Matlab Analysis
The Rockin' Roller
Engineering a safe and exciting carnival ride through spring-damper system analysis and MATLAB simulation
Design Process and Methods
Data Analysis
Motion Analysis with Runga Kutta Method
Data Analysis
The project began with known data about the spring the client would use and data about 3 different possible damper systems. Four data files containing spring and damper information were analyzed. Using linear regression with MATLAB's polyfit function, I determined the spring constant and damping coefficients from force-displacement and force-velocity relationships.
Mass Analysis
Motion Analysis with Runga Kutta Method
Data Analysis
The system hadn't been built but we needed a mass to work with. First, we found size constraints for the seat. Using several variations on the size and the density of the material we found the best match. I used both built-in MATLAB functions and manual Gaussian quadrature to compute the mass of the Rockin' Roller seat. The integration was performed over a complex function involving trigonometric and power terms.
Motion Analysis with Runga Kutta Method
Motion Analysis with Runga Kutta Method
Motion Analysis with Runga Kutta Method
Using the 4th-order Runge-Kutta method, I solved the differential equations governing the motion of the damped mass-spring system for each of the three damper configurations.
Plots
Damper 3 Plot
Damper 3 Plot
Damper 3 Plot
The linear regression model is used to fit the data of Damper 3. The data (c3.data) is in two columns of testing data, Velocity and Force. For the dampers, Force is proportional to the velocity with the relationship F = cv. So we can plot F and v and find c as the slope.
Damper 2 Plot
Damper 3 Plot
Damper 3 Plot
The motion of the seat followed the equation
m* d^2x./dt^2+ c*dx/dt+kx = 0. Since we are finding the mass of the seat with numerical integration, we need to find the c's and k's using this method. Then we can plot displacement and velocity vs time.
Damper 1 Plot
Damper 3 Plot
Damper 1 Plot
All three damper plots showed a very linear relationship between Velocity and Force, this was essential to finding C
Spring Plot
Displacement vs Time
Damper 1 Plot
The spring data was formatted into Force and Displacement columns. Using the relationship F=kd and the same linear regression techniques we can find the slope, K.
Displacement vs Time
Displacement vs Time
Displacement vs Time
Using MATLAB's built in Runga-Kutta method we could solve the differential equation. We put the initial conditions (x(0) = -1m and v(0) = 0 m/s) into state space equations and passed into the Runga-Kutta equation.
Velocity vs Time
Displacement vs Time
Displacement vs Time
We wanted a seat that crosses x=0 3 times and never exceeds v=1.5m/s. C1 and C2 both met the criteria of crossing over x=0 several times, but only C1 met the velocity criteria
Results
With this code we were able to quickly find vital information
Vital information about the mass of the seat, the spring constant and the three damping coefficients. Inputting this data and some known initial conditions into the differential equation m* d^2x./dt^2+ c*dx/dt+kx = 0 and we get displacement and velocity information about the seat. We want to use this data to understand what the rider will feel. We want a ride that moves in an exciting but safe way.
Damper C1 was the only damper to meet the criteria of passing over the centerline at least 3 times and having a max velocity under 1.5m/s. C1 was the choice of damper to move forward with.
