# Design and Analysis: Servo-Tube-Powered Liquid Jet Injector for Drug Delivery Applications
###### Abstract
In order to improve on the shortcoming of voice coil motors and to provide a platform with greater controllability, it is necessary to use a linear actuator with a slightly different topology. This study will examine the use of a classical three-phase linear motor consisting of three fixed coils and multiple permanent magnets. Each coil is controlled individually, i.e., commutated with respect to the permanent magnets. It should be noted that studies that examine this motor design have been conducted concurrently with the development of this prototype [50]. The studies conducted by [PERSON] et al. [51, 52] illustrate the optimization procedures for sizing a permanent magnet synchronous motor used for liquid jet delivery and test a custom-built motor in an open-loop configuration without current control. In this study, a prototype that utilizes a commercially available linear motor with well-established motor constants and parameters, as well as modern power electronics to provide true closed-loop control, is constructed. This prototype is then tested for its ability to reproduce specific plunger velocity profiles whilst compensating for factors that influence plunger motion via a PID loop. This will yield an accurate portrayal of the ability for linear permanent magnet motors to shape the pressure output of liquid jet injections. The motor chosen for the construction of a prototype injector was provided by Dunker-motoren GmbH, and the specifications of this motor are outlined in the following Table 1:  
In this actuator, magnets are enclosed within a circular actuator tube. The effective travel of this device can be increased or decreased as desired by lengthening the actuator tube. The core of the proposed actuator has two main components: a moving actuator rod and a fixed stator housing. The actuator rod consists of a non-magnetic stainless-steel tube filled with 13 high-quality, 25 mm circular neodymium NdFeB magnets. The actuator rod sits in a polymer (PTFE) bearing placed within the stator housing, which is encapsulated by a series of three windings that enable the actuator rod to be commutated. The process of commutation is an important attribute; despite adding an extra level of complexity, it aids in decoupling the relationship between the force output of the device and the velocity of the plunger. This means that, for a fixed velocity, the amount of force applied to the plunger can vary independently by increasing or decreasing the different phase currents. The process of commutation maintains an orthogonal relationship between the magnetic fields in order to maximize force output [53]. The actuator chosen for this study is equipped with three Hall effects sensors as well as a sinusoidal encoder. The Hall effects sensors determine the relationship of the magnetic field flux of the permanent magnets within the actuator tube upon motor start-up, and \begin{table}
\begin{tabular}{l l} \hline \hline
**Specification** & **Value** \\ \hline Peak Force & 624 N \\ Peak Current & 20 A \\ Force Constant & 44.1 N/Arms \\ (Sinusoidal-Comm) & \\ Pole Pitch & 51.2 mm \\ Peak Velocity & 4.7 m/s \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Dunkermotoren GmbH STA-2508 Linear Servo Tube Specifications (2022) [[https://www.dunkermotoren.com/](https://www.dunkermotoren.com/)]([https://www.dunkermotoren.com/](https://www.dunkermotoren.com/)), (accessed on 1 May 2022). the sinusoidal encoder is then used to vary the phase angle as a function of actuator tube displacement, knowing the fixed pole pitch of the magnets. Commutation of the coils and precise actuator motion are accomplished via an inverter/amplifier servo drive. In this study, the Parker Compax3 Servo Drive (Parker Hannifin Corporation, Cleveland, OH, USA) was utilized due to its ability to accurately drive linear motors; see Table 2 for its specifications. This unit converts an AC waveform into a DC square wave.