# A Linear Brushless Direct Current Motor Design Approach for Seismic Shake Tables
## 1 Introduction  
Linear motors are becoming increasingly favored in industry due to their simple structure and manufacturing [1, 2]. They are capable of high acceleration, precise positioning, low-maintenance operation and long life [3]. Linear BLDC motors have been used for applications ranging from rocket positioning and health operations to seismic table actuators [4, 5]. Especially, high speed and precision, fast response and zero backlash capabilities of PM linear motors are becoming considerably more important in seismic shake table actuator applications. The goal of a seismic vibrator is to exert a controlled time-varying high dynamic force on the structure [6]. In a basic vibrator, this force is provided by driving an actuator that moves a payload with respect to a base plate, which is in contact with the ground [7]. In contrast to hydraulic actuators, the linear electric motor performs equally well over the whole frequency range, especially at the low frequencies, making a small amount of signal distortion and can track various force-time profiles [8]. The usage of linear electric motors in seismicshake tables has enormously increased in the last years thanks to the aforementioned advantages [9]. Particularly, linear BLDC motors with high force densities come forward by having the qualities to meet the requirements of earthquake simulators. Modular structure of these motors is available with features including extendable stroke and increased thrust force. Thus, seismic waves that may have various displacement characteristics can be simulated [6; 9]. In recent years, the studies on linear motors have been concentrated on motor design topologies and control methods [10; 11; 12]. However, selection of the design criteria and approach is essential for different types of linear motor applications [13; 14]. The design approach may vary depending on the application, force/weight and force/volume ratios as performance measures and the variations in the displacement distance. As is known, efficiency is no longer a goodness measure for these type of motors because of low-speed applications. Various studies in the literature show different design targets. A linear flux switching permanent magnet with short double-side primary mover is proposed in [15]. The motor is particularly well suited to long stator applications including urban rail transport. An optimization approach, namely the sequential quadratic programming method, for the maximization of the thrust force and the minimization of force ripples in brushless PM motor, is proposed in [16]. By using this method, the normalized force ripple is reduced by 7.7% and the thrust force increase is 12.88 N in comparison with the design that is not optimized. To achieve the required thrust and optimal sinusoidal magnetic field, in [17], the authors altered the winding pitch and the current switching sequence, gaining required thrust, indicating that the harmonics and end effects of a linear motor are equal. The main aim is to obtain optimal sinusoidal magnetic field and required thrust. Some special phenomena involving transverse edge effect and end effect saturation of back iron are analyzed in [18]. The study includes the computation of the saturation by simple equations and iterative methods using Duncan model. In [19], a PM linear synchronous motor for ropeless elevator system is developed. The long stator double-sided slotted iron core type permanent magnet linear synchronous motor with fractional slot winding is selected for the superior performance using finite element analysis (FEA). In [20], a rotary motor with ball-screw table is retrofitted into a sub micro-meter stage. Moreover, a comparison between conventional drive and linear direct drive is conducted with sub-micron feedback. In [21], an alternative solution is formulated, defining the commutation as an optimization criterion for ironless linear motors, wherein it is shown that.