Centrifugal Pumps Design and Application 2nd ed - Val S. Lobanoff, Robert R. Ross (Butterworth-Heinemann, 1992)
16 Shaft Design and Axial Thrust Shaft Design The pump rotor assembly consists of the shaft, impellers, sleeves, bearing or bearing surfaces, and other components such as balancing disks, shaft nuts, and seals that rotate as a unit. The primary component of the rotor assembly is the shaft. The pump shaft transmits driver energy to impellers and consequently to the pumped fluid. This section will be concerned primarily with the sizing of the pump shaft. The pump shaft is subject to the combined effects of tension, compression, bending, and torsion. As a result of the cyclic nature of the load, when shaft failures occur they are almost exclusively fatigue-type failures. Therefore, the first consideration in sizing the shaft is to limit stresses to a level that will result in a satisfactory fatigue life for the pump. The degree of detail involved in the stress analysis will be dependent upon the intended application of the pump. The analysis can be a simple evaluation of torsional shear stress at the smallest diameter of the shaft or a comprehensive fatigue evaluation taking into consideration the combined loads, number of cycles and stress concentration factors. Sizing the shaft based on stress is not the only consideration. Shaft deflection, key stresses, fits for mounted components, and rotor dynamics must be evaluated by the designer. The analytic tools available range from simple hand calculations to sophisticated finite element computer programs. The following sections are intended to present the fundamental considerations with which the designer can begin the design of the pump shaft. In some situations, satisfying these fundamental requirements can be considered adequate for a complete shaft design. In other, more critical services, further analysis is required before finalizing the design. 333
334 Centrifugal Pumps: Design and Application Shaft Sizing Based on Peak Torsional Stress The stress produced in the shaft as a result of transmitting driver energy to the impellers is torsional. A simple technique for sizing pump shafts is based on limiting the maximum torsional stress to a semi-empirical value. The limiting-stress value is based on the shaft material, operating temperature, and certain design controls on key way geometry, diameter transitions, and type of application. Since only one stress value is calculated due to one type of load, the limiting stress is obviously kept low. Typical values range from 4,000 psi to 8,500 psi. With this method of shaft sizing, no attempt is made to calculate the effects of stress concentration factors, combined stresses resulting from radial and axial loads, or stresses due to start-up and off-design conditions. The peak torsional stress is equal to the following; The torque is calculated from the maximum anticipated operating horsepower. Special attention should be given to pumps operating with products having a low specific gravity. Shop performance testing will generally be conducted with water as the fluid, and overloading the shaft may occur; hence, performance testing at reduced speed may be required. The shaft diameter used for calculating the stress should be the smallest diameter of the shaft that carries torsional load. For most centrifugal pumps the shaft diameters gradually increase toward the center of the shaft span. This is necessary to facilitate mounting the impellers. As a result the coupling diameter tends to be the smallest diameter carrying torsional load. It is a good design practice to ensure that all reliefs and grooves are not less than the coupling diameter. On some designs, such as single-stage overhung pumps, the smallest shaft diameter is under the impeller, in which case, this diameter shall be used for calculating shaft stress. Reliefs and groove should not be less than this diameter, Example Determine the minimum shaft diameter at the coupling for a 4-stage pump operating at 3,560 RPM where the maximum horsepower at the end of the curve is 850 bhp. Use 4140 shaft material with a limiting stress value of 6,500 psi. Solution
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334 <strong>Centrifugal</strong> <strong>Pumps</strong>: <strong>Design</strong> <strong>and</strong> <strong>Application</strong><br />
Shaft Sizing Bas<strong>ed</strong> on Peak Torsional Stress<br />
The stress produc<strong>ed</strong> in the shaft as a result of transmitting driver energy<br />
to the impellers is torsional. A simple technique for sizing pump<br />
shafts is bas<strong>ed</strong> on limiting the maximum torsional stress to a semi-empirical<br />
value. The limiting-stress value is bas<strong>ed</strong> on the shaft material, operating<br />
temperature, <strong>and</strong> certain design controls on key way geometry, diameter<br />
transitions, <strong>and</strong> type of application. Since only one stress value is<br />
calculat<strong>ed</strong> due to one type of load, the limiting stress is obviously kept<br />
low. Typical values range from 4,000 psi to 8,500 psi. With this method<br />
of shaft sizing, no attempt is made to calculate the effects of stress concentration<br />
factors, combin<strong>ed</strong> stresses resulting from radial <strong>and</strong> axial<br />
loads, or stresses due to start-up <strong>and</strong> off-design conditions.<br />
The peak torsional stress is equal to the following;<br />
The torque is calculat<strong>ed</strong> from the maximum anticipat<strong>ed</strong> operating<br />
horsepower. Special attention should be given to pumps operating with<br />
products having a low specific gravity. Shop performance testing will<br />
generally be conduct<strong>ed</strong> with water as the fluid, <strong>and</strong> overloading the shaft<br />
may occur; hence, performance testing at r<strong>ed</strong>uc<strong>ed</strong> spe<strong>ed</strong> may be requir<strong>ed</strong>.<br />
The shaft diameter us<strong>ed</strong> for calculating the stress should be the<br />
smallest diameter of the shaft that carries torsional load. For most centrifugal<br />
pumps the shaft diameters gradually increase toward the center<br />
of the shaft span. This is necessary to facilitate mounting the impellers.<br />
As a result the coupling diameter tends to be the smallest diameter carrying<br />
torsional load. It is a good design practice to ensure that all reliefs<br />
<strong>and</strong> grooves are not less than the coupling diameter. On some designs,<br />
such as single-stage overhung pumps, the smallest shaft diameter is under<br />
the impeller, in which case, this diameter shall be us<strong>ed</strong> for calculating<br />
shaft stress. Reliefs <strong>and</strong> groove should not be less than this diameter,<br />
Example<br />
Determine the minimum shaft diameter at the coupling for a 4-stage<br />
pump operating at 3,560 RPM where the maximum horsepower at the<br />
end of the curve is 850 bhp. Use 4140 shaft material with a limiting<br />
stress value of 6,500 psi.<br />
Solution