Spool horns -
	Davis, Paul H. (Dukane Corp.) - US patent 4131505 (1978-12-26) - 'Ultra-Sonic Horn'

See Tab 4 of E. Holze "brown book" (bar horns & spool horns).

Cardoni -
	Discusses block horns - Chapter 5, p. 82..
	"A detailed strategy to control the vibration behaviour of block horns based on FE models was presented by 0' Shea [4]." (p. 84)
	Uniformity = the ratio of minimum to maximum response amplitude on the output surface, Umin/Umax (p. 84)
	Search for Adachi [51] & O'Shea [41] (effect of slots)
	
	Cardoni__'Enhanced_vibration_performance_of_ultrasonic_block_horns'
		The uniformity requirement for a block horn, measured as the ratio of minimum to maximum response amplitude on the output surface, Umin=Umax, is estimated to be 80% [3].The frequency separation should be at least 1 kHz from the longitudinal mode frequency.

Half-wave resonators attached to back of bar horn -
 	Elbert's patent

-------------------- Uniformity --------------------
Appendix A - Limitations of U eqn --
	- Currently consider cavitation load where power varies linearly with ampl. What about resistive type load where power varies with square of ampl?
	- U as RMS deviation from average -- sum(sqr[Ui - U_bar])
	
	- Appendix graph A2 - rose color plot line is too light, esp when printed.
	
	- AM 162 (Brush Wellman AlBeMet: 62% Be, 38% Al) - used in Chromealloy FEA:
		Density = 2100 kg/m^3
		E = 196.5 GPa
		==> Co = 9669 m/sec
		Nu = 0.17
		Fatigue = 138 MPa (20 kpsi) rotating beam @ 1e7 cycles

	- Al-Li 8024 Alloy (Osprey Metals):
		Density = 2410 kg/m^3
		E = 84 GPa
		==> Co = 5904 m/sec
		Nu = ?

	- Al-Si 4019 Alloy (Osprey Metals):
		Density = 2780 kg/m^3
		E = 98 GPa
		==> Co = 5928 m/sec
		Nu = ?

	- Al-Zn 7034 Alloy (Sandvik Osprey):
		Density = 2880 kg/m^3
		E = 74 GPa
		==> Co = 5069 m/sec
		Nu = ?
		Fatigue ~ 300 MPa (43.5 kpsi) (vs ~180 MPa (26 kpsi) for 7075-T6) [both from graph in Sandvik Osprey data sheet @ 5e6 cycles]
		
	- Link to pochhammer.html
	- Update pochhammer.html with pochhammer eqn - see:
		- poch_prn & pochhamer1.doc (appendix A to uniform.acu)
		- TP55\CARD\Equation\Poch* & PltPoch*
	- pochhammer.html has the following which may not be correct (for a thin radially vibrating disk, does U go to 0 or 1.0?)
<!--
<p>In actual fact, as the horn diameter becomes larger, the face uniformity continues to decrease to zero as the major component amplitude becomes progressively more radial.  At the largest possible horn diameter, the horn simply becomes a thin, flat, radially-resonant disk with essentially radial amplitude.  For Al&nbsp;7075&#8209;T6 aluminum, this happens at about 177&nbsp;mm at 20&nbsp;kHz.</p>
<p>This progressive decrease in face uniformity (above the limits of the Pochhammer equation) can be approximated by fitting a cubic spline curve between the largest Pochhammer diameter and the diameter at which the horn becomes radially resonant.  This is shown in figure&nbsp;&iacute;6&Ecirc;.
 Also shown in this figure are the diameters at which adjacent, nonaxial resonances may cause amplitude asymmetry or other unexpected amplitude variations.</p>
-->
<!--
<p>Notes to myself:  Note that ˆ is defined in terms of the circumference of the cylinder to the thin-wire half- wavelength.  Insights:  1) effect of nu on uniformity  2) relative variation of amplitude across the face.]</p>
-->

	- Find data where inserting a shim between the xdu & horn: the asymmetry pattern remained fixed wrt the horn reference mark. Check 100 mm horn (spool or unshaped).
	
	- Update Aerospace nu 0.319 --> 0.333 (see mat tests) [matweb gives nu = 0.33 for Al 7075-T6]

2/19/08: Currently, asymmetry is calc as (1 - Min ampl/Max ampl) where the ampls are measured at geometrically identical locations. However, may not be the best way to calc asymmetry. For example, consider 10mm dia and 100mm dia horns. Both might have the same asymmetry according to the above equation, but the slope of the amplitude change across the 100mm horn would be much less than but the slope of the amplitude change across the 10mm horn. For example, assume Min ampl = 90 and Max ampl = 100. Then the asymmetry is 90% for each. However, for the 10mm dia horn the ampl changes by 10 over a diameter of 10mm, whereas , for the 100mm dia horn the ampl changes by 10 over a diameter of 100mm. Therefore, perhaps should have an "asymmetry per unit length". If want to change the equation, then what to do about rectangular horns (what characteristic length should be used)?

If change U from % to decimal, the following files would need to be changed:
	- Pochhammer.html - OK
	- uniformity_basic_concepts.html - OK
	- uniformity1_dict.html (also, provide links to uniformity design pages) - OK

Asymmetry. The following horns have asymmetry:
	HRD-456-3, 100x100, 0 slots - see chapter on Uniformity p. 60 (have not been able to duplicate with FEA)
	HRD-472-1, 127x127, 2x slots 12.0 wide - See my paper, "Performance of 127 x 127 Aluminum Horns", 1991, p. 9 & figure 14. Asm = .238
	Look at 5x5 with frequency cross-overs as slots are lengthened.
	HRD-051-1, 101 dia unshaped, L = 119.26, xdu = CU90224D. Asm = .533
	HRD-051-1, 101 dia unshaped, L = 119.26, xdu = CU90224D. Asm = .314
	HRD-051-2, 101 dia unshaped, L = 119.26, xdu = CU90616D. Asm = .559
	HRD-064, 100 mm unshaped --> 100mm standard spool, L adjusted at back
	E. Holze 4" spool horn life test data --> "double-axial" resonance
	100 mm spool -- look at data in U/S seminar folders
	
Spool horns:
	See my doc "\Write\_Design\Resonators\Cylindrical horns\Unslotted\Spool horns\Spool Horn Design Procedure.doc" (2008)
	Does the face radial ampl depend on the flange thickness?
	
uniformity_improvement_methods_1a.html - Scotto patent --> see Derks, pp. 30-31	

Define -
	Transverse U = relative transverse ampl ("uniformity" probably not a good name) --> discuss with examples