Read Chapter 2 on sensor modeling. To control the motion of a moving carriage of

Question

Read Chapter 2 on sensor modeling. To control the motion of a moving carriage of a machine tool a DC motor is used with a rack-and- pinion mechanism (as shown). The input is an ideal current source Parameters include the motor torque constant K_m, motor armature inertia J_m, motor shaft damping B_m, shaft stiffness K, pinion gear inertia J_g, pinion gear radius r, rack (bar) mass m_0, and carriage mass mc. The friction in the rack-and-pinion mechanism has been lumped into a single linear damping force. The speed at the motor end of the shaft is Ohm_1- and the output is the velocity of the carriage, V_0, Develop the appropriate equation of motor for the system (go from i_s to v) Create a block diagram for the system (go from i_s to v) Use Matlabl Simulink to investigate the system behavior (find the step & frequency response [step function and bode plots]). Please comment on the behavior (What frequency inputs should be avoided? What is the rise time, settling time, maximum percent overshoot, etc.) Describe two ways you could measure the position and velocity of the mass, M_c.

Explanation / Answer

3)

The motor’s torque is provided by the electrical current through the windings, and is KmI(t). There are three torques counteracting the motor

Since at the moment we do not know how to express torque (iii), let us denote it by Tp. The time–domain equation of motion of the motor shaft then becomes

KmI(t) = J’ (t) + Bm(t) + Tp(t), Where w(t) is the motor shaft speed 1

Now let us find Force–balance on the translational part of the load, i.e. the pinion’s rack that carries the mass m. If Fp(t) denotes the force by the pinion on the rack, then in the time domain we have

Fp(t) = Mv’ (t) where M = mb+mc

Tp(t) = rFp(t),

v(t) = r2(t).

relates the pinion torque Tp to the pinion force Fp and the angular velocity 2 to the translational velocity v

Related Questions

Navigate

• Browse (All)
• Browse R
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.