ME 450 ME450 Computer Project 1 (Penn State University)

ME 450 ME450 Computer Project 1 (Penn State University)

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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: 

  1. 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. 
  2. 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. 
  3. Linearize the system model in the vicinity of the normal operating point, Tm=0. 
  4. 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. 
  5. For the linearized model, use dominant roots to validate your computer results. 
  6. 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? 

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