Simulate vibration damping, spring-mass-system

Okay, so i am trying to simulate a mechanical damper (a tuned mass damper, TMD) inside a handle on a power tool.

So, the power tool transfers a force to the handle. The handle transfers the force to the mechanical damper, which has an unknown mass and spring constant. The mass is going to be tried/tested iteratively, and from this we will have a value for the spring constant. As of now, i am using a force F(t)=F0*sin(w*t), where F0 is the force coming from the power tool, F0=m*a, where a=dw/dt. F(t) is transferred to the damper, which gives F2(t), the force that is dampened by the inner mass.

omega=2*pi*f;

a= (derivative of omega, respect to t);

F0=m(powertool)*a;

F=F0*sin(omega*t);

beta=omega/((2*k2/m2)^(1/2));

F2=F*1/(abs(1-beta^2));

The mechanical damper is INSIDE of the handle, which means that the deformation cant vary indefinately, only between 0-4mm.

The meaning of this system is to dampen the vibrations which are finally transferred to the tool operator.

I have been trying to simulate this using both matlab and simulink, but i cant make it work. I would like to simulate it so that it varies both upon time and the frequency of the vibrations (if possible).

Does anyone have any tips or inputs on how i could solve this?

Thanks!

Answer 1

[arushi]

I understand that you want to simulate the mechanical damper (TMD) inside the handle of a power tool. You can use MATLAB or Simulink to model the system and analyze its response. Here are some steps to help you get started:

1. Define the system dynamics: Start by defining the equations that describe the dynamics of the system. Based on your description, you can model the TMD as a mass-spring-damper system. The force from the power tool is transferred to the TMD, which dampens the vibrations. The equations of motion for the TMD can be written as:

where F(t) is the force from the power tool, c is the damping coefficient, k is the spring constant, and x(t) is the displacement of the TMD.

2. Implement the equations in MATLAB/Simulink: In MATLAB, you can define the equations of motion as a function and use numerical integration methods like ode45 to solve the differential equations. Alternatively, in Simulink, you can use the "Simulink-Function" block to implement the equations and simulate the system.

3. Specify the system parameters: Define the parameters of the system, including the mass, damping coefficient, and spring constant. Since you mentioned that the mass is unknown and will be iteratively tested, you can set an initial value for the mass and update it during the simulation based on the desired behavior.

4. Simulate the system: Set up the simulation time span and run the simulation. Vary the input force F(t) over time and/or frequency to observe the response of the TMD. You can analyze the displacement, velocity, or acceleration of the TMD to evaluate its effectiveness in dampening the vibrations.

5. Iterate and optimize: Based on the simulation results, iterate and optimize the system parameters, such as the mass and damping coefficient, to achieve the desired level of vibration damping. You can adjust the parameters and rerun the simulation until you achieve the desired behavior.

Find below documentation of Simulink blocks that might be helpful in your implementation of mechanical damper:

• Sine Wave Generator Block: https://www.mathworks.com/help/dsp/ref/sinewave.html
• Gain Block: https://www.mathworks.com/help/simulink/slref/gain.html
• Integrator Block: https://www.mathworks.com/help/simulink/slref/integrator.html
• Product Block: https://www.mathworks.com/help/simulink/slref/product.html
• Scope Block: https://www.mathworks.com/help/simulink/ug/simulation-data-display-and-capture-using-scopes.html

Hope this helps.