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SAE 2007 - Moving Magnet Technologies

SAE 2007 - Moving Magnet Technologies

T transition J π K =

T transition J π K = (2) The stiffness of the springs is defined in relation with the targeted transition time. We then have to size the magnetic circuit in order to achieve the minimum power consumption while generating enough torque to hold the armature against springs. Coil A Stator H Lc Armature Coil D Typical angular stroke between the two end positions is about 40° but smaller or higher stroke can be easily achieved. SIZING OF THE ACTUATOR The two key parameters are the spring stiffness K and the maximal induction allowed in the magnetic circuit B sat . The force to hold armature in closed position is directly proportional to B sat and K defines, with inertia J, the transition time. These two parameters are closely linked to the dimension of each part of the actuator (magnetic circuit and spring mechanism) that is why the sizing of such actuator is “tricky”. We give hereafter, in figure 2, the general strategy to size this actuator: Coil C e Figure 3: Magnetic circuit of rotary actuator L Coil B stator The solenoid structure is made of two pairs of coil that form two electrical independent phases: [coil_A, coil_B] & [coil_C, coil_D]. They are placed on two W shaped stators and act on a mobile armature linked to the shaft. At the equilibrium, the armature is in middle position as shown in figure 3. As depicted in figure 4, the first latching position is achieved when first set of coils is energized and acts on armature against spring stiffness. F1 Flux line paths l1 F2 l2 F2 F1 Figure 2: General strategy for dimensioning MMT rotary actuator In the following, we study the magnetic behavior of the rotary actuator. Magnetism Figure 4: Schematic magnetic principle – Latching in first end position The torque produced by the actuator is a function of the current in coils and active surfaces. One of the great interests of MMT rotary actuator is to provide important active surface into quite small dimensions since there are 4 surfaces at each position. The torque generated by the actuator is defined as follows (geometric parameters detailed in figure 3): Bsat Tlatching = × (2L − 2e − Lc ) × S µ 0 2 (3) With: B sat : induction at saturation in the almost closed airgap [T] µ o : Vacuum magnetic permeability [H/m] L: semi-length of armature [m] e: pole width [m]

L c : Coil width [m] S: pole section = e x H (with H stator depth [m²]) Closed position This expression of the latching torque gives important information in the aim to size the circuit. We can then adjust the different parameters to achieve the targeted performances as a function of specifications. Since the rotary actuator is of solenoid type, the magnetic induction is high when armature is in latching position due to the small airgap. In this position, the magnetic circuit is at its optimum operating point (induction is close to the saturation level). When coils are de-energized, the induction drops and spring torque becomes higher than holding torque. As a result, the armature is released and moves towards the other end position (cf. figure 5 below). Torque (Nm) Middle position Position (°) Increasing At Figure 6: Typical shape of torque evolution (simulation results) Of course, since magnetic saturation occurs when armature is at closed position and in the aim to optimize magnetic structure, it is highly recommended to use finite element software to visualize saturated sections and calculate effective torque (cf. figure 7 below). Figure 5: Schematic magnetic principle – Latching in second end position When armature is closed to the second end position, the second coil set is energized and this allows the capture of the armature. MMT’s rotary actuator is of solenoid type, so when there is no saturation, the induction in the airgap is a function of this airgap length between armature and stator pole. µ ni B 0 . = (4) 2. l With: ni: number of ampere-turns [At] l: average airgap between stator pole and armature [m] Figure 7: View of magnetic induction with Flux2D ® software. Mechanics The main difficulty is now in the spring sizing. Because stiffness has an impact on moving spring inertia, we must find the best compromise between inertia and stiffness. One of the most popular solutions is the use of spiral springs (cf. figure 8 below) because it leads to a very compact design and a simple integration. And equation (4) in (3) leads to: 2 µ ni C = 0 . × (2L − 2e − Lc ) × S 2 4. l (5) As a consequence, the generated torque over the complete stroke has the following shape (figure 6): Figure 8: Example of elastic system: spiral spring

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