Ultrasonic Resonators

The following are significant revisions. Minor rewrites are not included. (When viewing a particular page, the most recent revision date can be found at the bottom right of that page's footer.)

• 2019-05-19 —2019-05-25
  1. Joints —
     1. Added text descriptors to figure 4 ("Clamshell tightening fixture", previously figure 3a) and added descriptive text.
     2. Added text descriptors to figure 6 ("Metal welding stack supported by flexure elements").


• 2019-03-17 —2019-03-23
  1. Uniformity — methods for improving —
     1. Added topic Risers.
     2. Expanded topic Add additional half-wave resonators on the horn's input surface.
     3. Expanded other topics.


• 2018-12-23 — 2018-12-29
  1. Classic horns — Added catenoidal horn with 60 mm shoulder.


• 2018-12-16 — 2018-12-22
  1. Transducer design — Added figure Effect of prestress and temperature on d₃₃ for PZT4 piezoceramic.


• 2018-11-18 — 2018-11-24
  1. Added topic Classic horns.


• 2018-10-28 — 2018-11-03
  1. Steel materials —
     1. Added topic Temperature effects.


• 2018-09-23 — 2018-09-29
  1. Ultrasonic metal welding — Added topic Tooling materials.


• 2018-09-16 — 2018-09-22
  1. Ultrasonic metal welding — Expanded topic System comparisons.
  2. Joints — Added topic Joint clamp force distribution.
  3. Transducer design — Expanded topic Prestress pressure uniformity.


• 2018-09-09 — 2018-09-15
  1. Ultrasonic metal welding —
     1. Expanded topic System comparisons.
     2. Expanded topic Seam welding.


• 2018-09-02 — 2018-09-08
  1. Ultrasonic metal welding —
     1. Added topic System comparisons.
     2. Added figure "Lateral drive metal welding horn supported by two vertical members".
     3. Added figure "Microbonder".


• 2018-08-26 — 2018-09-01
  1. Added topic Ultrasonic metal welding.
  2. Titanium — added topic Diffusion surface hardening.
  3. Power supplies — added figure "Stack frequency during ultrasonic metal welding".


• 2018-08-19 — 2018-08-25
  1. Added topic Power supplies.
  2. Added topic Choosing the "best" operating frequency.


• 2018-08-12 — 2018-08-18
  1. Aluminum —
     1. Added figure "Ø125mm aluminum spool horn — Effect of Poisson's ratio on axial face amplitudes".
     2. Added figure "Ø110mm aluminum spool horn — Effect of Poisson's ratio on axial face amplitudes".
     3. Added figure "Directionality in flat rolled Al 7075-T6".
  2. Glossary —
     1. Metal welding— added figure "Ultrasonic metal welders — typical configurations".


• 2018-08-05 — 2018-08-11
  1. Added page Uniformity — methods for improving.
  2. Added page Ultrasonic plastics assembly.
  3. Glossary—
     1. Vacuum horn — added image
     2. Staking — expanded and added image
     3. Added Child horn and Daughter horn.


• 2018-07-29 — 2018-08-04
  1. Added glossary term Blade horn.


• 2018-07-22 — 2018-07-28
  1. Cavitation erosion —
     1. Added topic cavitation erosion resistance for stainless steel.
  2. Steel materials —
     1. Table "Loss measurements for various stainless steels" now lists the principal chemical components. The associated text discusses the possible relation of nickel content to loss (3xx series versus 4xx series).


• 2018-07-15 — 2018-07-21
  1. Steel materials —
     1. Added topic Loss measurements for stainless steels.
     2. Added topic Machinability of stainless steels.
  2. Added topic Tungsten.


• 2018-07-01 — 2018-07-07
  1. Transducer design —
     1. Expanded topic Back driver shape — effect on bandwidth.
     2. Added topic Secondary cooling.


• 2018-06-24 — 2018-06-30
  1. Added topic Ultrasonic Additive Manufacturing (UAM).
  2. Transducer design —
     1. Added topic Effect of frequency.


• 2018-06-17 — 2018-06-23
  1. Transducer design —
     1. Added topic Dual facing transducers.
     2. Added topic Power supply considerations.
     3. Clustered transducers — expanded to include splayed stacks.
     4. Electrical insulation — expanded to include Conap curing-loss information.
     5. Cooling — expanded to include water vapor requirements for cooling air.
  2. Aluminum—
     1. Added topic Endurance limit.


• 2018-06-03 — 2018-06-09
  1. Transducer design —
     1. Added data from Sonics & Materials.
     2. Multiple stacks — expanded to include limitations.


• 2018-05-27 — 2018-06-02
  1. Cavitation erosion —
     1. Added silver coating.


• 2018-05-20 — 2018-05-26
  1. Transducer design —
     1. Added Dukane information to table "Maximum recommended ceramic temperature".
     2. Added table "Transducer amplitudes for industrial applications".
     3. Multiple stacks — expanded to include information about "Compensating circuit for multiple stacks driving a single horn" (Roberts patent 5,828,156).
  2. Notes— Added table of units.


• 2018-05-13 — 2018-05-19
  1. Added Wear (encompasses cavitation, abrasion, and fretting).
  2. Cavitation erosion — Added Elbert's titanium information.
  3. Titanium — Added a cross-reference to cavitation erosion wear.
  4. Tips (replaceable) —
     1. Table 1 — Added tolerances on tip mass (Branson) and some maximum amplitudes (Qsonica).
     2. Added Materials.
     3. Added Lubricants.
     4. Added additional discussion of Use with organic solvents or low surface tension liquids.
  5. Abbreviations and symbols—
     1. Added Vickers hardness (HV).


• 2018-05-06 — 2018-05-12
  1. Joints — first release


• 2018-04-29 — 2018-05-05
  1. Cavitation erosion —
     1. Revised Table C1.
     2. Added information about the axes of Figure B1.
     3. Added titanium cavitation data from Hielscher.


• 2018-04-15 — 2018-04-21
  1. Added the following glossary terms —
     1. Fretting
     2. Head mass
     3. Mylar washer
     4. Spanner wrench
     5. Tail mass


• 2018-04-08 — 2018-04-14
  1. Transducer design —
     1. Added table "Maximum recommended ceramic temperature".


• 2018-04-01 — 2018-04-07
  1. Threads and threaded fasteners — Added Thread failures in steel horns.


• 2018-03-25 — 2018-03-31
  1. Titanium  — Added a figure that shows the effect of frequency on internal friction Q^-1.


• 2018-01-07 — 2018-01-13
  1. Titanium  —
     1. Added a table that shows the chemical composition of Ti-6Al-4V.
     2. Figure 2 (Ti-6Al-4V: Effect of raw stock diameter on Young's modulus) — added additional data and recalibrated the regression equation.
     3. Figure 3 (Effect of raw stock diameter on thin-wire wave speed) — recalibrated the regression equation based on added data from figure 2.
     4. The discussion of Ti-7Al-4Mo has been expanded.
  2. Composite horns —
     1. Expanded topic Design guidelines.


• 2017-11-12 — 2017-11-18
  1. Steel —
     1. Expanded topic CPM^® tool steel.
  2. Materials — Added niobium to the table.
  3. Titanium  — Added a figure that compares machinability of Ti-6Al-4V to various tool steels.


• 2017-11-05 — 2017-11-11
  1. Threaded fasteners —
     1. Expanded topic Bottomed versus unbottomed studs.
     2. Added table "Bottomed studs — torques".
     3. Added topic Anti-rotation means.
  2. Steel —
     1. Added tables "Tool steel machinability rating" and "Shock resistance comparison chart".
  3. Titanium  —
     1. Added Wuchinich data to topic Poisson's ratio.
     2. Expanded topic Ti-7Al-4Mo.


• 2017-10-29 — 2017-11-04
  1. Threaded fasteners —
     1. Added topic Cold-forming taps.
     2. Added topic Bottomed versus unbottomed studs.
     3. Added topic Cold-forming taps.
  2. Steel — added suggested heat treatment for Vertex.
  3. Added the following glossary items —
     1. Socket head cap screw
     2. Socket set screw
     3. Anisotropic material


• 2017-10-22 — 2017-10-28
  1. Steel
     1. Added topic Effect of grain size.
     2. Added topic Threads.
  2. Transducer design — continued preliminary release
     1. Added stainless steel to topic Electrodes.
     2. Added table "Effect of soft metal shims on transducer performance".
  3. Added topic Threaded fasteners.


• 2017-10-15 — 2017-10-21
  1. Added topic Steel.


• 2017-10-08 — 2017-10-14
  1. Added topic Isolation mounts.
  2. Titanium — added lists of figures and tables.


• 2017-10-01 — 2017-10-07
  1. Transducer design — continued preliminary release
     1. Expanded topic Electrical losses.
     2. Added topic Housing.
     3. Added figure "Cleaning transducer with conical back driver".
     4. Added list of tables.


• 2017-09-24 — 2017-09-30
  1. Transducer design — continued preliminary release
     1. In topic Compatible coefficient of thermal expansion, added figure "Transducer with Belleville springs" and associated discussion.
     2. Added topic Mechanical fits.
     3. Added topic Loss tests with subtopics Electrical losses and Mechanical losses.
     4. Added topic Number of ceramics.
     5. Topic Placement\Power considerations now includes the effect of the transducer's mechanical Q.


• 2017-09-17 — 2017-09-23
  1. Transducer design — seventh preliminary release (v. 7d)
     1. "Table 5. Front driver materials" has been rearranged.
     2. Expanded topic Multi-material front driver.


• 2017-09-03 — 2017-09-09
  1. Transducer design — seventh preliminary release (v. 7c)
     1. Added list of figures.
     2. Added topic Multi-material front driver.
     3. Expanded topic Prestress pressure uniformity and added a graph.
     4. Revised Appendix H: Effect of stack bolt on electromechanical coupling coefficient κ.


• 2016-06-26 — 2016-07-02
  1. Added Modal interaction.


• 2016-06-19 — 2016-06-25
  1. Added Mechanical—Electrical analogs.


• 2016-06-05 — 2016-06-11
  1. Contact emails are now active.


• 2016-05-22 — 2016-05-28
  1. Expanded discussion of Prismatic horns.


• 2016-05-15 — 2016-05-21
  1. Expanded definition of Q.


• 2016-05-08 — 2016-05-14
  1. Expanded definition Mori equation.
  2. Expanded definition Rayleigh equation.


• 2016-05-01 — 2016-05-07
  1. Transducer design — sixth preliminary release (v. 6a)
     1. Added animations showing the relative transducer amplitudes and von Mises stresses.
     2. Topic Loss — added information about voltages across individual ceramics.
     3. Expanded topic Individual ceramic thickness.
     4. Topic Electrical loading — added figure for transducer test arrangement.
     5. Appendix A: Comparison of 33 and 31 ceramic operation — added tables.
     6. Added Appendix B: Manufacturer's piezoelectric cross-reference.
     7. Appendix G — added compressed gas analogy for Young's modulus.
  2. Log decrement definition — corrected an error in equation 4 (replaced "\( n \)" with "\( \pi \)").
  3. Added definition Damping ratio.


• 2016-04-17 — 2016-04-23
  1. Added definition PZT.
  2. Updated definition Piezoelectric ceramic.


• 2016-04-10 — 2016-04-16
  1. Transducer design — fifth preliminary release (v. 5a)


• 2016-04-03 — 2016-04-09
  1. Added information for Tips (replaceable).


• 2016-03-27 — 2016-04-02
  1. Separate pages for Contents and Glossary.
  2. Added definition Bandwidth.
  3. Added definition Pochhammer equation.
  4. Corrected equation error in definition Dilitational wave speed.


• 2016-03-20 — 2016-03-26
  1. Added design for Shear-mode horn.
  2. Added Cavitation.


• 2016-03-06 — 2016-03-12
  1. Added images for Spool horn, Spool horn (standard), Spool horn (full), Bell horn, Prismatic.


• 2016-02-14 — 2016-02-20
  1. Added Cavitation erosion.


• 2016-02-07 — 2016-02-13
  1. Added Prismatic horns.


• 2016-01-31 — 2016-02-06
  1. Added Composite horns.
  2. Added Gain (preliminary).


• 2016-01-24 — 2016-01-30
  1. Abbreviations & symbols — added units.
  2. Uniformity & Asymmetry Calculations — added additional information with clarification.
  3. Added the following definitions:
     1. Dielectric constant
     2. Edge effect
     3. Symmetric resonance


• 2016-01-17 — 2016-01-23
  1. Added the following definitions:
     1. Langevin transducer
     2. Mass-loaded transducer


• 2015-11-29 — 2015-12-05
  1. Added the following definitions:
     1. Permittivity ε


• 2015-11-22 — 2015-11-28
  1. Added the following definitions:
  1. Electromechanical coupling coefficient к
  2. Piezoelectric capacitance — blocked
  3. Piezoelectric capacitance — clamped
  4. Piezoelectric capacitance — free
  5. Piezoelectric effect
  6. Piezoelectric direct effect
  7. Piezoelectric inverse effect
  8. Piezoelectric properties
  9. Piezoelectric charge constant d
  10. Piezoelectric voltage constant g
  11. Poling
  12. Relative dielectric constant K
  13. Transducer components


• 2015-11-15 — 2015-11-21
  1. Transducer design - third preliminary release (v. 3a)
  2. References
     1. Added table of contents.
     2. Added internal links (pdf) to all referenced U.S. patents.


• 2015-10-18 — 2015-10-24
  1. Transducer design - second preliminary release (v. 1b)


• 2015-10-11 — 2015-10-17
  1. Added Meyer (1) wave image to several glossary wave terms.


• 2015-09-06 — 2015-09-12
  1. Titanium. Added figure C2 (Branson Ultrasonics metal welding horn).


• 2015-08-23 — 2015-08-28
  1. Transducer design - first preliminary release (v. 1a)


• 2015-08-09 — 2015-08-15
  1. References. Added external patent links.


• 2015-06-28 — 2015-07-04
  1. Transducer. Added image showing transducer components.
  2. Notes: added Finite element analysis (FEA) color bar.
  3. Added the following definitions:
     1. Acoustic intensity
     2. Loss tangent


• 2015-06-21 — 2015-06-27
  1. Titanium. Added sintered Ti-6Al-4V to appendix E.
  2. Washer stud. Added reference to Scotto patent.
  3. Added the following definitions —
     1. Transducer (converter) with image
     2. Center bolt design
     3. Center stud design
     4. Peripheral bolt design
     5. Front driver (front mass)
     6. Back driver (rear driver, rear mass)
     7. Stack bolt
     8. Electrode
     9. Electrode tab
     10. Piezoelectric ceramic prestress
     11. Contour
  4. Flatted-cylindrical horn. Added image.


• 2015-06-14 — 2015-06-20
  1. Notes: added Finite element analysis (FEA) colors.
  2. Uniformity: split into two pages —
     1. Uniformity - Basic Concepts. Added section Cause of nonuniformity which includes a comparison of various materials, with images (some animated).
     2. Uniformity - Calculation


• 2015-06-07 — 2015-06-13
  1. Washer stud: added definition.


• 2015-05-31 — 2015-06-06
  1. Tapered slot: added machining dimensions and image.
  2. Aluminum: preliminary release.
  3. Titanium
     1. Added graphs 5a and 5b (Young's modulus data scatter for Ø7.9 mm and Ø12.7 mm rod stock, respectively).
     2. Added information about cross rolling.
     3. Added Appendix C - Titanium with Low Young's Modulus


• 2015-05-25 — 2015-05-30
  1. Preliminary release.
  2. Titanium
     1. Added additional information from Boyer about STA material (appendix C).
     2. Added a list of titanium alloys for medical use (appendix D).