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1 Shaft Design Section VI

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2 Shaft? Shaft Design ASME Shaft Equations Design of Shaft for Torsional Rigidity Standard Sizes of Shafts Bending and Torsional Moments Talking Points

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3 Rotating machine element that transmits power. Shaft? Shafts are usually circular in cross-section, and may be either hollow or solid.

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4 Shaft Design Consists of the determination of the correct shaft diameter to ensure satisfactory strength and rigidity when the shaft is transmitting power under various operating and loading conditions. Design of shafts for ductile materials, based on strength, is controlled by the maximum-shear stress theory (Tresca) or distortion-energy theory (von - Mises); while shafts of brittle materials would be designed on the basis of the maximum-normal stress theory. Shafts are usually subjected to torsion, bending, and axial loads. 1) For axial loads: The tensile or compressive stress is: 2) For bending loads: The bending stress (tension or compression) is: 3) For torsional loads: The torsional stress is:

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5 Shaft Design – Cont.

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7 ASME Shaft Equations The ASME code equation for hollow shaft combines torsion, bending, and axial loads by applying the maximum-shear equation modified by introducing shock, fatigue, and column factor as follows: For solid shaft having little or no axial loading, the equation is: Where:

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8 ASME Shaft Equations – Cont.

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Designing for Fully Reversed Bending and Steady Torsion ASME Method (ANSI/ASME Standard for Design of Transmission Shafting B106.1M- 1985, which is derived from distortion energy theory, can be applied only for: constant torque fully reversed moment. No axial load Designing for Fully Reversed Bending and Nearly Steady Torsion d = shaft diameter, m n d = design factor or safety factor K b = stress concentration factor M b = maximum bending moment, N.m Mt = maximum torsion, N.m S e = actual endurance strength, N/m 2 S y = yield strength, N/m 2

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A measure of the relative safety of a load-carrying component. For ductile materials: n d = 1.25 to 2.0: Design of structures under static loads for which there is a high level of confidence in all design data. n d = 2.0 to 2.5: Design of machine elements under dynamic loading with average confidence in all design data. n d = 2.5 to 4.0: Design of static structures or machine elements under dynamic loading with uncertainty about loads, material properties, stress analysis or the environment. n d = 4.0 or higher: Desire to provide extra safety to critical components. Design factor or Safety Factor (n d )

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Estimated Design Values for K b (bending case) (a) Profile keyseat (b) Sled runner keyseat (c) Well-rounded fillet K b = 2,0 for profile keyseat K b = 1,6 for Sled runner keyseat K b = 1,5 for well-rounded fillet

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Approximated reliability factors, ke Estimated Actual Endurance Strength, S e S e = k b k e S e S e = endurance strength k b = size factor k e = reliability factor Desired reliability ke 0.501,0 0,90 0,990,81 0,9990,75 Size factors, k b Size RangeFor d in mm d ≤ 7,62 k b = 1,0 7,62 < d ≤ 50 k b = ( d /7,62) -0,11 50 < d ≤ 250 k b = 0,859 – 0,000837 d NOTE: For simplification in determining the shaft diameter, the value of size factor can be estimated as k b = 0,75 ’

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Endurance strength (S e ) versus tensile strength (S u ) for various surface conditions of wrought steel ’

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Ultimate shear strength (S us ) and yield shear strength (S ys ) for wrought steel Both the yield strength and the ultimate strength in shear (Sys and Sus) are important properties of materials. Unfortunately, these values are seldom reported. We will use the following estimates: S ys = 0,50 S y Yield strength in shear: S us = 0,75 S u Ultimate strength in shear:

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15 Design of Shaft for Torsional Rigidity It is based on the permissible angle of twist. The amount of twist permissible depends on the particular application, and varies about 0.3 degree/m for machine tool shafts to about 3.0 degree/m for line shafting. Where:

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16 Standard Sizes of Shafts These sizes vary according to material specifications and supplier. Typical sizes for solid shafts are: Up to 25 mm in 0.5 mm increments 25 to 50 mm in 1.0 mm increments 50 to 100 mm in 2.0 mm increments 100 to 200 mm in 5 mm increments

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17 Bending and Torsional Moment These are the main factors influencing shaft design. One of the first steps in shaft design is to draw the bending moment diagram for the loaded shaft or the combined bending moment diagram if the loads acting on the shaft are in more than one axial plane. From the bending moment diagram, the points of critical bending stress can be determined. The torsional moment acting on the shaft can be determined from: 2) For gear drive: The torque is found by: 1) For belt drive: The torque is found by: Where:

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