**5.2. Experimental model**

268 Induction Motors – Modelling and Control

Linear winding data:

Rotary winding data:

Copper layer

Solid iron cylinder

**Table 1.** Winding and materials data for TARLIM.

Rotor

**Figure 24.** Winding diagram of the TARLIM, (a) rotary winding, (b) linear winding.

Number of phases 3 Number of poles 2 Number of slots per pole per phase 1 Number of wires per slot, Nw 215 Copper wire diameter 1.29 mm

Number of phases 3 Number of poles 4 Number of slots per pole per phase 2 Number of wires per slot, Nw 96 Copper wire diameter 0.7 mm Armature Core Laminated steel Air gap length, mm 0.5

> Thickness mm 1.1 mm Conductivity (�, @ 20C) 57.00x106 S/m

> Thickness mm 10.7 mm Conductivity (� , @ 20C) 5.91x106 S/m

To verify the modeling results, a real prototype of the motor was built (see Figs. 25 and 26) and tested. The laboratory model of TARLIM has a relatively short secondary length. Therefore, measuring motor performances at linear speed greater than zero was practically difficult so the test was carried out only at zero linear speed. The TARLIM operates practically at low rotary slip and at linear slip close to one. Thus the dynamic end effects does not influence much the motor performance but the static end effect caused by finite length of each of the armatures has a large impact on the linear motor performance.

**Figure 25.** Laboratory model of twin-armature rotary-linear induction motor.

**Figure 26.** Measurement stand for testing of rotary-linear motors.

### **5.3. Motor performance**

The analysis of each part of TARLIM performance is carried out separately as an independent tubular linear and rotary motor by 3-D FEM modelling.

The linear armature is being supplied from the constant voltage source of 86.6 V (rms), 50 Hz frequency. The results of simulation are shown in Figs. 27, 28 and 29 in form of the electromechanical force (Fem), mechanical power (Pm) and efficiency, respectively, versus linear slip of the rotor. These characteristics illustrate a significant impact of end effects on motor performance and are drawn as dashed line curves for the infinitely long motor when no end effects are considered, circles for the actual motor of finite armature length, when both static and dynamic end effects are taken into account and triangular sign for the experimental result.

Induction Motors with Rotor Helical Motion 271

cannot be higher the synchronous speed. In low-speed motors, the attenuation of the entry end-effect wave is quick, while in high-speed motors the attenuation is very slow and the entry-end-effect wave presents over the entire longitudinal length of the air-gap. As a consequence of the difference, the influence of the end-effect wave on motor performance is also quite different at high-speed motors and low-speed motors. In low-speed motors, the end effect wave may improve motor performance in low-slip region, the important motorrun region, increasing thrust, power factor and efficiency, and allowing net thrust to be generated even at synchronous and higher speeds. On the contrary, in high speed motors, thrust, power factor and efficiency are reduced to a large extent in the low-slip region, and it is not an over statement to say that high-speed applications of linear induction motors may not be feasible if the end effect is overlooked and is allowed to remain as an influence.

To study the performance of the motor at higher speeds, let us change the supply frequency to 3 times higher (synchronous speed, ݒ௦= 3 \* 6.15 m/s) and then recalculate the forces acted on rotor when all end effects are taken into account. Table 2 compares the output forces of

The simulation of rotary part of the motor is done for the winding being supplied by the

Due to closed magnetic circuit in rotary armature, static end effect does not exist in rotational direction. However, the performance of rotary armature might be affected by dynamic end

S=0.25 S=0.05

the low-speed and high-speed motor at relatively low operational slip region.

**Table 2.** Electromechanical force of low speed and high speed LIM.

three-phase voltage of 150 V (rms), 50 Hz frequency.

Synchronous speed Operational slip region

ݒ௦= 6.15 m/s 19 N 6 N ݒ௦= 3\*6.15 m/s 6 N 0 N

**Figure 29.** Characteristic of efficiency vs linear slip.

**Figure 27.** Characteristic of force vs linear slip.

**Figure 28.** Characteristic of output power vs linear slip.

The motor under study has a linear synchronous speed equal to 6.15 m/s and is considered as low-speed motor. In low-speed motors, the speed of the end effect wave can be higher than the motor speed and even much higher than the synchronous speed, while in highspeed motors the speed of the end effect wave is about the same as the motor speed and cannot be higher the synchronous speed. In low-speed motors, the attenuation of the entry end-effect wave is quick, while in high-speed motors the attenuation is very slow and the entry-end-effect wave presents over the entire longitudinal length of the air-gap. As a consequence of the difference, the influence of the end-effect wave on motor performance is also quite different at high-speed motors and low-speed motors. In low-speed motors, the end effect wave may improve motor performance in low-slip region, the important motorrun region, increasing thrust, power factor and efficiency, and allowing net thrust to be generated even at synchronous and higher speeds. On the contrary, in high speed motors, thrust, power factor and efficiency are reduced to a large extent in the low-slip region, and it is not an over statement to say that high-speed applications of linear induction motors may not be feasible if the end effect is overlooked and is allowed to remain as an influence.

**Figure 29.** Characteristic of efficiency vs linear slip.

270 Induction Motors – Modelling and Control

experimental result.

**Figure 27.** Characteristic of force vs linear slip.

**Figure 28.** Characteristic of output power vs linear slip.

The motor under study has a linear synchronous speed equal to 6.15 m/s and is considered as low-speed motor. In low-speed motors, the speed of the end effect wave can be higher than the motor speed and even much higher than the synchronous speed, while in highspeed motors the speed of the end effect wave is about the same as the motor speed and

The linear armature is being supplied from the constant voltage source of 86.6 V (rms), 50 Hz frequency. The results of simulation are shown in Figs. 27, 28 and 29 in form of the electromechanical force (Fem), mechanical power (Pm) and efficiency, respectively, versus linear slip of the rotor. These characteristics illustrate a significant impact of end effects on motor performance and are drawn as dashed line curves for the infinitely long motor when no end effects are considered, circles for the actual motor of finite armature length, when both static and dynamic end effects are taken into account and triangular sign for the

> To study the performance of the motor at higher speeds, let us change the supply frequency to 3 times higher (synchronous speed, ݒ௦= 3 \* 6.15 m/s) and then recalculate the forces acted on rotor when all end effects are taken into account. Table 2 compares the output forces of the low-speed and high-speed motor at relatively low operational slip region.


**Table 2.** Electromechanical force of low speed and high speed LIM.

The simulation of rotary part of the motor is done for the winding being supplied by the three-phase voltage of 150 V (rms), 50 Hz frequency.

Due to closed magnetic circuit in rotary armature, static end effect does not exist in rotational direction. However, the performance of rotary armature might be affected by dynamic end effects during rotor axial motion. This is the only influence of linear part of TARLIM on rotary motion and, as stated earlier, both armatures have no more influence on one another due to the relatively long distance and the lack of magnetic interaction in between. To determine the influence of rotor axial motion on the performance of rotary armature, the characteristics of electromagnetic torque (Tem) and mechanical power (Pm) versus rotary slip at three different linear speeds (u = 0 m/s, u =3 m/s and u =6 m/s) along with experimental results at zero linear speed (u = 0 m/s) are plotted in Figs. 30 and 31. These effects contribute to diminishing of torque and all other rotary motor performances. One can observe that, the higher axial speed leads to lower rotary torque and mechanical power.

Induction Motors with Rotor Helical Motion 273

experimental measurements, where the temperature changes during the experiment and FEM results is expected. On the other hand, FEM needs as dense mesh as possible to compute quantities accurately, but the execution time of such a complicated model is enormous. Therefore, some trade-off between accuracy and execution time is required to obtain a good solution at reasonable cost. However, the discrepancies between test and

Rotary-linear induction motor is one of a few types of motors with two degrees of mechanical freedom. It may find application in robotics and special types of drives like machine tools and drilling machines. One of its representatives, the TARLIM, with two solid layer rotor was modelled in 3-D FEMM and its performance has been determined. The operation of the motor does not differ from the operation of machine set consisting rotary and tubular linear motor of which rotors are firmly coupled. The electromechanical performances of the motor are affected by the end effects which are familiar phenomena in linear machines. Practically, the impact of these phenomena is not significant in low axial

The results obtained from the test carried out on the experimental model do not differ much from the ones got from simulations. Thus they validate the theoretical modeling of the motor. Motor with the rotor cage made in form of grid placed on the cylindrical core is another version of TARLIM and is expected to have a better performance with respect to the solid

Mendrela, E, Fleszar, J, Gierczak, E. (2003). *Modeling of Induction Motors With One and Two* 

Krebs, G, Tounzi, A, Pauwels, B and Willemot, D. (2008). *General overview of integrated linear* 

Bolognesi P, Bruno O, Landi A, Sani L, Taponecco L. (2004). *Electromagnetic actuators featuring multiple degrees of freedom:* a survey. In: ICEM conference, Krakow (Poland), 5–8

Giancarlo, B and Tellini, B. (2003). *Helicoidal electromagnetic field for coilgun armature* 

*Degrees of Mechanical Freedom*, Norwell, MA: Kluwer Academic Publishers.

*stabilization*, *IEEE Trans. Magn.*, vol. 39, no. 1, pp. 108–111, Jan. 2003. Anorad Corp., New York, USA. (2001). *Rotary linear actuator*, U.S. Patent 6 215 206.

Yamamura, S. (1972). *Theory of Linear Induction Motors*, John Wiley & Sons.

simulation results are relatively small which validates the simulation models.

speed of the rotor, what is expected for these types of motors.

**6. Conclusion** 

two layer rotor.

**Author details** 

**7. References** 

September.

Ebrahim Amiri and Ernest Mendrela *Louisiana State University, USA* 

*rotary actuators*, *in Proc. ICEM Conf.* 

**Figure 30.** Characteristic of Torque vs rotary slip with and without linear motion.

**Figure 31.** Characteristic of output power vs linear slip with and without linear motion.

Note, that the output quantities are extremely dependent on the property of materials. The conductivity of the materials used in 3D FEM analysis is kept constant, but in reality it might be influenced by the temperature. Therefore, minimal mismatch between experimental measurements, where the temperature changes during the experiment and FEM results is expected. On the other hand, FEM needs as dense mesh as possible to compute quantities accurately, but the execution time of such a complicated model is enormous. Therefore, some trade-off between accuracy and execution time is required to obtain a good solution at reasonable cost. However, the discrepancies between test and simulation results are relatively small which validates the simulation models.
