# A Linear Brushless Direct Current Motor Design Approach for Seismic Shake Tables
## 2 Design Approach  
In this study, the main output parameter is the maximum dynamic force production. To provide the proper dynamic force to seismic shake table, the force density of linear motor must be defined adequately. The starting force (zero speed) densities of PM linear and rotating machines (for rotating motor assuming shear force in air gap area) vary within 10-70 N/cm\({}^{2}\) depending on the PM materials and locked armature (or magnet assembly) current values. Of course, these values are for short circuit (no motion) operations, and, most of the time, actual electric sources and driver transistors may not cope with those extreme values. In practice, the terminal current must be limited and the operation is permitted only for short time intervals. In the study, considering the DC source constraints, the dimension constraints of the motor and heating effects, a 3-kN dynamic thrust force and 150-cm\({}^{2}\) active motor area (thrust force produced in the active air gap area, i.e., area below the armature), the dynamic force density is predetermined as 20 N/cm\({}^{2}\). The other design criterion of the linear motor is the electrical time constant. Recently, sub-fractional slot-pole type permanent magnet motors rose to prominence due to their high force (torque) production capabilities. However, because of sub-fractional concentrated winding structure, the motors have relatively higher winding inductance values, i.e., large electrical time constants, which hamper fast force production. Depending on the current density, losses and slot area constraints, the winding resistance cannot be made higher than a certain limit. Using all-teeth-wound winding topology is causing a lower value of winding inductance while alternate-teeth-wound structure results in higher winding inductance [27]. In this study, the application requires a fast acting, dynamic force production to simulate the mentioned earthquake movements. Therefore, a linear motor design with relatively lower winding inductance is selected intentionally, resulting in all-teeth-wound armature structure having half of the inductance value of alternate-teeth wound motor. It is of crucial importance to determine geometrical, mechanical and electrical constraints that are caused by the unique structure of the seismic shaker accurately while creating the design approach. These constraints play an important role in the assignment of the initial values of the design [28]. The linear slotted motor topology is used in high-force applications. The reason for this is that the iron core can stimulate higher force by concentrating the magnetic field created by the windings. To obtain high force density, sizes and materials have been optimized [29]. Thus, a high-quality electric steel with higher relative magnetic permeability is used to form the primary structure. It is expected that the ferromagnetic core provokes high magnetic flux density with low magnetic field intensity, and the iron loss is consequently low. The designed back iron has to be manufactured from high magnetic permeability and low-carbon cold-rolled soft steel. To specify the thickness of the back iron, some ampere-turn loss is permitted due to the saturation to avoid a bulky design. In other words, a non-saturated back iron results in heavier design. It is aimed to keep the losses at a minimum level by using M24/29G type material of high quality in the structure which will form the primary yoke and teeth. Moreover, it is important that the core ampere-turn loss must be a small percentage of air gap ampere-turn for enhanced performance. To obtain higher force production, N35 type rare-earth PMs with higher energy density are used. The maximum stroke force is determined by means of the required maximum acceleration for a specific payload, i.e., the moving mass of the system plus the mass of tested component. The open loop tests show that the damping of the system can be assumed as 10% of the total force.