Example: eigenfrequency computation
This example shows how to determine the Eigenfrequencies of a sewing machine.
We assume that you are familiar with the topic, but want to know
how to solve the mathematical side with MasterAllRound.
Here is a short version of an example from the manual showing some additional options in
MasterAllRound:
You obtain the Eigenfrequencies by solving the following equation:
with c defined as:
Input data are:
- L6 = 220 mm
- L7 = 120 mm
- M = 18 kg (mass of the machine)
- J = 0.18 kgm2 (mass moment of inertia)
- n = 1000 min-1 (nominal speed)
Units are [N], [mm] and [s].
First, we enter the above constants. Note that you can add comments when
defining constants in MasterAllRound:
- L6 = 220 ' [ mm]
- L7 = 120 ' [ mm]
- M = 18/1000 ' [N*s^2/mm]
- J = 0.18E3 ' [N*mm*s^2]
- OMI = 2*PI*1000/60 ' n = 1000 min^(-1)
We rewrite the equation using sub-equations:
- TC = 2*J*M*OMI^2/(M*(l6^2+L7^2)+2J)
- TG1 = (L6^2+L7^2)/(2J) + 1/M
- TG2 = (L6+L7)^2/(M*J)
That's all on the set-up side: we can solve the task by entering in
the formula input field our equation:
- f1 = (SQR(TC*(TG1-SQR(TG1^2-TG2))))/(2*PI) ' @
The "@" indicates that we are using sub-equations.
Finalizing our input with the return key, or clicking on the "Run!" button, gives us the result:
To obtain the second solution, we just edit the equation in the input field:
- "f1" in "f2"
- "-SQR" in "+SQR"
The second equation is:
- f2 = (SQR(TC*(TG1+SQR(TG1^2-TG2))))/(2*PI) ' @
We finalize our input with the return key and obtain the second frequency:
It's very easy to investigate changes in the Eigenfrequencies now. For example: all we have to do,
to study how f1 changes as a function of M, is to define M as a variable. As a result, we obtain
ordered pairs of M and f1. We can also plot this by saving the table and using the plot module of MasterAllRound.
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