Mechatronics Systems Design (MCT 317)
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Questions and Answers

What is the primary function of a servomotor?

  • To provide high-speed operation
  • To convert electrical energy into heat
  • To allow for precise control of position, velocity, and acceleration (correct)
  • To exclusively produce linear motion

    • According to Newton's second law of motion, which equation correctly represents the relationship between force, mass, and acceleration?

  • $F = m - a$
  • $F = m + a$
  • $F = m/a$
  • $F = ma$ (correct)

    • How is the displacement of an object traveling under constant acceleration calculated?

  • $s = ma^2$
  • $s = 1/2 a t^2$ (correct)
  • $s = F/m$
  • $s = 1/2 t^2$

    • What is the angular displacement equation analogous to that of linear motion?

    <p>$ heta = 1/2 at^2$</p> Signup and view all the answers

    For a mass rotating about a fixed axis, what does $T$ represent in the equation $T = J heta$?

    <p>Resultant torque acting on the mass</p> Signup and view all the answers

    What is required to determine the motor size for a given application with a rotary load?

    <p>The displacement and time required for motion</p> Signup and view all the answers

    In the rotary motion example, what is the total distance the load needs to travel for one cycle?

    <p>$1/4$ of a revolution</p> Signup and view all the answers

    What is the first step in the actuator sizing algorithm?

    <p>Define the geometric relationship between the actuator and load.</p> Signup and view all the answers

    What portion of the motion period is dedicated to acceleration in the example provided?

    <p>$50$ msec</p> Signup and view all the answers

    Which factors must be defined regarding the load in the sizing algorithm?

    <p>The inertia and torque/force characteristics of the load and transmission mechanisms.</p> Signup and view all the answers

    What should be calculated next after defining the inertia and torque of the load?

    <p>The reflected load inertia and torque/force for the actuator shaft.</p> Signup and view all the answers

    When guessing the actuator/motor inertia, what assumption can be made?

    <p>Make the first calculation with zero motor inertia.</p> Signup and view all the answers

    What is the relationship between the resistive load torques and the total torque when the load torque opposes motion?

    <p>The total torque is the motor torque minus the resistive torque.</p> Signup and view all the answers

    What does the peak torque and RMS torque depend on during the sizing process?

    <p>The torque history calculated for the desired motion cycle.</p> Signup and view all the answers

    What happens to the continuous torque capacity of a servo motor when the ambient temperature is above 25°C?

    <p>It should be de-rated.</p> Signup and view all the answers

    Which of the following formulas represents the total inertia reflected on the motor axis?

    <p>Jtotal = Jm + Jeff</p> Signup and view all the answers

    Why must the required peak and RMS torque be smaller than the continuous torque capacity of the stepper motor?

    <p>To ensure that the motor can operate continuously.</p> Signup and view all the answers

    What is the role of the reduction ratio (N) in the actuator sizing algorithm?

    <p>It defines the geometric relationship between the actuator and the load.</p> Signup and view all the answers

    What is considered an optimal inertia ratio between motor inertia and load inertia?

    <p>1:1</p> Signup and view all the answers

    What must be done if the initial actuator/motor selection does not meet the requirements?

    <p>Repeat the process with a different motor choice.</p> Signup and view all the answers

    How can the total torque, $T_{total}(t)$, be calculated if the resistive load torque, $T_R(t)$, is zero?

    <p>It is equal to $T_m(t)$.</p> Signup and view all the answers

    In the context of calculating net inertia, what does Jeff represent?

    <p>The total load inertia reflected on the motor shaft.</p> Signup and view all the answers

    What is essential to consider when determining the torque required to move a load?

    <p>All external and internal torques acting on the system.</p> Signup and view all the answers

    What should be done if the ambient temperature differs significantly from 25°C?

    <p>Adjust the continuous torque capacity according to de-rating guidelines.</p> Signup and view all the answers

    What is the formula to calculate the maximum speed required to define the motion profile?

    <p>$\theta_{max} = \frac{2\theta_{total}}{t_a + 2t_r + t_d}$</p> Signup and view all the answers

    What is the angular acceleration calculated in the content?

    <p>314 rad/sec²</p> Signup and view all the answers

    Which value represents the peak torque required?

    <p>0.7536 N.m</p> Signup and view all the answers

    Which of the following equations describes the relationship between displacement and maximum speed?

    <p>$\theta_{total} = \theta_{max} t_a + \theta_{max} t_r + \theta_{max} t_d$</p> Signup and view all the answers

    What does Trms represent in the motor calculations?

    <p>Root mean square torque over the entire cycle</p> Signup and view all the answers

    What values are required to ensure the motor is sufficient for the task?

    <p>Rotor inertia, maximum speed, peak torque, RMS torque</p> Signup and view all the answers

    During which motor operation mode is the torque equal to zero?

    <p>Dwell mode</p> Signup and view all the answers

    How is the acceleration described in relation to velocity?

    <p>Acceleration is the derivative of velocity.</p> Signup and view all the answers

    What does the term 'tcyc' represent in the motion profiles?

    <p>It represents the time to complete a full cycle.</p> Signup and view all the answers

    Which term defines the holding torque required during the dwell mode?

    <p>TH</p> Signup and view all the answers

    What does the term 'Jm' refer to in the torque equation?

    <p>The motor's inertia</p> Signup and view all the answers

    How is the root mean square torque represented mathematically in the content?

    <p>$Trms = \sqrt{\frac{1}{t_{cyc}}\int_{0}^{t_{cyc}} T_m^2(t) dt}$</p> Signup and view all the answers

    How are the time intervals for acceleration, constant speed, and deceleration represented?

    <p>ta, tr, td</p> Signup and view all the answers

    Study Notes

    Mechatronics Systems Design (MCT 317)

    • Course name: Design of Mechatronics Systems (1)
    • Instructor: Dr. Eng. Mohamed Nabil
    • Email: [email protected]

    Servomotors

    • A servomotor is a rotary or linear actuator for precise control of angular or linear position, velocity, and acceleration.
    • It combines a suitable motor with a sensor for position feedback.
    • Components usually include: DC Motor, Gearbox, Feedback Loop, Error Detection Amplifier, and Position Sensor.

    Cascade Control Structure of High Performance DC Servo System

    • A high-performance DC servo system employs a cascade control structure.
    • Key components: Desired Position Regulator, Speed Regulator, Current Regulator, Current Sensor, DC Motor, Position Sensor, and a 4-quadrant power supply.
    • The system regulates position, speed, and current to deliver the desired output.

    AC Servo System

    • This control method handles AC-based servo systems.
    • Components include AC Supply, Current Sensors, Permanent Magnet AC Motor, Position Sensor, Current Controlled Power Converter, Position Regulator, Speed Regulator components.
    • Control loops for position, speed, and current are evident.

    Actuator Sizing

    • This section covers sizing actuators for specific applications.
    • Key aspects: defining the relationship of the actuator and load, inertia and torque, desired motion profile of the load, reflected load inertia, torque, and forces on the actuator components.
    • Calculations consider motor inertia, torque requirements (peak and RMS).
    • Sizing considers continuous torque capacity given for a standard temperature (25°C).

    Types of Motion and Motion Conversion

    • Linear motion in a rigid object is controlled by Newton's second law of motion (F=ma).
    • Resultant force (F) affects the object's mass (m) and acceleration (a). A constant force produces a constant acceleration, moving the object a specific distance (s) over time (t) according to the equation s = 1/2at².
    • Angular motion is similarly calculated with respect to torque (T). The formula for angular motion is T = Jα, where T is torque, J is the moment of inertia, and α is the angular acceleration.

    Example: Rotary Motion Axis

    • The example concerns a rotary motion axis driven by an electric servo motor.
    • The load is a solid cylindrical steel shape. Dimensions given (diameter and length).
    • The desired motion of the load is cyclic.

    Example Calculations

    • The example provided includes detailed calculations for determining the necessary motor size for a specific cyclic motion of a mechanical system.
    • Specific figures like the period of motion (tcyc = 250 msec), dwell time (tdw = 100 msec) and the speed and acceleration times are given

    Actuator Sizing Algorithm and Procedure

    • A structured algorithm guides the process of actuator sizing.
    • Steps include defining the geometric relationship, characterising load and transmission inertias and torques, defining the motion profile, calculating reflected load inertia and torque, and guessing/calculating motor inertias and sizing the motor based on peak and RMS torque requirements

    Solution to Inertia Calculation

    • The example solution procedure details a step-by-step approach to determine the net inertia of the system involved.
    • Formulae applied include those for determining reflected load inertia from rotor inertia.

    Net Inertia Determination

    • This segment details the steps to calculate the net inertia in the system.
    • It considers total torque (Ttotal), motor torque (Tm) and resistive load torque (Tr) based on the direction of the assistance to motion.

    Fundamental Equations for Torque Calculation, Desired Cyclic Motion Profile

    • Fundamental equation for torque and motion relationships are established.
    • Calculations using these equations determine the total torque and acceleration.
    • Desired cyclic motion profiling is described, specifying acceleration, constant speed, and deceleration times.
    • Details like required distance per revolution are presented.

    Calculating Maximum Speed and Angular Acceleration

    • Maximum speed required to produce the desired motion profile determined from displacement-time and velocity-time profiles.
    • Specific values are shown for acceleration/deceleration stages.

    Torque Calculation at Each Mode, Peak Torque

    • Detailed method for torque calculation at different parts of motion cycle (e.g., acceleration, constant speed).
    • The maximum (peak) torque is calculated based on calculated values from profiles.

    Root Mean Square (RMS) Torque Calculation

    • RMS torque is derived over entire cycle.
    • Torque calculated using equations based on the torque diagram profile are explained and values shown

    Mechanisms and Drives

    • Concepts of gear drive, direct drive, ratio, inertia and torque are presented.
    • Relevant equations for inertia, velocity and speed relations.

    Conversion of Rotary to Linear Motion

    • Methods for converting rotary motion to linear motion using components like rack and pinion, lead screws and linkages.
    • Equations (and principles) to determine inertial parameters associated with these components are shown

    Calculations Involving Gravity and Inclinations

    • These formulas cover the forces acting on objects moving over inclines or in different inclinations accounting for mass and gravitational forces.
    • Examples (and related calculations) involve incline and pulleys.

    Move Profile

    • A move profile describing the typical speed vs. time profile is shown.
    • An example of a typical move profile has sections for Acceleration Time, Run Time and Deceleration Time

    Shape Relationships and Material Densities

    • A range of shapes (hollow cylinder, solid cylinder and solid block) are presented.
    • Expressions are provided for calculating moments of inertia and volumes. Various material densities are shown in a table format.

    Conversion Tables

    • Tables assist in converting between various units of length and mass.

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    Description

    Test your knowledge on the fundamentals of mechatronics systems including servomotors and high-performance DC servo systems. This quiz covers essential components and control structures used in both DC and AC servo systems. Understand the integration of motors, sensors, and feedback loops in mechatronic design.

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