# Design and Analysis: Servo-Tube-Powered Liquid Jet Injector for Drug Delivery Applications
###### Abstract
The design of the Lorentz force actuators used in these studies is based on simple voice coils, which have some significant drawbacks. This is revealed by examining the fundamental principles governing the force output of these actuators. In its simplest form, a voice coil can be considered a non-commutated DC motor, having one winding and one permanent magnet. In the case of the linear actuator utilized by [PERSON] et al. [40], the permanent magnet is chosen as the stationary component, with the coil providing motion. The force output is prescribed by \(F=B\times i\), where \(F\) is the force (N), \(B\) is the magnetic field flux (T) and \(i\) is the current (A) flowing through the coil. The magnetic field produced by the magnets permeates an air gap and is orthogonal to the coil, and thus produces a force that is prescribed by the cross-product of the magnetic field flux and the current energizing the coil. In an ideal scenario, the motor constant should exhibit an independent relationship between current, speed, position and temperature. However, because of the inherent construction of this type of motor, whereby only one coil can be energized, the velocity and force of the plunger on this type of actuator are dependent on the amount of current that is passed through the coil. This means that an increase in force will be accompanied by a proportional response in the speed of the plunger. When voltage is applied to the coil, the magnetic flux forces the coil to move in the direction normal to current flow. This motion will occur so long as the coil is energized. In order to provide precise motion, a control loop is created through the use of a simple LVDT, which returns the plunger's position as a function of time. The feedback from the LVDT is used in conjunction with a PID loop controlling both the magnitude and polarity of the voltage sent through the coil, ensuring that the proper plunger position is accomplished. The control loop must exhibit a relatively high-frequency response rate in order to ensure the plunger is following the proper trajectory, given that injections take place within milliseconds and the stroke of the plunger can be on the order of several centimeters depending on the volume of liquid delivered. However, when precise velocity control is required and the voice coil encounters higher forces due to the coupling between force and velocity, it becomes difficult for the control loop to follow the proper trajectory. This is a very important notion as the health care industry moves towards adopting newer technologies, such as DNA therapy [48; 49]; with more viscous formulations and larger injection volumes, the energy output for needle-free injectors will grow. Although voice coils exhibit very good high-speed response, increasing power output becomes difficult. Power output can be increased by increasing either the current or the magnetic field flux. This is usually accomplished by using more powerful and larger magnets, applying more current, which entails using larger coils, or diminishing the air gap between the magnet/coil. It should also be noted that optimizing a voice coil motor for power will inevitably affect the response times of the system, as larger magnets/coil assemblies represent larger moving masses of greater inertia. Furthermore, [PERSON] et al. [43] found that the coupling between voice coil stroke, size and efficiency interacts with the mechanics of pressurizing a fluid in a piston-cylinder apparatus to give a scaling law. For a given input power, the required voice coil mass grows faster than the injection volume, with \(M\) a \(V^{6/5}\). As a result, hand-held injectors delivering volumes of over 0.5 mL are not practical using voice coil actuation. Moreover, the voice coil design does not lend itself well to large travels, meaning that providing repeated large-volume injections as required by mass vaccination in the animal health industry would not be feasible.