13/Dec/2018 6:53 Equation 8 in Appendix H (appendix__effect_of_stack_bolt.html) and equation 5 in transducer_design.html -- Don't specify if Young's modulus Y if for short circuit or open ckt. For purposes of discussion, does this matter? However, Y for short ckt is lower than for open ckt so is the relative bolt stiffeness to ceramic stiffness is higher at short ckt ==> open ckt is nominally better? Add topic "max allow elect field strength" [v/m] Couldn't find anything in Philips book. Check Vernitron blue booklet. Add topic "adding d-c bias to reduce piezo loss" Sonobond - theoretical advantage of expo front driver (no reflected energy --> find derivation of this) 11/Nov/2018 4:34 transducer_design.html Replaced all "ceramic" with "piezoceramic". Do same for all appendices. Needs ref link for Conap. Renumber figures. Request - The Design of High-Power Ceramic Transducer-Assemblies August 1969IEEE Transactions on Sonics and Ultrasonics 16(3):132- 135 DOI: 10.1109/T-SU.1969.29515 SourceIEEE Xplore Nicholas Maropis https://www.researchgate.net/publication/3456215_The_Design_of_High-Power_Ceramic_Transducer-Assemblies Al-Sarraf__'A_Study_of_Ultrasonic_Metal_Welding'_(thesis_2013).pdf "A high power ultrasonic transducers was designed by Muhlen [46] whose design was based on the use of piezoelectric rings to produce high power." p. 19 [46] = S. S. Muhlen, "Design of an Optimized High-Power Ultrasonic Transducer," Ultrasonics Symposium, 1990. Proceedings., IEEE 1990, vol. 3, pp. 1631-1634, 1990. "Another study of high power ultrasound used in ultrasonic cutting and welding of thermoplastic textures was presented by Silva [50]. The FE analysis was used to predict the vibration amplitude for the wide blade horn through simulation. It confirmed that the electrical impedance was reduced due to the increase in the number of piezoceramic discs. However, the vibration amplitude was observed to be non-uniform along the horn working surface." p. 20 Effect of xdu on horn f - Power supply considerations Bandwidth (Q) In some cases the Q is so high that the PS has difficulty locking onto the resonance. Therefore, desireable to reduce Q (increase bandwidth). Use conical back driver. Xdu fp-fs determined by what? Dave Grewell Iowa State University North Dakota State University (NDSU) as of 8/1/2018 Fargo, ND Grewell, David - 'High Power Ultrasonics'.pdf Tips - used for high wear applications (inserting, glass filled staking) (slide 35) Xdu power vs f graph - est. 3500 W continuous @ 20 kHz (slide 48) Cavitation & liquid processing - slides 49-69, 116-117 Radially resonant ing resonators for continuous processing - slides 68-69 Metal welding - image for rotary system (slide 82) Defloming - pusonics.es (slide 92) Branson ceramic dims -- 500 series -- 2.0 (50.8mm) OD x 0.8 (20.32mm) ID x 0.2 (5.08mm) thick (FEA\Branson\Convertr\502\X5z32kx.3dm) Vol 1 ceramic = 8649 mm^3 = 8.649 cm^3 Vol 6 ceramics = 51893 mm^3 = 51.893 cm^3 Back driver -- FEA to see if steel and tungsten give better static stress across ceramics. These mats are stiffer but will also tune shorter. Shorter tuning has other advantages (e.g., freq separation)? 2018-07-21 -- Fig 25 (Comparative machinability of frequently used stainless steels and their free-machining counterparts) no longer used. Now in steel_properties.html Tungsten - Mathieson[1], pp. 62-63 Roberts, Allan (Branson Ultrasonics) - US patent 5828156 (1998), 'Ultrasonic Apparatus' Uses the term "transducer" instead of "converter" Gives 20 kHz nominal performance as 20 microns (p-p) @ 930 volts, 3 kW max (column 4, lines 9-16) Balun system use - Riedl, Jessica Ann, "Process optimization: Ultrasonic welding of coextruded polymer film" (2013). Iowa State University. Graduate Theses and Dissertations. 13323. https://lib.dr.iastate.edu/cgi/viewcontent.cgi?referer=https://www.google.com/&httpsredir=1&article=4330&context=etd http://lib.dr.iastate.edu/etd/13323 Tableÿ2. Nominal ceramic properties at low electric field conditions Loss tan is given as %. Is this correct since values seem low (but are at low drive levels)? ADACHI Kazunari (http://yudb.kj.yamagata-u.ac.jp/html/476_ronbn_en.html) Influence of Static Prestress on the Characteristics of Bolt-Clamped Langevin-Type Transducers, Japanese Journal of Applied Physics, 37(5B) 2982-2987, 1998.05 Experimental Evaluation of the Static Strain on the Clamping Bolt in the Structure of a Bolt-Clamped Langevin-Type Transducer, Japanese Journal of Applied Physics, 47(6) 4736-4741, 2008.06 Development of Bolt-Clamped Langevin-Type Transducer with High mechanical Quality Factor for Excitation of Large Torsional Vibration, Japanese Journal of Applied Physics, 33(2) 1182-1188, 1994.02 Excitation of Uniform Flexural Progressive Waves on a Large Rectangular Plate, Proceedings of Ultrasonics International 91, 523-526, 1991.07 The stability of resonant vibration to temperature change in modal vibration control of large ultrasonic tools using wave-trapped horns, The Journal of the Acoustical Society of America, 88(5) 2291-2297, 1990.11 Modal vibration control of large ultrasonic tools with the use of wave-trapped horns, The Journal of the Acoustical Society of America, 87(1) 208-214, 1990.01 Modal Vibration Control of Large Ultrasonic Tools in High Amplitude Operation, Japanese Journal of Applied Physics, 28(2) 279-286, 1989.02 Modal Vibration Control of Elastic Systems Using Wave-Trapped Horns, Japanese Journal of Applied Physics, 27(27-1) 183-185, 1988.06 Modal Vibration Analysis of Ultrasonic Plastic Welding Tools Using the Finite Element Method, Proceedings of Ultrasonic International 85, 727-732, 1986.07 https://www.researchgate.net/publication/289073596_High-power_ultrasonic_transducers-A_designing_method_for_bolt-clamped_langevin-type_transducers_and_its_application (Adachi) Analysis of screw pitch effects on the performance of bolt clamped Langevin type transducers, The Journal of the Acoustical Society of America, 2004.09 https://www.researchgate.net/publication/239646254_Analysis_of_screw_pitch_effects_on_the_performance_of_bolt-clamped_Langevin-type_transducers (Adachi) Bolt-clamped Langevin-type transducers (BLTs) are common vibration sources in high-power ultrasonic applications such as ultrasonic plastic joining. In this paper, the authors propose a low-aspect-ratio BLT shape based on numerical solutions of a complex elastic contact problem concerning the bearing stress (prestress) imposed on the interfaces between the parts by clamping with the screw bolt. The prestress distribution at the interface has significant influence on the mechanical quality factor (Q) of the BLT. It is found that the screw pitch of the clamping bolt heavily affects the prestress distribution in the simulation using the finite element method. The newly developed BLTs with a high resonance frequency of approximately 80 kHz has a relatively wide radiating face and sufficient volume ratio of the piezoelectric elements that convert electrical energy into mechanical energy. The average of their measured Q values exceeds 1000 despite their high resonance frequency when they are driven at a voltage higher than 17 V rms. Elastic contact problem of the piezoelectric material in the structure of a bolt-clamped Langevin-type transducer., The Journal of the Acoustical Society of America, 105(3) 1651-1656, 1999.03 https://www.researchgate.net/publication/243524441_Elastic_contact_problem_of_the_piezoelectric_material_in_the_structure_of_a_bolt-clamped_Langevin-type_transducer (Adachi) Bolt-clamped Langevin-type transducers (BLTs) are widely used in various fields of industrial application of high-power ultrasonics. One of the most crucial points in designing a transducer of this type is estimation of the bearing Stress imposed by clamping on the interface between the metal block and the piezoelectric element. This prestress, which compensates for low tensile strength of the piezoelectric materials used, must be larger than the dynamic vibratory stress at the interface between the components in high- amplitude operation. Precise estimation of it is virtually impossible, owing to an intricate elastic contact problem. However, with the use of the unique finite-element-analysis system developed by one of the authors, approximate solutions of the problem have been obtained. A BLT design based on the results of the prestress calculations is proposed. The results of its experimental verification have also been reported. (http://asa.scitation.org/doi/abs/10.1121/1.426704) SPS book, p. IX-8 "However, while the torque can be measured with a high degree of accuracy so many factors affect this method that in the average case clamping force can vary as much as +/- 25%." Alignment during assembly Use internal rigid PTFE tube that just clears stack bolt OD and ceramic ID. Tube fits into recesses in front driver and back driver. Tube also serves as insulator to stack bolt. George Bromfield - vacuum exoxy to close ceramic gaps. See if Morgan Matroc (now CeramTek?) has following in pdf - Guide to modern piezoelectric ceramics Piezoelectric technology data for designers Define PZT - "'PZT' is a registered trademark of Vernitron Corporation, formerly Clevite Corporation" (footnote p. 94) (https://books.google.com/books?id=wMbAK4Zv0vQC&pg=PA94&lpg=PA94&dq=pzt+vernitron+trademark&source=bl&ots=-hc6SKxwnr&sig=Juiwnv5_xLUIAofY5jRvw7JJDMw&hl=en&sa=X&ved=0ahUKEwj1t96X8ZPMAhXJ2T4KHagiBXYQ6AEILDAC#v=onepage&q=pzt%20vernitron%20trademark&f=false) Trademark search (United States Patent and Trademark Office) doesn't indicate that this is currently active (abandoned?). PZT mat props (for FEA) delpiezo.com Hampton (p. 32, appendix A) Morgan Matroc? Flow-thru designs Autoclaving (medical) Ageing - Burn-in Amplitude change Power - delPiezo.com shows tan-delta vs temperature. Some compositions are better than others ==> http://delpiezo.com/yahoo_site_admin/assets/docs/DL-45HD_K-T_dependence.106102124.pdf flat to ~140C but http://delpiezo.com/yahoo_site_admin/assets/docs/DL-43_K-T_dependence.1112830.pdf starts increasing significantly around 100C. Claims that DL-45HD (equiv Morgan PZT404) can handle at least 2x power of DL-43 (equiv Morgan PZT810). - Jones patent, p. 14 - shows power calc based on SWR (standing wave ratio) of 3.5 for metal welding. - Calc max continuous power for Branson 500 xdu based on allowed power/vol of ceramic Fig 9 (DeAngelis) - d33 increases with increasing static stress. However, Morgan TP-220 fig. 6 shows opposite for high temps. Also see Morgan TP-220 fig. 7. Rosenthal, Felix, p. 254 (my photocopy) - "Another interesting observation shown by the equations (not given in this presentation) is that the sound velocity in the piezoelectric medium for the d33 case is that corresponding to the compliance at constant electric displacement, and for the d31 case is that corresponding to the compliance at constant electric field. This velocity is independent of the boundary conditions. The well-known difference in resonant frequency between an open and short circuited piezoelectric bar is thus accounted for by different boundary conditions to be satisfied by the wave equation, but not by any difference in sound velocity within the material." --> Compare to Cady comments permittivity1_dict.html Nominal pzt dims - http://delpiezo.com/yahoo_site_admin/assets/docs/Nominal_size_and_tolerance.254654.pdf Miodrag table Thickness/number of pzt - Parallel -- t limited by max allowed electric field strength Series vs parallel - Q --> look at phase change eqn; quicker phase change as move slightly off resonance (series vs parallel) ==> higher Q Piezo material cross-references http://delpiezo.com/yahoo_site_admin/assets/docs/Cross_Reference_of_Material_Chart.36194230.pdf http://www.sparklerceramics.com/materialcross.html http://bostonpiezooptics.com/equivalent-ceramic-materials Miodrag - Ceramic temperature - "For welding transducers (when operating continuously in air) the piezoceramic temperature should not be higher than 50øC to 60øC (measured after very long time)." p. 4.4-4 Max current - p. 4.4-4 Tuning inductor - p. 3.3-2, 3.3-8 Difference between low f PZT capacitance and PZT capacitance at resonance - p. 3.3-7 "In most of cases of high quality piezoceramics we can neglect Rop as too high resistance, and Ros1, Ros2, as too low values, but we should also know that dielectric and resistive losses are becoming several times higher when converter is driven high power, in series or parallel resonance, comparing them to low signal measurements." p. 1-2 Insulation - p. 6-17 (blue font, may be from me) Mechanical branch losses - "The other dissipative power losses (R1 and R2) are belonging to the mechanical circuit branch and come from converter joint losses, from planar friction losses between piezoceramics and metal parts, from mounting elements and from material hysteresis-related losses (internal mechanical damping in all converter parts)." p. 1-4 Conformal insulation coatings - The following coatings have been suggested by Piezokinetics? Conap (Branson) Humiseal (see Butler, John L. - 'Piezoelectric ceramic mechanical and electrical stress study', p.ÿ1915, 1st paragraph, Smith) (contact Kenneth Rolt, co-author) Hysol (in patent) Paralyne - vapor deposited so covers all exposed surfaces; some surfaces must be masked (transducer face, face threads). Suitable for high volume production. Prokic - high temperature and high breakdown-voltage (p. 6-8) Housing - Antirotation Spirol pins Engaging teeth or flats Le Blanc - 'Dynamic Nonlinearities in Piezoelectric Sonar Ceramics' - "Initial measurements indicated that Navy Type-I ceramic materials from different suppliers differed substantially in output strain level (a 14 percent difference in strain amplitude for dimensionally similar rings at 8 kV/m) and fracture strength as well as in the onset and degree of nonlinear response." p. 3 DeAngelis__'Optimizing_piezoelectric_stack_preload_bolts_in_ultrasonic_transducers'_(2014).pdf From a static standpoint, the preload screw configuration should provide a uniform stress distribution over the piezoceramics to utilize this active material most efficiently; both the electromechanical coupling and maximum drive level are degraded with non-uniform stress (Woollett, 1957). (p. 13) R. S. Woollett, "Transducer Comparison Methods Based on the Electromechanical Coupling-Coefficient Concept," 1957 IRE National Convention, p. 23-27, IEEE Xplore. ==> I have this article but can't find any ref to ceramic uniform stress distribution. DeAngelis[2] "Optimizing Piezoelectric Crystal Thickness in Ultrasonic Transducers" - "To avoid unnecessarily complicated modeling of the joint interfaces and piezoelectric losses, a constant damping ratio (global) of 0.2% was used for all materials. This ratio was correlated to the impedance and phase window of the experimental results for the baseline 1 mm transducer." "For optimization, find the thickness that maximizes k and Qm, but minimizes Qe." p. 6 Someone suggested that high-E electrodes that prevent radial movement of the ceramics could be beneficial -- increased coupling coeff? Measuring capacitance --> at high f where xdu can't vibrate? Measuring dielectric loss -- drive 2 xdus back to back in-phase so no vibration (no mechanical losses, only dielectric losses) "True" piezo props (series vs parallel) - permittivity1_dict.html - "So far as one can speak of the "true" dielectric constant of the piezoelectric crystal, the value at constant strain [\( K^S \)] is the proper one to use." (Cady (1), p.ÿ161) Wave speed is measured in adiabatic (constant entropy) condition (corresponds to open ckt) (https://en.wikipedia.org/wiki/Speed_of_sound#Speed_of_sound_in_ideal_gases_and_air) Equivalent ckts - Radmanovic xdu pdf - "A very descriptive analysis of the BVD [Butterworth Van-Dyke] models ... together with their advantages and disadvantages was given by Ballato[55]". p. 16. -- [55] A. Ballato, "Modeling Piezoelectric and Piezomagnetic Devices and Structures via Equivalent Networks", IEEE Trans. Ultrason. Ferroelect. Freq. Contr., vol. 48, no. 5, September 2001, pp. 1189 - 1240. [54] K.S. Van Dyke, "The Electric Network Equivalent of a Piezo-electric Resonator", Phys. Rev., vol. 25, no. 26, 1925, p. 896 Jayasundre - 'Ultrasonic Transducer Standards' - discusses Mason (effect of negative capacitance) & Stepanishen. Draper resonator thesis Chapters 1 - 3 Butterworth Van-Dyke Model starts on p. 26 The impedance eqn is given by eqns 3.17 & 3.21 (p. 27) Q is given in terms of fs (eqn 3.20) Chapter 4 - Eqns 4.13 - 4.16 (p. 37) allow fitting equiv ckt params to impedance graph (knowing fs, fp, Zs, Zp). Chapters 5 - 6 -- nothing of interest 502 xdu 502-20kHz-3-kW-drawings.pdf (Prokic) 502 SPECIFICATION.pdf (measured range of equiv ckt params Amplitude Reference & Power-1.pdf -- gives Prokic's est. of max xdu power based on ceramic vol. George Bromfield "Design Limitations of Langeven Transducers" Slide 4 - Bias stress = 20 MPa [2900 psi] Test equipment Amplifiers - Instruments Inc L6 Krohn-Hite 7500 Constant Voltage Amplifier http://www.krohn-hite.com/htm/amps/PDF/7500%20Manual.pdf http://www.krohn-hite.com/htm/amps/PDF/7500Data.pdf HP 4194A analyzer (note nonlinear transducer response, probably at high drive levels) Petosic - 'Method for Measuring Acoustic Power of an Ultrasonic Neurosurgical Device' -- Fig 3, p. 4 shows connection of power amplifier to HP 4194A. Slide 5 - "Useage temperature range is typically limited to 1/2 Tc [Curie temperature]" Slide 9 - Reserve Power Index (IEC 6147 [Ultrasonic surgical systems, measurements and declaration of basic output characteristic, 1998-1A]) Ratio Of Maximum Electrical Power to Quiescent Electrical Power A measure of How Much Extra Power is Available to Maintain a Constant Tip Excursion Amplitude Under Various Load Conditions Slide 16 - Ti 6Al-4V fatigue limit given as 390 MPa [57 kpsi] Piezo cyclic stress should be <= 35.9 MPa [5200 psi] to prevent heating Slide 18, footnote - "IEC 60601 - applied parts that have localized heating exceeding 41C [106F] must be assessed in risk management" Slide 19 - Equation for power loss in thin element (probably from wave eqn) Q from dumbbell experimental data PZT 4 Q = 250 PZT8 Q = 380 Slide 27 - PZT8 superior to PZT4 (criteria not specified) Test conditions (previous slides) - 26 kHz series resonance Ceramic temperature const at 41C keff const at 0.230 by adjusting horn output dia (slide 26) Books, Articles - http://www.alibris.com/Ultrasonic-Transducer-Materials-Don-Berlincourt/book/9145653?qcondhi=5 (Berlincourt, Mattiat) $25 -- I have this book? Adhesives (glues) Ritter, Catharine (Westinghouse Electric) - US pataent 4530138 (1985-07-23), 'Method of Making a Transducer'.pdf Corrugated electrodes with vacuum. Epon 28-V40 expoxy from Shell Oil heated to 70C to reduce viscosity (col 4, line 55) Claims narrower f bands and more uniform coupling coeff unit-to-unit variation but no specific data (col 4 line 34). Unclear if this comparison is to other glued ceramics or to dry ceramics. "A typical anti-arcing compound which is utilized includes a solid such as an acrylic resin in combination with a solvent such as toluene and trichlorethane ..." (col 1, line 48) Electrode = 0.006" thick (peak-to-peak after corrugation) annealed Ni with 0.0015" peak-to-valley corrugations (col 4, line 45) Bromfield__'Evaluation_of_Joint_Losses_in_Langevin_Style_High_Power_Transducers'.pdf Vacuum epoxy Bromfield_George__US_patent_20060066181A1_(2006)_'Transducer_Assembly'.pdf Lapping to 10 nm (pp 0011) Epoxy (pp 0012) Heats during operation --> softening the joints --> increased transmission losses Difficult to control the initial application thickness Crush washers (pp 0013) Material - soft enough to allow deformation during preload but hard enough that it doesn't flow, thereby allowing the precompression to be relaxed Al, Pb, Zn, Sn, gold (annealed to be dead soft); Al is preferred Expense of stack construction --> unsuitable for mass production Use adherent coating instead (pp 0015). Electroplated (pp 0021). Electroplating alloys (0023) Electrode mats - BeCu, Ni, SS, Monel, Ni-Fe alloy, brass, phosphor-bronze. BeCu is preferred. Water vapor (allowed in cooling air) ------------------- Transducer --------------------- O-rings http://www.theoringstore.com/index.php?main_page=page&id=7 70-durometer hardness should be used whenever possible as it offers the best combination of properties for most o-ring applications. The surface indentation or hardness usually does not bear any relation to the ability of an elastomeric part to function properly. Hardness is a measure of an elastomer's response to a small surface stress. Stiffness and compressive modulus measure the response to large stresses of the entire elastomeric part. https://www.parker.com/literature/O-Ring%20Division%20Literature/ORD%205700%20Parker_O-Ring_Handbook.pdf Parker O-Ring Handbook.pdf 1.7.8 Cushion Installation (p. 1-6) Such an application requires that the O-ring absorb the force of impact or shock by deformation of the ring. Thus, forcible, sudden contact between moving metal parts is prevented. It is essentially a mechanical device. An example is the use of an O-ring to prevent metal-to-metal bottoming of a piston in a cylinder. The O-ring must be properly held in place as otherwise it might shift and interfere with proper operation of the mechanism. p. 2-9 - table that compares properties of various elastomers 2.4.7 Modulus (p. 2-13) Modulus, as used in rubber terminology, refers to stress at a predetermined elongation, usually 100%. It is expressed in pounds per square inch (psi) or MPa (Mega Pascals). This is actually the elastic modulus of the material. The higher the modulus of a compound, the more apt it is to recover from peak overload or localized force, and the bet- ter its resistance to extrusion. Modulus normally increases with an increase in hardness. It is probably the best overall indicator of the toughness of a given compound, all other factors being equal. 2.4.11 Compression Set (p. 2-14) Compression set is generally determined in air aging and reported as the percent of deflection by which the elastomer fails to recover after a fixed time under specifi ed squeeze and temperature. Tensile Strength (p. 2-30) Determine the minimum tensile strength necessary for the application. Always take into consideration the inherent strength of the elastomers most likely to be used to meet the specification (most silicones have tensile strengths in the range of 34.5 to 62.1 Bar (500 to 900 psi); For shielding purposes against electromagnetic interference (EMI), compounds filled with conductive-particles have been developed with a volume resistivity of < 10-2 Ohm- cm. (p. 2-29) Polyurethane elastomers, as a class, have excellent wear resistance, high tensile strength and high elasticity in com- parison with any other elastomers. (p. 2-6) silicone elastomers as a group, have relatively low tensile strength, poor tear strength and little wear resistance. (p. 2-6) 2.4.4 Tensile Strength (p. 2-9) Tensile strength is measured as the psi (pounds per square inch) or MPa (Mega Pascals) required to rupture a specimen of a given elastomer material when stressed. Tensile strength is one quality assurance measurement used to insure compound uniformity. It is also useful as an indication of deterioration of the compound after it has been in contact with a fluid for long periods. If fluid contact results in only a small reduction in tensile strength, seal life may still be relatively long, yet if a large reduction of tensile strength occurs, seal life may be relatively short. Exceptions to this rule do occur. Tensile strength is not a proper indication of resistance to extrusion, nor is it ordinarily used in design calculations. However, in dynamic applications a minimum of 1,000 psi (7 MPa) is normally necessary to assure good strength characteristics required for long-term sealability and wear resistance in moving systems. -------------- E:\websites\usr\misc\references\articles\Parker Chomerics - 'Conductive Elastomer Engineering Handbook'.pdf Silver-plated-copper filled (1215) gaskets have the highest resistance to EMP type currents, showing no loss of conductivity even at 2.5 kA/inch of gasket (peak-to-peak). Pure silver (1224) and silver-plated-aluminum filled (1285) gaskets have less current carrying capability than silver-plated- copper materials, but are generally acceptable for EMP hardened systems (depending on specific EMP threat levels, gasket cross section dimensions, etc.). (p. 41); see graph 4-12 Corrosion on Al (p. 45) - (exposure to salt fog - p. 11) 6502 - 5* 1215 - 1* (out of 5) 1285 - 3* Material Hardness (Shore A) Tensile strength (MPa) [Table 5-3, p. 46) Compression set (%) 6502 68 1.03 30 1215 65 1.38 32 1285 65 1.38 32 Piezo-ceramics - Property dependence on boundary conditions - Similar to gas specific heat (amount of energy needed to raise 1 mole of gas by 1 degree C) --> depends if measured under const volume condition or const pressure condition (see "Elementary Classical Physics", vol. 1 p. 522) Poisson's ratio - Ewart, Lynn - 'Investigation of the Compressive Material Properties of PZT and PMN' Table 1 - An unpoled Navy Type III PZT designated EC-69 from EDO Corporation --> 0.43 +/-.02 A poled Navy Type III PZT designated EC-69 from EDO Corporation --> 0.44 +/-.06 (Appears to be short circuit --> "Once in place, copper tape was attached to the two inserts, and the resistance was measured to confirm that a short circuit existed." p. 6 Unpoled vs poled - Yu, Yao - 'Effect of Polarization on Mechanical Properties of Lead Zirconate Titanate Ceramics' PZT8 - Modulus of poled generally > unpoled (fig. 2). Direction of poling and short ckt vs open ckt unknown. Questions: - What is Young's modulus for depoled ceramic - open circuit modulus or short circuit modulus? - When the ceramic is short circuited, is any piezoelectric energy stored (e.g., during static compression)? If not, then short-circuit coupling coeff = 0 since no energy is transformed? However, Berlincourt evaluates the effect of the bolt for s33^E (short circuit modulus). - Effect of stack bolt -- in my eqn H13, which Young's ceramic modulus to use (short ckt or open ckt)? (Eqn was derived at open ckt.) - Effect of coupling factor on max power? - Relation of coupling factor to ceramic capacitance & num ceramics (based on freq separation)? - Philips impedance circle (p. 161, bottom) shows (in order of increasing f): - fa = f when input impedance looks totally resistive - fp = f when real impedance is max (some capacitive impedance) - fn = f of max total impedance - Philips admittance circle (p. 161, top) shows (in order of increasing f): (also see Berlincourt, p. 244, fig. 30) - fm = f of max total admittance - fs = f when real admittance is max (some capacitive impedance); fp > fa - fr = 1st f when input admittance looks totally resistive (resonance) - fa = 2nd f when input admittance looks totally resistive (antiresonance) - fp = parallel resonance - fn = f of min admittance - Short circuit resonance --> only mechanical resonance (i.e., omega = sqrt(1/(L C)). Same as series resonance? (Waanders p. 9 & Philips p. 159 define series resonance as omega = sqrt(1/(L C)). However, at this frequency there is still some current flow thru Co.) Same as "resonance"? There is actually a lower resonance that involves Co where the input impedance is purely resistive w/o short circuiting. What is this called? See Philips impedance circles p. 161. Piezo coupling coefficient kappa - Why can drop superscripts E and T (my eqns 7 & 8, Appendix G ) - Waanders defn. of k - eqn A8 (p. 84) (also Cady, p.759; Berlincourt, eqn. 30, p. 190) vs eqn. on p. 12 @ low f . - eqn. on p. 12 @ low f --> - xdu strain energy is only due to static expansion of ceramics (members attached to ceramics have no effect: back driver, front driver, booster horn). However, these have an effect when calc from ký = 1 - (fs/fp)ý (Waanders, p. 85, eqn A19a). Then, is this last eqn keff rather than k? - If low f then inertial effects ignored & doesn't matter where ceramics are located in xdu (at node or all the way at end). However, ký = 1 - (fs/fp)ý would be significantly different for these 2 ceramic locations. - Berlincourt - p. 190 - "The static coupling factor from Eq. 30 is therefore: k31 = d31/sqrt(eps33^T s11^E). In dynamnic systems the coupling factors are dependent upon the stress distribution and are in general less than the static ones because not all the elastic energy is dielectrically coupled." "A piezoelectric bar heavily mass-loaded has identical dynamic and static coupling factors, because in this case also all elastic energy is dielectrically coupled." "Piezoelectric coupling factors characterize a piezoelectric material better for power transduction than do the sets of elastic, dielectric, and piezoelectric constants ..." - p. 173 - k is "the fraction of dielectric energy that can be extracted as elastic energy and vice versa .." - For a mass loaded transducer: "The metal mass loads ar considered infinitely rigid, and it is assumed that the mass of the ceramic elements is negligible compared to the loading masses. all elastic energy is dielectrically coupled and the static and dynamic coupling factors are identical." p. 246 - Wollett - electromechanical coupling coefficient "Also, it is evident that its use is transducers .." (p. 1) [chevrons indicate italics] What does "passive" mean? "Practical definitions of the electromechanical coupling coefficient are given in terms of equivalent circuit parameters (Figure 1). These circuits apply generally to lumped constant transducers, but for distrubuted-constant transducers they are approximate and apply only to a single mode of vibration." (p. 1) - coupling coeff = "ratio of motional capacity to total free capacity" (p. 1) - Effect of stack bolt on piezo coupling coefficient -- when calc piezo stiffness, should use Y^E or Y^D? d (charge const) - - If have rod, then statically the displacement for a given voltage is the same regardless of where the ceramic is placed . However, at resonance the max ampl is achieved when the ceramic is at the node where stress is max rather than at the free end where stress is min. How to explain? (This is related to the coupling factor k since d is proportional to k.) http://piezo.com/tech1terms.html#d "At resonance, the dielectric constant will be reduced by the factor (1 - ký) where k is the coupling coefficient of the mode in question. " Why? (Also see Cady, p. 473, eqn 483 - "effective dielectric constant") - Cady, p. 397 "C1 is usually derived from measurement of the crystal capacitance at a frequency low enough for the crystal vibrations to be inappreciable, say at 1,000 chcles/sec. The quantity thus measured is, however, the capacitance of the free crystal (plus the effect of leads and mounting), and for precise results it should be diminished by a certain amount, in order to allow for the fact that the effective dielectric constant of the crystal when vibrating near resonance is less than that of the free crystal. This diminution depends on the type of resonator." Note: Berlincourt, p. 237: Co = (wt/l)î^T(1 - ký) = (wt/l)î^S - Jay Sheehan, Prokic - dynamic capacitance: xdu capacitance changes when horn is added? Clamped (static) capacitance -- best way to measure? (See permittivity1_dict.html) - From HP analyzer equivalent ckt. However, curve fit may not accurately model the actual performance. Also, only gives low-level value which may be inaccurate at high drive voltage. - High-level back-to-back xdus driven in-phase. If xdus are identical then no vibration is possible. Adv: drive at high level -- also gives xdu capacitive loss. Disadv: if xdus are not identical then some vibration may be possible so cap. of motional branch would be included. - Drive at very high f (per Cady) so that no appreciable mode is excited. - Adjust variable tuning inductor to get best performance (what does this mean?) under load -- then calc Co from equiv. ckt. Best performance might be determined when xdu temp rise is minimum. Xdu power - how to specify? (contact Karl Graff) "EIAJ AE 4006A-2001 Measuring methods of vibration characteristics of a bolt clamped Langevin type ultrasonic transducer" - $59 at http://www.go4the.com/141633-EIAJ-AE-4006A-2001.html Tradeoff between electric field strength E & mechanical gain --> if increase G then less E is needed. Lower E reduces dielectric losses due to lower tan-delta. Note: tan-delta is a nonlinear fn of E. Use Don Hansen / Ed Hallabeck method? Gotmare - Processing of the ceramic has great impact on its properties and performance of piezoelectric ceramics. Processing of ceramics mainly consist of forming a green body by mixing of metal oxide powders and then producing dense structure by sintering. The two most widely used methods for piezoelectric ceramics are sol gel processing and solid state synthesis. Sol gel process is expensive; it produces very fine high purity powders which can sinter at much lower temperatures to achieve densities close to theoretical value. Solid state synthesis is more common due to its lower cost. Density is very important to achieve good piezoelectric and dielectric properties in a piezoelectric ceramic. In general bulk density of the ceramic after sintering should be more than 95% of theoretical densities. Processing parameters like milling time of the powders before and after calcinations and sintering time and temperature plays vital role in producing high density materials. (p. 19) General understanding was that, fine grain microstructure leads to significantly higher dielectric constant and remnant polarization and a much lower coercive field with slight improvement in piezoelectric constant. Recently Randall el al. 1998 studied the effect of grain size on the dielectric and piezoelectric properties of PZT.9 Results show that ferroelectric transition temperature is almost independent of grain size, dielectric constant K, piezoelectric coefficient d33 and d31 and electromechanical coupling coefficient kP and k31, remnant polarization PR decreases and coercive field EC increases with decrease in grain size. (p. 20) In order to minimize the thermal degradation, maximum application of piezoelectric materials is generally restricted to ?« Tc.[52,46] (p. 20) Aging is a process for a system to reach to an equilibrium state from a non-equilibrium state. More precisely aging can be defined as the spontaneous change of a material property with time, under zero external stress and constant temperature.[56] (p. 20) aged samples show lower dielectric constant, tanë, and electromechanical coupling factor, when mechanical quality factor and resonance frequency become higher (p. 20) Literature - https://www.researchgate.net/publication/258248496_Defining_the_coupling_coefficient_for_electrodynamic_transducers ------------------------------------------------------------------------------------- - Branson 500 c'bored stack bolt at front to reduce stress on Al front driver. - Branson 10k xdu - necked stack bolt dia to reduce thd failures - Mg front driver --> galvanic corrosion (see Elektron info) - Electrode & ceramic plating - Thickness? - Need to avoid edge buildup (like chrome plating) --> would cause non-flatness - Surfaces (flatness, finish) - Tierce, "Design of High Power Ultrasonic Transducers for Use in Macrosonics" (from Hamonic (ed, my book), Power Sonic and Ultrasonic Transducers Design) briefly discusses flatness (p. 202) - Difference between low-drive & high-drive piezo properties - "It should be noted that at high drive levels QE and Qm0 can no longer be treated as constants -- they are then often much lower than the low drive-level values." Waanders, p. 42 PZT4 vs PZT8 - PZT4 has higher dielectric const. Advantages (higher bandwidth?, higher coupling factor?) See my transducer_1b.html table. - Electrode plating - - Waanders p. 90 - Ni - vacuum-evaporated, 0.2 - 0.5 microns thick - Ag - burnt in silver paste, ~5 microns thick Electrode wires - Branson uses stranded Ni - Max power - Prokic (p. 4.4-5, 5-8) - Table T.1 (all at 20 kHz) - Continuous operation: 30W/cm^3 - Pulsed (50% duty cycle): 60W/cm^3) - Effect of temperature - Waanders p. 90 PXE41 - 1 hour at 200C: keff -10% - 1 hour at 280C: keff -20% - Prokic "Continuous and safe operating temperature of modern (PZT) piezoceramics (in ultrasonic cleaning) should be lower than 100øC (sometimes up to 120øC, for high temperature resistant piezoceramics), depending of water temperature in ultrasonic tank, but always lower than 150øC (for the best piezoceramics, found on the market at this time). It is recommendable to operate ultrasonic transducers on a lowest possible temperature. For welding transducers (when operating continuously in air) the piezoceramic temperature should not be higher than 50øC to 60øC (measured after very long time). The continuous operating temperature of piezoceramics can be measured using remote non-contact temperature infrared (laser beam) thermometers (directing the laser beam to the ceramics area)." 4.4-4 "Operating temperature of piezoceramic elements (in any operating regime) should be lover as possible (we can say between 20øC and 60øC is preferable situation, but in any case, for continuous and very long operation, no more than 90øC). If piezoceramics in operation reach temperatures between 150øC and 180ø, efficiency of transducer will drop significantly." p. 4.4-6; also 5-8 - My table comparing PZT4 & PZT8 - max temps are 165C & 175C respectively. Are these w/o prestress? (Prestress lowers the Curie temp.) - Need graph showing effect of temp on PZT8 props. (e.g., d33) - See graph in morgan3 for PZT8. Effect of prestress pressure - - Prokic - "Also: 1ø, as the prestress increases, the Curie temperature decreases; 2ø. Piezoelectric-Converters-Modeling-and-Characterization.pdf (p. 6-2) - Pressure impedance tests currently run at series resonance --> optimum when impedance is lowest. If run at parallel resonance then optimum should be when impedance is highest? Which tests are most sensitive (series or parallel)? - Hulst - need "clean" pdf for upload - Hulst's reference 8 - Mori, "Measurement of large amplitude vibrational characteristics of ultrasonic power transducers" (1968) - Wuchinich - email discusses prestress? - Prokic suggests sample testing by retorquing. Torque using torque wrench or d33? (Note: d33 changes due to prestress and age. d33 increases with age (Berlincourt fig. 19) and varies with prestress (Berlincourt fig. 17) --> 'Behaviour of Piezoelectric Ceramics under Various Environmental and Operation Conditions') Note: since d33 varies with prestress, using free d33 to predict the applied preload isn't entirely accurate. Stack bolt - I have a patent (besides Hulst) where the bolt is resonant. - DeAngelis - gives preferred f separation for bolt resonances - E:\Write\_Design\Transducers\Misc articles & books\Prokic\Piezo-transducers-FEM+characterization\An approach to design a high power piezoelectric ultrasonic transducer.pdf - Shows a cone of force at 45 degrees based on Charles Mischke's empirical criterion(p. 374). E:\Write\_Design\Joints & studs\Temitope - 'Condition Monitoring of Bolted Joints'.pdf - extensive graphs & discussion of interface force as a fn of bolt head dia, part thickness, etc. Hampton questions - - static bolt elongation 10 times greater than the total change in length during vibration (pdf p. 28). Reason? - Ti-6Al-4V Poisson = 0.334 (from where?) (pdf p. 43) - Appendix A. Props adjusted for 7500 psi preload (pdf p. 93). However, graphs (pdf p. 57+) show 70 - 80 MPa (10.0 kpsi - 11.6 kpsi) -- why such high prestress? - Preload = 44 kN (pdf p. 85) - A rule of thumb when designing ultrasonic transducers states that arcing will occur between 11-13 kilovolts/inch or 433-512 volts/mm [15]. ([15] = J. Sheehan, Converter Basics, Converter Materials, Converter Design Process Presentation, Iowa State University, (March 2010), Unpublished work) - FEA - used sliding elements when analyzing prestress. Significant difference if had just used rigid contact? - Ref. 15 "J. Sheehan, Converter Basics, Converter Materials, Converter Design Process Presentation, Iowa State University, (March 2010), Unpublished work" http://asa.scitation.org/doi/abs/10.1121/1.1777852 Back driver cone shape - - Look for other articles by Puskas (CAE Blackstone~Ney). Check Puskas patents. Change - "Stack bolt" --> "bias bolt" per Johnson patent or prestress bolt (since "stack" refers to entire U/S stack) Electromechanical coupling - - See DeAngelis, "Optimizing Piezoelectric Crystal Preload in Ultrasonic Transducers", p. 3 - See Woolett, esp. fig 2 for eqns. - See Waanders - explain k for single thin ceramic vs keff for entire xdu. Also, keff for xdu made entirely of ceramic where ceramic at antinodes is ineffective & therefore overall k is reduced. - Relate to bandwidth and ceramic capacitance - Lierke - Langevin xdu: "... the mechanical prestress can enhance the electromechanical coupling ..." (p. 935) - keff should not be taken to indicate the available power --> depends on (fp - fs) but this freq difference will change depending on the horn, even the power of the transducer doesn't change. Series vs Parallel resonance - - Prokic 3.2-6 "... the loading interval of a converter operating in parallel resonance is much wider (and acoustically much different) than the loading interval of a converter operating in series resonance. From mechanical quality factors changes in the function of water loading (Fig. 16.5) we conclude that for low and moderate loads, it is more convenient to operate in parallel resonance (since Qm2 > Qm1), and for heavy mechanical-load situations, series resonance becomes more favorable operating regime (since Qm1 > Qm2)." Using a bell horn (3.2-1). Data from impedance plots. - See "Mathieson - 'Nonlinear characterisation of power ultrasonic devices used in bone surgery' (thesis, 2012).pdf", p. 56 (favors parallel resonance; refers to article by Hirose "High power characteristics at antiresonance frequency of piezoelectric transducers" [192]) - If ceramic dia is limited to ~1/4 wavelength then parallel resonance allows larger dia ceramics due to higher wave speed. Offset ceramics - - Allan Roberts, Jay Sheehan, US Patent 6,434,244 B1 - "In many prior designs, it is not uncommon to excite third harmonic motions within the converter. These third harmonics typically occur in the mounting flange or in the back driver of the converter. Such harmonic motions produce no useful work and contribute to localized losses and temperature increases." (p. 3) - Check out the referenced Cunningham patent 5,590,866 (prior art) - booster & xdu rigid mounting Questions for Lierke - - For the xdu of figure 4, 5, & 6 - what is the passive material (see fig 5)? Unpoled PZT? What modulus (short ckt or open ckt)? To duplicate - what are all mat props? - Results would be different if passive material were Mg vs W. In these cases, Lpiezo/Ltotal would be different for the same Lpiezo. - Mechanical Q - includes dielectric effects? What dissipation factor used? - Fig 5 - determined theoretically (what is eqn?), by impedance matching, or by FEA? "To understand the basic behavior of piezoelectric elements and their coupling to their environment, simplifying models can be helpful. For example, the electromechanical characteristics of a bolted Langevin transducer, which is driven in its longitudinal resonance, can easily be modeled by using a mechanical mass-spring-damper system or an equivalent electronic circuit. If the vibration shape is to be investigated, an off-resonance drive is wanted or higher harmonics should be included, one-dimensional continuum models are still sufficient. The mathematical background for such a kind of modeling is given in e.g. Ref. 11." p. 935 D. A. Berlincourt, D. R. Curran and H. Jaffe, Piezoelectric and Piezomagnetic Materials and Their Function in Transducers (Academic Press, N. Y., 1964) - Fig 6 - what is the eqn for Q? Q includes both dielectric and mechanical loss? Of both the piezo & passive materials? "For high-power applications, e.g. plastics welding, the piezoelectric material should cover one third of the /2-transducer in the middle of the transducer." p. 937 http://www.americanpiezo.com/products_services/stack_actuators/principles_stack_ring.pdf (2010). Amplitude - - If the ceramics induce a certain level of strain then will the front driver or back driver materials affect the amplitude, assuming that their wave speeds remain unchanged. Analyze with CARD or FEA. See Neppiras3, figs 5 & 6; also, discussion at top 2nd column p. 298 - What is the effect on amplitude if the ceramics are moved away from the node, assuming that they are always driven with the same electric field strength? - How does a short vs long ceramic stack (number of ceramics) affect the amplitude, assuming all ceramics have the same thickness & nodal ceramics have the same strain? - Make back driver dia larger than ceramics for +amplitude & better stress distribution? (I have an article - Morgan or Clevite?.) - Use Piezotran? Other free software? Assembly - - Prokic p. 6-5+ Other references - - R. S. Woolett, Scientific and Engineering Studies : Section II The Longitudinal Vibrator, Naval Underwater Systems, Newport, Rhode Island, pp 66 - 79 (per Prokic paper "The Ultrasonic Hammer Transducer") Also, Hulst reference (I can get Prokic's copy?). - Need Mathieson's Ph. D. thesis "Nonlinear characterisation of power ultrasonic devices used in bone surgery" --> list in references "However, studies of power ultrasonic devices have reported that the width of the hysteretic region can be significantly influenced by elevated piezoceramic element temperature and joint preloading in ultrasonic devices [19]. " mathieson2, p. 1131 - What joint preload used? "It can also be assumed that joint preloading in the piezoceramic stack did not significantly vary for the different piezoceramic stack locations." p. 1131 - Pulse waveform - see Waanders, fig 6.23a Nonlinear behavior - "Through experimental characterisation it has been observed that the tuned devices under investigation exhibited; resonant frequency shifts, jump amplitudes, hysteretic behaviour as well as autoparametric vibration. The source of these behaviours have been found to stem from device geometry, but also from heating within the piezoceramic elements as well as joints with different joining torques." matheison1, p. ii - See Cardoni, pp. 9-10 (pdf p. 28 - 29) - "The detection and characterisation of the nonlinear vibration behaviour of single- and multi-component ultrasonic tools usina ESPI and LDV were also investigated by Lucas and Graham [8,9]. In these publications the importance of identifying in-plane responses via ESPI was demonstrated by the measurement of jump phenomena, frequency shifts, and hysteresis cycles, typical features of nonlinear systems." Cardoni, p. 23 (pdf p. 42) - "The nonlinear response characteristics of systems were also determined. Ultrasonic transducers are inherently nonlinear at high power and tend to exhibit cubic softening characteristic, with a jump phenomenon typical of a Duffing oscillator. To find a practical design solution to the effects of nonlinear responses, it was first necessary to measure the linear regime and nonlinear response at a range of input voltages to the transducer. The effect on this response of attaching different tuned components was assessed, as well as the attachment method. It was found that some tuned components, including some wavelength blades and block horns, tended to reduce the softening response when attached to the transducer and result in the system increasing its linear threshold, and operating with a near linear response. In other cases, including half-wavelength blades, the blade-transducer system response was softer than the transducer alone, had a lower linear threshold and wider instability region. A bank of information on the nonlinear characteristics of transducers, bar horns, and blades had been obtained, providing valuable data for understanding serially-coupled multi-component system configurations which assist the control of the nonlinear response in the design of ultrasonic devices. Additionally, the width of the instability region could be manipulated by altering the tightness of joints and by altering the position of the stud between attached components." Cardoni, p. 178 Search Mathieson & Cardoni for "autoparametric". Amplitude saturation: Cardoni, p. 11 (pdf p. 30) Bleed resistor - to discharge xdu due to temperature rise.