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Let's think of the following: we want to build an electrical circuit that is a model of the mechanical circuit we would like to evaluate! We wish to do it so, that all the measurements and computations we do in the electrical domain are right away suitable to the mechanical equivalent - building services engineer. The first agenda: how do we map our measureable quantities torques and speeds to voltages and currents? The natural mapping originates from the circuit laws.




2: For any loop in the system the amount of the speed-differences on all the elements making that loop is 0. The first law is comparable to Kirchhoff's existing law: at any node in an electrical circuit, the amount of currents flowing into and out of that node is 0.




We have to create ratios between torque and existing and speed and voltage. Considering that we're building only electrical models that make it simple to us to make estimations and predictions about mechanical systems, this aspect can be anything hassle-free. We can state that 1A of existing represents 1Nm of torque, but we might simply as well as state that 1mA of existing represents 1 oz" of torque, it doesn't matter.

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The only thing that matters is that we pick one conversion and we stay with it (building services engineer). In the following I will use the mapping that 1A existing represents 1Nm of torque and 1V voltage represents 1rad/s speed, but as I said before, this is approximate. The next order of company is to come up with electrical elements that can be replaced for our mechanical ones.


Drag has a really basic one: T = d * s We understand now, that will represent torque with present and speed with voltage, so our electrical equivalent ought to have a particular equation of the following type: I = d * V This is a, with a resistance of 'd'. Friction is a bit more complex, being a non-linear part.




And simply as in the mechanical variation, this model can be streamlined to a continuous current source if you assume that voltage never changes polarity. Fixed friction is even more frustrating. The characteristic equation is not just non-linear however hysteretic as well: s = 0 if abs( T) < d; T = 0 if s > 0 After replacement we get: V = 0 if abs( I) < d; I = 0 if V > 0 This is either a depending on the state of the aspect.

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It is probably not a huge surprise after all this that springs can be represented by with an inductance of '1/K', bacuse dT/dt = K * s ends up being dI/dt = K * V Sources are almost insignificant to convert: considering that torque becomes present, torque sources become. Likewise, speed sources are converted into.


This most current step is not actually relevant. In reality, when you change the mechanical ground, you can change it with any consistent voltage node. Simply make certain you keep some outright and continuous referral around for the mechanical part. You now have a completely electrical circuit, that you can reason about using all the familiar strategies of circuit analysis.


From that: Rm = 2. 3 Lm = 26 HKE = 0. 215 mV/rpm = 0. 002 V/( rad/s) KT = view website 2. 05 mNm/A = 0. 002 Nm/AJm = 0. 12 gcm2 = 0. 11 * 10-6 Nm2Fm = 0. 03 mNm = 0. 03 * 10-3 Nm If we represent 1Nm torque with 1A of present and 1rad/s of speed with 1V of voltage, we get the following electrical equivalent: This is a circuit that you can put in a circuit simulator (if you do, take care about the polarities of the sources!) and outline the frequency response for instance (here I plot the anonymous generator voltage): You see the anticipated low-pass characteristics, with two corner-frequencies.

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This is really similar to what we've seen with our easy motor modeling exercise. Naturally the values are different as we're dealing here with a different motor. building services engineer. The intriguing thing in this model however, is that it maintains the mechanical quantities too. For example, in the following I'll put a 3V pulse for ones on the motor and plot the voltage across the capacitor: Now, we understand that we designed speed with voltage, so we remain in fact looking at a speed-over-time graph here.


When the short-term is lastly over, we measure 1. 48kV on the capacitor. (Don't hesitate of the huge numbers, these are not genuine voltages, just equivalent numbers.) We've represented 1rad/s speed with 1V, so it should be 1480 rad/s speed. Transforming it to rpm, we get 14132. This is close to the 13800 rpm value, specified in the datasheet.


3% precision is pretty great for such a basic model. We can also outline the current through the capacitor: Here you see that the torque decreases to 0 (in reality the only torque transformed on the motor is utilized up by friction) after the initial short-term. The peak current is at 2.

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This corresponds to 2. 5mNm torque on the turning disc. There's a little quantity of torque that's consumed by the fiction so the motor requires to output a little more than that. While this example is not terribly enlightening unless our plan is to utilize the motor without any load, however shows that we can directly get mechanical residential or commercial properties from the equivalent electrical circuit.


So, if we want to now tie a load to the motor (let's state a large wheel with some friction), we can do that. All we need to do is extend our mechanical additional resources model with the brand-new components: Here Jw and fw are the inertia and the friction of the wheel respectively.