engineering studies

Motor Modeling Project Week 1 Assignment EGR202

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Week 1 Problem Description The purpose of this week’s motor assignment is to understand the mechanical power required to propel your hoverboard and rider up a hill at constant velocity. Remember that power is the scalar dot product of force and velocity or torque and angular ve- locity:

p = f⃗ · v⃗ = τ⃗ · ω⃗

This gives you several ways to compute the mechanical power required. If you know the torque at the wheels, then you will need to know how fast the wheels are spinning. If you know the equivalent force at the wheel bearings, then you must find out the velocity of that point. Either way you will need to find a force / torque term and the matching velocity / angular velocity term. One way to find the forces involved in your system is with a free body diagram.

Steps 1. Create a free body diagram for the wheel. Draw and label all important variables and design

parameters in your diagrams. This includes things like dimensions, forces, velocities, an- gles, vectors. Identify all forces acting upon each subsystem, including gravity, interaction forces between subsystems, and ground reaction forces.

2. Use static force / moment balance equations to solve for static equilibrium in each subsys- tem. In planar systems, ∑

Fx = 0∑ Fy = 0∑ M = 0

Please expand these equations, using all forces and torques acting upon the wheel. 3. Using the above equations, solve for fT , the force required to push the mass(m) of board

and rider up the hill. 4. Using the above equations, solve for the torque required at the wheels to achieve static

equilibrium. 5. Given the velocity specification given in the assignment, how fast do the wheels spin?

Remember the releationship between linear and angular velocity, v⃗ = ω⃗ × r⃗, where v⃗ is linear velocity, ω⃗ is angular velocity, and r⃗ is the vector to the point on the wheel’s radius.

6. Given the equations for power mentioned above, please calculate how much power is re- quired to maintain the board’s velocity up the hill.

Assumptions and Notes • It may be beneficial to use the B frame rather than the A frame to sum forces and torques • Assume a planar system, ie 2D. • Assume the rider is stationary on the board, with the mass of the system centered about the wheel.

• Keep all dimensions as variables throughout your work, ie, if we say the velocity of the rider is 5 m/sec, use a variable like v as you work through your equations.

• Important terms are terms that are used in equations.