325-midterm-solutions-part 2 solutions 2 (2008w)

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Q4/ A compressor is driven motor by mean of a flat belt of thickness 10 mm and a width of 250 mm. The motor pulley is 300 mm diameter and run at 900 rpm and the compressor pulley is 1500 mm diameter. The shaft center distance is 1.5 m. The angle of contact of the smaller pulley is 220° and on the larger pulley is 270°. The coefficient of friction between the belt and the small pulley is 0.3, and between the belt and the large pulley is 0.25. The maximum allowable belt stress is 2 MPa and the belt density is 970 kg/m³. (a) What is the power capacity of the drive and (b) If the small pulley replaced by V-grooved pulley of diameter 300 mm, grooved angle of 34° and the coefficient of friction between belt and grooved pulley is 0.35. What will be the power capacity in this case, assuming that the diameter of the large pulley remain the same of 1500 mm.

A 2:1 speed reduction drive (Fig Q4) between two parallel shafts at 1200 mm centre distance is being provided by a V-belt of mass 0.5 kg/m. The diameter of the driving pulley is 200 mm and the driving shaft rotates at 900 rev/min. The driven pulley is 400 mm diameter. The angle of the pulley grooves is 40°, and the coefficient of friction between belt and pulleys is 0.35. If the maximum beit tension is 400 N determine: (i) The linear belt speed and the centripetal tension due to that belt speed. (ii) The angle of lap on each pulley (iii) The maximum power that may be transmitted Ø200 1200 Ø400

Power is transmitted between two shafts by a V-belt whose mass is 0.9 kg/m length. The maximum permissible tension in the belt is limited to 2.2 kN. The angle of lap is 170° and the groove angle 45°. If the coefficient of friction between the belt and pulleys is 0.17, find : 1. velocity of the belt for maximum power; and 2. power transmitted at this velocity. Note: Sketch the belt drive system for both parts and label the given data on it.

A horizontal belt conveyor arranged as shown in the figure P1 below operates at a speed of 270fpm and requires 25 Hp at the 40-inch-diameter driving drum. The drum receives power from a countershaftthrough a pair of spur gears. A motor operating at 860 rpm delivers power to the countershaft through aroller chain. The mechanical efficiency of the chain drive is 94 % and of the gears is 96 %. a) Determine theHp of the motor you would recommend. b) Determine the rpm of the driving drum and the countershaft. c)Calculate the number of teeth on the large sprocket required running the conveyor belt at the speedspecified. d) Determine the transmitted torque on the countershaft, in in-lb.

3. A motor is connected by a belt to pulley B. T, is the tight-side tensile force equal to 1800 N. The shaft spins at a constant speed, 650 rpm. The power delivered by the motor is 12.6 kW. On pulley A, connected to the load, the slack side of the belt has a tension equal to th of the tight side. b T T, B d shaft Dimensions are as follows: da 200 тm 300 тт | 250 тm |180 тm | 250 тm 26 тm dB dahaft a We analyzed a problem similar to this on Test 01 using static failure theories. Is this strictly correct? Because the shaft is spinning, would not a material particle see a time-varying reversal of the the bending stress as in the R.R. rotating beam test? Would a particle see a reversal of the torsional shear stress? Assume Sut = 370 MPa and Sy = 300 MPa. Ignore Marin factors. Ignore stress concentrations. Ignore direct shear stress (that due to V). Find the safety factors with respect to fatigue and yielding. Be guided by section 6-14 on combined loading.

Q1/ A 6-in-wide polyamide F-1 flat belt is used to connect a 2-in-diameter pulley to drive a larger pulley with an angular velocity ratio of 0.5. The center-to-center distance is 9 ft. The angular speed of the small pulley is 1750 rev/min as it delivers 2 hp. The service is such that a service factor Ks of 1.25 is appropriate. (a) Find Fc, Fi, Fla, and F2. (b) Find Ha, nfs, and belt length. (c) Find the dip.

The larger diameter and face of the disk of a multiple disk chutch are 225 mm and 20 mm respectively. The load applied to the spring of the clutch axially is 1500 N. Assuming that there are 8 pairs of friction 0.18 and tuning 800 rpm. Find the power transmitted by the clutch using uniform pressure method. (Ans, 13.67 kW)

Theory of machines

A blower is driven by an electric motor though a belt drive. The motor runs at 750 r.p.m. For this power transmission, a flat belt of 8 mm thickness and 250 mm width is used. The diameter of the motor pulley is 350 mm and that of the blower pulley 1350 mm. The center distance between these pulleys is 1350 mm and an open belt configuration is adopted. The pulleys are made out of cast iron. The frictional coefficient between the belt and pulley is 0.35 and the permissible stress for the belt material can be taken as 2.5 N/mm2 with sufficient factor of safety. The mass of a belt is 2 kg per meter length. Find the maximum power transmitted without belt slipping in any one of the pulleys. Note: Sketch the belt drive system for both parts and label the given data on it.

A blower is driven by an electric motor though a belt drive. The motor runs at 750 r.p.m. For this power transmission, a flat belt of 8 mm thickness and 250 mm width is used. The diameter of the motor pulley is 350 mm and that of the blower pulley 1350 mm. The center distance between these pulleys is 1350 mm and an open belt configuration is adopted. The pulleys are made out of cast iron. The frictional coefficient between the belt and pulley is 0.35 and the permissible stress for the belt material can be taken as 2.5 N/mm2 with sufficient factor of safety. The mass of a belt is 2 kg per meter length. Find the maximum power transmitted without belt slipping in any one of the pulleys.

A flat belt is to consist of 2 m diameter and 1.5 m diameter cast iron pulleys spaced at 4.8 m apart. It is to transmit 50 kW at a pulley speed of 380 rev/min. By using a service factor of 1.1 and a design factor 1277 ks 60 of 1.0: (a) Calculate the hoop tension, F. due to centrifugal force. (b) (c) b Find the torque,T due to the design power and pulley speed. Design and select a suitable belt type and dimension for the above application.

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calculate the power transmitted and the rotational speed in r/min of the small pulley of a belt drive where the diameter of the deriven pulley is 275 mm and rotates  at 750 r/min. the driving pulley size is 125 mm. the tension is the tight side of the belt is 500 N, with the tension ratio between the tight and slack side side being 4.33:1

Q4/ A single V belt is to be selected to deliver engine power to the wheel-drive transmission of a riding tractor. A 5-hp single-cylinder engine is used. At most, 60 percent of this power is transmitted to the belt. The driving sheave has a diameter of 6.2 in, the driven, 12.0 in. The belt selected should be as close to a 92-in pitch length as possible. The engine speed is governor-controlled to a maximum of 3100 rev/min. Select a satisfactory belt and assess the factor of safety and the belt life in passes.

A V-belt drive transmits 20kW from an electric motor running at 1440rpm to the main shaft of a roving machine. The motor and main shaft pulleys have 300 & 600 rpm respectively. The coefficient of friction between belt and pulley is 0.25. The centre distance between the shafts is 1000mm. The top width, thickness, section angle and density of belt and permissible tension on the belt are 22mm, 14mm and 40deg, 0.97gcm-2 and 600N respectively. How many belts are needed? Calculate the length of a belt needed

A steel shaft 800 mm long transmitting 15 kW at 400 Q5: r.p.m. is supported at two bearings at the two ends. A having 80 teeth and 500 mm pitch circle diameter is mounted at 200 mm from the left hand side bearing and receives power from a pinion meshing with it. The axis of pinion and gear lie in the horizontal plane. A pulley of 300 mm diameter is mounted at 200 mm from right hand side bearing and is used for transmitting power by a belt. The belt drive is inclined at 30° to the vertical in the forward direction. The belt lap angle is 180 degrees. The coefficient of friction between belt and pulley is 0.3. Design and sketch the arrangement of the shaft assuming the values of safe stresses as: t gear wheel 55 MPa; o, = 80 MPa. Take torsion and bending factor 1.5 and 2 respectively. [Ans. 120 mm]