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**Exercise.**

**Numerical.**

**1]** The arcs of a porter governor are 250 mm long and pivoted or the governor axis. The mass of each ball is 5kg and mass of central sleeve is 30kg. the radius of rotation of the ball is 150mm when sleeve begins to rise reaches a value of 200mm for maximum speed. Determine the range of speed of the governor. If the friction of sleeve is equivalent to 20N load. Determine how the speed range is modified? **(MU/Dec 2011/10 marks)**

**2]** In an engine governor of the porter type, the upper and lower arms are 200mm and 250mm respectively and pivoted on the axis of rotation. The mass of the central load is 15kg, the mass of each ball is 2 kg and friction of the sleeve together with the resistance of the operating gear is equal to a load of 25N at the sleeve. If the limiting inclinations of the upper arms to the vertical are 30° and 40°, find taking friction into account, range of speed of the governor.

**3]** All the arms of a porter governor are 178 mm long and are hinged at a distance of 38mm from the axis of rotation. The mass of each ball is 1.15 kg and mass of the sleeve is 20 kg. the governor sleeve begins to rise at 280 r.p.m. when the links are at an angle of 30° to the vertical. Assuming the friction force to be constant. Determine the minimum and maximum speed of rotation when the inclination of the arms to the vertical is 45°.

**4]** The arms of a porter governor are 300 mm long. The upper arms are pivoted on the axis of rotation. The lower arms are attached to a sleeve at a distance of 40mm from the axis of rotation. The mass of the load on the sleeve is 70kg and the mass of each ball is 10kg. determine the equilibrium speed when the radius of rotation of the balls is 200 mm, if the friction is equivalent to a load of 20N at the sleeve, what will be the range of speed for this position?

**5]** A Hartnell governor having a central sleeve spring and two right angled bell crank levers moves between 290 r.p.m. and 310 r.p.m. for a sleeve lift of 15mm. the sleeve arms and the balls arms are 80mm and 120 mm respectively. The levers are pivoted at 120mm from the governor axis and mass of each ball is 2.5 kg. the ball arms are parallel to the governor axis at the lowest equilibrium speed. Determine: 1. Loads on the spring at the lowest and the highest equilibrium speeds, and 2. Stiffness of the spring.

**6]** In a spring loaded Hartnell type governor, the extreme radii of rotation of the balls are 80mm and 120mm. the ball arm and the sleeve arm of the bell crank lever are equal in length. The mass of each ball is 2kg. if the speeds at the two extreme positions are 400 and 420 r.p.m. find: 1. The initial compression of the central spring and 2. The spring constant.

**7]** In a spring loaded governor of the Hartnell type, the mass of each bell is 1kg, length of vertical arm of the bell crank lever is 100 mm and that of the horizontal arm is 50mm. the distance of fulcrum of each bell crank lever is 80mm from the axis of rotation of the governor. The extreme radii of rotation of the balls are 75mm and 112.5mm. the maximum equilibrium speed is 5 percent greater the minimum equilibrium speed which is 360 r.p.m. find, neglecting obliquity of arms, initial compression of the spring and equilibrium speed corresponding to the radius of rotation of 100 mm.

**8]** In a spring loaded governor of the Hartnell type, the mass of each ball is 5kg and the lift of the sleeve is 50 mm, the speed at which the governor begins to float is 240 r.p.m. at this speed the radius of the ball path is 110mm and 100mm. the mean working speed of the governor is 20 times the range of speed when friction is neglected. If the lengths of ball and roller arm of the bell crank lever are 120mm and 100mm respectively and if the distance between the centre of pivot of bell crank lever and axis of governor spindle is 140mm, determine the initial compression of the spring taking into account the obliquity of rms. If friction is equiailevent to a force of 30 N at the sleeve, find the total alteration in speed before the sleeve begins to move from mid-position.

**9]** A porter has equal arms each 250mm long pivoted on the axis of rotation. Each ball has a mass of 5kg and the mass of the central load or the sleeve is 25 kg. the radius of rotation of the ball is 150 mm when the governor begins to lift and 200 mm when the governor is at maximum speed. Find the range of speed, sleeve lift, governor effort and power of the governor in the following cases: 1. When the friction at the sleeve is neglected and 2. When the friction at the sleeve is equivalent to 10N.

**10]** The upper arms of a porter governor have lengths 350mm and are pivoted on the axis of rotation. The lower arms have lengths 300 mm and are attached to the sleeve at a distance of 40 mm from the axis. Each ball has a mass of 4 kg and mass on the sleeve is 45 kg. determine the equilibrium speed of a radius of rotation of 200mm and find also the effort and power of the governor for 1 percent speed change.

**11]** The radius of rotation of the balls of a Hartnell governor is 80mm at the minimum speed of 300 r.p.m. neglecting gravity effect, determine the speed after the sleeve has lifted by 60 mm. also determine the initial compression of the spring, the governor effort and the power.

The particulars of the governor are given below:

Length of ball arm = 150 mm, length of sleeve arm = 100 mm, mass of each ball = 4kg, and stiffness of the spring = 25 N/mm.

**12]** In a Hartnell governor, the lengths of ball and sleeve arms of a bell crank lever are 120 mm and 100mm respectively. The distance of the fulcrum of the bell crank lever from the governor axis is 140mm. each governor ball has a mass of 4kg. the governor runs at a mean speed of 300 r.p.m. with the ball arms vertical and sleeve arms horizontal. For an increase of speed of 4 percent, the sleeve moves 10 mm upwards. Neglecting friction, find:

The minimum equilibrium speed if the total sleeve rover is limited to 20mm.

The spring stiffness.

The sensitiveness of the governor and

The spring stiffness if the governor is to be isochronous at 300 r.p.m.