I- Introduction

II- IPMSM Model

III- Grid On/Off Search Method

IV- Simulation Results

V- Structural Analysis

VI- CONCLUSION

REFERENCES

Abstract

Interior permanent-magnet synchronous motors (IPMSMs) have been widely used due to their high-efficiency and high-power densities. Minimization of torque pulsation resulting in vibration and acoustic noise is one of the important design considerations for IPMSMs. In this paper, a grid on/off search method for the rotor profile is proposed to mitigate torque pulsation. Selection of the rotor profile is due to the fact that air gap is the most sensitive parameter in electric machines wherein changes in flux densities can cause substantial differences in the distribution of forces. A layer comprised 20 partitions with a 0.1 mm thickness and 3° wide grids have been introduced to the rotor surface for each pole, and the possible geometries have been analyzed using the finite-element method in ANSYS Maxwell. An optimal design was found that has the lowest torque ripple with a higher average torque compared to the original design. Genetic algorithm has also been applied to the method to automate the coupling between Maxwell and MATLAB, thereby saving the simulation time. Complete structural analysis has been done for both of the original and optimal designs to verify the superiority and feasibility of the proposed design.

INTRODUCTION

INTERIOR permanent-magnet synchronous motors (IPMSMs) have broad applications in electric vehicles, home appliances, and robotics due to their high-power densities, high torque densities, and large speed ranges [1], [2]. Permanent magnets are buried inside the rotor, which leads to an unequal permeability for the d-axis and q-axis leading to magnetic saliency. Given the presence of reaction torque, caused by the magnetomotive force (MMF) of the stator and its interaction with permanent magnets, the torque of IPMSM is a combination of reaction and reluctance torques, which provides a higher torque density and wider speed range during field weakening compared to other conventional machines [3]. However, torque pulsation is one of the most important design considerations in IPMSMs, since it can cause unwanted byproducts such as vibrations and acoustic noise. Mitigation of torque pulsation has been studied by many scholars. There are mainly two categories of methods, namely, control techniques such as the current profiling method [4], [5], and the optimal design method. However, reducing torque pulsation based on power electronics and control method heavily depends on the accuracy of the power electronics circuits as well as the need for high-end microcontrollers to guarantee a timely execution of the control algorithm. This paper proposes a torque ripple minimization method from the design point of view. Many techniques have addressed this topic, such as rotor or stator skewing [6]–[8], magnet skewing and shape optimization [7], slot/pole number combinations [7], [9], [10], optimization of flux barrier such as asymmetric flux barriers [11], rotor shape optimization, such as Kiyoumarsi and Moallem [12], Kioumarsi et al.

I- Introduction

II- The Mathematical Model

III- The Numerical Modeling of The Hybrid Stepper Motor

IV- Experimental Results

V- Conclusions

References

Abstract

The design of a hybrid stepper motor for achieving a specific performance requires its adequate geometrical sizing that may be performed through numerical modeling. With this aim, the current study documents several aspects of the three– dimensional numerical modeling that was used to predetermine the holding torque for a stepper motor and presents different approaching methods used to reduce redundancies. The results for holding torque calculation are compared with experimental measurements in order to validate the numerical model. Moreover, optimal economic and technical solutions were obtained through successive improvements made in the design phase and concurring to the requirements of the product specification are included.

INTRODUCTION

The increased demand towards motion control of stepper motors (SMs) play a key role in a wide range of applications demanding for accuracy and repeatability [1]. SMs are increasingly used as digital actuators because they do not require digital‒to‒analog (D/A) conversion. For instance, SMs are utilized as actuators in a spacecraft instrumentation system [2], or to control drum actuators [3]. Consistently, theoretical and experimental work was devoted to study and compare the SMs with conventional closed–loop positioning systems [4] and to deploy the SMs to a variety of applications. The SM main parameters are: parasitic torque, holding torque and running torque. Parasitic torque sums up the hysteresis torque, the irreversibility torque and the detent torque. The SM is largely presented in [5], where a study regarding the detent torque (the torque with the windings not energized) is presented. In SMs, position holding must occur without energy consumption [6–10]. This paper is focused on another important parameter of the SM, namely the holding torque (the torque with the windings energized). Numerical modeling and experimental results are presented and discussed.

I- Introduction

II- SRM Analytical Torque Model

III- Comparison Study of Six-Phase Topologies

IV- Copper Loss for Multiphase Machine

V- Experimental Validation

VI- CONCLUSION

References

INTRODUCTION

SWITCHED reluctance machines (SRMs) have excellent features such as simple and robust structures, high manufacturability, good fault-tolerant capability, and also low cost. In addition, without permanent magnets or field windings on the rotor, they are particularly suitable for harsh environmental operations such as high speed and high temperature. Due to these significant advantages, SRMs have attracted increasing interest in electric vehicles, aerospace, and other safety-critical applications [1], [2]. However, the doubly salient structure together with the special rectangular wave current supply causes high torque ripple, high vibrations, and acoustic noise compared with other types of machines. Therefore, in past decades, the torque ripple reduction is one of the most popular research topics for SRMs. This can be achieved from two aspects: machine design [3]–[5] and also advanced control [6], [7]. One effective and simple way to reduce the torque ripple is to increase the phase number. This method can be applicable not only to SRMs but also to synchronous (reluctance) machines and induction machines. Multiphase machines provide additional benefits apart from the torque ripple reduction because the machines with higher phase numbers (m > 3) can also have higher torque density and better faulttolerant capability compared with conventional three-phase machines [8]. In addition, different winding configurations for multiphase machines can be selected to achieve even better torque performance [9], [10]. The conventional SRMs, with three-phase or multiphase, are supplied with rectangular wave current. However, recent studies have shown that they can be supplied with sine wave currents as well [11], [12]. It has been found that the sine wave excitations can bring benefit to the radial force reduction for SRMs, which are the primary source of vibrations and acoustic noise. One of the other advantages of sine wave excitation is that the standard three-phase voltage source inverter as that used in synchronous (reluctance) machines or induction machines can be employed, which can help reduce the system cost. It also provides a more flexible control strategy for SRMs to improve the torque performance. However, it is worth noting that the SRMs with sine wave current supply are actually doubly salient synchronous reluctance machines (DS-SRMs) [13]–[15].

A method of cutting permanent magnets with circular arcs of offset center was proposed on the basis of the principle of similarity under the condition of slip drive to obtain a permanent magnet transmission scheme for low permanent magnet torque fluctuations. The magnetic flux distribution of each region in the magnetic circuit was altered by changing the shape of the permanent magnet. Different magnetic torque curves were obtained by selecting silicon steel sheet with different thicknesses. The relationship between the magnetic flux distribution and the relative rotation angle in the silicon steel sheet was further analyzed, and the direct cause of the influence of the thickness of the silicon steel sheet on the magnetic torque was obtained. The parameters of different eccentric arcs were selected for simulation calculation, and a smooth magnetic torque curve was obtained after fixing the thickness of the silicon steel sheet. On the basis of the results of the former two, the parameters of the eccentric arc were obtained by the magnetic torque value volatility using an approximation method, and the magnetic torque value was measured by making the physical object. According to the results of the simulation and experiment, the permanent magnets with eccentric arcs can be used to obtain the smooth magnetic torque in the range of a 0◦–90◦ relative rotation angle, which has a certain application value.

Introduction

The magnetic transmission concepts dated back to the early 20th century [1]. Recently, many studies on permanent magnet transmission have emerged. The axial-flux modulated superconducting magnetic gear has currently been specifically studied using a superconducting bulk magnet replacing conventional permanent magnet [2]. The coaxial magnetic gear with an eccentric pole of the inner rotor and Halbach arrays of the outer rotor was proposed and studied to improve the torque density of a coaxial magnetic gear (CMG) [3]. Substantial studies on the CMG were performed in [4]–[6]. Magnetic gears that were well suited to execute high-torque direct-drive operations for oceanic wave energy harvesting applications were designed [7]. The shape of the flux modulators of the concentric magnetic gear affects the torque capability and ripples [8]. A new geometry was proposed for the magnetic gear to reduce the eddy-current loss of permanent magnets and improve the torque transfer efficiency [9]. The permanent magnet shape is one of the main factors affecting the performance of permanent magnet transmission. The CMG has a great advantage when a large radius and a small axial length are permissible. Hence, the CMG is suitable for the drivetrain of vehicles [10]. A novel topology of a planetary magnetic gear having only two rotating parts demonstrated a torque density of 187 kN · m/m3 [11]. The air-gap magnetic fields and eddy-current densities of a non-rotary mechanical flux adjuster (MFA) were investigated under the different shifting distances of a MFA, which reveals the fairly good torque regulation effects [12].

LOCOMOTION plays a crucial role on the capacity to perform activities of daily living, personal functional abilities, and independent development in the community. However, clinical conditions such as stroke, spinal cord injury, Parkinson disease and loss of a member by amputation can affect the human locomotion with varying degrees of severity [1], [2]. To overcome or attenuate human gait disorders, devices such as prostheses [3], exoskeletons [4], and smart walkers [5] have been employed for assistance and rehabilitation purposes. Lower limb exoskeletons are being used for gait assistance and rehabilitation therapies. Robotic exoskeletons are successfully employed for rehabilitation exercises due to its higher repeatability and the quantitative feedback of the patient recovery [6]. Furthermore, the embedded sensors can also be used for continuous monitoring and evaluation of patient progress with predefined objectives and allowing the customization of treatment with increasing levels of personalization and difficulties. This customization is achieved through the dynamic interaction between the exoskeleton and the patient, which happens with the transition between passive, active-assisted, and active-resisted movements of the robotic device controller [7]. Considering the human safety, it is desirable that the exoskeleton actuators have low output impedance [7]. Otherwise, there is a risk of accident with the patient [7]. Furthermore, the actuators must have a bandwidth close to the one of human movement in order to perform the desired movements of the physiotherapy section. A straightforward manner to achieve these requirements is by placing an elastic element between the load (human limb) and the actuator. This is the series elastic actuator (SEA) principle proposed in [8]. Although the spring placed between the load and the actuator can significantly reduce the system output impedance, it also reduces the system bandwidth [9]. Since the human movement occurs in low frequencies [10], SEAs have been successfully employed as exoskeletons actuators [11], [12], [7], among others. Another advantage of SEAs is the possibility of estimating the output torque from spring deflection. For this reason, sensors for spring deflection can be employed instead of the torque sensors, which may simplify the actuator instrumentation. However, sensors used to measure these deflections are generally encoders [7] and potentiometers [13] that require mechanical supports precisely assembled due its sensitivity to misalignments. This may result in a less compact system. Additionally, potentiometers may also result in noisy measurements.

Among various control techniques, the direct torque control schemes are proven to provide simplicity, fast dynamic response and less parameter dependency compared to the current vector control schemes [1–4]. The classical direct torque control (DTC) scheme which uses hysteresis controllers and a switching table is widely used in driving electrical motors position sensorlessly, because the estimation of torque and flux can be carried out in the stationary reference frame [5]. However, one of the main drawbacks of classical DTC is the unavoidable large ripple in the torque and flux responses. As an alternative, a modified DTC scheme which reduces torque and flux ripples was proposed in [6– 8] for an interior permanent magnet synchronous machine (IPMSM) drive. The proposed method replaces hysteresis controllers and the switching table of classical DTC with a PI controller and space vector modulation. Even though this method is known to provide reduced flux and torque ripples, it is comparatively noisy and complex [7]. The modified DTC later evolved as direct torque and flux control (DTFC) scheme and gained the attention of the research community as it can provide far less torque and flux ripples while retaining the desirable features of classical DTC [9]. In the DTFC scheme, two PI controllers are used in order to regulate the torque and flux individually. Many high-performance industrial drives prefer interior permanent magnet synchronous motors due to their desirable characteristics such as high efficiency, flux-weakening capability and compact size. The flux-weakening capability is indeed an advantage to an IPMSM, because it allows the motor to achieve a wide speed range under the system constraints. Ability to operate in a wide speed range brings the benefit of efficient energy utilisation. Typically, trajectory control is implemented in IPMSM drives to achieve optimum torque performance at the constant torque and power regions [10–12]. Current vector controlled IPMSM drives use maximum torque per ampere (MTPA) trajectory, current and voltage limit trajectory and maximum torque per voltage (MTPV) trajectory defined on id–iq plane for the efficient operation of the motor over a wide speed range. It is noteworthy that the MTPV trajectory control can be applied only if the characteristic current (ratio of magnet flux-linkage over the daxis inductance) of the IPMSM is less than the rated current. If the characteristic current happens to be larger than the rated current, MTPV trajectory lies outside to the current limit circle in the id–iq plane as shown in Fig. 1a and cannot be incorporated in the control algorithm.

1. مقدمه
با الزامات موجود درباره کاهش انتشار و بهبود اقتصاد سوخت، وسایل نقلیه الکتریکی و وسایل نقلیه الکتریکی هیبریدی (HEVها) توجهات بیشتری را معطوف بخود کرده اند، که انتظار بر این است در آنها قابلیت اطمینان بالا، چگالی قدرت زیاد، و قابلیت های اضافه بار بحد کافی باشد. همچنین، موتورهای مغناطیس دائم شار سوئیچینگ (FSPM) با توجه به چگالی های قدرت و گشتاور بالا علاقمندی های قابل ملاحظه ای را برای کاربردهای درایو با عملکرد بالا جذب کرده اند [2]-[9]. علاوه بر این، از آنجا که سیم پیچ های آرمیچر و آهنرباها هر دو در استاتور واقع هستند، یک ساختار ساده و قوی از روتور موجب می شود که ماشین های FSPM برای کاربردهای سرعت بالا مناسب باشد [10].
در این مقاله، یک موتور FSPM مدولار سه فازه تولید شده همراه با جریان بالا و ولتاژ پائین استفاده شده برای HEVها با استفاده از آنالیز اجرای محدود (FEA) طراحی می شود. مدل ابتدائی FEA بصورت تدریجی با در نظر گرفتن منحنی های B-H لمینیت تحت شرایط فرکانس های مختلف الکتریکی، دمای عملیاتی، اثر پایان سه-بعدی، و همچنین ملاحظه روتور خارج از مرکز بهبود می یابد. تاثیرات مربوطه در عملکردهای الکترومغناطیسی بطور عمیق، بخصوص برای نیروی ضد محرکه فاز، و گشتاورهای الکترومغناطیسی تحت عملیات مجاز بررسی می-شود. در مقایسه با مدل اولیه FEA، یک افت کلی 40 درصدی از گشتاور الکترومغناطیسی در مدل FEA بهبود یافته دیده می شود که بطور همزمان عوامل طراحی ذکر شده را در نظر می گیرد.

هدف این مطالعه ارزیابی تأثیر زمان سپری‌شده روی خواص رئولوژیکی و تیکسوتروپی مخلوط‌های بتن خودتحکیم (SCC) حاوی افزودنی‌های معدنی مختلف است. برای این منظور، تغییرات زمان روانی T50، لزجت پلاستیک گشتاور پیچشی، تنش تسلیم ظاهری و تیکسوتروپی به‌صورت تابعی از زمان در شرایط سکون بررسی شد. مقادیر مختلف فوم سیلیکا (SF)، متاکائولن (MK)، خاکستر بادی رده F(FAF) و سرباره دانه‌ای شده کوره آهن‌گدازی (BFS) به‌صورت مخلوط‌های دوتایی، سه‌تایی و چهارتایی سیمانی در 17 SCC مختلف با مقدار روانی اسلامپ ثابت استفاده شدند. نتایج حاکی از این بود که مخلوط‌های SCC حاوی افزودنی‌های معدنی مختلف در زمان صفر براساس استاندارد ASTM C1611 دارای پایداری زیاد یا متوسطند (VSI بین صفر و 1). هرچند، در مخلوط‌های حاوی FAC، FAF و BFS در زمان 50 دقیقه فرار سیال و تفکیک ذرات بتن مشاهده شد. در شرایط سکون، تنش تسلیم ظاهری و تیکسوتروپی با گذر زمان تا حد زیادی افزایش پیدا کرد، درحالی‌که، لزجت پلاستیک گشتاور پیچشی تنها در دامنه محدودی تغییر یافت. افزون بر این، با گذر زمان، مشخص شد که MK و FAC در مقایسه با سایر افزودنی‌ها تأثیر بیشتری روی لزجت پلاستیک گشتاور پیچشی و تنش تسلیم دارند. هرچند، افزایش مقادیر تنش نسبت به لزجت پلاستیک گشتاور پیچشی محسوس‌تر بود. افزایش در تیکسوتروپی با گذر زمان برای مخلوط‌های حاوی SF و MK در قیاس با مخلوط‌های کنترل و مخلوط‌های حاوی سایر افزودنی‌های معدنی بیشتر بود.