machine construction Exam
Exercise 1 (((50%))) Figure 1 shows a transmission system that transmits power from an electric motor to an industrial machine by means of V-belt and gear transmission. The gears have a straight-toothed tooth profile. The electric motor is delivered with a V-belt mounted on the shaft journal. The following data are given for the electric motor: Nominal power, P = 60 kW, speed n1 = 625 rpm. Due to the tension wheel, it can be assumed that the pull in the tight part (T1) of the belt on the pulley is twice as large as the pull in the slack part (T2) and that both act parallel to the z-axis (see Fig. 1 (b)) . The intermediate shaft is made of steel (E335) and carries a pulley and a gear. It is supported by a single-row ball bearing and a cylindrical roller bearing. The shaft of the industrial machine and the intermediate shaft lie in the same vertical plane. a) What is the effective torque of the industrial machine if the belt drive is assumed to have an efficiency of 90%? b) Assume module m = 5 and that there is clearance engagement between the gears, and determine the base circle diameter (db), number of teeth (z1) and tooth thickness (s) on gears 1. c) A simplified calculation model of the intermediate shaft together with mounted pulley, bearings and gears are shown in FIG. 1 (c) above. Fig. 1 (c) Simplified calculation model for the intermediate shaft Based on the nominal power of 60 kW and the dimensions given in the figure: i) Draw the torque diagram for loading the intermediate shaft in both x-y and x-z planes. How big is the largest bending moment? The weight of the shaft, gears and pulley can be neglected. ii) At a point on the intermediate shaft, the voltages acting on a voltage element have been calculated as shown next to it. Use Mohr's circle and find the magnitude and direction of the main voltages for this voltage element. Enter the voltages on a sketch of a main voltage element. d) An examination shows that the machine runs at almost full load for 75% of the operating time and otherwise with half load. What will be the nominal service life of bearing A, in number of hours, if you choose bearing type 6310 which has the following bearing capacities: C = 65.0 kN, C0 = 38.0 kN? e) FIG. 1 (d) shows a curvature surface diagram for the intermediate shaft (see also Fig. 1 (a)) calculated on a plane where the shaft is most loaded. The diagram is based on a shaft with a constant diameter (Ø50). Use the linker (curvature surface) method and calculate the max. the displacement C at end C of the shaft. Tip: the weight of the shaft, gears and pulley is neglected. Fig. 1 (d) Deformation image and curvature surface diagram f) The pulley is rigidly connected (mounted) to the intermediate shaft by a single-shrink connection. As shown in Fig. 1 (a), the connection is dimensioned with fit tolerance Ø45H6 / p5. The following data are given for the shrink connection: - Diametral press nozzle in mounted condition: min = 10 μm, max = 37 μm. - Influence coefficients are calculated and specified as follows: Shaft: a = 5.0 * 10-5 Belt pulley (hub): n = 6.5 * 10-5. How large must the width of the contact surface between the pulley and the intermediate shaft be in order to transmit a torque of 1.5 kNm? Exercise 2 A design draft for a manual water pump is shown in FIG. 2 below. In order to be able to optimize the water flow, it is recommended that the piston has a vertical speed of vs = 50 mm / s. The pumping force F is assumed to be perpendicular to the crank arm BD at all times. a) Determine the number of instantaneous poles for the mechanism, and state the location of these at the moment shown in the figure on a sketch of the mechanism to scale. b) Use graphical method and find the angular velocity 2 of the crank arm BD. c) The column CE is made of aluminum alloy (E = 70 GPa, Rp02 = 160 MPa) with an outer diameter of 20 mm and a wall thickness of 4 mm. i) Make the necessary assumptions and assess whether the column is in the Euler area. ii) How great is the safety against buckling of the column with respect to Euler voltage when the angle θ = 00? Fig. 2 Design draft of manual water pump Exercise 3 Figure 3 shows the calculation model for a wheel suspension in a trolley. The axle is bolted to the car body at A and is supported against the car body by a helical spring at B. The axle cannot rotate, but it can swing in the vertical plane, the plane shown in the figure. The wheel, which is in contact with the road surface at all times, is mounted on the axle at C. By a random check, an imbalance has been found in the wheel which can be stated as if the wheel's mass of m = 25 kg is placed eccentrically in relation to its axis of rotation at a distance e = 2 mm. Due to the fact that the mass of the car body is so large in relation to the mass of the wheel, one can disregard vibrations in the car body. a) Neglect the mass of the axle and critically calculate the angular velocity of the wheel in the axle suspension. Tip: By considering the relationship between an arbitrary force F (centrifugal force) acting in C and the deformation at the same point, one can derive the resulting spring constant indicated by: b) How large is the deformation amplitude of the helical spring at B when the wheel turns at an angular velocity of = 120 rad / s. Also determine the alternating force that is transmitted to the car body via the coil spring due to. the unbalanced mass of the wheel. We now consider that the following data are known about the helical spring: Material: cold drawn steel wire with 2 mm diameter Number of active turns: n = 10 Spring length in unloaded condition: L0 = 56 mm Spring index: C = 10. c) To avoid buckling in the spring, its compression should not exceed 25 mm. i) How large is then the largest shear stress in the spring. ii) Also determine the safety against tight turns in this case.