calculate the maximum bending stress when the shaft is rotating at 80% of the critical speed
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calculate the maximum bending stress when the shaft is rotating at 80% of the critical speed
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- A turbine rotor is mounted on a stepped shaft that is fixed at both ends as shown in The torsional stiffnesses of the two segments of the shaft are given by k = 3.000 N-m/rad and k2 = 4,000 N-m/rad. The turbine generates a hamonic torque given by M(1) = Mo cos ot about the shaft axis with Mg = 200 N-m and as = 500 rad/s. The mass moment of inertia of the rotor about the shaft axis is h = 0.05 kg-m. Assuming the equivalent tosional damping constant of the system as e, = 2.5 N-m-s/rad, determine the steady-state response of the rotor, 6(1). ka M() = Ma cos e Turbine rotor, Jo A 50-kg turbine is mounted on four parallel springs, each of stiffness of 3 x 10° N/m When the machine operates at 40 Hz. its steady-state amplitude is observed as 1.8 mm What is the magnitude of the excitation? Given m = 50 kg. k = 3x 10 Nm. e = 40 Hz. X= 1.8 mm Find: FeA turbine rotor is mounted on a stepped shaft that is fixed at both ends as shown in The torsional stiffnesses of the two segments of the shaft are given by ka = 3,000 N-m/rad and k2 = 4,000 N-m/rad. The turbine generates a harmonic torque given by M(t) = Mo cos wt about the shaft axis with M, = 200 N-m and w = 500 rads. The mass moment of inertia of the rotor about the shaft axis is Jo = 0.05 kg-m. Assuming the equivalent torsional damping constant of the system as c, = 2.5 N-m-s/rad, determine the steady-state response of the rotor, 6(1). O(1) ke M(1) = M, cos ot Turbine rotor, JoTurning moment 1mm = 60NM: crank angle, 1 mm = 1°. The turning moment shows the maximum energy that needs to be stored by the flywheel in unit area is 2850 m?. The flywheel rotates at an average speed of 220 rpm with a total speed change of 2.5%. If the mass of the flywheel is 500 kg, find the appropriate dimensions (inner diameter, outer diameter and thickness) of the flywheel. Given that inner diameter of the flywheel is 0.9 outer diameter and the density is 7.2 Mg/m3. Reply.
- 15 mm diameter shaft rotates in long fixed bearings 60 cm apart. A rotor of mass 20 kg is mounted at mid span. The mass center of rotor is 0.5 mm from the shaft axis. If the bending stress in the shaft is not to exceed 120 MPa. Find range of speed over which the shaft must not run. Take modulus of elasticity for the shaft material as 200kN/m².A turbine rotor is mounted on a stepped shaft that is fixed at both ends as shown in The torsional stiffnesses of the two segments of the shaft are given by k = 3,000 N-m/rad and k2 = 4,000 N-m/rad. The turbine generates a harmonic torque given by M(1) = Mo cos wt about the shaft axis with M, = 200 N-m and w = 500 rad/s. The mass moment of inertia of the rotor about the shaft axis is J, = 0.05 kg-m?. Assuming the equivalent torsional damping constant of the system as e, = 2.5 N-m-s/rad, determine the steady-state response of the rotor, 0(1). O(1) M(1) = Mg cos etr %3! Turbine rotor, JoA vertical shaft 20 mm in dia and 100 cm long is mounted in long bearings and carries a rotor of mass 10 kg midway between bearings. The center of rotor is 0.5 mm away from axis of shaft. Neglect the weight ofshaft and take E-200 GPa forshaft material. Determing whirling speed of shaft and bending stress induced in it when it is rotating at 2000 rpm.
- A thin circular disc is fitted to a shaft as shown in figure. Weight of the disc is 500 N and diameter is 1.2 m. Shaft rotates at 300 r.p.m in anticlockwise direction when seen from the right side. Find the effect of the gyroscopic couple on the shaft and the bearing reactions at A and B taking the effect of the weight of the disc. 1 m. 1.5 m FigureA shaft having length equal to 10 m and diameter equal to (50+ 01) mm is simply supported at both ends. The shatt carries four masses (150 + 01) kg, (200 + 01) kg, (250 +01) kg and (300 + 01) kg. These masses are located at a distance of 1.5m, 2.5 m, 5.5 mand 7.5 m from the left hand side support, respectively. The modulus of elasticity, E, for the material of the shaft is 200 GN/m? and mass density for the shaft material is 7500 kg/m?3. Determine critical speed of the shaft in revolutions per minute for the following two cases: 1. Effect of the mass of the shaft is neglected. 2. Effect of the mass of the shaft is considered. What is the usefulness of the answers determined in this problem?The length of the smooth circular shaft with a solid cross-sectional area of 315nm2 is 1 meter. Instead of this shaft, it is desired to use an evacuated circular-section shaft with a wall thickness of 3 mm with the same length and weight. For these two cases, compare the angles of rotation that would occur if a moment M = 600 (N.m) was applied to the end of the shaft made of material G-80 GPa.
- A motorcar front wheel brake system consists of a master cylinder with a diameter of 20 mm and a brake pedal with a mechanical advan- tage of 5:1. The master cylinder feeds four slave cylinders with 50 mm diameter pistons on the disc brake callipers. Each slave cylinder must be able to exert a maximum force of 6,25 kN. The isothermal bulk modulus of the fluid is 1,9 GPa, Calculate: (a) the force that must be applied to the pedal to apply the brakes. [1.000,38 N] (b) the distance the pedal must be moved to apply the brakes if the slaye cylinders must move 1 mm each. . (c) the play on the pedal due to compressi- bility of the fluid when the brakes are fully applied and the system has a total volume of 500 ml of fluid. [13,3 mm] (d) the play on the pedal due to compressi- bility in the system when the brakes are fully applied and 2 ml of air is present in the system. [125 mm] [36,06 mm]An aluminum pole for a street light weighs4600 N and supports an arm that weighs 660 N (seefigure). The center of gravity of the arm is 1.2 m from theaxis of the pole. A wind force of 300 N also acts in the (-y)direction at 9 m above the base. The outside diameter ofthe pole (at its base) is 225 mm, and its thickness is 18 mm. Determine the maximum tensile and compressivestresses σt and σc, respectively, in the pole (at its base)due to the weights and the wind force.Turning moment 1mm = 60 Nm: crank angle, 1 mm = 1° . The turning moment shows the maximum energy that needs to be stored by the flywheel in the unit area is 2850 m² . The flywheel rotates at an average speed of 220 rpm with a total speed change of 2.5%. If the mass of the flywheel is 500 kg, find the appropriate dimensions (inner diameter, outer diameter and thickness) of the flywheel. Given that inner diameter of the flywheel is 0.9 outer diameter and the density is 7.2 Mg/m³ .