Report 1 Electromagnetic cannon 知物達理隊 劉富蘭克林 儲君宇 葉星佑 黃奕立 郭潔恩

Problem # 1 Electromagnetic cannon A solenoid can be used to fire a small ball. A capacitor is used to energize the solenoid coil. Build a device with a capacitor charged to a maximum 50V. Investigate the relevant parameters and maximize the speed of the ball. 2018/11/12 Reporter: 知 物 達 理

Overview Introduction Experiment Results and Discussion Observation Problem Analysis Experiment Experimental Setup Results and Discussion Conclusions & Summary References 2018/11/12 Reporter: 知 物 達 理

Introduction Observation 1. A steel ball is loaded near one end of a coil. 2. When a sudden current is released from a capacitor and passed through a coil, the coil can project a steel ball. 3. The apparatus cannot project a solder ball aluminum ball or copper ball. 2018/11/12 Reporter: 知 物 達 理

5. Steel ball experiences no backward magnetic force and flies forward Sudden current generates strong magnetic field in solenoid Steel ball becomes temporary magnet due to magnetic field 3. Steel ball is accelerated by magnetic field 4. Before steel ball reaches mid-point of solenoid, most of the current has already passed 2018/11/12 Reporter: 知 物 達 理

Experimental Setup 1. Power supply unit 2. Capacitor 3. Solenoid and cannon tube 4. Photogates and phototimer 2018/11/12 Reporter: 知 物 達 理

Experimental Setup Firing state Charging state 2018/11/12 Reporter: 知 物 達 理

Experiment Parameters: the total capacitance: 2200, 3300, 4700, 6800, 10000 uF the initial position of the steel ball Steel ball edge -0.1, 0, 0.1, 0.2, 0.3 cm from coil edge the layers of coil around the firing tube 4, 5, 6 layers 2018/11/12 Reporter: 知 物 達 理

Experiment Results 2200uf 3300uf 4700uf 6800uf 10000uf -0.1 0.2 0.2 2018/11/12 Reporter: 知 物 達 理

Experiment Results 2018/11/12 Reporter: 知 物 達 理

SIMetrix simulation SIMetrix , a circuit simulation program, is used in order to obtain knowledge of the current in the solenoid during discharge. A few parameters are required : Resistance: measured to be approx. 0.4 Ohms Inductance: Calculated to be approx. 398.5 uH Capacitance: Specified 2200, 3300, 4700, 10000 uF under 50V r: mean radius N: number of turns l: length of coil d: coil thickness Accurate to about 1% * Harold A. Wheeler, “Simple Inductance Formulas for Radio Coils”. Proc. I.R.E, October 1928, pp.1398~1400 2018/11/12 Reporter: 知 物 達 理

The circuit is an RLC circuit, and exhibits oscillatory behavior. For an RLC oscillation, 2018/11/12 Reporter: 知 物 達 理

As shown in the graph, the discharge curve is a sharp peak which is steep on one side and less steep on the other. The discharge takes place in only a few milliseconds, yielding a maximum current of 60~100 Amps. The next step is just to know the force experienced by the steel ball for any location. 2018/11/12 Reporter: 知 物 達 理

FEMM Simulation FEMM is a finite element method program which can simulate the magnetic force experienced by a steel ball in a solenoid for any given current and steel ball location For a constant 66A (2200uF max current), the steel ball experiences different force magnitudes at different positions. 2018/11/12 Reporter: 知 物 達 理

SIMetrix FEMM Force experienced by Steel Ball in I(t1) coil at position X(t1) 2018/11/12 Reporter: 知 物 達 理

Euler’s algorithm to obtain position of steel ball at a given time 2018/11/12 Reporter: 知 物 達 理

Prediction of steel ball speed with SIMetrix-FEMM-Euler simulation: 2018/11/12 Reporter: 知 物 達 理

Same trend Decreased speed -> Drag Friction Spark dissipates energy hysterisis Actual acceleration process Firing in 8 ms, more than the predicted 2ms ->influence on final velocity 2018/11/12 Reporter: 知 物 達 理

Conclusions & Summary The speed of the steel ball shows an increasing trend with total electric capacity. When the steel ball is placed a particular distance away from the coil, it has the maximum speed because the discharge time of the capacitor plays an important role on the force on the ball. 2018/11/12 Reporter: 知 物 達 理

Conclusions & Summary A SIMetrix-FEMM-Euler method is used to theoretically show the same trend in accordance with experiments. Drag, hysterisis and spark dissipation of energy may also play an important role in the final velocity of steel ball. 2018/11/12 Reporter: 知 物 達 理

Conclusions & Summary Since the ball would be temporarily magnetized by the coil, it would be best to know the hysteresis curve of the steel ball. This way a more accurate model could be built up. 2018/11/12 Reporter: 知 物 達 理

劉富蘭克林 儲君宇 黃奕立 葉星佑 郭潔恩 Thank you 2018/11/12 Reporter: 知 物 達 理