A Novel Linear Switched Reluctance Machine: Analysis and Experimental Verification

The important problems to be solved in Linear Switc hed Reluctance Machines (LSRMs) are: (1) to design the shape and size of poles in s tator and translator cores; (2) to optimize their geometrical configuration. A novel stator geometry for LSRMs that improved the force profile was presented in this study. In the new geometry, pole shoes were affixed on the stator poles. Static and dynamic characteristics for the proposed structure had been highlighted using Two Dimensional (2-D) Finite Element Analyses (FEA). Motor performance fo r variable load conditions was discussed. The finite element analyses and the experimental result s of this study proved that, LSRMs were one of the strong candidates for linear propulsion drives. Problem statement: To mitigate the force ripple without any loss in average force and force density. Approach: Design modifications in the magnetic structures. Results: 2-D finite element analysis was used to predict th e performance of the studied structures. Conclusion/Recommendations: The proposed structure not only reduces the force ripple, also reduced the volume and mass. The future study is to make an attempt on vibration, thermal and stress analyses.


INTRODUCTION
Linear switched reluctance motors are an attractive alternative to linear induction or synchronous machines due to lack of windings on the stator or translator structure, easier manufacturing and maintenance, good fault tolerance capability (Miller, 1993). LSRMs are classified as (a) longitudinal flux (b) transverse flux. This study is dedicated to the longitudinal flux LSRM. A design procedure for longitudinal-flux LSRM has been described in (Byeong-Seok et al., 2000). Other types of longitudinal-flux LSRMs are presented in (Chayopitak and Taylor, 2005), with coupled flux paths and in (Sun et al., 2008) with uncoupled flux paths for a magnetic levitation system. A high force longitudinalflux double-sided double-translator LSRM has been analyzed in (Deshpande et al., 1995). Longitudinal-flux LSRMs have been proposed for applications such as precise motion control (Pan et al., 2005;Zhao et al., 2007) and as propulsion systems for railway vehicles (Kolomeitsev et al., 2008) or vertical elevators (Lim and Krishnan, 2007;Lim et al., 2008;Lobo et al., 2008). Recently, a detailed sensitivity analysis of double sided LSRM parameters based on (Arumugam et al., 1988) has been presented in (Amoros and Andrada, 2010).
In despite of the various advantages, LSRMs has some drawbacks such as high force ripple, vibration, acoustic noise and need of power electronic converters. Several efforts to reduce or eliminate the torque ripple of the Rotary Switched Reluctance Motors (RSRMs) have been presented in the literature (Schramm et al., 1992;Hussain and Ehsani, 1996;Rabinovici, 2005). Multi phase excitation to reduce the force ripple in the LSRM has been explained in (Bae et al., 2000). However, the previous method considerably increases the copper losses. In this study a novel stator structure for a longitudinal flux LSRM is proposed to reduce the force ripple.
A control strategy for the proposed LSRM is dynamically simulated, which consists of force and velocity control loops. A trapezoidal velocity profile is used to control travel position smoothly during acceleration, deceleration and stop of the motor. Conventional proportional-integral controller is used for the current and velocity control loops .

MATERIALS AND METHODS
Force ripple analysis using an alternative geometry: Definition, sources of the force ripple and techniques to reduce it: Assuming that the maximum value of the static force as F max , the minimum value that occurs at the intersection point of two consecutive phases as F min and the average force as F avg , the percentage force ripple may be defined as: The causes of the force ripple in LSRMs are mainly due to the switching of phase currents into its windings and the highly nonlinear nature of the phase inductance variation when the translator moves. These force pulsations contribute to vibrations and acoustic noise in LSRMs. There are two approaches to force profile improvement. One approach is to suitably shape the input excitation current profile by using an electronic control of the power controllers. The second approach is to modify the geometry of the poles of the stator and translator. This research makes an attempt to examine the force profile by the geometry modifications approach, by providing pole shoes on the stator poles.

Effect of stator pole shaping on the force profile:
This sensitivity study aims mainly to determine the improvement in the force profile when the stator pole width gets varied. The conventional LSRM which is considered in this study is shown in Fig. 1. The specifications of the conventional machine are given in Table 1.   The width of the stator pole is varied from 16-21 mm in steps. The translator geometry remains unchanged throughout the sensitivity study. The height of the stator pole is fixed. The field analysis has been carried out for a phase excitation of 10 A. The predicted propulsion force, normal force, inductance profiles and average force are shown in Fig. 2. Table 2 summarizes the comparison of the studied configurations.  Table 2 it can be observed that, when the stator pole width is increased, there is a reduction in the average force, which is not large after a certain point. Figure 2d shows the stator pole length/pole pitch Vs average force. From Fig. 2d, we inferred that, the maximum average force and the low force ripple occurs, when the pole width is 19 mm.
Force ripple minimization using stator pole shoes: Improving the force profile using stator pole shoes is investigated by a 2-D finite-element analysis. The difference between the conventional and the proposed stator poles are shown in Fig. 3. The cross sectional view of the proposed LSRM with pole shoes is shown in Fig. 4. The analysis is carried out on the conventional LSRM with a pole shoe, which is affixed on the stator poles. The width of the stator pole shoe is 4 mm. The stator pole width is varied from 16-20 mm in steps. The width of the pole shoe and overall height of the stator pole are maintained constant. The mutual inductance and leakage effects are neglected. The simulation is presented for an excitation current of 10 A.
The predicted propulsion force, normal force, inductance profiles and the average force are shown in Fig. 5. Table 3 summarizes the comparison of the studied configurations with pole shoes. The stator volume, stator mass and the % force ripple reduction are compared in Table 4. Figure 5d shows the stator pole length/pole pitch vs. average force. From Fig. 6, the maximum average force occurs when the stator pole width is 19 mm with a 4 mm pole shoe.  During starting, the deceleration command is given at 0.5 m and during stopping; the deceleration command is given at 0.1 m. The duration for holding at the stop position is set to 1sec. Figure 7 shows the simulation results of the position, velocity, phase current and generated force of the LSRM at 0.15 m sec −1 . Dynamic simulation: Force and current control: For a vertical or horizontal applications, the LSRMs needs a precise control strategy consisting of force, current, velocity and position controls, as shown in Fig. 6. Force control with a Force Distribution Function (FDF) is used to control the LSRM. A trapezoidal velocity profile is used to obtain the desired response curve of the position. In addition, current and velocity controls with Proportional-Integral (PI) control for the proposed LSRM are explained. The proposed LSRM is simulated at 0.15 m sec −1 velocity. The data for the dynamic simulation is obtained from the FEA, which is shown in Fig. 5. The remaining motor parameters and input specifications are summarized in the Table 1. In Fig. 7a the designed LSRM successfully carries the load at 0.15 m sec −1 producing an excellent velocity and position control performance. After the deceleration command is given at 0.5 and 0.1 m during starting and stopping respectively, the motor stops at 0.49 and 0.1 m, where the velocity command from the velocity profile is zero. Under continuous operation, the current amplitude values in starting and stopping are 9.6 and 8.4 A/phase, respectively. In addition, the average force produced is 119.7 N during acceleration and 113.6 N during deceleration.   Motor performance for variable load conditions: In practice, motors operate with changing load conditions. The influence of load variation on some of the parameters like the velocity, current and the efficiency of the motor are studied. The results shown in Table 5 are obtained when the circuit is turned ON at the point when the inductance starts to increase and turned OFF before it starts to decrease. Figure 8a shows the velocity and current variation for different load conditions. The velocity steadily decreases with an increase in load. This characteristic reminds of the speed-load characteristic of a series DC motor.   Figure 8b shows the characteristics of mechanical power P m and the efficiency with change in load. It can be seen that, initially as the load increases the efficiency increases and when load is further increased the efficiency started to decrease. Figure 8c shows the characteristics of the efficiency with change in mechanical power P m . It can be seen that, the efficiency is high at most cases, encourages the proposal of the pole shoe concept in LSRM. Figure 9 shows the actual experimental setup for the prototype LSRM with the stator pole shoe that is used as a material carrying vehicle in the laboratory. The experimental road is 2 m long and translator weight is 12 kg. It should be noted that the present setup is intended for development purposes only.

RESULTS
The inductance for the different positions at rated current is measured by locking the translator at each position. A constant current is applied to a phase and is turned off and the falling current profile is computed. The time constant is measured from the profile and hence the inductance is calculated. The measured values of inductance are plotted alongside the FEA results in Fig. 10. A comparison of inductance values at aligned and unaligned positions are given in Table 6 at the rated current. Figure 11 shows actual phase voltage and phase current waveforms of the LSRM.

DISCUSSION
The provision of stator pole shoes improves the force profile and reduces the force ripple at the maximum force regions. Hence, the maximum force is allowed to remain the same for more positions of the translator. The extent of the low force region around the unaligned position is reduced due to the addition of pole shoes. From Table 3 it can be observed that, as the stator pole width is increased, keeping the stator pole shoe width as constant, there is a reduction in the average force, which is not large after certain a point. The sensitivity study also depicts that any reduction in the width of the stator pole for the same variations of the pole shoe arcs, contributes to a loss of the average force. It is generally accepted that decreasing the stator pole width will decrease the aligned inductance with negligible effect on the unaligned inductance. This is reflected in Table 2. Finally, from the Table 4 we inferred that, the proposed LSRM (19 mm stator pole width) has high force density, less force ripple and volume when compared to the conventional machine. So only, for the other analysis in this study we prefer LSRM with pole shoe having 19 mm pole width.

CONCLUSION
A modification of the stator geometry by the provision of stator pole shoes has been presented. A prototype LSRMs is modeled, simulated, analyzed, developed and experimentally validated with the conventional control strategy. The following conclusions are observed when compared to the conventional machine: • Force ripple is reduced by 5.44% • Volume of the stator is reduced by 2.35% • Mass of the stator is reduced by 2.44% • Force density is high in the proposed structure • The maximum efficiency occurs at a load force of 5 N, which is also high when compared to the conventional LSRM • There is a good agreement between measurement results and FEA values of the inductance profile The proposed stator pole shoe geometry research can be further extended to study the thermal, stress and vibration analyses.