Mixer Vibration – Design Considerations
Posted by: Robert Higbee, P.E.
A mixer is a complex mechanical system consisting of both rigid and flexible components. For the purposes of this vibration discussion, please consider a top-entry single-impeller mixer which consists of an A/C motor driving a mixer-duty gear reducer (one that can handle high bending moments) whose output shaft is rigidly coupled to an agitator shaft that extends unsupported into a mixing vessel and which drives a mixing impeller connected to the bottommost end. The lower portion of the gear box is typically bolted to a tank flange, support bridge or concrete. For this configuration, the shaft and impeller can be thought of as a large tuning fork.
Like a tuning fork, the agitator shaft has a fundamental vibration frequency. The type of shaft-impeller movement associated with the lowest vibration frequency is similar to that of a pendulum – all portions of the agitator-impeller assembly move back and forth in the same direction, more motion at the impeller and less as you approach the upper bearing. The agitator-impeller assembly also has higher vibration modes (harmonics). The rate of vibration for these modes is also fixed for a given shaft geometric configuration. The motion of the second mode has a characteristic motionless node, often just a few feet above the impeller. At a given instant in time, those portions of the shaft above and below the node move in opposite directions. An almost infinite number of harmonics exist; although the visible deflection associated with each higher harmonic drops off exponentially (first mode has the largest deflection). Therefore, vibrations at the first and second modes are the most problematic and are the key modes to consider when designing an agitator shaft.
The primary design concern involving a mechanical system’s modes of vibration, a.k.a., natural frequencies, is that very little excitation energy is required to induce the system to vibrate at its natural frequency. A hammer strike will excite several of the lower natural frequencies. The most common excitation source is related to the rotational speed of the agitator shaft. An agitator assembly design, where the mixer revolutions per minute (RPM) equals the cycles per minute (CPM) of the shaft-impeller system’s first natural frequency, can experience excessive vibration/deflection which can lead to the catastrophic failure of the mixer. The next most important excitation source is called “blade-pass” and is caused by the interaction of the blades with the shaft or an internal tank feature that might lie close to the impeller. The blade-pass excitation frequency equals (RPM) multiplied by the number of blades.
Mathematical computations exist which predict the frequencies at which the modes of shaft-impeller vibrations occur. Such computations have the ability to account for geometric features such as steps in shaft diameter, hollow shafts, or the added weight of additional impellers at specific locations. The judicious mixer designer will chose a shaft of sufficient diameter, or locate shaft steps at specific locations, in order to tune the shaft-impeller system to avoid any natural frequencies or harmonics.
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About the author: Mr. Higbee has been with PMSL for 20 years. He has a Masters degree in Mechanical Engineering and is a Professional Engineer registered in Pennsylvania. He also holds several mixing related patents.