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One of the major problems in coilgun-building is synchronization of current pulses in coils with the position and velocity of projectile. Traditionally, the signals for sensors set in appropriate positions along the barrel are used (the sensors are usually fixed, although the positions may be variable sometimes as it is done in EM-3 "electric bow"). Unfortunately, even the simplest optical sensors are in fact rather complicated constructions. The reason is that they must have some features to function stably: be strobed by external circuitry (to avoid false triggering), have power outputs to drive SCR gates, maintain logic and power signals of different amplitude etc. It is desirable to have also some circuits to visualize the state of the sensor (it is useful while tuning inside the coilgun). Examples of such detectors are here and here.
Fig. 1. Optical sensor of rhte starting stage of EM-3 coilgun.
Besides all that, the presense of detectors puts additinal demands to construction of the accelerator (for instance, in case of optical sensors the coilgun 's barrel must be drilled where they are installed, or be transparent to according light spectre).
It is no wonder that many gauss-builders try to remove any sensors from their constructions and utilize acceleration timing from external source. I.e. transition from close-loop system to open-loop (sensorless) one. In latter case the moments of beginning and durations of the driving pulses are determined while tuning the accelertor and saved in appropriate memory IC (usually microcontroller). Examples of such decisions are here and here.
Fig. 2. Sensorless coilgun realization from Future weapons forum.
It is clear that the more stages a coilgun has - the more temptation exists to utilize such an approach. The main poblem is: what if little variation of initial parameters takes place - will it be catastrophical consequence to efficiency of the accelerator, or no? In fact, not-in-time activated stage can not only to decrease the total efficiency, but even retard the projectile.
To examine this speculation, I decided to execute some FEMM calculations in process of construction of EM-4 coilgun. The results are below.
Special script coilgun.ucoz.ru/FEMM_calc/EM-4/bistage.lua was used describing so-called "bistage" system utilized in EM-4. The features of this design are highlighted on the dedicated page. I will only remark here that it consists of two consequently powered coils. The original script was used to simulate the optically-aided coilgun with 16 mm distance between the coordinate of activation of the first and second coils, and initial projectile velocity 30 m/s.These conditions lead to active state duration of the first coil of about 500 mcs. Hence, to simulate the sensorless system, the script was modified by replacement of 16 mm way mark to fixed 500 mcs time mark as a moment of deactivation of the first coil. So, we have the model of the coordinate-based feedback to simulate optically-triggered coilgun in first case, and the model of fixed-time-triggered (sensorless) coilgun in the latter one.
The investigation itself was conducted as follows: the set of initail parameters ensuring the optimal (i.e. maximum efficiency) case was established (it can be found on the page dedicated to FEMM calculation of EM-4). Then, one of the parameters was changed to 10 % (for example), and new calculation was executed both for the sensorless and closed-loop systems. Those cases are marked as "constant T" (meaning constanct time intervals preserved in coilgun) and "constant CA" (suggesting constant coordinates of activation according to the fixed optical sensors) on the graphs below.
The parameters subjected to variation were chosen from those which could change unwillingly during construction or exploitation of the coilgun. For instance, the length of the projectile, or the position of the sensors may be suggested constant (as the constructor can set them to any value he wants). But the capacitance doesn't always correspond to the nominal one. Another situation can happen: the gauss-builder has projected a coilgun, but there is no wire of the predetermined gauge, and he used any off-the-shelf one with close (but not "optimal") diameter.
Below are graphs illustrating the results for some cases.
First, I tried to model the variation of the capacitance. It is interesting because of question of practice: how would a coilgun behave at winter open-air shooting? It is well known that electrolytic caps tend to drift with temperature. Here is what we have for basic capacitance of 300 mcF varied in both directions for 50 and 150 mcF:
Fig. 3. The influence of capacitance variation on efficiency and speed.
It is seen that the curves for deterctor-equipped coilgun and sensorless one coincide. I.e. these systems are equally stable to thw capactitance variation! Some unexpected result...
Other features of the graph are easily explained. With capactitance (i.e. energy) increase the efficiency decreases (because of deeper saturation of the projectile), ans viсe versa.
Secondly, the most common and interesting case was investigated - the variation of initial velocity of the projectile (its basic value was 30 m\s).
Fig. 4. Efficiency vs Initial speed variation from its optimal value 30 m/s.
The sensorless system is much less stable here. Only 5 m/s variation causes the substantial decrease of speed. Note that the activation coordinate of the bistage was set - 2 mm constantly in this model, independently of the initial speed change. It is reasonable to suggest that, in sensorless mode, the desynchronization would grow sequentially from stage to stage leading to outrunning activation of the coils (before the projectile reaches the "optimal" position). So, in reality the parameters of the open-loop gauss gun will probably be much worse (in comparison to the system with sensors) than it is shown on fig. 4.
Then, the case of "parastitc" mass change was studied. What is it about? The projectile in EM-4 is arrow-shaped body with ferromagnetic blade (its mass is about 2,7 g) and plastic tube as a stabilizer. This stabilizer doesn't paticipate in acceleration, so it is "parasitic'" element from the point of view of the efficiency. Its mass was calculated to be 0,3 g. But what if I used an arrow with other parameters (for example, longer one) ?
The answer is on fig. 5.
Fig. 5. Efficiency and velocity vs "parasitic" mass of the projectile.
The closed-loop system is somewhat better, but I was surprised by another thing - a weak influence of "parasitic" mass on the efficiency. Indeed, it drifts only from 7.5 to 7 % when the stabilizer is as massive as ferromagnetic blade, and ranges from 6.5 to 6.9 % when the stabilizer has triple mass as the blade. It means that the projectile in gauss gun can be equipped with additional elements quite boldly.
Fig. 6. shows how deviation of the outside diamters of the coils from their optimal values 14 mm decreases the efficiency. It is clear that the influence is substantional and approximately the same for both modes.
Fig. 6. Speed (efficiency) vs coil diameters.
At last, I varied wire gauge around its optimal values 0,3/0,5 mm (1st and 2nd coils of the bistage). The result is shown on fig. 7.
Fig. 7. Speed (efficiency) vs wire gauge (1st/2nd stage).
The system with detectors, and sensorless one have close parameters here, too.
1) In most of examined cases the closed-loop and open-loop systems have nearly the same parameters of stability to variation of the initial parameters of the accelerator.
2) When the initial speed is varied, the sensorless coilgun is much less stable.
The reasonable questions arise: what can be a source of such deviation of the velocity from the precalculated value? What construction of the coilgun hepls to avoid this variation?
More calcultions and experiments are obviously to be conducted to answer these questions. Yet, I decided not to remove the optical sensors from EM-4.
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