Mixing should be a process operation, not a mechanical problem. Yet, some plants push a mixer beyond the capability of its mechanical design and then get themselves into trouble. While most mixers can provide a long service life — for instance, some are still operating after more than 30 years — mechanical problems can shorten life or even break parts. Often, the processing capabilities of the mixer fail before the equipment does, but poor processing can cause mechanical problems.
Usually, equipment manufacturers know the limits of their equipment and design to specified conditions. However, over the life of a mixer, process requirements and conditions may change from those specified for design. So, here, we will explore some of the mechanical problems that may befall mixing equipment.
Most everyone appreciates the danger of overloading a mixer, usually by trying to mix a material that is more viscous than the mixer can handle. Actually, many mixers are designed to cope with a wide range of materials and have considerable overload capabilities. Some portable mixers and high-speed dispersers can handle very high viscosities without overloading. Such mixers only may draw less than 10% of the motor power when operated in water. However, other mixers are designed for 85% or 90% of motor capacity and so are less tolerant of upset conditions. While high viscosity is an obvious load factor in mixing, fluid density has a direct effect on the motor load in turbulent conditions. A high density fluid, such as a mineral slurry, can overload a motor that is not designed for process conditions. In any case, gear reducers, shafts, impeller blades and other basic components should be chosen to match the maximum motor load. Still process overloads can occur and may damage the motor or shorten the life of other components.
A mixer component, such as a shaft, shaft seal, impeller blade or gear reducer, may fail for several reasons. Differences between actual process conditions and original design criteria often can cause problems. In other cases, installation shortcomings can contribute to equipment failures.
The “wetted” parts of the mixer must be designed to handle mechanical loads, process conditions and potential vibrations. Most mechanical loads come from an interaction between the mixer and the fluid (Figure 1). Obviously, a force is necessary to rotate the impeller. That force is represented by a torque load transmitted by the shaft from the drive to the impeller. Besides the fluid forces that resist the rotating impeller, moving fluid creates random hydraulic forces that act perpendicularly to the shaft.
These forces create a bending moment on the shaft. A typical cantilevered shaft, which is supported only by the mixer drive, can experience significant bending loads. So, selection of shaft diameter requires consideration of both the torque and bending loads.
Torque is easily calculated from the basic relationship of power divided by speed, with an appropriate conversion factor for units:
TQ = 63,025 Pmotor/N (1)
where TQ is torque, in-lbf; Pmotor is motor power, hp; and N is rotational speed, rpm.
Hydraulic loads are based on empirical relationships. An expression for the bending load on a mixer shaft with a single impeller is:
M = 19,000 PmotorLfH/ND (2)
where M is the bending moment, in-lbf; L is the “shaft length to support,” in; fH is the hydraulic load factor; and D is the impeller diameter, in. The “shaft length to support” may exceed the shaft length inside the tank because the nearest support bearing may be in the drive or seal above the tank mounting or flange. Multiple impellers require separate bending-load calculations for each, using the fraction of the motor power at each impeller and at the appropriate shaft length, and then summing of the individual bending loads.
The hydraulic load factor may surpass 1.0 for cases where loads fluctuate, as in gas dispersion or boiling systems (fH = 2.0 to 3.0), or where extreme external loads may occur, as with impacting large clumps of solids (fH = 3.0 to 7.0). The severe load most often overlooked is prolonged operation at the liquid level, as when filling or emptying the tank. Operation near the liquid level may result in a significant hydraulic load factor (fH = 2.0 to 3.5), depending upon impeller type and mixing intensity.
Once the torque and bending loads have been estimated, basic calculations can be made for the shear and tensile stresses in the mixer shaft.
The expression for shear stress is:
σs = 16(TQ2 + M2)½/πd3 (3)
where σs is shear stress, psi; and d is shaft diameter, in.
A typical allowable shear stress for carbon and stainless steels is 6,000 psi. This stress level takes into account the effects of fluctuating mixing forces that could result in a fatigue failure.
A similar expression for tensile stress is:
σt = 16(M + (TQ2 + M2)½)/πd3 (4)
where σt is tensile stength, psi.
A reasonable allowable tensile stress level for steels is 10,000 psi. Higher-than-allowable stress levels may lead to a fatigue failure of the mixer shaft. Other factors, such as welds or steps in the shaft, may cause stress risers that may increase local stresses, which, in turn, could result in failures. Fluctuating loads also act on the impeller blades and may cause other component failures.
The vertical forces on the mixer, such as weight, pressure and thrust, have little impact on the shaft design but may affect mixer mounting. Axial flow impellers create some axial thrust, enough to occasionally lift an impeller off shaft mounts.
Bearings on the output shaft of the mixer drive must resist the lateral forces of the bending loads and the axial forces of weight and pressure. Bending loads also are transmitted up the shaft and may result in deflections between the bearings, causing gear misalignment. Shaft deflections also can lead to failures in the shaft seals, since mechanical seals are especially susceptible to damage by large deflections.