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To maintain internal clearances at the wearing rings, it is usually desirable to limit the shaft deflection under the most adverse conditions to between 0.005 and 0.006 in (0.127 and 0.152 mm). It follows that a shaft design with a deflection of 0.005 to 0.006 in will have a first critical speed of 2,400 to 2,650 rpm. This is the reason for using rigid shafts for pumps that operate at 1,750 rpm or lower. Multistage pumps operating at 3,600 rpm or higher use shafts of equal stiffness (for the same purpose of avoiding wearing ring contact). However, their corresponding critical speed is about 25 to 40 percent less than their operating speed.

Lomakin Effect All the previous material refers to the behavior of a rotor and its shaft operating in air. In reality, the rotor operates immersed in the liquid being pumped, and this liquid flows through one or more of the small annular areas created by clearances separating regions in the pump under different pressures, such as at the wearing rings, interstage bushings, or balancing devices. This flow of liquid creates what is called a hydrodynamic bearing effect and essentially transforms the rotor from one supported at two bearings external to the pump to one with several additional internal bearings lubricated by the liquid pumped. This phenomenon is generally called the Lomakin effect.

The result of the Lomakin effect is that the deflection of the shaft when a pump is running is reduced somewhat from the value calculated for the shaft operating in air and the critical speed is increased. The advantage of this effect, particularly in the design of some multistage pumps, is that it permits the use of longer and more slender shafts. Whether this is sound practice remains a controversial subject. The supportive effect of the hydro-dynamic hearings depends on (a) the pressure differential, which disappears completely when the pump is at rest, and (b) the clearance, which decreases substantially as the internal clearances increase with erosive or contact wear. Thus, contact between rotating and stationary parts will take place every time a pump is started if the internal clearances are initially less than the shaft deflection in air. This contact will again take place as the pump coasts down after being stopped. Furthermore, as wear takes place at the running joints, the shaft assumes a deflection closer and closer to its deflection in air, unsupported by the Lomakin effect.

In view of all these facts, it is recommended that pump users acquaint themselves not only with the calculated shaft deflections with a pump running in new condition, but also with the shaft deflections in air. This way they can compare these with the internal clearances.

Shaft Sizing Shaft diameters are usually larger than what is actually needed to transmit the torque. A factor that assures this conservative design is a requirement for ease of rotor assembly.

The shaft diameter must be stepped up several times from the end of the coupling to its center to facilitate impeller mounting (see Figure 65). Starting with the maximum diameter at the impeller mounting, there is a step down for the shaft sleeve and another for the external shaft nut, followed by several more for the bearings and the coupling. Therefore, the shaft diameter at the impellers exceeds that required for torsional strength at the coupling by at least an amount sufficient to provide all intervening step downs.

One frequent exception to shaft oversizing at the impeller occurs in units consisting of two double-suction, single-stage pumps operating in a series, one of which is fitted with a

FIGURE 65 Rotor assembly of a single-stage, double-suction pump (Flowserve Corporation)

double-extended shaft. As this pump must transmit the total horsepower for the entire series unit, the shaft diameter at its inboard bearing may have to be larger than normal.

The shaft design of end-suction, overhung impeller pumps presents a somewhat different problem. One method for reducing shaft deflection at the impeller and seal chamber, where the concentricity of running fits is extremely important, is to considerably increase the shaft diameter between the bearings.

Except in certain smaller sizes, centrifugal pump shafts are protected against wear, erosion, and corrosion by renewable shaft sleeves. In small pumps, however, shaft sleeves present a certain disadvantage. As the sleeve cannot appreciably contribute to shaft strength, the shaft itself must be designed for the full maximum stress. Shaft diameter is then materially increased by the addition of the sleeve, as the sleeve thickness cannot be decreased beyond a certain safe minimum. The impeller suction area may therefore become dangerously reduced, and if the eye diameter is increased to maintain a constant eye area, the liquid pickup speed must be increased unfavorably. Other disadvantages accrue from greater hydraulic and seal losses caused by increasing the effective shaft diameter out of proportion to the pump size.

To eliminate these shortcomings, very small pumps frequently use shafts of stainless steel or some other material that is sufficiently resistant to corrosion and wear that it does not need shaft sleeves. One such pump is illustrated in Figure 66. Manufacturing costs, of course, are much less for this type of design, and the cost of replacing the shaft is about the same as the cost of new sleeves (including installation).

Shaft Sleeves Pump shafts are usually protected from erosion, corrosion, and wear at seal chambers, leakage joints, internal bearings, and in the waterways by renewable sleeves.

The most common shaft sleeve function is that of protecting the shaft from wear at packing and mechanical seals. Shaft sleeves serving other functions are given specific names to indicate their purpose. For example, a shaft sleeve used between two multistage pump impellers in conjunction with the interstage bushing to form an interstage leakage joint is called an interstage or distance sleeve.

In medium-size centrifugal pumps with two external bearings on opposite sides of the casing (the common double-suction and multistage varieties), the favored shaft sleeve construction uses an external shaft nut to hold the sleeve in an axial position against the impeller hub. Sleeve rotation is prevented by a key, usually an extension of the impeller key (see Figure 67). The axial thrust of the impeller is transmitted through the sleeve to the external shaft nut.

In larger high-head pumps, a high axial load on the sleeve is possible and a design similar to that shown in Figure 68 may be preferred. This design has the advantages of simplicity and ease of assembly and maintenance. It also provides space for a large seal chamber

FIGURE 66 Section of a small centrifugal pump with no shaft sleeves (Flowserve Corporation)

IMPELLER SLEEVE SHAFT NUT

FIGURE 67 A sleeve with external locknut and impeller key extending into the sleeve to prevent rotation

IMPELLER SLEEVE SHAFT NUT

FIGURE 67 A sleeve with external locknut and impeller key extending into the sleeve to prevent rotation

IMPELLER SHAFT GLAND

IMPELLER SHAFT GLAND

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