Solve and show solution for answer -Show that for a "broken in" clutch, the maximum torque transfer through the clutch occurswhen the inner radius of the clutch "r" is equal to the outer radius of the clutch "ro" dividedby the "√3" (i.e. r₁ = 12). Start with equation 18.6 (i.e. T = (π)(Pmax)(µ)(N)(ro²ri — r₁³)). Treat"r" as the independent variable, "T" as the dependent variable, and the remaining parametersas "constants" (Note: Essentially, the torque "T" is a cubic function (3rd degree polynomial) ofthe inner radius "r"). "Maximize" this "cubic function" over a realistic domain usingdifferential calculus. Be sure to show the "critical point" r₁ = 1/3 corresponds to a "relativemaximum" (Hint: This can be done by using either the 1st derivative test or the 2nd derivativetest).

Step 1: Step 2: Step 3: Step 4:

Answered: - Show that for a "broken in" clutch,…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Q1) For a cone clutch, see figure (Q1), when the wear is uniform (Pr=constant), show that the transmitted torque is equal to: T = π *μ*csc(B)* C* (r² − r₂²) Where T: Transmitted torque, u: coefficient of friction, C:Constant, 2ß: Cone angle, ₁: Inner radius, ₂: Outer radius driving Shaft お 3 (rad/sec) or (rpm) 90° driven shaft. W (rpm) (read /sea) total axial force.
on the driving shaft and 1 on the drive shaft, the outer radius is 100 cm and inside diameters 600 mm. The maximum intensity of pressure at any point is 0.2 N/mm². If the u is 0.25, determine the speed of the clutch if the power generated = 31582.807 kW, 03/ A multi plate clutches an included angle of 120°. A multi plate clutch, has 2 discs Use both the uniform wear theory and the uniform pressure theory %3D
2) A shaft of a diameter of 30 mm is transmitting 14,9 kW at 400 rpm. The shaft is connected to a pulley of an axial length of 160 mm with the help of a rectangular key 16 mm x 12 mm ( b=16 mm, t=12mm). (The spokes are connected to the pulley, but the pulley is not shown in the figure). Axial length of the key, hub and pulley are 160 mm. Determine the shear and normal stresses developed in the rectangular key. Rectangular key Spokes A R Hub Shaft
EFx=0= (0.433 F1) - (0.667 F2) - (0.866 F3) + (0.342 P) EFy=0= - (0.250 F1) + (0.667 F2) EFz=0= (0.866 F1) + (0.333 F2) + (0.500 F3) - (0.940 P) Find the magnitude of F1, F2, and F3
The max speed for the servo shown is 130RPM when connected to 6V. Assume that the gearbox on your servo is able to output a torque of 1.5 kg-cm while turning at this speed. Using the number of teeth on each gearprovided in the table, determine the torque and rotational speed of the output shaft on the DC motor. HINT: Work backwards from the output shaft and use the equations developed in class that relate the number of teeth to the torque. When working back from the output shaft to gear 7/6, realize that the “torque” transmitted by gear 7 is the SAME as the torque transmitted by gear 6 since they are joined. Then, relate the torque of gear 6 to gear 5 based on their numbers of teeth. Since gears 5 and 4 are actually one piece, the torque in 4 and 5 will be the same (as was the case for gears 6 and 7). Repeat for the other gears, working your way all the way back to the DC motor.
Q 16- Find the length of a belt necessary to drive a pulley of 80 cm diameter running parallel at a distance of 12 m from the driving pulley of 480 cm diameter ?
Q4/ A multi plate clutches an included angle of 90°. A multi plate clutch, has 2 discs or the driving shaft and 1 on the drive shaft, the outer radius is 100 cm and inside diameters 600 mm. The maximum intensity of pressure at any point is 0.2 N/mm?. If the determine the speed of the clutch if the power generated = 31582.807 kW. Use both the uniform wear theory and the uniform pressure theory . is 0.25, D
Question (2) The followings are the compression spring particulars in slip clutch unit. You are asked to:- Axial force Spring mean Diameter 25 mm Compression Spring Particulars Og of SAE 6150 O, of Cr-Mo-Ni Steel 1600 MPa 1400 MPa 8 FDK 1000 N Spring index Shear stress in spring wire 5 8 FD3N Y= Gdt No. of active turns, N Modulus of rigidity of spring material, G Spring deflection 10 8 x 10* MPa Wahl factor, K 1.3 1. Calculate the shear stress in spring wire. 2. Choose the suitable spring material. . 3. Calculate the spring stiffness. 4. Determine the spring length in the system in working condition if the spring free length is 100 mm. 5. Recalculate the shear stress in spring wire if the axial force increases to 2000 N without changing the spring material (obtained in no. 2). Comment on your results.
Q1/ An open belt drive connected two pulleys 120 cm and 50 cm diameter on parallel shafts 4 m apart. The belt weights 0.9 kg/m length and maximum tension in it is not to exceed 2000 N. 0.3. The 120 cm pulley, which is the driver, runs at 200 rpm. Due to belt slip on one of the pulleys, the velocity of the driven shaft is only 450 rpm. Calculate the torque on each of the two shafts and power transmitted.
A steel shaft has a diameter of 25 mm. The shaft rotates at a speed of 600 r.p.m. and transmits 30 kW through a gear. The tensile and yield strength of the material of shaft are 650 MPa and 353 Mpa respectively. Taking a factor of safety 3, select a suitable key for the gear. Assume that the key and shaft are made of the same material. 3. [Ans. I = 102 mm]
A 220 mm diameter of 14.5 degrees involute gear is used to transmit 50 kW at 580 rpm Find the total force transmitted on the gear.
Q3/ A multi plate clutches an included angle of 120°. A multi plate clutch, has 2 discs on the driving shaft and1 on the drive shaft, the outer radius is 100 cm and inside diameters 600 mm. The maximum intensity of pressure at any point is 0.2 N mm. If the u is 0.25, determine the speed of the clutch if the power generated = 31582.807 kW. Use both the uniform wear theory and the uniform pressure theory %3D

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