Below are some of the simple shaft calculations.
The basics and the text notations are also given.
Shaft Design and Analysis
A shaft is the component of a mechanical device that transmits rotational motion and power. It is integral to any mechanical system in which power is transmitted from a prime mover, such as an electric motor or an engine, to other rotating parts of the system. There are many examples of mechanical systems incorporating rotating elements that transmit power: gear-type speed reducers, belt or chain drives, conveyors, pumps, fans, parts of a car, machines around workplace and many types of automation equipment.
Visualize the forces, torques, and bending moments that are created in the shaft during operation. In the process of transmitting power at a given rotational speed, the shaft is inherently subjected to a torsional moment, or torque. Thus, torsional shear stress is developed in the shaft. Also, a shaft usually carries power-transmitting components, such as gears, belt or chain sprockets, which exert forces on the shaft in the transverse direction (perpendicular to its axis). These transverse forces cause bending moments to be developed in the shaft, requiring analysis of the stress due to bending. In fact, most shafts must be analyzed for combined stress.
Because of the simultaneous occurrence of torsional shear stresses and normal stresses due to bending, the stress analysis of a shaft virtually always involves the use of a combined stress approach. The recommended approach for shaft design and analysis is the distortion energy theory of failure. Vertical shear stresses and direct normal stresses due to axial loads also occur at times, but they typically have such a small effect that they can be neglected. On very short shafts or on portions of shafts where no bending or torsion occurs, such stresses may be dominant.
Procedure for Design and analysis of a Shaft
1. Determine the rotational speed of the shaft, n (rpm).
2. Select the material from which the shaft will be made, and specify ultimate tensile strength Su, yield strength Sy and its surface condition: ground, machined, hot-rolled and as-forged. At the moment, due to lack of database for endurance strength, this module should be used to design and analysis only steel shafts Use the database in selection of a material.
3. Apply a desired reliability for definition of reliability factor,CR.
4. Apply a design factor ,N.
5. Propose the general form of the geometry for the shaft, considering how each element on the shaft will be held in position axially and how power transmission from each element to the shaft is to take place. Design details such as fillet radii, shoulder heights, and keyseat dimensions must also be specified. Sometimes the size and the tolerance for a shaft diameter are dictated by the element to be mounted there. For example, ball bearing manufacturers' catalogs give recommended limits for bearing seat diameters on shafts.
6. Specify the location of bearings to support the shaft. The reactions on bearings supporting radial loads are assumed to act at the midpoint of the bearings. Another important concept is that normally two and only two bearings are used to support a shaft. They should be placed on either side of the power-transmitting elements if possible to provide stable support for the shaft and to produce reasonably well-balanced loading of the bearings. The bearings should be placed close to the power-transmitting elements to minimize bending moments. Also, the overall length of the shaft should be kept small to keep deflections at reasonable levels.
7. Determine the design of the power-transmitting components or other devices that will be mounted on the shaft, and specify the required location of each device.
8. Determine the power to be transmitted by the shaft.
9. Determine the magnitude of torque at point of the shaft where the power-transmitting element is.
where:
P = transmitted power
T = torque
n = rotational speed
10. Determine the forces exerted on the shaft.
Spur and helical gears, tangential force
where:
D = pitch diameter of gear;
Radial force
where:
= normal pressure angle for helical gears and pressure angle for spur gears
= helix angle
11. Preparing a torque diagram.
12. Resolve the radial forces into components in perpendicular directions, vertically and horizontally.
13. Solve for the reactions on all support bearings in each plane.
14. Produce the complete shearing force and bending moment diagrams to determine the distribution of bending moments in the shaft.
15. Analyze each critical point of the shaft to determine the minimum acceptable diameter of the shaft at that point in order to ensure safety under the loading at that point. In general, the critical points are several and include those where a change of diameter takes place, where higher values of torque and bending moment occur, and where stress concentrations occur.
If a vertical shearing force V is the only significant loading present, this equation should be used to compute the required diameter for a shaft.
where:
Kt = stress concentration factor;
S’n = modified endurance strength, depends on ultimate tensile strength Su
where:
Cs = size factor
CR = reliability factor
Sn = endurance strength
In most shafts, the resulting diameter will be much smaller than that required at other parts of the shaft where significant values of torque and bending moment occur. Also, practical considerations may require that the shaft be somewhat larger than the computed minimum to accommodate a reasonable bearing at the place where the shearing force is equal to the radial load on the bearing.
Most shafts are subjected to bending and torsion. The power being transmitted causes the torsion, and the transverse and radial forces on the elements cause bending. In the general case, the transverse forces do not all act in the same plane. In such cases, the bending moment diagrams for two perpendicular planes are prepared first. Then the resultant bending moment at each point of interest is determined.
A design equation is now developed based on the assumption that the bending stress in the shaft is repeated and reversed as the shaft rotates, but that the torsional shear stress is nearly uniform.
where:
M = bending moment
T = twisting moment
You can refer a book on Machine Design by V.B. Bhandari.
there are 2 books by the same author one of them will be having a seperate chapter on shaft design... 😀
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