centrifugal pumps - design and application (2nd edition): part 2
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Part3 Mechanical Design This page intentiTonally left blank 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 keyway 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 Shaft Design and Axial Thrust 335 Solving for D: For design round up to nearest Vs-in. increment: D = 2.375. Example A 2-stage pump has been designed with a 25/8-in. shaft diameter at the coupling. The maximum horsepower at 3,560 RPM is 900. What is the maximum operating speed for a limiting stress of 7,000 psi? Solution Using the pump affinity laws described in Chapter 2: 336 Centrifugal Pumps: Design and Application Substituting and solving for N: Shaft Sizing Based on Fatigue Evaluation Pump shafts are subjected to reversing or fluctuating stresses and can fail even though the actual maximum stresses are much less than the yield strength of the material. A pump shaft is subject to alternating or varying stresses as a result of the static weight and radial load of impellers, pressure pulses as impeller vanes pass diffuser vanes or cutwater lips, driver start-stop cycles, flow anomalies due to pump/driver/system interaction, driver torque variations, and other factors. In order to perform a fatigue analysis, it is first necessary to quantify the various alternating and steady-state loads and establish the number of cycles for the design life. In most cases, the design life is for an infinite number of cycles; however, in the case of start-stop cycles, the design life might be 500 or 1,000 cycles depending on the application. Once the loads have been defined and the stresses have been calculated, it is necessary to establish what the acceptable stress values are. The use of the maximum-shear-stress theory of failure in conjunction with the Soderberg diagram provides one of the easier methods of determining the acceptable stress level for infinite life (Peterson; Shigley; Roark). Since the primary loads on pump shafts are generally torsion and bending loads, the equation for acceptable loading becomes: Shaft Design and Axial Thrust 337 Where ra and era = alternating stress components rm and om = mean stress components Se = fatigue endurance limit for the shaft material corrected for the effects of temperature, size, surface roughness, and stress concentration factors Sy = yield strength for the material at the operating temperature A safety factor is generally applied to Se and Sy to account for unanticipated loads. Equation 16-2 is applied at the location(s) where stresses are the highest. There are circumstances where it is not necessary to have infinite-life for certain loads. The designer must review all the operating modes and possible upset conditions before a load is classified as a finite-life load. Loads that might be placed in this category are start-stop cycles, and offdesign flow, speed, or temperature transients. If the event has an anticipated occurrence of less than 1,000 cycles, it can be considered as a static load with no effect on fatigue life, providing the stresses are less than the material yield strength. For loading conditions of more than 1,000 cycles, but less than 107 cycles, the designer has the option to perform a cumulative fatigue damage analysis. Example It has been determined that the maximum stresses occur at an impeller-locating ring groove shown in Figure 16-1. The steady state torque is 28,(XX) in.-lb. The bending moment due to radial hydraulic load is 10,700 in.-lb. Due to axial thrust, there is a tensile force in the shaft of 20,000 Ib. Are the stresses at the locating ring acceptable? Solution The steady-state loads are the torque and axial load. The alternating bending stress is: 338 Centrifugal Pumps: Design and Application Figure 16-1. Shaft section. Yield strength of 4140 steel is 80,000 psi. The endurance limit for 4140 steel is 52,500 psi. This limit must be adjusted to account for the service condition (Shigley). For 99% reliability use Kc = .814. For ground surface finish use Ka = .9. For stress concentration due to locating ring groove radius: where Kt is the stress concentration factor from Peterson. Shaft Design and Axial Thrust Torsional stress: Axial stress: Hence from Equation 16-2: Stresses are satisfactory. 339 340 Centrifugal Pumps: Design and Application Figure 16-2. Schematic representation of horizontal overhung pump. Shaft Deflection Shaft deflection calculations are usually performed on single-stage overhung pumps to establish a relative measure of shaft stiffness. Deflection calculations are also performed on horizontal multi-stage pumps when the potential of galling at wear ring or sleeves exists during start-up or coastdown. The calculation for single-stage overhung pumps assumes that the loading on the shaft consists of weight (for a horizontal pump) and the dynamic radial thrust due to the pump hydraulics. Figure 16-2 schematically represents a typical horizontal overhung pump (Figure 16-3). The deflection at any point along the shaft between the impeller and the radial bearing can be calculated from the following equation. This equation does not account for any support the shaft might receive from the hydrostatic stiffness at the impeller wear rings and shaft throttle This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.
Centrifugal Pumps Design and Application 2nd Edition Pdf
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