Question: 1 . ?A DC motor is used to drive a Il = 1 8 ?kg - m 2 ?load as shown in the schematic.

$1 .$ ?A DC motor is used to drive a Il $= 18$ ?kg $-$ m $2$ ?load as shown in the schematic. The system includes two gear trains $($ to modify the applied torque and speed $)$ ?and viscous damping of cl $= 36$ ?Nm $-$ s $/$ rad and c $= 8$ ?Nm $-$ s $/$ rad as shown. The number of teeth on gear $1$ ?is N $1 = 10,$ ?gear $2$ ?is N $2 = 20,$ ?gear $3$ ?is N $3 = 10,$ ?and gear $4$ ?is N $4 = 20 .$ ?The torque $-$ speed curve for the motor is shown in Figure $2 .$ ?Assume that the inertial of the motor, Im $,$ ?is negligible when compared to the other components of the system.

$($ a $)$ ?Derive the differential equation that models the angular displacement of the load, $\$ theta $($ t $)$ ?as a function of input motor voltage, v $($ t $) .$

$2 .$ ?Repeat problem $1$ ?for the case that the inertia of the gears are not negligible. Assume that gear $1$ ?has an inertia of I $1 = 1$ ?kg $-$ m $2,$ ?gear $2$ ?has an inertia of I $2 = 2$ ?kg $-$ m $2,$ ?gear $3$ ?has an inertia of I $3 = 2$ ?kg $-$ m $2,$ ?gear $4$ ?has an inertia of I $4 = 3$ ?kg $-$ m $2 .$ Figure $1$ : Schematic of the DC motor driven system.

+ v(t) Motor Im T [Nm] Tstall = 5 Gear 2 Gear 1 Gear 3 Gear 4 POT Figure 1: Schematic of the DC motor driven system. w [RPM] Wno load 600/

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Solutions Step 1 The following actions must be taken in order to solve the mentioned issue 1 Differential Equation Derivation First Case In this insta... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mechanical Engineering Questions!

Cinder Inc. is a Canadian-controlied private corporation based in your province The company operates a wholesale business. The following information is provided for its year ended May 31,2023 1. Net...

Quinoa Farms just paid a dividend of $3.05 on its stock. The growth rate in dividends is expected to be a constant 5 percent per year indefinitely. Investors require a return of 12 percent for the...

Your two-part essay question is based on the following: Over the long-run in the US, from the late 19th century to the present, the number of births per woman has fallen, married womens labor force...

TIM produces and sells two products, the MK and the KL. The organisation expects to sell 2 MK for every 2 KLs and have monthly sales revenue of GHe150,000. The MK has a C/S ratio of 20% whereas the...

Group Design Assignment Design and Implementation of a Control and Interface Unit for A Simple Microwave Oven using MPLAB IDE and Proteus This design assignment is worth 15% of your final grade. It...

IBL ( Chapter 1 4 - covered using problem based learning method ) ME 3 0 2 - Machine Design IIGear Design Chapters 1 3 and 1 4 , from textbookProblem StatementThe Figure 1 below shows an electric...

Hello, you already did chapter 1 and 2 of my MASTERS Thesis already for me. (See attached) So normally you know masters thesis consist of 5 chapters right ??..... But in this case my thesis will be 4...

please explain with details how to get the dynamic diferrntial equation, Why is 7 the coefficient of y ' ( t ) , why is 6 the coefficient of y ( t ) and why - 1 2 is the coefficient of X ( t ) Table...

Week 3: No Plagiarism No content from other students papers. Post should be in APA 6th edition format, I will need References and in-text citations. This website should be useful for all APA...

( please note in the first page, motor internal gears with a 1 4 : 1 ratio! not 1 : 1 4 ! ) In this first homework, you are to derive a mathematical model that describes the dynamic response of a...

In this first homework, you are to derive a mathematical model that describes the dynamic response of a Quanser Consulting SRV - 0 2 ( Servo - 0 2 ) system. Figure 1 depicts a schematic diagram of...

Find the tension in wire CD and the reactions at pins A and B. The uniform plate weighs 210b. Assume the pin at B cannot support any thrust load (B,). As always, include a FBD(s) and clearly label...

Using the notation scheme for defining manipulator configurations, draw diagrams (similar to Figure 8.1) of the following robots: (a) TRT:R, (b) TVR:TR, (c) RR:T.

Find the following derivative 3 . 9 . 3 1 d d x ( l n ( x ) l n ( x ) + 4 ) d d x ( l n ( x ) l n ( x ) + 4 ) =

In many population growth problems, there is an upper limit beyond which the population cannot grow. Many scientists agree that the earth will not support a population of more than 16 billion. There...

Given the changes to compliance and regulations across multiple industries, what do you feel are critical attributes to a successful board member?

Suppose we have two coins: one is fair and the other one is two-headed. We choose one coin to throw: the fair coin is chosen with probability 34 . We toss the chosen coin and it lands heads. Use the...

Suppose an unfair (weighted) die takes values 1,2,3,4,5, 6 with respective probabilities p1,p2,p3,p4,p5,p6. The die is rolled once. If the die result is i, a fair coin is thrown I times. Find the...

Search an annual financial report for a public U.S. company. Read the Notes to the Financial Statements to determine the criteria for cash equivalents and how cash and cash equivalents are handled....

Design a minimum-mass symmetric three-bar truss (the area of member 1 and that of member 3 are the same) to support a load P, as was shown in Fig. 2.9. The following notation may be used: Pu = P cos...

In an industrial research on extraction of flavoring oils, raw materials were sourced from five different countries and each of was subjected to extraction using vessels of five different sizes, each...

An experimenter wanted to compare the effects of four chemicals A, B, C, and D on water hardness. Hard water from three different locations was used in the study, but the location of hard water was...

In phytochemical research, the percentage content of a plant chemical extract used for drug production was being studied. It was believed that the contents could vary according to the country of...