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Slotted cylindrical horns

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For cylindrical horns whose diameter is greater than about 0.5 * wavelength (about 5" at 20 kHz), longitudinal slots must be used to reduce the transverse coupling due to the Poisson effect. Such slots are usually radial, although other configurations are sometimes useful. Without such slots the horn will either have very uneven amplitude across the face or may even resonate in a nonaxial manner. Slotted cylindrical horns generally have low-to-moderate gain (1:1 to 2:1). Cylindrical horns are used for plunge welding.


The following example shows a 20 kHz 6.5" diameter slotted cylindrical horn. The horn has a face cavity that extends deep within the horn in order to increase its gain. The axial resonance is the desired resonance. The horn is one half-wavelength long at axial resonance, as indicated by the single node that is generally transverse to the principal direction of vibration.

For all images, the output surface (face) is at the top and the input surface is at the bottom. The warmest colors indicate the highest amplitudes. The darkest color traces the axial node(s).

All results are from finite element analysis.

Original design

The following shows the original (unoptimized) design and the resulting amplitude distribution.

Ultrasonic horn -- cylindrical, unoptimized Original design -- No optimization
Ultrasonic horn -- cylindrical, axial mode, unoptimized Axial resonance, relative amplitudes -- The amplitude at the outer face is much higher than at the center. This will cause over-welding at the outside or reduced welding at the center.

View actual vibration

Improved design

The following shows an improved design that has substantially better amplitude uniformity across the horn's face.

Ultrasonic horn -- cylindrical, optimized

Improved design -- Uses optimized cavity, slots, and back extension

Ultrasonic horn -- cylindrical, axial mode, optimized

Axial resonance, relative amplitudes -- The amplitude is now very uniform across the horn's face.

View actual vibration

Design considerations

Although the slots help to improve the face amplitude uniformity, other refinements are often necessary to further improve the uniformity, depending on the particular application. Also, the required slots can introduce additional secondary resonances and can cause stress problems, although these problems can be reduced through careful design.

(Note: depending on the application requirements, many smaller diameter horns will not require slots. For example, see spool horns.)

Secondary resonances

Slots often introduce additional secondary resonances. The following image shows a typical secondary resonance, although many others are possible.

Such secondary resonances may interfere with the vibration of the axial resonance. In some cases, the power supply may prefer to start on a secondary resonance or may jump to a secondary resonance during the weld cycle. The effects of secondary resonances can be minimized by designing the horn so that the secondary resonances are sufficiently far from the axial resonance.

Slot stresses

In slotted cylindrical horns, the stresses are generally highest at the end of the slots. The cause of this problem can easily be seen by watching the slots  deform as the horn vibrates (see the animation). High cyclic stresses can cause the horn to fail by fatigue. This problem can be reduced by proper slot design and by machining the horn from high-strength materials.


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Krell Engineering
212 E. Medwick Garth    Baltimore, MD  21228    USA

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