Asymmetry — Details

Causes

Asymmetry may occur because:

1. The horn may have machining errors so that the horn is not actually symmetric.
2. The primary resonance may be affected by a close secondary resonance.
3. There were errors in measuring the amplitude.
4. For FEA simulation, the mesh may not be identical at geometrically equivalent locations. This error will generally be minimized as the mesh is refined.

Another possible cause is that the output amplitude from the transducer could be asymmetric, thereby affecting the horn. However, this does not appear to be true. Several horns with significant asymmetry have been tested as follows:

1. Choose a transducer with known asymmetry.
2. Measure the horn amplitudes with respect to the horn's reference mark.
3. Insert a 0.025" thick shim at the horn-transducer joint so that the tightened transducer was rotated 180° with respect to the horn.
4. Again measure the horn amplitudes with respect to the horn's reference mark.

If the transducer were affecting the horn's asymmetry then rotating the transducer by 180° should have also rotated the amplitudes of the horn's face. However, in all cases the horn asymmetry remained unchanged with respect to the horn's reference point. In fact, this was true even when there was a node on the horn's face due to an adjacent asymmetric resonance (for example, a Ø100 mm spool horn).

Asymmetry measurements are given in table å1Ï. You will note that all of the horns have at least some asymmetry. In some cases the asymmetry is very severe. For instance, the horns whose diameters are 101.3 mm have asymmetries ranging from 0.302 to 0.559. These horns would not be useable for most applications.

Is it possible that the asymmetry readings could be a statistical fluke, possibly due to improper measurement technique? Looking at table å1Ï, we see that horns that have been remeasured without any change (except disassembly from and reassembly to the converter) show very repeatable measurements. For instance, horn HRD 052 gave asymmetry measurements of 0.302 and 0.314. Also, note that most horns of similar size have similar asymmetries. This all suggests the asymmetry cannot be attributed to random error. There is apparently some underlying phenomena that is causing the asymmetries. Also: Horn asymmetry stays same wrt mark on horn, regardless of converter. Asymmetry also shows sinusoidal pattern, which does not indicate random measurement error. Figure.

Of course, it is known that an asymmetrical horn design can cause asymmetric amplitudes. However, all of these horns are symmetric, within normal machining tolerances. If machining tolerances are the problem then you would expect the asymmetries to be randomly distributed among the horn sizes. Instead, the horns of about 100 mm have considerably higher asymmetry than horns of other sizes.

Could it be the converter be causing the asymmetry? Well, let's look first at cases where the same converter has been used on different horn sizes. For instance, the converter CU90215D was used on three 75.0 mm horns (average asymmetry = 0.032), two 100.0 mm horns (average asymmetry = 0.154), one 110.0 mm horn (asymmetry = 0.011), and two 125.0 mm horns (average asymmetry = 0.02check). Also, converter CU90651D was used on the 38.1 mm titanium standard (asymmetry = 0.018), on a 50.8 mm full-wave (asymmetry = 0.054), and on a 101.3 mm horn (asymmetry = 0.559). Neither converter produces consistently good or consistently bad asymmetries, except that the asymmetries are similarly poor when the horn diameter is near 100 mm.

What about cases where the same horn was tested with different converters? HRD 052 (101.3 mm) was tested with converter CU90224D (figure í11Ê) and CU90651D (.f.figure í11aÊ). The face asymmetries produced by the respective converters were 0.314 and 0.559. The difference between these asymmetry values is substantial, but both values are still large compared to horns of other diameters. Also, note that the face amplitudes showed the same pattern with respect to the horn reference mark, regardless of which converter was used. For instance, the highest amplitudes occurred at the 12 o'clock and 6 o'clock positions, while the lowest amplitudes occurred at the 3 o'clock and 9 o'clock positions. Thus, the asymmetry seems to be somehow associated with the horn, rather than with the converter. (Note, however, that the full-wave horn HRD 053 does not seem to maintain this pattern when its converter is changed. See .f.figure í12Ê«».)

Tests on another horn (HRD 051­1, 6/23/82) of nominally identical design using the same converter (CU90224D) showed similar axial and radial amplitude distributions.

So what is the cause of the asymmetry? First, a small part of each horn's amplitude asymmetry is likely due to mesurement error. For instance, if an amplitude of 20 microns was misread by 0.2 microns, then this by itself would give a 0.01 asymmetry, even though no asymmetry was actually present. One method of checking for such measurement error is to see if the amplitudes are random around the edge of the horn or whether, on the other hand, the amplitudes form a consistent pattern. For instance, if we look at the amplitude measurements at the edge of HRD 454 (figure í13Ê«»), we see that the amplitude progresses steadily from a low of 21.9 microns at position 1 to a high of 22.3 microns at position 4 and then back again to the low at position 1. Thus, the smooth progression of amplitudes indicates that the asymmetry (0.018) is apparently real and not due to principally to measurement error.

Second, a small portion of the asymmetry is probably due to machining tolerances and the influence of the converter. For instance, measurements on converter back drivers show that most converters, by themselves, are asymmetric. Some of this converter asymmetry may be transferred to the horn. [E. Holze and F. Dibble data on converter asymmetry.]

I believe, however, that the main cause of asymmetry in most horns is the presence of adjacent resonances that influence the axial resonance. The strength of these resonances is often small quite small compared the axial resonance. I will not present evidence here to support this position. Instead, I will wait until the discussion of spool horns and bar horns.

Effect of asymmetry on uniformity

According to the chosen method of calculating uniformity (equation ó1Â), table å1Ï and figure í4Ê show that horns of similar diameter have similar uniformities, regardless of the asymmetry. For instance, horns of approximately 100 mm diameter have uniformities ranging from 0.655 to 0.736 (a difference of 8.1%) while the asymmetries range from 0.152 to 0.559 (a difference of 40.7%).

Because horns of similar diameter have similar uniformities, a single curve-fit equation can be used for all of the data. However, suppose that we had chosen not to use equation ó1Â to calculate the uniformity, but instead had adopted the following definition of uniformity:

Ö Minimum measured amplitude Ì
²¹) Uniformity = °                            ° 100
Ŵ Maximum measured amplitude ì

Using this equation, the horns of approximately 100 mm diameter would have uniformities ranging from 0.405 for HRD 052 (see figure í11Ê) to 0.669 for HRD 064 (see figure í2Ê) for a difference of 26.4%. Thus, using equation ó26Â would tremendously increase the data spread and would essentially rule out any reasonable curve-fit of the uniformity data. Neither would equation ó26Â really provide any additional useful information beyond that of equations ó1Â and ó4Â. Therefore, equation ó1Â is the rational choice for calculating the uniformity.

Any implication of having same asm pattern as horn is being tuned?