Assignment 3
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1. This document provides numerical and theory questions related to governors used in steam engines. Numerical questions involve calculating speed ranges, forces, and other parameters for various governor configurations. 2. Theory questions explain governing concepts like governor height, types of governors including Watt, spring loaded, and Proell, factors that affect stability, and how stability is determined from controlling force curves. 3. Questions also cover topics such as how governing is done in steam engines, effects of friction and central weights, controlling forces that determine stability, and comparing ball weights between Porter and Proell governors.
![Assignment 3
[Module 2–Governor]
Last Date of Submission is 10/10/2017
Numerical Question:
1. In a simple Watt Governor, the length of the upper arm is 10mm and its inclination on the
vertical is 300
. Estimate the percentage change in speed for a rise in the level of balls by 20 mm.
[Ans: 3%]
2. The arms of a Porter governor are 300 mm long. The upper arms are pivotedon the axis of
rotation. The lower arms are attached to a sleeve at a distance of 40 mm from the axisof rotation.
The mass of the load on the sleeve is 70 kg and the mass of each ball is 10 kg. Determinethe
equilibrium speed when the radius of rotation of the balls is 200 mm. If the friction is
equivalentto a load of 20 N at the sleeve, what will be the range of speed for this position?
[Ans: 167 rpm, 4.2 rpm]
3. A loaded Porter governor has four links each 250 mm long, two revolvingmasses each of 3 kg
and a central dead weight of mass 20 kg. All the links are attached to respective sleeves at radial
distances of 40 mm from the axis of rotation. The masses revolve at a radius of 150mm at
minimum speed and at a radius of 200 mm at maximum speed. Determine the range of speed.
[Ans: 19 rpm]
4. A Proell governor has equal arms of length 300 mm. The upper and lowerends of the arms are
pivoted on the axis of the governor. The extension arms of the lower links areeach 80 mm long
and parallel to the axis when the radii of rotation of the balls are 150 mm and200 mm. The mass](https://image.slidesharecdn.com/assignment3-180530110715/85/Assignment-3-1-320.jpg)
![of each ball is 10 kg and the mass of the central load is 100 kg. Determine therange of speed of
the governor. [Ans:10 rpm]
5. A Proell governor has all four arms of length 305 mm. The upper arms are pivoted on the axis
of rotation and the lower arms are attached to a sleeve at a distance of 38 mmfrom the axis. The
mass of each ball is 4.8 kg and are attached to the extension of the lower armswhich are 102 mm
long. The mass on the sleeve is 45 kg. The minimum and maximum radii ofgovernor are 165 mm
and 216mm. Assuming that the extensions of the lower arms are parallel to thegovernor axis at
the minimum radius, find the corresponding equilibrium speeds. [Ans:165 rpm, 170 rpm]
6. In a spring loaded governor of the Hartnell type, the mass of each ball is1kg, length of vertical
arm of the bell crank lever is 100 mm and that of the horizontal arm is 50 mm.The distance of
fulcrum of each bell crank lever is 80 mm from the axis of rotation of the governor.The extreme
radii of rotation of the balls are 75 mm and 112.5mm. The maximum equilibrium speedis 5 per
cent greater than the minimum equilibrium speed which is 360 r.p.m. Find, neglecting
obliquityof arms, initial compression of the spring and equilibrium speed corresponding to the
radius ofrotation of 100 mm. [Ans: 28.6 mm, 373 rpm]
7. A Porter governor has all four arms 200 mm long. The upper arms are pivoted on the axis of
rotation And the lower arms are attached to a sleeve at a distance of 25 mm from the axis. Each
ball has a mass of 2 kg and the mass of the load on the sleeve is 20 kg. If the radius of rotation of
the balls at a speed of 250 r.p.m. is 100 mm, find the speed of the governor after the sleeve has
lifted 50 mm. Also determine the effort and power of the governor. (IES 2007)
[Ans. 275.6 r.p.m.; 22.4 N ; 1.12 N-m]
8. A Porter governor has arms 250 mm each and four rotating flyballs of mass 0.8 kg each. The
sleeve movement is restricted to ± 20 mm from the height when the mean speed is 100 r.p.m.
Calculate the central dead load and sensitivity of the governor neglecting friction when the
flyball exerts a centrifugal force of 9.81 N. Determine also the effort and power of the governor
for 1 percent speed change. [Ans. 11.76 N; 11.12; 0.196 N; 7.7 N-mm]
9. The upper arms of a Porter governor are pivoted on the axis of rotation and the lower arms are
pivoted to the sleeve at a distance of 30 mm from the axis of rotation.The length of each arm is
300 mm and the mass of each ball is 6 kg. If the equilibrium speed is 200 r.p.m. when the radius](https://image.slidesharecdn.com/assignment3-180530110715/85/Assignment-3-2-320.jpg)
![of rotation is 200 mm, find the required mass on the sleeve. If the friction is equivalent to a force
of 40 N at the sleeve,find the coefficient of insensitiveness at 200 mm radius. (IES 2001)
[Ans. 61.1 kg. ; 6%]
10. A Hartnell governor has two rotating balls, of mass 2.7 kg each. The ball radius is 125 mm
in the mean position when the ball arms are vertical and the speed is 150 r.p.m. with the sleeve
rising. The length of the ball arms is 140 mm and the length of the sleeve arms 90 mm. The
stiffness of the spring is 7 kN/m and the total sleeve movement is 12 mm from the mean
position. Allowing for a constant friction force of 14 N acting at the sleeve, determine the speed
range of the governor in the lowest and highest sleeve positions. Neglect the obliquity of the ball
arms. (IES 1999) [Ans. 10.7 r.pm., 6.6 r.pm.]
Theory Questions:
1. Explain the term height of the governor. Derive an expression for the height in the case of
a Wattgovernor. What are the limitations of a Watt governor?
2. How is governing done in steam engine.
3. Explain with neat line diagram the working of the spring loaded type governor.
4. What are the effects of friction and of adding a central weight to the sleeve of a Watt
governor?
5. Discuss the controlling force and stability of a governor and show that the stability of a
governordepends on the slope of the curve connecting the controlling force (FC) and
radius of rotation (r) andthe value (FC /r).
6. What is stability of a governor? Sketch the controlling force versus radius diagrams for a
stable,unstable and isochronous governor. Derive the conditions for stability.
7. Explain clearly how you would determine from the controlling force curve whether a
governor is stable, unstable or isochronous.
8. For given equilibrium speed, weight of the sleeve and the governor height, which
governor shall have balls of less weight:Proter or Proell ? Why?
9. Why are two balls and not just one ball provided in centrifugal governor?](https://image.slidesharecdn.com/assignment3-180530110715/85/Assignment-3-3-320.jpg)
Assignment 3
- 1. Assignment 3 [Module 2–Governor] Last Date of Submission is 10/10/2017 Numerical Question: 1. In a simple Watt Governor, the length of the upper arm is 10mm and its inclination on the vertical is 300 . Estimate the percentage change in speed for a rise in the level of balls by 20 mm. [Ans: 3%] 2. The arms of a Porter governor are 300 mm long. The upper arms are pivotedon the axis of rotation. The lower arms are attached to a sleeve at a distance of 40 mm from the axisof rotation. The mass of the load on the sleeve is 70 kg and the mass of each ball is 10 kg. Determinethe equilibrium speed when the radius of rotation of the balls is 200 mm. If the friction is equivalentto a load of 20 N at the sleeve, what will be the range of speed for this position? [Ans: 167 rpm, 4.2 rpm] 3. A loaded Porter governor has four links each 250 mm long, two revolvingmasses each of 3 kg and a central dead weight of mass 20 kg. All the links are attached to respective sleeves at radial distances of 40 mm from the axis of rotation. The masses revolve at a radius of 150mm at minimum speed and at a radius of 200 mm at maximum speed. Determine the range of speed. [Ans: 19 rpm] 4. A Proell governor has equal arms of length 300 mm. The upper and lowerends of the arms are pivoted on the axis of the governor. The extension arms of the lower links areeach 80 mm long and parallel to the axis when the radii of rotation of the balls are 150 mm and200 mm. The mass
- 2. of each ball is 10 kg and the mass of the central load is 100 kg. Determine therange of speed of the governor. [Ans:10 rpm] 5. A Proell governor has all four arms of length 305 mm. The upper arms are pivoted on the axis of rotation and the lower arms are attached to a sleeve at a distance of 38 mmfrom the axis. The mass of each ball is 4.8 kg and are attached to the extension of the lower armswhich are 102 mm long. The mass on the sleeve is 45 kg. The minimum and maximum radii ofgovernor are 165 mm and 216mm. Assuming that the extensions of the lower arms are parallel to thegovernor axis at the minimum radius, find the corresponding equilibrium speeds. [Ans:165 rpm, 170 rpm] 6. In a spring loaded governor of the Hartnell type, the mass of each ball is1kg, length of vertical arm of the bell crank lever is 100 mm and that of the horizontal arm is 50 mm.The distance of fulcrum of each bell crank lever is 80 mm from the axis of rotation of the governor.The extreme radii of rotation of the balls are 75 mm and 112.5mm. The maximum equilibrium speedis 5 per cent greater than the minimum equilibrium speed which is 360 r.p.m. Find, neglecting obliquityof arms, initial compression of the spring and equilibrium speed corresponding to the radius ofrotation of 100 mm. [Ans: 28.6 mm, 373 rpm] 7. A Porter governor has all four arms 200 mm long. The upper arms are pivoted on the axis of rotation And the lower arms are attached to a sleeve at a distance of 25 mm from the axis. Each ball has a mass of 2 kg and the mass of the load on the sleeve is 20 kg. If the radius of rotation of the balls at a speed of 250 r.p.m. is 100 mm, find the speed of the governor after the sleeve has lifted 50 mm. Also determine the effort and power of the governor. (IES 2007) [Ans. 275.6 r.p.m.; 22.4 N ; 1.12 N-m] 8. A Porter governor has arms 250 mm each and four rotating flyballs of mass 0.8 kg each. The sleeve movement is restricted to ± 20 mm from the height when the mean speed is 100 r.p.m. Calculate the central dead load and sensitivity of the governor neglecting friction when the flyball exerts a centrifugal force of 9.81 N. Determine also the effort and power of the governor for 1 percent speed change. [Ans. 11.76 N; 11.12; 0.196 N; 7.7 N-mm] 9. The upper arms of a Porter governor are pivoted on the axis of rotation and the lower arms are pivoted to the sleeve at a distance of 30 mm from the axis of rotation.The length of each arm is 300 mm and the mass of each ball is 6 kg. If the equilibrium speed is 200 r.p.m. when the radius
- 3. of rotation is 200 mm, find the required mass on the sleeve. If the friction is equivalent to a force of 40 N at the sleeve,find the coefficient of insensitiveness at 200 mm radius. (IES 2001) [Ans. 61.1 kg. ; 6%] 10. A Hartnell governor has two rotating balls, of mass 2.7 kg each. The ball radius is 125 mm in the mean position when the ball arms are vertical and the speed is 150 r.p.m. with the sleeve rising. The length of the ball arms is 140 mm and the length of the sleeve arms 90 mm. The stiffness of the spring is 7 kN/m and the total sleeve movement is 12 mm from the mean position. Allowing for a constant friction force of 14 N acting at the sleeve, determine the speed range of the governor in the lowest and highest sleeve positions. Neglect the obliquity of the ball arms. (IES 1999) [Ans. 10.7 r.pm., 6.6 r.pm.] Theory Questions: 1. Explain the term height of the governor. Derive an expression for the height in the case of a Wattgovernor. What are the limitations of a Watt governor? 2. How is governing done in steam engine. 3. Explain with neat line diagram the working of the spring loaded type governor. 4. What are the effects of friction and of adding a central weight to the sleeve of a Watt governor? 5. Discuss the controlling force and stability of a governor and show that the stability of a governordepends on the slope of the curve connecting the controlling force (FC) and radius of rotation (r) andthe value (FC /r). 6. What is stability of a governor? Sketch the controlling force versus radius diagrams for a stable,unstable and isochronous governor. Derive the conditions for stability. 7. Explain clearly how you would determine from the controlling force curve whether a governor is stable, unstable or isochronous. 8. For given equilibrium speed, weight of the sleeve and the governor height, which governor shall have balls of less weight:Proter or Proell ? Why? 9. Why are two balls and not just one ball provided in centrifugal governor?