single-side detent forces with the opposite phase angle, which is obtained by optimizing the unequal end-teeth width of the primary two-sides. In the proposed machine, the symmetry three-phase flux linkage of the toroidal winding also can be obtained by optimizing the unequal end-teeth width. Therefore, the low thrust ripple of DSTWLPMVM is achieved by optimizing the unequal end-teeth width for obtaining the low detent force and symmetry three-phase flux linkage. The vertical magnetic force in the proposed LPMVM is also considered by finite element analysis (FEA) in this paper. Via optimizing the unequal end-teeth width, the detent force is reduced by 90% while the peak-to-peak thrust ripple is reduced by 69% than that of DSTWLPMVM with the equal end-teeth width, respectively. In this paper, the thermal and PM demagnetization behavior of the proposed machine are also analyzed by FEA.

Modified Primary Flux Linkage for Enhancing the Linear Induction Motor Performance Based on Sliding Mode Control and Model Predictive Flux Control

This paper proposes a modified primary flux linkage and an improved weighting less model predictive control for linear induction motors (LIMs) to enhance the drive system in terms of linear speed response, wide speed range, efficiency, and computation time. Sliding mode controller is presented in this work to get quick response instead of the use of the PI controller. A weighting less model predictive flux control (MPFC) is employed to eliminate the weighting factor and reduce the computation time. Furthermore, the optimum value of the primary flux linkage is calculated to guarantee higher efficiency under the operation of maximum thrust per ampere, loss minimization control and wider speed range in the field weakening region. The FCS-MPFC uses only the primary flux in the cost function independent on the weighting factor. Moreover, simplified calculation process can be executed greatly in the αβ-coordinates without transformation matrix, where the end-effect is fully taken into consideration. In comparison with the PI controller under different conditions, the proposed control method can achieve faster dynamics with lower thrust ripple, computation time, and so on. Comprehensive simulation and experimental results based on one prototype with 3 kW linear induction machine have verified the advantages of the proposed strategy in this work.

A Low Detent Force DS-PMSLM Based on the Modulation of Cogging and End Forces

This article presents a low detent force double-sided permanent-magnet synchronous linear motor (DS-PMSLM), which contains two flat-type stators and a mover. The mover is constituted of a fiberglass support plate and Halbach array permanent magnets attached on both surfaces of this plate, which provides a large thrust force and low mover mass for high dynamic response. For the sake of reducing the thrust ripple, a modulation method of the cogging and end forces is proposed based on the destructive interference. The even-order harmonics in cogging and end forces are reduced by adjusting the width of the side slots and the lengths of end teeth, respectively. In order to reduce the odd-order harmonics of the detent force, the cogging force and end force are modulated to reverse phases and identical amplitudes by changing the equivalent lengths of four end teeth. An integrated subdomain analytical model considering the cogging and end effects is built to optimize five structural parameters of the stators for low detent force. Finally, the prototype and testing platforms are set up and the experimental results validate that the proposed DS-PMSLM can achieve a low thrust ripple of less than 1.5 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ \%$</tex-math></inline-formula> .

A Non-Permanent Magnet DC-Biased Vernier Reluctance Linear Machine with Non-Uniform Air Gap Structure for Ripple Reduction

Thrust ripple and density greatly impact the performance of the linear machine and other linear actuators, causing positioning control precision, dynamic performance, and efficiency issues. Generalized pole-pair combinations are difficult to satisfy both the thrust and ripple for double salient reluctance linear machines. In this paper, a DC-Biased vernier reluctance linear machine (DCB-VRLM) is proposed to solve the abovementioned issues. The key to the proposed design is to reduce the ripple and enhance the thrust density with non-uniform teeth by utilizing and optimizing the modulated flux in the air gap. To effectively verify the proposed design, the DCB-VRLMs with different winding pole pairs and secondary poles are compared. The 12-slot/10-pole combination is chosen to adopt a non-uniform air gap structure. Moreover, the energy distribution of AC/DC winding is studied and optimized to further enhance the performance of the proposed DCB-VRLM. The results indicate that the DCB-VRLM with the non-uniform air gap has a lower thrust ripple, better overload capability, and higher thrust density, which confirms its superiority in long-stroke linear rail transit and vertical elevator applications.

A Novel Consequent-Pole Modular-Mover Linear Permanent Magnet Vernier Machine for Thrust Ripple and Cost Reduction

Recently, linear permanent magnet vernier machine (LPMVM) is attracting more and more attention due to its high thrust density, high efficiency, and simple structure at low-speed operation, which makes it a preferable solution for direct-drive linear motion applications. In order to further reduce the thrust ripple and the cost of LPMVM, a novel consequent-pole modular-mover LPMVM (CM-LPMVM) is proposed and analyzed in this article. Due to the dual-flux-modulation effect, the proposed CM-LPMVM can exhibit a low thrust ripple (∼3.2% of the average thrust) and high thrust density (∼387 kN/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) at a low current density of 3 A/mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , as well as reduce nearly half of the PM usage at the same time. The performance improvement of the proposed CM-LPMVM is verified by the comparison to a regular modular-mover LPMVMs, using the finite-element method. Finally, three prototypes are built and tested. The experimental results match well with the analytical data, showing the superiority of the proposed CM-LPMVM.

Design and Modeling of a Novel Permanent Magnet Width Modulation Secondary for Permanent Magnet Linear Synchronous Motor

High-speed linear motor with low thrust ripple is one of the research focuses of high-performance systems. This article proposes a novel secondary topology for permanent magnet (PM) linear synchronous motor (PMLSM) with high speed, to suppress the thrust ripple. PM width modulation secondary adopts several PMs to excite the main magnetic field per pole. The issues from a big pole pitch, which is generally used by high-speed PMLSM, are solved. These PMs have various longitudinal lengths based on the pulsewidth modulation principle, to achieve a magnetic field with excellent sinusoidal features. First, the topology structure of PM width modulation secondary is designed. The analytical model of the main magnetic field excited by PMs in this novel secondary is established, and the electromagnetic thrust is calculated. Furthermore, the influences of PM width modulation secondary on the main magnetic field and thrust properties are analyzed. The comparisons between two PMLSMs employing PM width modulation secondary and Halbach secondary, respectively, are provided. Finally, prototypes are manufactured and tested, to verify the effectiveness of the topology proposed in this article.

Analysis and Design Optimization of Tubular Linear Voice Coil Motor for High Thrust Force and Low Copper Loss

In recent years, studies on the design of the tubular linear voice coil motor (TLVCM) have increased considerably. These studies propose to obtain high thrust force, high efficiency, low thrust ripple, low cost, or low volume. The magnetic equivalent circuit of the motor is created, and for any objective, only one or some parameters are emphasized. In fact, the effect of each geometric parameter of the TLVCM on performance is different and important. This study proposes multiparameter and multiobjective design optimization for high thrust force and low copper loss using a complex magnetic equivalent circuit model and nondominated sorting genetic algorithm II. Besides, the optimized motor design is analyzed by the finite element method. The average thrust force has been increased, and copper loss has been reduced with multiple interactive changes of the motor geometry, while the thrust ripple has also been reduced. According to the obtained results, a multiparameter design approach is thought to contribute to the performance of the TLVCM with the proposed approach.

Improved Analytical Modeling of a Novel Ironless Linear Synchronous Machine With Asymmetrical Double-Layer Winding Topology

The Ironless Permanent Magnet Linear Synchronous Motor (ILPMLSM) with nonoverlapping windings is widely used in precise applications due to its simple structure, low thrust ripple, and fast response, while the disadvantage is low thrust density. The novel asymmetrical double-layer winding ILPMLSM with quasi-Halbach magnets can improve the thrust density while keeping simple structure. However, the double-layer windings are asymmetric and the primary has finite length. To solve the problem of this asymmetry and investigate its influences on electromagnetic characteristics, an improved 2-D analytical model is proposed, which introduces “virtual periodic primary” and solves the magnetic field of each winding layer. By the results of finite element and experiments, the proposed analytical model is verified. Moreover, the analytical model requires less computation time, which is helpful for optimizing design of this motor.

Thrust Performance Improvement for PMSLM Through Double-Layer Reverse Skewed Coil and WRF-MKH Method

This article is dedicated to achieving the best thrust performance of high thrust and low thrust ripple of permanent magnet synchronous linear motors (PMSLMs), which are used in precision positioning system. To achieve this, a novel PMSLM with double-layer reverse skewed coil (DRSC) is designed and optimized. First, the topological structure of the DRSC-PMSLM is introduced, and the effectiveness of the DRSC is analyzed qualitatively according to the analytic model. Certain hypotheses that are more suited to qualitative analysis can lead to the low accuracy of the analytic model. Therefore, for the subsequent optimization, the weighted random forest (WRF), an enhanced random forest (RF) algorithm by assigning different weights to different regression trees, is proposed to fit the sample data generated by the finite element method to establish a high-precision proxy model. Accuracy test proves that the WRF model has higher accuracy than the standard RF model and the analytical model. Subsequently, a new global optimization algorithm, call the modified Krill Herd (MKH) algorithm is proposed to iteratively optimize the WRF model to obtain the optimal structure parameters. The MKH algorithm is a modified KH algorithm that two strategies are used to improve the convergence rate and avoid premature convergence. Comparative experiments are performed by using genetic algorithm, particle swarm optimization, and standard Krill herd, which prove that the MKH has faster convergence speed and stronger global search capability. The thrust performance of the optimized motor is improved considerably compared with that of the initial motor, which further proves the effectiveness of the MKH used in this article. Finally, the prototype experiment proves that the PMSLM with DRSC has the best thrust performance.

Robust Design Optimization of Permanent Magnet Linear Synchronous Motor Based on Quantified Constraint Satisfaction Problem

This study focuses on the robust design optimization of permanent magnet linear synchronous motors (PMLSM) considering the effect of uncertainties (noise factors) such as manufacturing errors, installation errors and working wears. A robust design optimization approach based on quantified constraint satisfaction problem (QCSP) is proposed. It establishes a robust PMLSM thrust ripple model considering noise factors by QCSP, and obtains the optimal design parameters that have lower thrust ripple and smaller thrust ripple fluctuation within their error range by branch-and-prune algorithm. First, an analytical model of thrust ripple for PMLSM is established. Second, the robust QCSP model of thrust ripple is established by quantifier concept based on analytical model. It defines the design parameters and noise variables as existential and universal quantifiers, respectively, defines the variables of QCSP model as quantifier parameters that are composed of existential and universal quantifiers, then QCSP model are established by quantifier parameters. Third, the algorithm of branch-and-prune based on interval arithmetic is proposed to optimize the QCSP model. This approach is proven to be robust and superior compared with traditional deterministic approach and another robust approach. Finally, Finite element analysis and motor prototype experiments confirm the feasibility and validity of the proposed method.

Analysis of the Fractional Pole-Pair Linear PM Vernier Machine for Force Ripple Reduction

Linear permanent magnet Vernier machine (LPMVM) is attracting more and more attentions recently due to its simple structure, high efficiency, and high thrust density at low speed. In this article, a novel fractional pole-pair linear permanent magnet Vernier machine (FP-LPMVM) is proposed, which gives more freedom in the design of the LPMVM to reduce the force ripple of the machine. The operation and force ripple reduction principles of the FP-LPMVM are also given in this article with the help of analytical equations. It is found that some of the proposed FP-LPMVM exhibit inherent good performances such as high EMF symmetry and low thrust ripple due to the combining of the flux modulation effect and the FP-LPMVM. In order to verify the theoretical analysis in this article, two LPMVM prototypes (i.e., 12 slots 20 poles integer pole-pair LPMVM and 18 slots 29 poles fractional pole-pair LPMVM) are manufactured, tested, and compared with each other. The experimental results are consistent with the FEA results, and the validity of the analysis and the superiorities of the proposed FP-LPMVM are verified.

MTPA-Based Finite-Set Model Predictive Control Without Weighting Factors for Linear Induction Machine

The efficiency of the linear induction machine (LIM) is considerably low due to the large air-gap length and the additional losses resulting from the end-effects. However, so far, a little concentration has been done to increase the efficiency of this kind of motor. Therefore, the main objectives of this article are to eliminate the weighting factor, reduce the calculation steps, and increase the efficiency of the LIM aiding with a proposed finite-set model predictive direct flux control (FS-MPDFC), depending upon the maximum thrust per ampere (MTPA) strategy. The proposed FS-MPDFC is only based on the primary flux-linkage with the help of a novel cost function that does not require any weighting factors in order to considerably reduce the calculation steps. Moreover, the proposed FS-MPDFC is better than the model predictive current control in reducing the calculation step and decreasing the dependence on the transformation matrix and the machine parameters. In order to illustrate the effectiveness of the proposed MTPA-based FS-MPDFC, a comparison between the FS-MPDFC, with and without MTPA, and the previously suggested control techniques is presented and discussed. Moreover, a test bench platform of two 3-kW arc induction machines is constructed to emulate the drive performance of the actual LIM. Comprehensive simulation and experiments have fully demonstrated that the proposed FS-MPDFC with MTPA has lower calculation step, lower thrust ripple by 7%, and lower primary flux-linkage ripple by 0.4% compared to those of the FS-MPDTC. Moreover, the efficiency-based FS-MPDFC with MTPA is increased by 4% compared to that of the FS-MPDFC without MTPA.

An Efficient Multiobjective Design Optimization Method for a PMSLM Based on an Extreme Learning Machine

This paper focuses on the multiobjective design optimization of the permanent magnet synchronous linear motors (PMSLMs), which are applied to a high-precision laser engraving machine. A novel efficient multiobjective design optimization method for a PMSLM is proposed to achieve optimal performances as indicated by high average thrust, low thrust ripple, and low total harmonic distortion at different running speeds. First, based on the finite-element analysis (FEA) data, a regression machine learning algorithm, called an extreme learning machine (ELM), is introduced to solve the calculation modeling problem by mapping out the nonlinear and complex relationship between input structural factors and output motor performances. Comparative simulation experiments conducted using the traditional analytical modeling method and another machine learning modeling method, i.e., support vector machine, confirm the superiority of the ELM. Then, a new bionic intelligent optimization algorithm, called the gray wolf optimizer algorithm, is used to search the best optimization performances and structural parameters by performing iteration optimization calculation for multiobjective functions. Finally, FEA and prototype motor experiments prove the effectiveness and validity of the proposed method.

Thrust Ripple Analysis on Toroidal-Winding Linear Permanent Magnet Vernier Machine

Linear permanent magnet Vernier machines (LPMVM) have received more and more attention in recent years due to the advantages of high thrust density and low thrust ripple, which are both required in many direct-drive applications. In this paper, a double-sided toroidal-winding LPMVM (DSTWLPMVM) is proposed, and the thrust ripple sources for this type of machine are analyzed. To emphasize the specificity of LPMVM in aspect of thrust ripple optimization, a traditional fractional-slot linear permanent magnet synchronous machine is selected as a reference. Two indexes [amplitude difference (AD) and phase shifting (PS)] are defined to quantify the thrust ripple caused by the AD and the PS among three-phase electromotive force (EMF), respectively. Additionally, detent force is also considered when optimizing the three-phase EMF. Finally, a prototype of DSTWLPMVM is manufactured and tested. The measured EMF is basically symmetrical sinusoidal waveforms and the peak-to-peak value of the detent force is lower than 10 N.

Design and Analysis of an Interior Permanent Magnet Linear Vernier Machine

A novel interior permanent magnet linear vernier machine (IPM-LVM) is proposed and analyzed in this paper. Compared to the existing surface-mounted permanent magnet linear vernier machine (SPM-LVM) and the SPM-LVM with Halbach arrays, the proposed machine can offer higher flux density in both the air-gap and armature iron core, which lead to a higher back electric motive force (back EMF) and higher thrust density under the same mover volume and heat capacity. Besides, it is proven that the proposed IPM-LVM also has a lower demagnetization risk compared to the SPM-LVM. Furthermore, in order to reduce the thrust ripple of the proposed machine, the three-sectional structure is adopted in this paper, which makes the proposed IPM-LVM exhibit high thrust density and low thrust ripple at the same time.

Design and Performance Investigation of Novel Linear Switched Flux PM Machines

A novel partitioned primary linear switched flux permanent magnet (PLSFPM) machine is presented, which adopts an odd number of primary poles. For the design objective of minimum thrust ripple, the optimized novel PLSFPM machine with 9 primary/10 secondary (9/10) pole combination is obtained. To this optimized PLSFPM machine, the electromagnetic performance is analyzed in detail and compared with that of the original one. The merits of this 9/10 pole combination are also proved by comparative study with other three available pole combinations. Moreover, comparison between the proposed PLSFPM machine and a conventional linear switched flux permanent magnet machine has been performed, which shows that the proposed machine can achieve better performances under both open-circuit and load conditions. The corresponding prototype is manufactured and the influences of possible machining errors during manufacture on thrust force performance are discussed. Finally, the experiment is carried out, which verifies the predicted results. The research shows that the proposed PLSFPM machine with 9/10 pole combination has high thrust force and low thrust ripple.

Research on Permanent Magnet Linear Synchronous Motors With Ring Windings for Electromagnetic Launch System

Since permanent magnet linear synchronous motor (PMLSM) has a bright future in electromagnetic launch (EML), moving-magnet PMLSM with multisegment primary is a potential choice. To overcome the end effect in the junctions of armature units, three different ring windings are proposed for the multisegment primary of PMLSM: slotted ring windings, slotless ring windings, and quasi-sinusoidal ring windings. They are designed for various demands of EML, regarding the load levels and force fluctuations. Auxiliary iron yokes are designed to reduce the mover weights, and also help restrain the end effect. PMLSM with slotted ring windings has a higher thrust for heavy load EML. PMLSM with slotless ring windings eliminates the cogging effect, while PMLSM with quasi-sinusoidal ring windings has very low thrust ripple; they aim to launch the light aircraft and run smooth. Structure designs of these motors are introduced; motor models and parameter optimizations are accomplished by finite-element method (FEM). Then, performance advantages of the proposed motors are investigated by comparisons of common PMLSMs. At last, the prototypes are manufactured and tested to validate the feasibilities of ring winding motors with auxiliary iron yokes. The results prove that the proposed motors can effectively satisfy the requirements of EML.

Design and Analysis of a New Ring Winding Structure for Permanent Magnet Linear Synchronous Motors

With the quick development of electromagnetic propulsion systems, permanent magnet linear synchronous motors (PMLSMs) have been the focus of research for high-performance propulsion systems. Compared with traditional windings, two ring windings with novel structures and better performance for PMLSMs are proposed: the single-layer ring windings are suitable for high-power systems; the double-layer ring windings can be adopted in low fluctuation systems. This paper first analyzes the electromagnetic parameters of the ring windings based on the equivalent magnetizing current method to verify the availabilities of ring windings. The main parameters of two ring windings are compared to achieve the optimization guides. Then, the magnetic fields and thrust characteristics of ring windings and traditional lap windings are analyzed by the finite-element method, and the independent magnetic field of ring winding ends is verified. And then a prototype motor with double-layer ring windings was manufactured and experimentally tested, the measurement data were matched with the theoretical calculations. The results illustrate that the PMLSM with ring windings has higher thrust density and lower thrust ripple, ring winding structure is more suitable for electromagnetic propulsion systems.