It is desirable to control the angular velocity w(t) of a rotor turbine of moment of...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
It is desirable to control the angular velocity w(t) of a rotor turbine of moment of inertia J=60 kgm2. The rotational motion of the rotor is excited by a step input torque TEng 50 N-m, generated by an engine. It is assumed that the rotor experiences a linear damping torque proportional to the angular velocity of the rotor and the coefficient of proportionality is DL=10 N-m-s/rad. The rotor also experiences a nonlinear damping torque whose mathematical form is quadratic i.e the magnitude of the torsional damping torque is proportional to the square of the angular velocity of the rotor. The coefficient of proportionality for the nonlinear damping is DNL 20 Nm-s²/rad². 2.1. 2.2. 2.3. 2.4. Providing the free body diagram of the rotor turbine, derive the differential equation of motion of the rotor turbine Derive the expression for the angular velocity w(t) of the rotor turbine. Construct a detailed block diagram to control the angular velocity w(t) of the rotor turbine. (9) Assuming the final value of the time response for the angular velocity of the system to be reached when the maximum value is attained, calculate the final angular velocity of the rotor turbine. (6) (3) (4) It is desirable to control the angular velocity w(t) of a rotor turbine of moment of inertia J=60 kgm2. The rotational motion of the rotor is excited by a step input torque TEng 50 N-m, generated by an engine. It is assumed that the rotor experiences a linear damping torque proportional to the angular velocity of the rotor and the coefficient of proportionality is DL=10 N-m-s/rad. The rotor also experiences a nonlinear damping torque whose mathematical form is quadratic i.e the magnitude of the torsional damping torque is proportional to the square of the angular velocity of the rotor. The coefficient of proportionality for the nonlinear damping is DNL 20 Nm-s²/rad². 2.1. 2.2. 2.3. 2.4. Providing the free body diagram of the rotor turbine, derive the differential equation of motion of the rotor turbine Derive the expression for the angular velocity w(t) of the rotor turbine. Construct a detailed block diagram to control the angular velocity w(t) of the rotor turbine. (9) Assuming the final value of the time response for the angular velocity of the system to be reached when the maximum value is attained, calculate the final angular velocity of the rotor turbine. (6) (3) (4)
Expert Answer:
Answer rating: 100% (QA)
21 Free body diagram and differential equation of motion of the rotor turbine The free body diagram of the rotor turbine is shown below Free body diag... View the full answer
Related Book For
Fundamentals of Ethics for Scientists and Engineers
ISBN: 978-0195134889
1st Edition
Authors: Edmund G. Seebauer, Robert L. Barry
Posted Date:
Students also viewed these databases questions
-
Given a resonator consisting of two mirrors with radii of curvature R and R2, and separation d. The wavelength is 500 nm. Find the Rayleigh range, the location and radius of the beam waist as well as...
-
It is desired to control the angular displacement ( of a space vehicle by controlling the applied torque T supplied by thrusters (Figure PI2.8a). The plant model is Gp (s) = ( (s) / T (s) = 10 / s2...
-
It is desired to control the angular displacement ( of a space vehicle by controlling the applied torque T supplied by thrusters (Figure PI2.3). The plant model is Gp (s) = ( (s) / T (s) = 5/s2...
-
. What is the output of the following program? Write your answer in the box below. #include using namespace std; int main() { int a=4; int b=6; int i; int j; } int** k; i = &a; j = &b; *j = 8; if...
-
Use a three-time-step tree to value an American floating lookback call option on a currency when the initial exchange rate is 1.6, the domestic risk-free rate is 5% per annum, the foreign risk-free...
-
Wilson is now evaluating the expected performance of two common stocks, Furhman Labs Inc. and Garten Testing Inc. He has gathered the following information: The risk-free rate is 5%. The expected...
-
Go to the library and select five empirical research articles (those that contain actual data) from your area of interest. For each one, list the following: a. What is the null hypothesis (implied or...
-
On March 1, 2011, Dora Corporation began operations with a charter from the state that authorized 50,000 shares of $4 par value common stock. Over the next quarter, the firm engaged in the...
-
Mark Cuban Corporation purchased a truck at the beginning of 2025 for $51,500. The truck is estimated to have a salvage value of $2,060 and a useful life of 164,800 miles. It was driven 23,690 miles...
-
Determine the moment of each force about the bolt located at A. Given: FB = 40 lb a = 2.5 ft α = 20 deg γ = 30 deg FC = 50 lb b = 0.75 ft β = 25 deg Fc FB
-
What is the beta coefficient for a firm? What does it tell us about the firm? Why do similar firms have different beta coefficients?
-
A message digest is the result of hashing. Which of the following statements about the hashing process is true? a. It is reversible. b. Comparing the hashing results can ensure confidentiality. c....
-
The computer sums the first four digits of a customer number to calculate the value of the fifth digit and then compares that calculation to the number typed during data entry. This is an example of...
-
The steps in business intelligence include a. analyze data for patterns, gather information, make decision. b. create data warehouse, query data warehouse, make decision. c. query data warehouse,...
-
Why would a company need a SOC report? a. The external auditor needs to know the effectiveness of internal controls of the companys service provider(s). b. The company wants to use it for marketing...
-
Incentive to commit fraud usually will include all of the following, except a. inadequate segregation of duties. b. financial pressure. c. personal habits and lifestyle. d. feelings of resentment. e....
-
A certain television is advertised as a 59-inch TV (the diagonal length ). If the width of the TV is 49 inches, how tall is the TV? Round to the nearest tenth of an inch.
-
After graduating from college and working a few years at a small technology firm. Preet scored a high-level job in the logistics department at Amex Corporation. Amex sells high-quality electronic...
-
A man is stranded in the middle of an ice rink that is perfectly frictionless. How can he get to the edge?
-
One of Jupiters moons, Io, has a mean orbital radius of 4.22 x 10 8 m and a period of 1.53 x 10 5 s. (a) Find the mean orbital radius of another of Jupiters moons, Callisto, whose period is 1.44 x 10...
-
In figure the objects are attached to spring balances calibrated in newtons. Give the reading of the balances in each case, assuming that the strings are massless and the incline infrictionless 10kg...
-
The UK government has recognized the importance of information and behavioural economics to decision-making. The government partly funds the Behavioural Insights Team (BIT) in conjunction with an...
-
What are the four subfields of anthropology?
-
Who was Jean-Baptiste Lamarck, and how did his ideas contrast with those of Darwin?
Study smarter with the SolutionInn App