Desarrollo Suspensión
Josecisneros001 opened this issue · 3 comments
- Diseño de Suspensión para mejorar agarre
Entregable:
- Investigación/Cálculos
- Modelaje Solidworks
To begin the model of the robot suspension system first we need to calculate the teoretical values of the spring and damping constants that satisfy a smood displacement. Mathematical modeling of the four wheel system is complicated. We can simplify the sistem by only analysing one wheel as show below.
A mass-spring damper system is model by the following equation:
where m is the mass that holds a wheel, K the spring constant, b the damping coeficient and r(t) the external forces.
Using Laplace transform we can conclude:
The transfer function is given by:
Once having the model of the system we substitute the values we have, such as the mass. As we want a smood movement the
spring must be a systm with critical damping, So the poles of the system must be equals:
s^2 +(b/m)*s + (k/m) = (s + p)^2
giving us the value of b as function of k and m
b= 2* m* sqrt (k/m)
By using Matlab and WolframAlpha programs I model the system to give the reaction of any input to the system with knowing the constants.
My task of this week is to find the most suitable constant K for our robot, mantaining the desire stability.
Continuing with the calculus of the suspension, We develop a MATLAB program in which by a given estability time we can know the values of the spring and damping constants. The first program is simulating a Step input with a variable magnitud and the second we can give the traslational function of the wheel.
UNIT STEP
Response with unit step magnitud of 10
Given Function
Response with Sin (t) input
Now by just given the Stability Time we can know the important constants with a critical damping
