How to determine the mass of the load on the motor shaft?

Question

Electronics

We have a FI regulator (triac controlled by MK) of the speed of the AC motor.
If we consider two cases:
1) the rotation of the engine at idle (more precisely, with a minimum load)
2) the rotation of the engine with an additional load
in both cases, the "power" is set the same, or rather not the power, but the moment the triac is turned on, but for obvious reasons, the engine rotation speed in the second case, it will be less, while the current and power consumed by the motor will increase in proportion to the load.
Question: how to determine the mass of the same additional load if the engine speed is known in both cases?
Here the essence is not in the choice of the engine and its parameters, the engine has already been selected.
I'm sorry, I corrected the typo in the word "rotation".

Answer 1

Option "on the forehead" to find the formula for the moment under the engine.
As far as I remember, the moment is directly proportional to the current through the motor, and the coefficients that will need to be dug / calculated / obtained experimentally.
It will be necessary to obtain the root mean square value of the current, calculate the moment M (N * m) from it.
Using the moment M (N * m) and the length of the arm l (m) to the load - calculate the load on the shaft \u003d M / l and convert it from Newtons to kg or immediately calculate the moment in kilograms.
If the speed is known, and the thyristor opens for the same time, then you can simply make a table:
We use a set of impromptu loads and measure what speeds are.
We build a table, then a graph and estimate a function that will approximately reflect the dependence of speed on load for a given engine. Let's use it.

Answer 2

there can be "torque" on the shaft, not "mass". in calculators like https://kataltim.ru/krmom.php substitute values, selecting them for your data. efficiency is written for most "standard" motors on the nameplate, along with rated voltage/current and cos(f)

Answer 3

In the general case, the shaft rotation speed will decrease only due to an increase in friction, etc.
And so - the rate of change of speed will change aka acceleration (derivative of speed)

Answer 4

Maybe a PI controller? The power consumed
by the engine will be calculated according to the formula:
P=Mkr*n, where P is the power, Mkr is the torque, n is the revolutions . - the moment of inertia of the motor rotor with the entire load. With dn / dt = 0, Mcr = Mload (all further calculations subject to constant rotation speeds) As far as I understood from the condition, the power is the same in both cases (conditionally, the same current will pass at the same supply voltage) Then: P = Mcr1 * n1 = Mkr2*n2
It follows that knowing two rotational speeds and power / torque for one case, we will find the torque for the other case using the formulas Mkr2 \u003d P / n2; Mkr2=Mkr1*n1/n2.
If the power is in watts, the rotational speed is in rad/s, the torque will be measured in newton*meters. Multiplying N * m by 0.102, you can get kgf * m. 1 kgf * m is equivalent to 1 kilogram suspended on the motor shaft with a shoulder of 1 meter. When the arm is shortened, the suspended mass increases proportionally. However, in the case of a real application, I recommend, in addition to your description, to lay out briefly the initial data and the final task (I did not understand the essence of your task based on the question). And also calculate the load depending on its type, in fact, you don’t hang weights on a meter stick.