(30 points) In order to compute numcrical valucs of the nominal stcady-state gain and time constant,...

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(30 points) In order to compute numcrical valucs of the nominal stcady-state gain and time constant, we will start by determining the equivalent moment of inertia, Jeg. As shown in (2.2.15), Jeg is a function of the moment of inertia of the motor, Jm, and the moment of inertia of the load, J. The inertia of the motor, Jm, is provided in Table 2.2.1 and includes both the inertia of the rotor and of the tachometer attached to the motor shaft. The inertia of the load, Ji, is the sum of the inertia of the gear train, J,, (provided in Table 2.2.1) and the inertia of the external load attached to the load shaft Jeat. In this lab, the external load is the disc shown in Fig. 2.1.1 with properties provided in Table 2.2.1. Compute the moment of inertia of a) the disc, Jert; b) the load shaft, J; and c) the entire system, Jeq. Jeg = NgK, Jm + Jt, (2.2.15) SUAN ER SAVOR Figure 2.1.1: Servo Unit system with bar and disc inertial loads. Description Value Units Symbol kg - m² kg - m² Moment of inertia of gearbox 5.52 × 10–5 Jg Jm Moment of inertia of motor Gearbox efficiency 4.61 × 10-7 0.9 Ng K9 Gear ratio 70 2.6 Ω Rm Motor armature resistance 0.69 Motor efficiency Motor current-torque constant Motor back-emf constant N• m/A V/(rad/s) N·m/(rad/s) kg 7.68 × 10-3 kit 7.68 × 10-3 km Equivalent damping coefficient Mass of disc 0.015 Beg 0.04 mdisc Radius of disc 0.05 m T'disc Table 2.2.1: Servo Unit nominal parameter values. (30 points) In order to compute numcrical valucs of the nominal stcady-state gain and time constant, we will start by determining the equivalent moment of inertia, Jeg. As shown in (2.2.15), Jeg is a function of the moment of inertia of the motor, Jm, and the moment of inertia of the load, J. The inertia of the motor, Jm, is provided in Table 2.2.1 and includes both the inertia of the rotor and of the tachometer attached to the motor shaft. The inertia of the load, Ji, is the sum of the inertia of the gear train, J,, (provided in Table 2.2.1) and the inertia of the external load attached to the load shaft Jeat. In this lab, the external load is the disc shown in Fig. 2.1.1 with properties provided in Table 2.2.1. Compute the moment of inertia of a) the disc, Jert; b) the load shaft, J; and c) the entire system, Jeq. Jeg = NgK, Jm + Jt, (2.2.15) SUAN ER SAVOR Figure 2.1.1: Servo Unit system with bar and disc inertial loads. Description Value Units Symbol kg - m² kg - m² Moment of inertia of gearbox 5.52 × 10–5 Jg Jm Moment of inertia of motor Gearbox efficiency 4.61 × 10-7 0.9 Ng K9 Gear ratio 70 2.6 Ω Rm Motor armature resistance 0.69 Motor efficiency Motor current-torque constant Motor back-emf constant N• m/A V/(rad/s) N·m/(rad/s) kg 7.68 × 10-3 kit 7.68 × 10-3 km Equivalent damping coefficient Mass of disc 0.015 Beg 0.04 mdisc Radius of disc 0.05 m T'disc Table 2.2.1: Servo Unit nominal parameter values.

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