ME 450 ME450 Computer Project 1 (Penn State University)
ME450 Computer Project 1 (Penn State University)
Shown below is a schematic of a partial gear train used in common helicopter gear drive boxes. J1 is the rotational inertia which the input torque Tm is applied. Rotational stiffness is K1 and gears 1 and 2 are represented by J2 and J3 respectively. The nonlinear friction torque between the ground and gear 2 is:
- Develop the nonlinear state variable equations for this system. Use q1=1, q2=1- 2, and q3=3 as the state variables. Also, construct the simulation diagram.
- Use the MATLAB program ode45 to calculate and
plot the response of the system to a step torque(Tm) with magnitude 1 N-m and then to a step torque with magnitude 30 N-m. For both inputs, determine the steady-state value, maximum overshoot, and period of oscillations of the rotational displacement (1-2). Include a print out of your MATLAB program. - Linearize the system model in the vicinity of the normal operating point, Tm=0.
- Obtain step responses of the linearized model for the same two step inputs. Again,
for both inputs determine steady-state value, maximum overshoot, and period of oscillations. Compare these values with the nonlinear system. Include a print of your MATLAB program. - For the linearized model, use dominant roots to validate your computer results.
- Write your conclusions regarding all important aspects of this project. Specifically, is
the linearized model a good representation of the nonlinear model? What improvements can be made to the system parameters to enhance system performance?
