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| 1 catalog #3, 1998 custom design and engineering product development 2 products electronics piezo linear amplifier 4 piezo switching amplifier 6 proportional voltage booster 8 dc to ac inverter drive circuit 9 motion instruments linear motion heavy duty piezo vibration table 10 2 - axis, linear positioner, 200 ? 12 2 - axis, linear positioner, 1 ? 14 angular motion 1 - axis, mirror tilter, 0.75 16 2 - axis, mirror tilter, 1.5 18 ultrasonic rotary motion ultrasonic rotary motor & driver 20 acoustic sources lightweight acoustic source 22 fans and resonators piezoelectric fan 24 piezoelectric resonant blade element 25 piezoelectric chopper 26 design and prototyping piezoelectric motor/actuator kit 27 piezoelectric generator/sensor kit 28 piezo design aid software diskette 29 transducer elements low voltage piezoelectric stacks 30 piezoceramic bending elements 32 piezoceramic single sheets 42 solder / flux kit 46 piezoceramic application data introduction to piezoelectricity 47 motor transducer relationships 50 generator transducer relationships 51 typical thermal properties of piezoceramic 52 table of contents p iezo s ystems ,i nc . 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com service and warranty : all piezo systems, inc. products are warranted against defective materials and workmanship. this warranty applies for a period of time of one year from the date of delivery to the original purchaser. any instrument or part that is fou nd within the one year period not to meet these standards, will be repaired or replaced. no other warranty is expressed or implied. note : prices and specifications subject to change without notice.
2 p iezo s ystems ,i nc . 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com catalog #3, 1998 custom design and engineering fea modeling 2 - axis rotational positioner high frequency tuning fork pr pr oduct development oduct development piezoceramic actuator design is based on customer speci- fications which include as a minimum: n motion and force requirements n space available n voltage available n stability n thermal operating range n frequency operating range n response time customer specifications using extensive computer software and experience, piezo systems inc. can move directly from your specifications to a complete optimized design.the actuator geometry, elec- troactive material, internal lamination, polarization, elec- trode configuration, mount, power take-off, and produc- tion process is designed to ensure repeatable and reliable performance. piezo systems inc. can also design and build the electronic system which drives the actuator and fabricate (or mold) the structure to which the piezo actuator is mounted. actuator & system design piezo systems inc. offers a phased development program for custom device and product development. our experi- ence allows the elimination of potential design flaws which plague those unfamiliar with piezoceramic technol- ogy, especially in the areas of lamination bonding, flexure design, ceramic stress and fatigue criteria, thermal stabili- ty, mounting, power take-off attachments, electronic drive, testing, and evaluation. this service reduces the customer s need to dedicate highly qualified personnel during the development period, and development time is typically reduced from years to months. financial and technical risks are minimized. the following phases are quoted on a fixed price basis: n analysis and design phase: communication of specifi- cations, analysis, and optimized design of actuator. n prototype phase: samples built to specification. n pre-production phase: pre-production samples for exhaustive testing. n production phase: production pieces at desired volume. phased development program 3 catalog #3, 1998 custom design and engineering areas of exper areas of exper tise tise piezo systems offers consultation on an hourly, daily, weekly, and monthly basis. consulting & analysis combined with proprietary processing techniques, piezo systems works closely with a network of highly specialized vendors. as a result piezo systems is capable of supplying highly sophisticated single parts or hundreds of thousands of parts per year. production piezo systems?proprietary bonding process and ceramic quality testing program leads to consistent performance, high-strength, thermally stable, void free laminations. our advanced cutting techniques produce actuators with dimensional tolerances within ?001 inch if necessary; widths as narrow as .020 inch; chip free edges; non-linear shapes; and contamination free surfaces. piezo systems ships parts to performance specifications, not merely to dimensional tolerance. our bending actuators are employed in piezo valves, choppers, modulators, fans, tunneling microscopes, and soil testers. our bending sen- sors are used in implantable pacemakers and industrial equipment. bending actuators & sensors resonant devices are an effective way of achieving high periodic motion at low voltage and power. products designed to operate at a single frequency require special attention be paid to shape uniformity, material consisten- cy, and process control. a careful balance is sought between minimizing strain on the piezoceramic and maxi- mizing the dynamic amplitude. energy losses due to inter- nal dissipation, external attachments, and output loading are addressed. resonant devices ultrasonics resonators bending elements resonant devices resonant devices ultrasonic devices ultrasonics, a special portion of the resonant spectrum, find extensive use over a wide range of application areas. these devices are designed according to the same princi- ples guiding resonant devices. however, additional consid- eration is given to amplitude stability, power consumption, over-heating, resonance tracking, and electronic drive. piezo systems has developed a monolithic construction which eliminates many of the problems associated with precompressed bolt together systems. electronics p iezo s ystems ,i nc . 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com piezo linear piezo linear amplifier amplifier piezo linear amplifier, 200 vp/200ma (115 vac, 60 hz) epa-102-115 $2,399 piezo linear amplifier, 200 vp/200ma (230 vac, 50 hz) epa-102-230 $2,399 ordering information part no. price piezo systems offers a single channel high frequency ampli- fier for driving a variety of piezo actuators, including stacks, bimorphs, and single sheets. the ability of an amplifier to drive a piezo device statical- ly is determined primarily by the voltage level and stabili- ty. its ability to drive a piezo device dynamically is deter- mined by the capacitance of the actuator, the voltage to which it must be charged, and the number of times it must be charged and discharged per second.these establish the current, voltage, and frequency requirements of the ampli- fier. the epa-102 is a high voltage ( 200 vp), high current ( 200 ma), and high frequency (dc to 300 khz) amplifier designed to drive higher capacitive (low impedance) loads, such as low voltage stacks, at moderate frequencies or lower capacitive loads, such as ultrasonic devices, at high frequencies. lo w electrical noise , lo w distor tion: the amplifier is made with a high quality apex?high voltage hybrid operational amplifier, and utilizes high regulation linear power supplies. they are housed in a heavy high conduc- tivity aluminum case which provides an excellent shield from external electromagnetic interference. input and output pr otection: piezo loads present special problems to electronic drivers. the epa-102 provides heavy input and output protection to take care of all shorting, turn-on, turn-off, and load generated voltage occurrences which can damage either the amp or your actuator. man ual bias contr ols (p olarity and dc offset): useful for making manual adjustments of drive voltage to verify piezo actuator static motion, for static setting, or for applying dc bias to dynamically driven piezo actuators such as piezo stacks. external contr ol (via analog signal to the bnc input con - nector): accepts up to 10 vp signal waveforms from external signal generators, computer controllers, or feed- back networks from dc to rated frequency. the com- bined ac plus dc offset voltage is adjustable from zero to the maximum rated voltage. description piezo amplifier model 80.102 piezo systems, inc. cambridge, ma power off on dc polarity 0 + dc offset voltage input 10 v max caution high voltage ouput 200 volt 200 ma 12 (305) sq 5 (127) 4 catalog #3, 1998 electronics specifications electrical maximum voltage ?00 volts peak maximum current ?00 ma peak output power 40.0 watts peak frequency range dc to 300 khz bandwidth into 1 k resistive load . . . . flat: dc to 275 khz 3db roll-off: 350 khz into capacitive load . . . . . . see chart below voltage gain fixed at x20 slew rate (no load) 180 volts / ?ec maximum input voltage ?0 volts peak maximum dc component ?0 volts dc input coupling direct dc coupling only input impedance 10k ohm output coupling dc coupling variable dc offset normally zero volts. adjustable to volts peak load impedance capable of driving any load within the voltage and current limitations of the amplifier. load power factor 1 to 0, leading or lagging ac power source 115/120vac, 50/60 hz or 230/240vac, 50/60 hz circuit protection overload short circuit mechanical controls power switch; dc polarity (+,0,-); dc offset level terminals bnc for input; binding posts for output weight 16 lbs. dimensions 12?l x 12?d x 5?h epa-102 piezo linear amplifier 10 10 10 10 10 1 23 4 5 c = 10 f c = 1 f c = .1 f c = .01 f c = .001 f 10 0 10 6 0 25 50 75 100 125 150 175 200 frequency (hertz) volts peak peak voltage delivered to capacitive load at peak current rating as a function of operating frequency (steady state sinusoidal waveforms; temperature = 25 ?) 5 catalog #3, 1998 electronics p iezo s ystems ,i nc . 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com piezo switching piezo switching amplifier amplifier l l ightweight ightweight - e - e nergy nergy e e fficient fficient - c - c omp omp a a ct ct piezo switching amplifier, 180 vp/?00ma (115 vac, 60 hz) esa-208-115 $1,799 ordering information part no. price description piezo systems inc. dc offset input out gnd model esa-203 + polarity power 7.4" (188) 2.7" (69) 9.6" (244) 0 over current reset the esa-208 achieves its flat response and wide band- width by employing a unique technology which is patent pending. it is the first of its kind to be offered for sale, and demonstrates concretely a future trend in miniatur- ization for high voltage power circuitry that will open up new practical applications for piezo actuators. the esa-208 is a lightweight (3 lbs.), compact (7.4? x 2.7? x 9.6?), high voltage ( 180 vp), high current ( 500 ma), and audio frequency (dc to 5 khz) amplifier designed to drive high capacitive loads, such as low volt- age stacks, at moderate frequencies or low capacitive loads, such as acoustic sources, at high frequencies. principle of operation: the input signal to the amplifier is converted into a train of width modulated pulses. the polarity and duration of these pulses alternately control the turn on and turn off of two (high and low) high volt- age power switches operating at 200 khz. the high fre- quency carrier is filtered out to pass the audio signal. high cur r ent ca pability: a typical linear amplifier achieves voltage control by intelligently adjusting the resistance value of the output stage which is in series with the load. if the load draws .5 amps, all that current must flow through the output stage resistance and be turned into heat. by contrast, the switching amplifier has an out- put stage which is either fully on of fully off (never in between), and so is capable of metering out far higher currents for the same size circuit with a minimum of heat loss. input and output pr otection: piezo loads present special problems to electronic drivers. the esa-208 provides input and output protection to take care of turn-on, turn- off, and load generated voltage occurrences which can damage either the amp or your actuator. man ual bias contr ols (p olarity and dc offset): useful for making manual adjustments of drive voltage to verify piezo actuator static motion, for static setting, or for applying dc bias to dynamically driven piezo actuators such as piezo stacks. external contr ol (via analog signal to the bnc input con - nector): accepts up to 10 vp signal waveforms from external signal generators, computer controllers, or feed- back networks from dc to rated frequency. the com- bined ac plus dc offset voltage is adjustable from zero to the maximum rated voltage. piezo systems offers a single channel audio frequency switching amplifier for driving a variety of piezo actuators, including stacks, bimorphs, and single sheets. 6 catalog #3, 1998 electronics specifications mechanical dimensions 7.4?w x 9.6?d x 2.7?h (188 x 244 x 69) weight 3 lbs. (1.6 kg) controls power switch; dc polarity (+, zero, -); dc offset terminals bnc for input; binding posts for output electrical maximum output voltage 180 volts peak maximum output current 500 ma peak (see graph below) variable dc offset 180 volts peak, adjustable frequency range dc to 5 khz voltage gain x 20, +10% / -5% maximum input voltage ?0 volts peak maximum input, dc component ?0 volts dc input coupling dc coupled input impedance 47k ohm output coupling dc coupled load impedance any capacitive loads and resistive loads above 500 w ac power source 115-125vac, 50-60 hz circuit protection current limit, short circuit, and thermal protection with manual reset. ?this is a new technology and specifications are subject to change. esa-208 piezo switching amplifier c=100 f c=10 f c=1 f c=0.1 f 210 180 150 120 90 60 30 0 1 10 100 1,000 5,000 voltage esa-208 peak output voltage versus frequency for various capacitive loads (sinusoidal waveform). frequency (hz) 7 catalog #3, 1998 electronics p iezo s ystems ,i nc . 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com pr pr opor opor tional tional v v ol ol t t a a ge booster ge booster proportional voltage booster evb-304 $299 ordering information part no. price description booster specifications the proportional voltage booster is a simple means for obtaining the higher voltage used for driving piezo devices, such as sheets, benders and stacks, at static or quasi static frequency. it requires only a low voltage dc supply (such as the output of an op-amp), commonly avail- able in the laboratory. the booster is small in size, pc board mountable, and suited for low current / high voltage applications. output voltage is proportional to the input voltage and is linear from ~ 10% to the maximum output voltage. output rip- ple is low. floating output enables the user to choose either positive or negative drive. and, it is short circuit and reverse polarity protected. input voltage: 0 - 12 vdc input current: 85 ma nominal output voltage: 0 - 250 vdc nominal output current: 2 ma load regulation: 5% (1/2 to full load) ripple: < 0.5% p-p insulation resistance: 3500 vdc weight: ~1.5 oz temperature range: -20? to +70? input voltage (vdc) output voltage (vdc) 250 300 200 150 100 50 0 01 234 56789101112 no load 120 k load 50 k load 1.25 (31.8) .325 (8.3) .60 (15.2) .80 (20.3) .125 (3.2) 1.00 (25.4) .125 (3.2) 1.25 (31.7) .55 (14.0) typical .04 (1.0) dia. typical .63 (1.6) max in out + _ _ + bottom view 8 catalog #3, 1998 electronics dc dc t t o o a a c inver c inver ter drive circuit ter drive circuit inverter drive circuit ( 75 hz - 200 hz) ein-405 $129 inverter drive circuit (150 hz - 400 hz) ein-406 $129 ordering information part no. price .125 (3.2) 1.50 (38.1) 1.00 (25.4) 1.25 (31.8) a a #2-56 tapped 2 plcs. b b gnd +12 the inverter drive circuit converts a dc voltage input into an oscillating ac output. the inverter circuit is provided for driving low voltage (up to 56 vp-p), low frequency ( 75 hz - 400 hz) resonant piezo devices such as fans, choppers, and vibrators. the output frequency is adjusted manually by turning the trimmer pot on the pcb. optimum tuning is accomplished by visual observation of the device motion or inspection of the output waveform on an oscilloscope during operation. description input / output waveform ein-405 ein-406 input voltage range vdc 3 - 30 3 - 30 output voltage range vp-p 0 - 56 0 - 56 frequency range hz 50 - 200 150 - 400 temperature range ? 0 -60 0 - 60 inverter specifications 12vdc piezo fan: the 12 vdc fan (see page 24) can be bolted directly to the ein-406. two wires from terminal ??connect to the two solder dots on the piezo fan, and the metal spacer bolts directly to terminal ?? piezo resonant element: the resonant blade element (see page 25) may be driven using the ein-406. piezo chopper. the piezo chopper (see page 26) may be driven using the ein-405. piezo benders: bending elements (see pages 32 - 37) may be driven at resonance using the appropriate inverter circuit. driving piezo resonators p iezo s ystems ,i nc . 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com input voltage (vdc) output voltage ( vpeak) 0 + - 0 + time time input voltage (vdc) output voltage (vpeak-peak) 50 60 40 30 20 10 0 0 5 10 15 20 25 30 9 catalog #3, 1998 motion instruments p iezo s ystems ,i nc . 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com piezo vibration table (english version) ivb1-003-e $4,500 piezo vibration table (metric version) ivb1-003-m $4,500 vibration table electronic driver ivb1-003-c01 $3,250 ordering information part no. price hea hea vy duty piezo vy duty piezo vibra vibra tion tion t t able able l l o o w w v v ol ol t t a a ge ge , , l l arge arge l l o o ad ad c c ap ap a a city city & n & n on on - - m m a a gnetic gnetic the heavy duty piezoelectric vibration table requires only 15 vrms to deliver a peak to peak amplitude of 9 ? from dc to 200 hertz. the system consists of a low fre- quency vibration table and electronic driver. the vibration table is driven by piezoelectric stacks locat- ed symmetrically about the outer diameter of the table top. piezoelectric stacks provide a means of generating oscillations electrostatically rather than magnetically. a spring-plate assembly provides stack compression, tor- sional resistance, and moment compensation. both english and metric bolt patterns are available. the base plate bolts to ground using 1/4" (or m6) hardware on 6" (or 150 mm) centers. a load up to 150 lbs. may be bolted to the table top using the 1/4-28 unf (or m6) tapped holes located on the 1.0" (or 25 mm) centers. note: the shake table can be driven statically from 0 to +100 vdc and achieve a motion range of 0 to + 30?. description the vibration table driver accepts 0 to ?0 vp input sig- nals from a frequency generator, computer, or feedback network and delivers 0 to 15 vrms to the vibration table, allowing the operator to scan through an operating fre- quency range from 0 to 200 hz. since the stack motors cannot tolerate appreciable volt- age in the antipoling direction, the electronic package pro- vides both an ac drive voltage and a dc bias voltage. the bias voltage superimposes a positive dc voltage greater than the peak negative swing introduced during maximum ac operation. the driver protects the table from excessive voltage, cur- rent, and frequency. driver 1.0 (25.4) 6.5 (165) 3.5 (88.9) 1.00 (or 25) 3.00 (75) 3.4 (86) #1/4-28 or m6 tapped hole on a 2.0" (50 mm) bcd 90 apart, 4 plcs. plus center #1/4-20 or m6 clr. hole on a 6.0" (or 150 mm) bcd 45 apart, 8 plcs. n no magnetic field generation. n all non-magnetic materials n safe operating voltage, 15 vrms n high load capacity features 10 catalog #3, 1998 motion instruments specifications dimensions dimensions (h x od) inches 3.43 x 6.50 mm 87 x 165 table top diameter inches 3.00 mm 76 weight n 22 mounting, base plate english 1/4 clearance holes on 6.0?bcd metric m6 clearance holes on 150mm bcd mounting, table top english 1/4-28 tapped holes, 1.0?centers, 9 places metric m6 tapped holes, 50mm centers, 9 places electrical rated input voltage (at 200 hz with 30 vdc bias voltage applied) vrms 15 input capacitance farad 45 x 10-6 bleed resistance 10k power cable rg 174/u, 10 feet (3 m), 4 pin connector thermal operating temperature range ? 10 to 40 storage temperature range ? 0 to 50 performance dynamic deflection (150 lb. load, 200 hz, 15vrms) ? peak ?.5 static deflection (150 lb. load, 0 hz, 0 - 100vdc) ? peak 0 - 28 frequency range hz 0 - 200 rated load n 660 maximum compressive load n 4,400 input power source 115vac, 60 hz or 230vac, 50/60hz dimensions inches 12 x 12 x 5 mm 305 x 305 x 127 input signal maximum input voltage vp 10 output signal dc offset voltage vdc 30 ac drive voltage vrms 0-15 output current arms 1.25 frequency range hz dc - 200 protection output terminal protected from back emf. power amplifier thermally protected. input voltage and current protection frequency protection. vibration table electronic driver piezo vibration table 11 catalog #3, 1998 p iezo s ystems ,i nc . motion instruments 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com 1/4-20 or m6 tapped hole 4 plcs. 1/4-20 or m6 clearance hole 6 plcs. 1.50 or (37.5) (46.3) 1.82 3.5 (88.9) .25 (6.4) 1.29 (32.8) (6.4) .25 2.0 (50.8) .50 or (12.5) .50 or (12.5) 2.0 or (50.8) 1.25 or (31.8) 2-axis linear positioner, 2-axis linear positioner, 200 200 m m the piezoelectric 2-axis linear positioner is a low fre- quency device designed for delicate manipulations of rela- tively light loads. the piezoelectric motors are configured to provide linear motion along the x and y axis without rotation and shortening commonly associated with stan- dard cantilever devices. the design leads to higher dis- placements than normally associated with piezoelectric devices, while delivering the fine resolution generally sought. the positioner produces displacements of 200 ? with no time lag, vibration, or backlash. when used under a microscope, voltage may be reversed to com- pensate for inverted optics. the motors produce no mag- netic fields and are clean room compatible. the positioner may be electronically driven with the epa- 102 piezo amplifier . two hole patterns are available for mounting: 1/4-20 on 1 inch centers or m6-1.0 on 25 mm centers. custom configurations: other piezo linear positioner features are available in custom configurations, including: single axis, higher and lower motions, totally non-mag- netic constructions, and custom sizes. description n scientific research: invitro fertilization n biology: micro dissection, gene splicing n precision engineering: robotics n electronics: microchip circuitry testing n microscopy: slide manipulation applications 2-axis linear positioner (1/4-20 on 1 inch centers) iln2-001-e $2,499 2-axis linear positioner (m6-1.0 on 25mm centers) iln2-001-m $2,499 ordering information part no. price scale: x1/2 12 catalog #3, 1998 motion instruments specifications mechanical dimensions (l x w x h) inches 3.5 x 2.0 x 1.5 mm 89 x 51 x 46 weight (without platform) grams 140 (with platform) grams 175 mounting english 1/4-20 clr. holes on 3?centers, 6 plcs. metric m6 clr. holes on 75mm centers, 6 plcs. electrical rated input voltage vp 180 capacitance / channel nf 35 input cable 2.1 meters (7 feet) input connector 6 pin, rj12 modular plug thermal operating temperature range ? 10 - 60 storage temperature range ? 0 - 70 performance free deflection @ 180 vp ? 200 resolution nm 25 load capacity grams 50 frequency range (no load) hz dc - 10 2 - axis linear positioner, ?00 ? 13 catalog #3, 1998 motion instruments p iezo s ystems ,i nc . 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com 2-axis linear positioner, ?? (english version) iln2-002-e $2,999 ordering information part no. price 2-axis linear positioner, 2-axis linear positioner, 1 1 m m the 2-axis linear positioner is a solid state high frequen- cy device designed for optical fiber alignment or general micropositioning. the power take-off block is driven by piezoelectric motors configured to provide linear motion along the x and y axes. the positioner delivers extremely fine displacements (in the nm range) by adjusting the applied voltage. the piezoelectric motors produce no contamination or magnetic fields and show no wear over time. the positioner can be mounted to ground using mounting holes on the bottom or sides. power take-off can be accessed from the top or side. a power cable exits from the rear edge. the positioner may be electronically driven with the epa- 102 piezo amplifier. custom configurations: other piezo linear positioner features are available in custom configurations, including: single axis, higher and lower motions, totally non-mag- netic constructions, custom sizes and hole patterns. description #4-40 tapped 0.3" deep one side, 4 plcs. #4-40 tapped 0.2" deep, 4 plcs. #4-40 tapped 0.3" deep both sides, 6 plcs. 2.50 (63.5) .95 (24.1) 1.75 (44.5) .25 (6.4) 2.20 (55.9) 1.00 (25.4) 1.24 (31.5) .01 (.25) .50 (12.7) .90 (22.9) .95 (24.1) .75 (19.1) .75 (19.1) .475 (12.1) wire exit 1.48 (37.6) .50 (12.7) .50 (12.7) .38 (9.5) 1.25 (31.8) .25 (6.4) 1.375 (34.9) .225 (5.7) #4-40 tapped 0.3" deep, 2 plcs. axis-1 axis-2 14 catalog #3, 1998 motion instruments specifications mechanical dimensions (l x w x h) inches (mm) 2.5 x 1.0 x 2.2 (63.5 x 24.1 x 55.9) weight grams 153 electrical rated input voltage vp 70 input capacitance (per axis) nf 82 input resistance (per axis) m 10 environmental operating temperature c 10-40 ? storage temperature range ? 0 - 50 ? performance motion (x direction) ? ? motion (z direction) ? ? resolution nm ? frequency limit (no load) hz 5,000 load capacity grams 200 2 - axis linear positioner, 1? 15 catalog #3, 1998 motion instruments p iezo s ystems ,i nc . 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com 1 - axis mirror tilter (english version) i ag1-004-e $2,000 $1,250 $750 $400 1 - axis mirror tilter (metric version) i ag1-004-m $2,000 $1,250 $750 $400 ordering information part no. 1 pc. 5 pc. 25 pc. 100 pc. 1-axis mirr 1-axis mirr or or til til ter, ter, 0.75 0.75 angle mirror 5mm sq. .50 or (12.9) 1.00 or (25) .50 or (12.9) 1.00 (25.4) .25 or (6.5) .50 or (12.5) .43 (10.9) .50 (12.7) .38 (9.7) #1/4-20 or m6 tapped 3/8 (9.5) deep, 4 plcs. the piezoelectric 1-axis mirror tilter is a high frequency device designed to produce angular motion at high speed and low power. because of its small size, this device is capable of being directly bolted to a gimbal mount and replaces bulky galvanometer systems. the piezoelectric motors provide reasonable displacement while delivering the fine resolution associated with piezoelectric devices. the motors produce no magnetic fields and are clean room compatible. a 5mm x 5mm x 1mm crown glass mirror with a protec- tive gold coating is directly attached to the motor assem- bly. the tilter may be electronically driven using the epa- 102 piezo linear amplifier .two hole patterns are available for mounting: 1/4-20 on 1 inch centers, or m6-1.0 on 25 mm centers. custom tilter configurations: other piezo single axis tilter features are available in custom configurations, including: different angles and frequencies, custom mirror attachment, high temperature operation (up to 150?), low temperature / low vacuum operation, totally non- magnetic constructions, and custom sizes. description 16 catalog #3, 1998 frequency (khz) amplitude versus frequency angle (relative amplitude) 0 .1 .2 .3 .4 .5 .6 .7 01 23 angle versus voltage voltage (vrms) angle (degrees) 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 20 40 60 80 100 120 140 motion instruments specifications mechanical dimensions (l x w x h) inches 2.0 x 1.0 x 0.5 mm 50 x 25 x 12.5 mirror material crown glass, protective gold coating dimensions (l x w x t) mm 5 x 5 x 1 flatness 3 l per 25 mm weight grams 30 mounting english #1/4-20 tapped holes, 4 places, .5?x 1.0 metric m6 tapped holes, 4 places, 12.5mm x 25mm electrical maximum input voltage (vp) v peak ?80 capacitance nf 22 performance angular range (@ 180 vp) degrees .72 broadband operating range hz 0 - 1,500 resonant frequency hz 2,200 thermal operating range c -20 to 60 thermal storage range c -30 to 70 1 - axis piezoelectric mirror tilter, ?.75 17 catalog #3, 1998 motion instruments p iezo s ystems ,i nc . 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com 2 - axis mirror tilter (english version) iag2-005-e $2,999 $1,999 $999 $599 2 - axis mirror tilter (metric version) iag2-005-m $2,999 $1,999 $999 $599 ordering information part no. 1 pc. 5 pc. 25 pc. 100 pc. 2-axis mirr 2-axis mirr or or til til ter, ter, 1.5 1.5 u u l l tra tra t t hin hin p p r r ofile ofile the piezoelectric 2-axis mirror tilter is a low profile device designed for insertion between closely spaced components in an optical path. it may be used for either reflective or refractive optical elements. the tilter deliv- ers precise angular motions for dynamic beam steering, adjustment, or stabilization. large angular deflections 3 ?5 milliradians and resolution better than 5 radians are obtained. mirror elements may be provided separately for individual application needs. drive electronics: each axis my be driven using the epa- 102 linear amplifier described on page 4 and 5. custom tilter configurations: other piezo double axis tilter features are available in custom configurations, including: different angles and frequencies, mirror attach- ments, high temperature operation (up to 150?), low temperature / low vacuum operation, non-magnetic, and custom sizes. description 1.41 (35.9) 1.50 (38.1) 1.414 (35.9) 1.50 (38.1) 3.50 (88.9) square mirror diameter .984 (25.0) .06 (1.6) .10 (2.5) axis-1 axis-2 mirror diameter .984 (25.0) 18 catalog #3, 1998 motion instruments specifications mechanical dimensions (l x w x h) inches 3.5 x 3.5 x .090 (89 x 89 x 2.3) round flat mirror material crown glass, aluminum coating dimensions (dia. x t) inches .984 x .039 ( 25.0 x 1.0) flatness 3 l per 25 mm weight grams 28 mounting english #1/4-20 clr holes on 3?centers (and 4? metric m6 clr holes on 75mm centers (and 100mm) electrical rated input voltage (vp) vp 180 capacitance (per axis) nf 35 environmental thermal operating range c -20 to +60 thermal storage range c -30 to +70 performance angular range (@ 180 vp) degrees 1.5 radians .026 resolution radians 25 broadband operating range hz 0 - 200 resonant frequency hz ~400 2 - axis piezoelectric mirror tilter, ?.5 frequency (hz) amplitude versus frequency angle (degrees) 0 .25 .50 .75 1.00 1.25 1.50 1.75 0 100 200 300 400 500 input voltage = 2 v rms angle versus voltage voltage (vrms) angle (degrees) 2.00 1.75 1.50 1.25 1.00 0.75 0.50 0.25 0 0 20 40 60 80 100 120 140 input frequency = 100 hz 19 catalog #3, 1998 motion instruments p iezo s ystems ,i nc . 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com ultrasonic motor ru30-001 $499 $399 $329 $249 electronic driver circuit ru30-001-c01 $349 $249 $179 $99 ultrasonic motor kit ru30k-001 $1,499 ordering information part no. 1 pc. 5 pc. 25 pc. 100 pc. ul ul trasonic trasonic r r o o t t ar ar y y mo mo t t or or phased excitation of a piezoelectric ring produces pro- gressive elastic oscillations (travelling waves) along its sur- face. this wave induces rotational motion to the rotor pressed against it. when excitation is stopped, the shaft is held in place by friction force. by reversing electrical excitation, the rotor turns in the opposite direction. unique features of the ultrasonic motor are: compact size, low rpm without the need for gear reduction, quick response, quiet operation, holding torque greater than driving torque, and lack of magnetic field generation. the ultrasonic motor / electronic driver require a ?4 vdc power supply, switches and wiring. description the ultrasonic motor kit is intended primarily as a conve- nient demonstration device. it consists of an ultrasonic motor mounted to a stand, an electronic driver, and a controller. the controller houses the electronic driver, power supply, on-off switching, direction switch, and speed control. ultrasonic motor kit motor performance 0.98 (25) .63 (16) .08 (2.0) .55 (14) .31 (8) .02 (0.5) 1.13 ( 28.7) 1.19 ( 30.3) .98 (25) 4 - .031 (4 - 0.8) 3 - 0.98 pitch (3 - 2.5 pitch) .43 ( 11) .47 (12) m2 tapped mounting hole, .551" (14) bcd 4 plcs., 90 apart .16 ( 4) .27 (6.9) 300 200 100 0 0.05 0.10 speed (rpm) torque (n-m) continuous operating range short-time operating range (during acceleration & deceleration 0 motor speed versus output torque 20 catalog #3, 1998 motion instruments specifications motor motor size 30.3 mm dia., 11 mm thick, shaft size 4 mm dia., 14 mm long mounting holes m2-3 on a 14 mm bcd, 90 apart rated torque 0.05 nm holding torque 0.1 nm response (no load) starting response ttime ~ 50 ms stopping response time ~ 1 ms direction reversl response time ~ 10 ms direction of rotation cw, ccw continuous operation 2,000 hrs. steady state operating range no load 30 - 300 rpm 0.05 nm 30 - 250 rpm transient operating range 0.1 nm 30 - 150 rpm operating temperature range -10 to 55 ? allowable temperature rise 65 c at stator surface storage temperature range -20 - 80? humidity 75% weight 20 grams driver required input power 24 vdc, 0.7 amps driver output 110 vac, 2 phase, ~50 khz operating temperature range -10 - 55 ? storage temperature range -20 - 80? size 71mm x 56mm x 22mm weight 240 gram controller (kit only) required input power 115 vac, 60 hz driver output 24 vdc, 0.7 amps power switch on / off start / stop control cw, off, ccw speed control variable, b10k , 0.1w potentiometer operating temperature range -10 - 55 ? storage temperature range -20 - 80? ultrasonic motor & driver 21 catalog #3, 1998 acoustics p iezo s ystems ,i nc . 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com lightweight lightweight a a coustic source coustic source the lightweight acoustic source is a rugged, high output, low mass acoustic source. it is a ceramic-metal compos- ite structure. unlike conventional speakers, it has no frag- ile cone or moving coils. the front face of the abs mounting ring allows attachment and electrical isolation from the structure to which it is mounted. twelve #6-32 tapped metal inserts located 30 apart on a 4.15?bolt circle are provided for this purpose. description applications features piezoelectric lightweight acoustic source das-001 $799 $499 $299 $199 ordering information part no. 1 pc. 5 pc. 25 pc. 100 pc. n useful output band of one octave starting at 1 khz. n precision manufacturing method ensures close phase response matching from one unit to the next for large array noise cancellation experiments. n shallow mechanical envelope for tight spaces. n light weight and rigid metal diaphragm makes the acoustic source impervious to air buffeting and frame vibrations that compromise plastic and paper cone speaker outputs. n exposure to repetitive high ??forces will not change speaker properties or shorten life. n plastic ring mount electrically isolates piezo actuator from mechanical ground, giving flexibility and safety to electronic drive schemes. n can be driven with piezo systems?small light weight switching amplifier (2 lbs). custom acoustic source configurations: other acoustic source features are available in custom configurations, including: different sound levels and frequencies, high temperature operation (up to 150?), low temperature / low vacuum operation, non-magnetic, and custom sizes. n noise cancellation n high intensity sound experimentation n high ?? environment acoustic experimentation n warning speaker 1.25 (31.8) 1.12 (28.4) 4.40 (111.8) 30 #6-32 tapped mounting holes on a 4.15" (105.4) bcd. 0.45" (11.4) deep. 30 apart. 12 plcs. 22 catalog #3, 1998 acoustics specifications mechanical dimensions dia. x thickness inches (mm) 4.50 x 1.25 (114 x 32) weight grams 241 mounting #4-40 screws, front mounted 12 places, 30 apart electrical rated input voltage vp ?00 capacitance nf 132 environmental thermal operating range ? 0 to +70 thermal storage range ? -10 to +70 performance operating frequency range see graph below nominal output, spl db 125 (70 vrms, 6 inches from source) lightweight acoustic source 70 80 90 100 110 120 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 frequency (khz) sound pressure level (db) 10 vrms 6" from source, on axis 23 catalog #3, 1998 fans & resonators p iezo s ystems ,i nc . 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com piezo fan blade, 115 v / 60 hz rfn1-005 $149 $79 $49 $34 piezo f piezo f an blade, an blade, 115 115 v / 60 h v / 60 h z z version version ordering information part no. 1 pc. 5 pc. 25 pc. 100 pc. .50 (12.7) blade swing #2-56 clr. 2 plcs. 1.0 (25.4) .085 (2.2) .312 (7.9) .25 (6.4) 2.52 (64.0) 3.02 (76.7) wires, 6" (152) airflow input voltage: 115 vac, 60 hz capacitance: 15 nf power consumption 30 mw volume flow rate: 2 cfm, (0.9 l/s) peak air velocity: 400 fpm, (2.0 m/s) weight: 2.8 grams mounting : #2-56 clr. holes, 2 places temperature range: -20 c to 70 c emi / rfi: none fan specifications piezo fans are solid state devices without wearing parts. their oscillating mylar blade is driven at resonance by a piezo bending element. in free air, high amplitude resonant vibration of the plastic blade causes formation of high velocity unidirectional flow stream. maximum airflow occurs on axes of the fan s centerline, relative to both width and height dimensions. air intake is above and below the swept out plane of the blade. its?simple design lends itself to low cost in high volume production. piezo fans offer advantages over conventional fan technol- ogy. these include: instant starting with no power surge, making them especially desirable for spot cooling; ultra- light weight; thin profile; and extremely low magnetic per- meability. they produce almost no heat dissipation mak- ing them ideal for sealed enclosures. the 115 v / 60 hz version piezo fan requires no drive circuit and can be driv- en directly off the power bus. custom piezo fan configurations : other piezo fan features are available in custom configurations, including: different flow rates and sizes, high temperature operation (up to 150?), low temperature / low vacuum operation, totally non-magnetic versions, dc operation, flow- through, and water-proof configurations. description of piezo fan 24 catalog #3, 1998 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com performance measured while driving the resonant blade element with inverter drive circuit (pn: ein-406). input voltage (to inverter): 30 v current: 5.1 ma power consumption: 153 mw nominal resonant frequency: 185 hz tip amplitude (p-p): .2 inches weight: 3.8 grams mounting : #2-56 clr. holes temperature range: -40 c to 70 c specifications fans & resonators the piezoelectric resonant blade element can be used as a single fan blade, a vibration source, a chopper, or mod- ulator. the resonant element is easy to use and install. its low profile, small size, low power consumption, low emi, and thermal operating range make it possible to install in places forbidden to electro-magnetic devices. the element resonates at approximately 185 hz. mass may be added to the tip of the element. to increase ampli- tude and decrease resonant frequency, or, metal may be trimmed from the tip to decrease amplitude and increase resonant frequency. the elements are particularly useful for establishing feasibility of a piezoelectric device for a resonant application, such as a chopper. custom configurations: other piezo resonator features are available in custom configurations, including: different amplitudes, frequencies, sizes , thermal operating ranges (up to 150?), low temperature / low vacuum operation, and non-magnetic constructions. description of resonator piezoelectric piezoelectric resonant blade resonant blade element element the piezoelectric resonant element is powered electro- statically rather than magnetically. the metal portion of the blade is driven at resonance by a piezoelectric bender section at the base of the blade. principle of operation the resonant blade element requires an oscillating drive signal matched to the resonant frequency of the blade. this may be provided by a frequency generator / amplifier or inverter circuit. piezo systems provides a simple inverter circuit (pn: ein-406 described on page 9). output frequency of the inverter is adjusted manually by turning a trim pot on the pcb. inverter drive circuit the resonator evaluation kit includes one piezoelectric resonant element and one inverter drive circuit. resonator evaluation kit .125 (3.2) .75 (19.1) 1.50 (38.1) .375 (9.5) 1.75 (44.5) #4-40 clr hole, 2 plcs. .50 (12.7) .075 (1.9) piezoelectric resonant blade element rbl1-006 $149 $99 $60 $35 piezoelectric resonant blade evaluation kit rbl1k-006 $250 ordering information part no. 1 pc. 5 pc. 25 pc. 100 pc. p iezo s ystems ,i nc . 25 catalog #3, 1998 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com the piezoelectric chopper is a resonant device which moves a shutter attached to the front tip of its blade. piezoceramic on one side of the blade can be used for excitation while the piezoceramic on the other side can be used for drive circuit feedback. compared to electro-magnetically driven wheels and tun- ing forks, the piezo chopper is lightweight, small, pro- duces no emi, operates over a wide temperature range, low power, reliable, and cost effective. custom configurations: other piezo chopper features are available in custom configurations, including: different amplitudes and frequencies, high temperature operation (up to 150?), low temperature / low vacuum operation, and non-magnetic constructions, and two bladed (tuning fork configurations. chopper description specifications piezoelectric chopper piezoelectric chopper piezoelectric choppers are powered electrostatically rather than magnetically. the oscillating blade and shutter is driven by a piezoelectric bending element operating at resonance. principle of operation the evaluation kit includes a 100 hz piezo chopper and an inverter drive circuit. chopper evaluation kit fans & resonators piezo chopper rch1-005 $249 $199 $59 $39 piezo chopper evaluation kit rch1k-005 $350 ordering information part no. 1 pc. 5 pc. 25 pc. 100 pc. p iezo s ystems ,i nc . when being driven sinusoidally, the 100 hz piezo chop- per requires an oscillating drive signal matched to the res- onant frequency of the blade. this may be provided by a frequency generator/amplifier or inverter circuit. piezo systems provides a simple inverter circuit (pn: ein-405 described on page 9). output frequency is adjusted man- ually by turning a trim pot on the pcb. inverter drive circuit 2.52 (64.0) .50 (12.7) .25 (6.4) .66 (16.8) .130 (3.3) .235 (6.0) .375 (9.5) .25 (6.4) .550 (14.0) .125 (3.2) .125 (3.2) shutter resonator mount #2-56 tapped 3 plcs. 20 30 40 50 60 10 0 drive voltage (vp-p) shutter displacement (inches p-p) 0.1 0.2 0.3 0.4 0.5 0 drive voltage: 60 vp-p nominal resonant frequency: 100 hz shutter amplitude: .42 inches p-p feedback voltage: 20 vp-p weight: 4.8 grams mounting holes: #2-56 tapped holes, 3 plcs. temperature range: 0 to 60 c 26 catalog #3, 1998 design and prototyping piezoelectric motor/actuator kit kma--005 $499 ordering information part no. price piezoelectric mo piezoelectric mo t t or/a or/a ctu ctu a a t t or kit or kit the motor actuator kit is designed as a development tool for those who wish to quickly verify the feasibility of a piezoelectric approach to an idea or application. the piezoelectric materials provided in this kit represent some of the basic building blocks employed in constructing bending motors, extension motors, and stack motors. emphasis is placed on designing and building bending actu- ators. because the piezoelectric effect is reversible, the same elements are used as sensors and generators. psi- 5a-s4-enh piezoceramic was chosen for the kit because it offers the fewest voltage, temperature, and stress restrictions. it is, by far, the most commonly used piezo- ceramic in the industry. the manual is intended to help the user model, fabricate, and test a prototype actuator as rapidly as possible. quick and simple techniques for cutting piezoceramic elements to desired size are described, as well as, attaching leads to the electrodes. equations for free deflection, block force , resonant frequency, maximum stress, and capacitance allow the user to scale experimental results to many actu- ator designs. description n micro actuators and manipulators for optical, robotic, fluidic, biomedical, electronic, and process engineering. n vibrating shutters and dithering devices. n acoustics and ultrasonics. n micro-pumps for process control and medical instru- mentation. n small size, light weight, low power, solid state, actua- tors of all types for aerospace and battery powered devices. piezo motor applications n piezoceramic single sheets; psi-5a-s4-enh 2 pieces: 1.25" x 2.5" x .0075" n 2?layer standard brass piezo motor elements poled for series operation 1 piece: 2.50" x 1.250" x .020" 1 piece: 1.25" x 0.500" x .020" 1 piece: 1.25" x 0.250" x .020" 1 piece: 1.25" x 0.125" x .020" poled for parallel operation 1 piece: 2.50" x 1.250" x .020" 1 piece: 1.25" x 0.500" x .020" 1 piece: 1.25" x 0.250" x .020" 1 piece: 1.25" x 0.125" x .020" n piezoelectric motor/actuator manual introduction to piezoelectricity designing piezoelectric actuators building piezoelectric actuators n wires, solder and flux the kit includes 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com p iezo s ystems ,i nc . 27 catalog #3, 1998 design and prototyping n piezoceramic single sheets; psi-5a-s4-enh 2 pieces: 1.25" x 2.5" x .0075" n 2?layer standard brass piezo motor elements poled for series operation 1 piece: 2.50" x 1.250" x .020" 1 piece: 1.25" x 0.500" x .020" 1 piece: 1.25" x 0.250" x .020" 1 piece: 1.25" x 0.125" x .020" poled for parallel operation 1 piece: 2.50" x 1.250" x .020" 1 piece: 1.25" x 0.500" x .020" 1 piece: 1.25" x 0.250" x .020" 1 piece: 1.25" x 0.125" x .020" n piezoelectric generator / sensor manual introduction to piezoelectricity designing piezoelectric generators building piezoelectric generators n wires, solder and flux the kit includes piezoelectric generator/sensor kit kgs-006 $499 ordering information part no. price piezoelectric genera piezoelectric genera t t or/sensor kit or/sensor kit the generator / sensor kit is designed as a development tool for those who wish to quickly verify the feasibility of a piezoelectric approach to an idea or application. the piezoelectric materials provided in this kit represent some of the basic building blocks employed in constructing bending generators, extension generators, and stack gen- erators. because the piezoelectric effect is reversible, the same elements are used as motors and actuators. psi-5a- s4-enh piezoceramic was chosen for the kit because it offers the fewest voltage, temperature, and stress restric- tions. it is, by far, the most commonly used piezoceramic in the industry. the manual is intended to help the user model, fabricate, and test a prototype generator as rapidly as possible. for example, quick and simple techniques for cutting ceramic elements to desired size are described. equations for open circuit voltage, closed circuit current , resonant frequency, maximum stress, and capacitance allow the user to scale experimental results to many actuator designs. description n self energized accelerometers n activity & rate response sensors n vibration control & damping n dynamic strain instrumentation n small size, light weight, self-power, solid state sensors piezo generator applications p iezo s ystems ,i nc . 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com 28 catalog #3, 1998 piezo applic a tion module menu screen 2.0 module interest areas 1 ?extender-motor ?icro positioners, optics robotics 2 ?extender-generator force sensors, push-buttons robotics 3 ?bimorph-motor ?illi positioners, shutters 4 ?bimorph-generator motion sensors, cmos power supplies 5 ?monomorph-motor ?illi positioners, shutters, noisemaker 6 ?strain gage vibration and impact sensing 7 ?stack-motor ?icro positioners, optics 8 ?stack-generator impact triggered power supplies 9 ?retrieve previous display a previous calculation select your choice and press 5 10 15 0 0 50 100 25 75 displacement ( m) voltage (vdc) tsi8-h5-104 & tsi8-h5-202 transducer elements low voltage piezoelectric stack (small) ts18-h5-104 $350 $300 $250 $200 low voltage piezoelectric stack (large) ts18-h5-202 $499 $425 $350 $275 ordering information part no. 1 pc. 5 pc. 25 pc. 100 pc. lo lo w w v v ol ol t t a a ge piezoelectric st ge piezoelectric st a a cks cks a low voltage piezoelectric stack is a monolithic ceramic construction of many thin piezoceramic layers which are connected in parallel electrically. the principal character- istics of the stack are: a high energy conversion efficiency, low voltage operation, large force, low motion, fast response, and no emi. motion may be increased, at the expense of force, by mechanical amplification. the stack offers a high energy density in a small package. due to its superior compres- sive strength, it provides a high load bearing capability. however, it is relatively weak in tension. generally, excitation should be applied only in the direc- tion of polarization. hysteresis is typically about 15% in static applications. description 100 v 80 60 40 20 10 100 1000 sine wave frequency (hz) temperature rise ( c) 40 v ts18-h5-104 ts18-h5-202 stack performance 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com tsi8-h5-104 p iezo s ystems ,i nc . + force (newtons) 10 24 6 8 12 14 16 0 0 + deflection ( m) ts18-h5-104 ts18-h5-202 1,000 2,000 3,000 4,000 .71 (18) .71 (18) .44 sq. (11) sq. .39 sq. (10) sq. coating .20 sq. (5) sq. coating .23 sq. (6) sq. 30 catalog #3, 1998 specifications ts18-h5-104 ts18-h5-202 mechanical dimensions (l x w x h) inches 0.2 x 0.2 x 0.72 0.4 x 0.4 x 0.72 mm 5 x 5 x 18 10 x 10 x 18 compressive strength n/m 2 8.8 x 10 8 8.8 x 10 8 tensile strength n/m 2 4.9 x 10 6 4.9 x 10 6 young s modulus n/m 2 4.4 x 10 10 4.4 x 10 10 poisson ratio 0.34 0.34 density kg/m 3 7,900 7,900 weight grams 4.5 16. wires .002 x 50 stranded, red wire positive electrical rated voltage (positive only) +100 vdc +100 vdc capacitance nf 1600 6,500 performance (@ =100 vdc) free deflection ? +14.5 +14.5 blocked force n 840 3,388 response time ? 50 50 environmental thermal operating range c -20 to +80 thermal storage range c -30 to +85 humidity % < 50% piezoelectric stacks 31 catalog #3, 1998 p iezo s ystems ,i nc . 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com transducer elements intr intr oduction oduction t t o bending o bending transducers transducers the piezoceramic bender is a versatile low power electro- mechanical transducer. as a motor, electrical excitation (voltage and current) leads to a mechanical response (motion and force). the application of an electric field across the two layers of a bender causes one layer to expand while the other con- tracts. the net result is a curvature much greater than the length or thickness deformation of the individual layers. a simple bender is actually a nine layer device consisting of four electrode layers, two piezoceramic layers, two adhesive layers, and a center shim. crucial electro- mechanical properties of all individual sheets utilized for bending motors (or generators) are monitored. piezo systems proprietary bonding process leads to high- strength, uniform, void free laminations. our advanced cutting techniques produce actuators with dimensional tolerances within ?001 inch if necessary, widths as nar- row as .020 inch, chip free edges, non-linear shapes, and contamination free surfaces. piezo systems provides design, engineering, and produc- tion capabilities to develop custom bimorph actuators based on performance specifications rather than simple part geometry. bending motors as a generator (or sensor), mechanical excitation (motion and force) leads to an electrical response (volt- age and current). when a piezoceramic bender is forced to flex, one layer will be in tension while the other in compression. the stresses in each layer will produce electrical outputs which will simply be the summation of the outputs of each layer. benders may be used as strain gauges for easy and rapid determination of the characteristics of dynamic strains in structures. they exhibit extremely high sensitivities, in the order of 50 times that of wire strain gauges and are small enough that on most structures they will not mate- rially affect the vibrational characteristics of the structure. bending generators piezo devices are ideal for use as ?mart?devices. that is, part of the piezo volume is able to sense its surroundings while the other portion is able to respond as necessary. each layer of a bender may be used for each purpose. ?mart? devices bending motors 32 catalog #3, 1998 transducer elements to convert cantilever to simple beam performance: xf, free deflection = 1/4x cantilever motion fb, blocked force = 4x cantilever force tr, response time 1/3x cantilever response c, capacitance = same as cantilever capacitance characteristics: center moves up and down. simple beam configuration t w ? x + f la bending bending transducer choices transducer choices to convert cantilever to ??beam performance: xf, free deflection = 1/2x cantilever motion fb, blocked force = 2x cantilever force tr, response time 0.6x cantilever response c, capacitance = same as cantilever capacitance characteristics: right end moves ~ linearly. ?? beam configuration + t la w ? x f bending configurations typically psi-5a piezoceramic is the first choice of most designers. 5a is the most temperature insensitive and offers the widest temperature range. psi-5a achieves motion similar to psi-5h if higher voltage is available. psi-5h is recommended only when low voltage operation is essential. piezoceramic material totally non-magnetic piezo transducers are specially fabricat- ed using non-magnetic electrode and center shim materials. non-magnetic high temperature piezo actuators are specially construct- ed to operate up to 150 c. high temperature cryogenic piezo actuators are specially constructed to operate below 4.2 c. motor performance is reduced by ~1/5 at 77 k and ~1/7 at 4.2 k. however, much higher voltages may be applied to the bender, thereby recovering lost performance. cryogenic vacuum compatible piezo actuators are constructed to be baked-out up to 150? and have a low cross-section for outgassing. vacuum series operation refers to a bender with voltage applied across both piezoceramic layers. it is a two wire device, with one wire attached to each of the outside surfaces. parallel operation refers to a bender with voltage applied across each piezoceramic layer individually. it is a three wire device, with one wire attached to each of the outside surfaces and a third wire attached to the center shim . for the same motion, a bender polarized for series operation requires twice as much voltage as a bender poled for par- allel operation (see page 46). polarization is depicted graphically as an arrow pointing from the positive elec- trode to the negative electrode. series & parallel operation the common bending configurations, piezoceramic mate- rials, bender thicknesses, and methods of mounting are shown below. center shim materials are available for enhancing strength (stainless steel), thermal range, non-magnetism (brass), and economy (brass). specially designed center shims promote unique composite properties. center shim materials t la w ? x + f standard materials: psi-5a type or psi-5h type piezoceramic standard thickness,t: .015?(.38 mm) .020?(.50 mm), .026?(.66 mm) characteristics: right end moves along arc. simplest to mount. cantilever configuration 33 catalog #3, 1998 p iezo s ystems ,i nc . 186 massachusetts avenue cambridge, ma 02139 ? phone: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: s ales@piezo.com transducer elements quick mount bending element, 1325 m m, 5a type t220-a4-503-qm $199 $129 $79 $54 quick mount bending element, 1240 m m, 5h type t220-h4-503-qm $199 $129 $79 $54 ordering information part no. 1 pc. 5 pc. 25 pc. 100 pc. 2.25 (57.2) 2.75 (69.9) .085 (2.2) .125 (3.2) .750 (19.1) 1.25 (31.8) _ + #4-40 clr. 2 plcs. wires, 6" (152) the ?300 m m version quick mount bending element may be used as an actuator and / or sensor. it is ready to be used immediately. the standard t220-a4-503 bending element is wired for low voltage operation and the pcb to which it has been mounted may be attached to mechanical ground using the two #4-40 mounting holes provided. a bleed resistor across the terminals protects the transduc- er from thermal transients. the user must provide the mechanical connection between the transducer tip and their load. as an actuator, the transducer provides large deflection and moderate force at low frequencies. it exhibits low magnetic permeability and generates no magnetic fields. positioners constructed of 5a or 5h type piezoceramic are stocked for ?ff-the-shelf?delivery. custom sizes and configurations are available on request. description quick mount bending element quick mount bending element , , 1300 1300 m m m m version version p art n umber p iezo w eight c apacitance m aximum r esonant r esponse f ree b locked m aterial v oltage f requency t ime d eflection f orce grams nf ?p hz ms m m n t220-a4-503-qm 5a-s4-enh 9.4 290 ?0 70 5.0 1325 .33 t220-h4-503-qm 5h-s4-enh 9.4 480 ?0 70 5.0 1240 .31 specifications & bending motor performance (in the cantilever configuration) force (newtons) deflection (mm) 10.2 20.4 30.6 40.8 .010 .020 .030 .040 .050 ( inches) ( grams) 1.25 .25 .50 .75 1.0 1.50 .20 .40 .10 .30 .060 0 0 5a type @ 90 v 5h type @ 60 v 34 catalog #3, 1998 transducer elements p iezo s ystems ,i nc . 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com quick mount bending element, 320 m m, 5a type t220-a4-303-qm $149 $79 $49 $34 quick mount bending element, 300 m m, 5h type t220-h4-303-qm $149 $79 $49 $34 ordering information part no. 1 pc. 5 pc. 25 pc. 100 pc. .50 (12.7) #2-56 clr. 2 plcs. .085 (2.2) .312 (7.9) .25 (6.4) 1.125 (28.6) 1.625 (41.3) wires, 6" (152) quick mount bending element quick mount bending element 300 300 m m m m version version p art n umber p iezo w eight c apacitance m aximum r esonant r esponse f ree b locked m aterial v o ltag e f requency t ime d eflection f orce grams nf ?p hz ms m m n t220-a4-303-qm 5a-s4-enh 2.5 58 ?0 280 1.2 ?20 .27 t220-h4-303-qm 5h-s4-enh 2.5 96 ?0 280 1.2 ?00 .25 specifications & bending motor performance (in the cantilever configuration) force (newtons) deflection (mm) 5.1 10.2 15.3 20.4 25.5 .002 .004 .006 .008 .010 ( inches) ( grams) .25 .05 .10 .15 .20 .30 .10 .20 .25 .05 .15 .012 0 0 5a type @ 90 v 5 h type @ 60 v the ?00 m m version quick mount bending element may be used as an actuator and / or sensor. it is ready to be used immediately. the standard t220-a4-303 bending ele- ment is wired for low voltage operation and the pcb to which it has been mounted may be attached to mechani- cal ground using the two #2-56 mounting holes provided. a bleed resistor across the terminals protects the trans- ducer from thermal transients. the user must provide the mechanical connection between the transducer and their load. as an actuator, the transducer provides medium range deflection and force. it exhibits low magnetic permeabil- ity and generates no magnetic fields. positioners constructed of 5a or 5h type piezoceramic are stocked for ?ff-the-shelf?delivery. custom sizes and configurations are available upon request. description 35 catalog #3, 1998 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com transducer elements p art n umber w idth l ength inches (mm) inches (mm) elements made with psi-5a-s4 piezoceramic t215-a4-103 .125 (3.2) 1.250 (31.8) t215-a4-203 .250 (6.4) 1.250 (31.8) t215-a4-303 .500 (12.7) 1.250 (31.8) t215-a4-503 1.250 (31.8) 2.500 (63.5) elements made with psi-5h-s4 piezoceramic t215-h4-103 .125 (3.2) 1.250 (31.8) t215-h4-203 .250 (6.4) 1.250 (31.8) t215-h4-303 .500 (12.7) 1.250 (31.8) t215-h4-503 1.250 (31.8) 2.500 (63.5) p art n umber w eight c apacitance r ated v o ltag e r esponse t ime f ree b locked (f ull a mplitude )d eflection f orce series parallel series parallel active cantilever length, mm operation operation operation operation 25.4 50.8 25.4 50.8 25.4 50.8 grams nf nf ?p ?p ms ms ?m ?m ? ? t215-a4-103 .30 5. 20. ?20 ?0 1.5 - ?.3 - ?04 - t215-a4-203 .60 10. 40. ?20 ?0 1.5 - ?.3 - ?08 - t215-a4-303 1.2 20. 80. ?20 ?0 1.5 - ?.3 - ?16 - t215-a4-503 6.0 100. 400. ?20 ?0 1.5 6.0 ?.3 ?.2 ?40 ?20 t215-h4-103 .30 8. 32. ?0 ?0 1.5 - ?.3 - ?04 - t215-h4-203 .60 16. 64. ?0 ?0 1.5 - ?.3 - ?08 - t215-h4-303 1.2 32. 128. ?0 ?0 1.5 - ?.3 - ?16 - t215-h4-503 6.0 160. 640. ?0 ?0 1.5 6.0 ?.3 ?.2 ?40 ?20 l w top view (scale: x1) t215-a4-303 and t215-h4-303 t215-a4-203 and t215-h4-203 t215-a4-103 and t215-h4-103 t215-a4-503 and t215-h4-503 + .015" (0.38) .005" (0.13) side view (exaggerated) nickel electrode psi-5a-s4 piezoceramic, or psi-5h-s4 piezoceramic adhesive bond layer brass center shim poled for series operation (standard) poled for parallel operation (on request) p p the t215 standard brass shim bending elements are .015?(0.38 mm) thick and sized to be produced economically. they are general purpose actuators designed to produce high deflections and moderate forces at low voltage, and exhibit low mag- netic permeability. the parts are stocked for ?ff-the-shelf?delivery. custom sizes are available on request. description specifications & bending motor performance (in the cantilever configuration) p iezo s ystems ,i nc . 36 catalog #3, 1998 t215 brass shim bending elements t215 brass shim bending elements s s t t and and ard ard s s izes izes t215 brass shim bending elements t215 brass shim bending elements s s t t and and ard ard s s izes izes transducer elements force (newtons) deflection (mm) 10.2 20.4 30.6 40.8 50.9 ( grams) 1.0 0.2 0.4 0.6 0.8 1.2 0.2 0.4 0.5 0.1 0.3 .008 .0016 .024 .031 .039 ( inches) .047 0 0 0.6 61.0 0.7 la t215-a4-503 la = 2.0" (50.8mm) t215-a4-503 la = 1.0" (25.4mm) t215 brass shim bending element (?03?size) t215-a4-103 $90 $40 $22 $12 t215 brass shim bending element (?03?size) t215-a4-203 $90 $45 $25 $15 t215 brass shim bending element (?03?size) t215-a4-303 $90 $50 $30 $20 t215 brass shim bending element (?03?size) t215-a4-503 $125 $90 $60 $40 t215 brass shim bending element (?03?size) t215-h4-103 $90 $40 $22 $12 t215 brass shim bending element (?03?size) t215-h4-203 $90 $45 $25 $15 t215 brass shim bending element (?03?size) t215-h4-303 $90 $50 $30 $20 t215 brass shim bending element (?03?size) t215-h4-503 $125 $90 $60 $40 ordering information part no. 1 pc. 5 pc. 25 pc. 100 pc. bending motor performance (in the cantilever configuration) force (newtons) deflection (mm) 5.1 10.2 15.3 20.4 25.5 .002 .004 .006 .008 .010 ( inches) ( grams) .25 .05 .10 .15 .20 .30 .10 .20 .25 .05 .15 .012 0 0 la t215-a4-303 t215-a4-203 t215-a4-103 t215 -a4-103, -203, -303 b ending e lements voltage: ?20 vp (series) or ?0 vp (parallel) active cantilever length: 1.0?(25.4mm) t215 -a4-503 b ending e lement voltage: ?20 vp (series) or ?0 vp (parallel) active cantilever length: 1.0?(25.4mm) & 2.0?(50.8mm) force (newtons) deflection (mm) 10.2 20.4 30.6 40.8 50.9 ( grams) 1.0 0.2 0.4 0.6 0.8 1.2 0.2 0.4 0.5 0.1 0.3 .008 .0016 .024 .031 .039 ( inches) .047 0 0 0.6 61.0 0.7 la t215-h4-503 la = 2.0" (50.8mm) t215-h4-503 la = 1.0" (25.4mm) force (newtons) deflection (mm) 5.1 10.2 15.3 20.4 25.5 .002 .004 .006 .008 .010 ( inches) ( grams) .25 .05 .10 .15 .20 .30 .10 .20 .25 .05 .15 .012 0 0 la t215-h4-303 t215-h4-203 t215-h4-103 t215 -h4-103, -203, -303 b ending e lements voltage: ?0 vp (series) or ?0 vp (parallel) active cantilever length: 1.0?(25.4mm) t215 -h4-503 b ending e lement voltage: ?0 vp (series) or ?0 vp (parallel) active cantilever length: 1.0?(25.4mm) & 2.0?(50.8mm) 37 catalog #3, 1998 t215 brass shim bending elements t215 brass shim bending elements s s t t and and ard ard s s izes izes transducer elements p iezo s ystems ,i nc . 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com l w top view (scale: x1) t220-a4-303 and t220-h4-303 t220-a4-203 and t220-h4-203 t220-a4-103 and t220-h4-103 t220-a4-503 and t220-h4-503 + .020" (0.51) .0075" (0.19) side view (exaggerated) nickel electrode psi-5a-s4 piezoceramic, or psi-5h-s4 piezoceramic adhesive bond layer brass center shim poled for series operation (standard) poled for parallel operation (on request) p p the t220 standard brass shim bending elements are .020?(0.5 mm) thick and sized to be produced economically. they are general purpose actuators designed to produce moderate deflections and forces, and exhibit low magnetic permeability. the parts are stocked for ?ff-the-shelf?delivery. custom sizes are available on request. description p art n umber w eight c apacitance r ated v o ltag e r esponse t ime f ree b locked (f ull a mplitude )d eflection f orce series parallel series parallel active cantilever length, mm operation operation operation operation 25.4 50.8 25.4 50.8 25.4 50.8 grams nf nf ?p ?p ms ms ?m ?m ? ? t220-a4-103 .40 3.6 14. ?80 ?0 1.2 - ?25 - ?07 - t220-a4-203 .80 7.4 29. ?80 ?0 1.2 - ?25 - ?14 - t220-a4-303 1.6 14.5 58. ?80 ?0 1.2 - ?25 - ?28 - t220-a4-503 8.0 72.5 290. ?80 ?0 1.2 4.8 ?25 ?.0 ?70 ?35 t220-h4-103 .40 6.0 24. ?20 ?0 1.2 - ?25 - ?7 - t220-h4-203 .80 12.0 48. ?20 ?0 1.2 - ?25 - ?14 - t220-h4-303 1.6 24. 96. ?20 ?0 1.2 - ?25 - ?28 - t220-h4-503 8.0 120. 480. ?20 ?0 1.2 4.8 ?25 ?.0 ?70 ?35 specifications & bending motor performance (in the cantilever configuration) p art n umber w idth l ength inches (mm) inches (mm) elements made with psi-5a-s4 piezoceramic t220-a4-103 .125 (3.2) 1.250 (31.8) t220-a4-203 .250 (6.4) 1.250 (31.8) t220-a4-303 .500 (12.7) 1.250 (31.8) t220-a4-503 1.250 (31.8) 2.500 (63.5) elements made with psi-5h-s4 piezoceramic t220-h4-103 .125 (3.2) 1.250 (31.8) t220-h4-203 .250 (6.4) 1.250 (31.8) t220-h4-303 .500 (12.7) 1.250 (31.8) t220-h4-503 1.250 (31.8) 2.500 (63.5) 38 catalog #3, 1998 t220 brass shim bending elements t220 brass shim bending elements s s t t and and ard ard s s izes izes transducer elements t220 brass shim bending element (?03?size) t220-a4-103 $75 $30 $18 $10 t220 brass shim bending element (?03?size) t220-a4-203 $75 $35 $20 $12 t220 brass shim bending element (?03?size) t220-a4-303 $75 $40 $25 $15 t220 brass shim bending element (?03?size) t220-a4-503 $100 $75 $50 $35 t220 brass shim bending element (?03?size) t220-h4-103 $75 $30 $18 $10 t220 brass shim bending element (?03?size) t220-h4-203 $75 $35 $20 $12 t220 brass shim bending element (?03?size) t220-h4-303 $75 $40 $25 $15 t220 brass shim bending element (?03?size) t220-h4-503 $100 $75 $50 $35 ordering information part no. 1 pc. 5 pc. 25 pc. 100 pc. force (newtons) deflection (mm) 10.2 20.4 30.6 40.8 50.9 ( grams) 1.0 0.2 0.4 0.6 0.8 1.2 0.2 0.4 0.5 0.1 0.3 .008 .0016 .024 .031 .039 ( inches) .047 0 0 0.6 61.0 0.7 la t220-a4-503 la = 2.0" (50.8mm) t220-a4-503 la = 1.0" (25.4mm) bending motor performance (in the cantilever configuration) force (newtons) deflection (mm) 5.1 10.2 15.3 20.4 25.5 .002 .004 .006 .008 .010 ( inches) ( grams) .25 .05 .10 .15 .20 .30 .10 .20 .25 .05 .15 .012 0 0 la t220-a4-303 t220-a4-203 t220 -a4-103 t220 -a4-103, -203, -303 b ending e lements voltage: ?80 vp (series) or ?0 vp (parallel) active cantilever length: 1.0?(25.4mm) t215 -a4-503 b ending e lement voltage: ?80 vp (series) or ?0 vp (parallel) active cantilever length: 1.0?(25.4mm) & 2.0?(50.8mm) force (newtons) deflection (mm) 10.2 20.4 30.6 40.8 50.9 ( grams) 1.0 0.2 0.4 0.6 0.8 1.2 0.2 0.4 0.5 0.1 0.3 .008 .0016 .024 .031 .039 ( inches) .047 0 0 0.6 61.0 0.7 la t220-h4-503 la = 2.0" (50.8mm) t220-h4-503 la = 1.0" (25.4mm) force (newtons) deflection (mm) 5.1 10.2 15.3 20.4 25.5 .002 .004 .006 .008 .010 ( inches) ( grams) .25 .05 .10 .15 .20 .30 .10 .20 .25 .05 .15 .012 0 0 la t220-h4-303 t220-h4-203 t220 -h4-103 t220 -h4-103, -203, -303 b ending e lements voltage: ?20 vp (series) or ?0 vp (parallel) active cantilever length: 1.0?(25.4mm) t220 -h4-503 b ending e lement voltage: ?20 vp (series) or ?0 vp (parallel) active cantilever length: 1.0?(25.4mm) & 2.0?(50.8mm) 39 catalog #3, 1998 t220 brass shim bending elements t220 brass shim bending elements s s t t and and ard ard s s izes izes 40 catalog #3, 1998 p iezo s ystems ,i nc . 186 massachusetts avenue cambridge, ma 02139 ? phone: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: s ales@piezo.com transducer elements non-magnetic bending element, 5a type t220-a3bs-304 $100 $75 $50 $35 non-magnetic bending element, 5h type t220-h3bs-304 $100 $75 $50 $35 ordering information part no. 1 pc. 5 pc. 25 pc. 100 pc. + .020" (0.51) .0075" (0.19) side view (exaggerated) silver electrode psi-5a-s3 piezoceramic, or psi-5h-s3 piezoceramic adhesive bond layer brass center shim poled for series operation (standard) poled for parallel operation (on request) p p p art n umber p iezo w eight c apacitance m aximum r esonant r esponse f ree b locked m aterial v o ltag e f requency t ime d eflection f orce grams nf vp hz ms m m n t220-a3bs-304 5a-s3 2.3 17 180 150 2.5 635 .22 t220-h3bs-304 5h-s3 2.3 30 120 150 2.5 595 .21 specifications & bending motor performance (cantilever configuration, la = 1.5? force (newtons) deflection ( m m) 5.1 10.2 15.3 20.4 25.5 .004 .008 .012 .016 .020 ( inches) ( grams) 500 100 200 300 400 600 .10 .20 .25 .05 .15 .024 0 0 5a type @ 180 v 5h type @ 120 v la active length = 1.5" (38.1mm) 1.75 (44.5) .500 (12.7) top view (scale: x1) the non-magnetic bending element may be used as either an actuator or sensor. as an actuator, the transducer provides medium range deflection, frequency, and force. it exhibits no magnetic permeability and generates no magnetic fields. it is well suited for use in high magnetic field environments such as nmr machinery and particle accelerators positioners constructed of 5a or 5h type piezoceramic are stocked for ?ff-the-shelf?delivery. custom sizes and configurations are available upon request. ?uick mount configurations are also available. description t220 brass shim bending element t220 brass shim bending element t t o o t t all all y y n n on on -m -m a a gnetic gnetic v v ersion ersion 41 catalog #3, 1998 p iezo s ystems ,i nc . 186 massachusetts avenue cambridge, ma 02139 ? phone: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: s ales@piezo.com transducer elements the superior construction of the narrow stainless steel shim bending element allows use as either a motor or sensor in applications requiring high strength and reliability at operating temperatures up to 100 c. these elements are used in activity sensors and as rate response sensors in implantable pacemakers. description .700" .040" top view (scale: x2) + .020" (0.51) .0075" (0.19) side view (exaggerated) nickel electrode psi-5a-s4 piezoceramic adhesive bond layer stainless steel shim poled for series operation (standard) poled for parallel operation (on request) p p t220 stainless steel shim bending element narrow width (.040? t220-a4-105 $99 $50 $30 $25 ordering information part no. 1 pc. 5 pc. 25 pc. 100 pc. p art n umber p iezo w eight c apacitance m aximum r esonant r esponse f ree b locked m aterial v o ltag e f requency t ime d eflection f orce grams nf vp hz ms m m n t220-a4-105 psi-5a-s4 .07 0.6 180 ~1,250 0.3 75 .04 specifications & bending motor performance (cantilever configuration, la = 0.5? force (newtons) deflection ( m m) 1 2 3 4 5 .001 .002 ( inches) ( grams) 25 50 75 .02 .04 .05 .01 .03 .003 0 0 5a type @ 180 v active length = 0.5" (12.7mm) la t220 st t220 st ainless steel shim bending element ainless steel shim bending element n n arr arr o o w w w w idth idth transducer elements 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com psi-5a-s4-enh (2.85?square x .005?) t105-a4e-602 $100 $70 $50 $35 psi-5a-s4-enh (2.85?square x .0075?) t107-a4e-602 $100 $60 $40 $30 psi-5a-s4-enh (2.85?square x .010?) t110-a4e-602 $100 $70 $50 $35 psi-5a-s4-enh (2.85?square x .020?) t120-a4e-602 $125 $85 $60 $45 psi-5a-s4-enh (2.85?square x .040?) t140-a4e-602 $150 $115 $80 $60 psi-5a-s4-enh (2.85?square x .080?) t180-a4e-602 $200 $150 $100 $75 ordering information part no. 1 pc. 5 pc. 25 pc. 100 pc. psi-5a-s4-enh piezoelectric single sheet psi-5a-s4-enh piezoelectric single sheet piezoelectric and material properties piezoelectric composition lead zirconate titanate material designation psi-5a-s4-enh relative dielectric constant (@1khz) k t 33 1800 piezoelectric strain coefficient d 33 390 x 10 -12 meters/volt d 31 -190 x 10 -12 meters/volt piezoelectric voltage coefficient g 33 24.0 x 10 -3 volt meters/newton g 31 -11.6 x 10 -3 volt meters/newton coupling coefficient k 33 0.72 k 31 0.32 polarization field ep 2 x 10 6 volts/meter initial depolarization field ec 5 x 10 5 volts/meter mechanical density 7800 kg/meter 3 mechanical q 80 elastic modulus y e 3 5.2 x 10 10 newtons/meter 2 y e 1 6.6 x 10 10 newtons/meter 2 thermal thermal expansion coefficient ~4 x 10 - 6 meters/meter ? curie temperature 350 ? piezoelectric single sheet 2.85 (72.4) 2.85 (72.4) nickel electrodes both sides .005 .0005 (.127 .013) .0075 .0005 (.191 .013) .0105 .0005 (.267 .013) .020 .0005 (.508 .013) .040 .0005 (1.016 .013) .080 .0005 (2.032 .013) p art n umber t hickness c apacitance mm nf (?0%) t105-a4e-602 .127 650 t107 -a4e-602 .191 430 t110 -a4e-602 .267 315 t120 -a4e-602 .508 162 t140 -a4e-602 1.02 80 t180 -a4e-602 2.03 40 p iezo s ystems ,i nc . 42 catalog #3, 1998 transducer elements p iezo s ystems ,i nc . 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com psi-5h-s4-enh (2.85?square x .005?) t105-h4e-602 $100 $70 $50 $35 psi-5h-s4-enh (2.85?square x .0075?) t107-h4e-602 $100 $60 $40 $30 psi-5h-s4-enh (2.85?square x .0105?) t110-h4e-602 $100 $70 $50 $35 ordering information part no. 1 pc. 5 pc. 25 pc. 100 pc. psi-5h-s4-enh piezoelectric single sheet psi-5h-s4-enh piezoelectric single sheet piezoelectric and material properties piezoelectric composition lead zirconate titanate material designation psi-5h-s4 enh relative dielectric constant (@1khz) k t 33 3800 piezoelectric strain coefficient d 33 650 x 10 -12 meters/volt d 31 -320 x 10 -12 meters/volt piezoelectric voltage coefficient g 33 19.0 x 10 -3 volt meters/newton g 31 -9.5 x 10 -3 volt meters/newton coupling coefficient k 33 .75 k 31 .44 polarization field ep 1.5 x 10 6 volts/meter initial depolarization field ec 3.0 x 10 5 volts/meter mechanical density 7800 kg/meter 3 mechanical q 30 elastic modulus y e 3 5.0 x 10 10 newtons/meter 2 y e 1 6.2 x 10 10 newtons/meter 2 thermal thermal expansion coefficient ~3 x 10 -6 meters/meter ? curie temperature 250 ? piezoelectric single sheet .005 .0005 (.127 .013) .0075 .0005 (.191 .013) .0105 .0005 (.267 .013) 2.85 (72.4) 2.85 (72.4) nickel electrodes both sides p art n umber t hickness c apacitance mm nf (?0%) t105-h4e-602 .127 1250 t107 -h4e-602 .191 850 t110 -h4e-602 .267 610 43 catalog #3, 1998 transducer elements 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com 2.15 (54.6) 2.15 (54.6) silver electrodes both sides (+) polarity mark r 0.18 (r4.6) r 0.20 (r5.1) 2.03 (51.6) border .0075 .0005 (0.191 .013) psi-5a-s3 single sheet (0.0075" thick) t107-a3-502 $70 $40 $25 $20 ordering information part no. 1 pc. 5 pc. 25 pc. 100 pc. psi-5a-s3 piezoelectric single sheet psi-5a-s3 piezoelectric single sheet piezoelectric and material properties piezoelectric composition lead zirconate titanate material designation psi-5a-s3 relative dielectric constant k t 33 1800 k t 11 1700 piezoelectric strain coefficient d 33 450 x 10 -12 meters/volt d 31 -180 x 10 -12 meters/volt piezoelectric voltage coefficient g 33 25.0 x 10 -3 volt meters/newton g 31 -11.5 x 10 -3 volt meters/newton coupling coefficient k 33 0.71 k 31 0.34 polarization field ep 2 x 10 6 volts/meter initial depolarization field ec 5 x 10 5 volts/meter mechanical density 7700 kg/meter 3 mechanical q 70 elastic modulus y e 3 5.0 x 10 10 newtons/meter 2 y e 1 5.7 x 10 10 newtons/meter 2 tensile strength, static 6.3 x 10 7 newtons/meter 2 tensile strength, dynamic 2.1 x 10 7 newtons/meter 2 compressive strength 5.2 x 10 8 newtons/meter 2 thermal thermal expansion coefficient ~4 x 10 -6 meters/meter ? curie temperature 350 ? psi-5a-s3 piezoceramic sheet with silver elec- trodes is suitable for total- ly non-magnetic devices. note: silver electrodes are not recommended for stat- ic high field dc applica- tions. piezoelectric single sheet c apacitance (?0%) 190 nf p iezo s ystems ,i nc . 44 catalog #3, 1998 transducer elements psi-5a-s3 single sheet (0.0075" thick) t107-h3-502 $70 $40 $25 $20 ordering information part no. 1 pc. 5 pc. 25 pc. 100 pc. psi-5h-s3 piezoelectric single sheet psi-5h-s3 piezoelectric single sheet piezoelectric and material properties piezoelectric composition lead zirconate titanate material designation psi-5h-s3 relative dielectric constant k t 33 3800 k t 11 2550 piezoelectric strain coefficient d 33 380 x 10 -12 meters/volt d 31 -260 x 10 -12 meters/volt piezoelectric voltage coefficient g 33 12.5 x 10 -3 volt meters/newton g 31 -8.0 x 10 -3 volt meters/newton coupling coefficient k 33 0.52 k 31 0.34 polarization field ep 1.9 x 10 6 volts/meter initial depolarization field ec 3.0 x 10 5 volts/meter mechanical density 7700 kg/meter 3 mechanical q 65 elastic modulus y e 3 4.8 x 10 10 newtons/meter 2 y e 1 6.1 x 10 10 newtons/meter 2 tensile strength, static ~4.8 x 10 7 newtons/meter 2 tensile strength, dynamic ~1.6 x 10 7 newtons/meter 2 compressive strength ~3.9 x 10 8 newtons/meter 2 thermal thermal expansion coefficient ~4 x 10 -6 meters/meter ? curie temperature 220 ? piezoelectric single sheet 2.15 (54.6) 2.15 (54.6) silver electrodes both sides (+) polarity mark r 0.18 (r4.6) r 0.20 (r5.1) 2.03 (51.6) border .0075 .0005 (0.191 .013) psi-5a-s3 piezoceramic sheet with silver electrodes is suitable for totally non- magnetic devices. note: silver electrodes are not recommended for stat- ic high field dc applica- tions. c apacitance (?0%) 470 nf p iezo s ystems ,i nc . 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com 45 catalog #3, 1998 design & prototyping 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com solder n tin/lead solder for nickel electrodes, or tin/lead/silver solder for silver electrodes, 12? length. flux n liquid flux for soldering to nickel or silver electrodes, 7 ml. n liquid flux for soldering to stainless steel & brass center shims , 7 ml. wires n red wires, #30 gauge, stripped & tinned, 6?length, 5 pieces. n black wires, #30 gauge, stripped & tinned, 6?length, 5 pieces. piezoceramic sheet small piezoceramic n sheet with nickel or silver electrode to practice technique, 1 piece description of electrodes description of center shims solder & flux kit (for nickel electrodes) msf-003-ni $49 solder & flux kit (for silver electrodes) msf-003-ag $59 ordering information part no. 1 pc. soldering wires to the electrodes of piezoceramic sheet and/or the center shim of a 2-layer bending element can be difficult if the proper materials are not used. there is a vast array materials to choose from. the solder & flux kit offers the right materials to get started at once and pro- vides information to procure materials directly from the manufacturer later. recommended procedure is described. materials in the kit are for soldering to nickel electrodes unless specifically requested for silver. piezoceramic electrodes will be either fired silver or nick- el. silver electrodes are flat white in color while nickel electrodes are grey. silver electrodes are not recommended for high electric field dc applications where the silver is likely to migrate and bridge the two electrodes. it is often used in non- magnetic and ac applications. silver used as an electrode is in the form of flakes suspended in a glass frit. it is gen- erally screened onto the ceramic and fired. the glass makes the bond between the ceramic and the silver par- ticles. silver is soluble in tin and a silver loaded solder should be used to prevent scavenging of silver in the elec- trode. nickel has good corrosion resistance and is a good choice for both ac and dc applications. it can usually be sol- dered to easily with tin/lead solder. electroless nickel, used for plating piezoceramic, contains phosphor. sometimes the phosphor content in a plating run can make it hard to solder. vacuum deposited nickel elec- trodes are usually very thin, making soldering tricky. choice of the correct flux (to remove surface oxidation) generally makes soldering to electrode surfaces easy even under adverse conditions. generally, the center shim layer of a 2-layer piezoelec- tric bending element is either brass or stainless steel. a wire is attached to the center shim if the element is used in parallel operation. shims are soldered in the same way as the nickel electrode. the proper liquid flux choice must be made depending on the shim material. solder & flux kit solder & flux kit p iezo s ystems ,i nc . bending motors kit includes: bending motors purpose of the kit 46 catalog #3, 1998 piezoceramic application data p iezo s ystems ,i nc . 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com the piezoelectric constants relating the mechanical strain produced by an applied electric field are termed the strain constants, or the ??coeffi- cients. the units may then be expressed as meters per meter, per volts per meter (meters per volt). it is useful to remember that large d ij constants relate to large mechanical displacements which are usually sought in motional transducer devices. conversely, the coefficient may be viewed as relating the charge collected on the electrodes, to the applied mechanical stress. d 33 applies 2 1 3 p + 2 1 3 p + q or v f + p + q or v f + p + q or v f + p + figure - 1a figure - 1b figure - 2a figure - 2b figure - 2c when a piezoceramic element is stressed electrically by a voltage, its dimensions change. when it is stressed mechanically by a force, it generates an electric charge. if the electrodes are not short-circuited, a voltage associated with the charge appears. a piezoceramic is therefore capable of acting as either a sensing or trans- mitting element, or both. since piezo- ceramic elements are capable of gen- erating very high voltages, they are compatible with today s generation of solid-state devices ?rugged, com- pact, reliable, and efficient. the following text describes the ter- minology of piezoceramics and the relationship among variables for func- tional applications. relationships between applied forces and the resultant responses depend upon: the piezoelectric properties of the ceramic; the size and shape of the piece; and the direction of the electri- cal and mechanical excitation. to identify directions in a piezoce- ramic element, three axes are used. these axes, termed 1, 2 and 3, are analogous to x,y and z of the classi- cal three dimensional orthogonal set of axes (figure 1a) the polar or 3 axis is taken parallel to the direction of polarization within the ceramic. this direction is estab- lished during manufacturing by a high dc voltage that is applied between a pair of electroded faces to activate the material. the polarization vector ??is represented by an arrow point- ing from the positive to the negative poling electrode. in shear operations, these poling electrodes are later removed and replaced by electrodes deposited on a second pair of faces. in this event, the 3 axis is not altered, but is then parallel to the electroded relationships faces found on the finished element (figure 1b). when the mechanical stress or strain is shear, the subscript 5 is used in the second place. piezoelectric coefficients with double subscripts link electrical and mechan- ical quantities. the first subscript gives the direction of the electrical field associated with the voltage applied, or the charge produced. the second subscript gives the direction of the mechanical stress or strain. several piezoceramic material con- stants may be written with a ?uper- script?which specifies either a mechanical or electrical boundary condition. the superscripts are t, e, d and s, signifying: t = constant stress = mechanically free e = constant field = short circuit d = constant electrical displacement = open circuit s = constant strain = mechanically clamped as an example, k t 3 expresses the relative dielectric constant (k), mea- sured in the polar direction (3) with no mechanical clamping applied. "d" constant d = strain developed applied electric field intr intr oduction oduction t t o piezoelectricity o piezoelectricity 47 catalog #3, 1998 piezoceramic application data 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com electromechanical coupling k 33 ,k 31 , k p , and k 15 describe the conversion of energy by the ceramic element from electrical to mechanical form or vice versa. the ratio of the stored converted energy of one kind (mechanical or electrical) to the input energy of the second kind (electrical or mechanical) is defined as the square of the coupling coeffi- cient. when the force is in the 3 direction (along the polarization axis) and is impressed on the same surface on which the charge is collected (figure 2a). d 31 applies when the charge is collected on the same surface as before, but the force is applied at right angles to the polarization axis (figure 2b). the subscripts in d 15 indicate that the charge is collected on electrodes which are at right angles to the origi- nal poling electrodes and that the applied mechanical stress is shear (figure 2c.) the units for the d ij coefficients are commonly expressed as coulombs/square meter per new- ton/square meter. when the force that is applied is dis- tributed over an area which is fully covered by electrodes (even if that is only a portion of the total electrode) the units of area cancel from the equation and the coefficient may be expressed in terms of change per unit force, coulombs per newton. to view the dij coefficients in this manner is useful when charge generators are contemplated, e.g., accelerometers. k = mechanical energy stored electrical energy applied whereas the relative dielectric cons- tant is strictly a material property, the capacitance is a quantity dependent on the type of material and its dimen- sions. capacitance is calculated by multiplying the relative dielectric con- stant by the permittivity of free space capacitance the relative dielectric constant is the ratio of the permittivity of the material, e , to the permittivity of free space, e 0 , in the unconstrained condition, i.e., well below the mechanical resonance of the part. dielectric constants the piezoelectric constants relating the electric field produced by a mechanical stress are termed the volt- age constants, or the ??coefficients. the units may then be expressed as volts/meter per newton/square meter. output voltage is obtained by multi- plying the calculated electric field by ??constant the thickness of ceramic between electrodes. a ?3?subscript indicates that the electric field and the mechan- ical stress are both along the polariza- tion axis. (figure 2a.) a ?1?sub- script signifies that the pressure is applied at right angles to the polariza- tion axis, but the voltage appears on the same electrodes as in the ?3 case. (figure 2b.) a ?5?subscript implies that the applied stress is shear and that the resulting electric field is perpendicular to the polarization axis. (figure 2c.) high g ij constants favor large voltage output, and are sought after for sen- sors. although the g coefficient are called voltage coefficients, it is also correct to say the g ij is the ratio of strain developed over the applied charge density with units of meters per meter over coulombs per square meter. d = short circuit charge density applied mechanical stress g = open circuit electric field applied mechanical stress g = strain developed applied charge density c = k e 0 a t k = permittivity of material = e permittivity of free space e 0 k = electrical energy stored mechanical energy applied k 3 is related to the capacitance between the original poling elec- trodes. k 1 is related to the capaci- tance between the second pair of electrodes applied after removal of the poling electrodes for the purpos- es of shear excitation. at frequencies far below resonance, piezoelectric ceramic transduc- ers are fundamentally capacitors. consequently, the voltage coefficients g ij are related to the charge coeffi- cients d ij by the dielectric constant ki as, in a capacitor, the voltage v is related to the charge q by the capacitance c. the equations are: q = cv d 33 = k t 33 e 0 g 33 d 31 = k t 33 e 0 g 31 d 15 = k t 11 e 0 g 15 ( e 0 = 8.9 x 10 -12 farads/meter) and electrode surface area, and then dividing by the thickness separating the electrodes. units are expressed in farads. coupling coefficients p iezo s ystems ,i nc . or 48 catalog #3, 1998 piezoceramic application data p iezo s ystems ,i nc . 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com a measure of the dielectric losses in the material-defined as the tangent of the loss angle or the ratio of parallel resistance to the parallel reactance, expressed in percent. dissipation factor the ratio of the mass to volume in the material, expressed in kg/m 3 density the ratio of reactance to resistance in the equivalent series circuit repre- senting the mechanical vibrating res- onant system. the shape of the part affects the value. mechanical (qm) the temperature at which the crystal structure changes from a non-sym- metrical (piezoelectric) to a symmet- rical (non-piezoelectric) form, expressed in degrees celsius. curie temperature aging is the attempt of the ceramic to change back to its original state prior to polarization. aging of piezoelectric ceramics is a logarithmic function with time. the aging rate defines change in the material parameters per decade of time, i.e., 1-10 days, 5-50 days, etc. aging rate deflection and force: piezoelectric actuators are usually specified in terms of their free deflection and blocked force. free deflection, x(f), refers to displacement at a given volt- age level without the actuator work- ing against any external load. blocked force, f(b), refers to the force exerted at a given voltage level when the actu- ator is not allowed to move. since the force at maximum deflection is zero, all other values of simultaneous dis- placement and force (for a given volt- age level) are determined by a line drawn between these points on a force versus deflection diagram as shown below. in practice, a bending motor must move a specified amount and exert a specified force, which determines its operating point on the force versus deflection diagram.work is maximized when the deflection per- formed permits one half the blocked force to be developed. this occurs when the deflection equals one half the free deflection. for cantilevered bending motors, x(f) and f(b) are approximated by observ- ing the tip deflection after energizing, and by holding a force gauge against the tip during energization. performance as with all solids, piezoelectric ceram- ics have mechanical stiffness proper- ties described as young s modulus. young s modulus is the ratio of stress (force per unit area) to strain (change in length per unit length). because mechanical stressing of the ceramic produces an electrical response which opposes the resultant strain, the effective young s modulus with electrodes short circuited is lower than with the electrodes open circuited. in addition, the stiffness is different in the 3 direction from that in the 1 or 2 direction. therefore, in expressing such quantities both direc- tion and electrical conditions must be specified.y e 33 is the ratio of stress to strain in the 3 direction at constant field e (electrodes shorted). y d 33 is the equivalent with the electrodes open circuited.y e 11 and y d 11 are the moduli in the 1 or 2 direction. y e 55 and yd55 are the ratios of shear young? modulus y = stress strain r = mass volume stress to shear strain. units are usu- ally newtons/square meter. it should be clearly understood that the piezoceramic properties described above are defined for ideal shapes measured under ideal mechanical and electrical boundary conditions. when put to use under practical device operating condi- tions, the predicted performance is approached but seldom realized. non-ideal shapes and non-ideal boundary conditions contribute to transduction losses due to such things as standing waves, interfering vibrational modes, pseudo-clamping, stray electric and dielectric resis- tances. since the possibilities are infinite, the designer must evaluate each component under the use con- ditions for which it is intended. v2 > v1 v1 force deflection direction of increasing voltage operating point optimized to produce maximum work x f f b subscripts denote the relative direc- tions of electrical and mechanical quantities and the kind of motion involved. they can be associated with vibratory modes of certain simple transducer shapes; k 33 is appropriate for a long thin bar, electroded on the ends, and polarized along the length, and vibrating in a simple length expansion and contraction. k 31 relates to a long thin bar, electroded on a pair of long faces, polarized in thickness, and vibrating in simple length expansion and contraction. k p signifies the coupling of electrical and mechanical energy in a thin round disc, polarized in thickness and vibrat- ing in radial expansion and contrac- tion. k 15 describes the energy con- version in a thickness shear vibration. since these coefficients are energy ratios, they are dimensionless. 49 catalog #3, 1998 piezoceramic application data 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com mo mo t t or or transducer rela transducer rela tionships tionships parallel expansion & contraction motor shear motor bending motor l+ ? l t- ? t l t w ? t l? ? l t+ ? t ? t p + p + p + v + v + ? x ? x p + p + p + v + v + ? x ? x + p p + l t + p p + + p p + v v + + + + p p + + p p + + p p l t v + v + p iezo s ystems ,i nc . series connection parallel connection x = vd 15 parallel expansion x = 2l 2 v d 31 t 2 x = 4l 2 v d 31 t 2 ? t = vd 33 transverse expansion & contraction motor l+ ? l t- ? t l t w ? t l? ? l t+ ? t ? t p + p + p + v + v + transverse expansion ? l = ? w = vd 31 l w t 50 catalog #3, 1998 piezoceramic application data genera genera t t or or transducer rela transducer rela tionships tionships parallel compression or tension generator parallel shear generator transverse shear generator bending generator transverse compression or tension generator l t w p + q or v f f + q or v + p + p + l t w q or v f f + q or v + p + p + p + l t w p + p + p + q or v f f + q or v + w l t + p p + f q or v + + + p p f q or v + l t w q or v f f + q or v + p + p + p + p iezo s ystems ,i nc . 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com q = 3fl 2 d 31 t 2 parallel connection series connection v = f g 33 t lw q = fd 33 q = f d 31 lw tw v = f g 31 t tw v = f g 15 t lw q = fd 15 q = f d 15 lw tw v = f g 15 t tw v = 3fl g 31 4wt q = 3fl 2 d 31 2t 2 v = 3fl g 31 2wt 51 catalog #3, 1998 piezoceramic application data 186 massachusetts avenue cambridge, ma 02139 ? tel: (617) 547-1777 ? fax: (617) 354-2200 ? web: www.piezo.com ? e-mail: sa les@piezo.com typical typical thermal pr thermal pr oper oper ties of piezoceramic ties of piezoceramic temperature (c) -100 -50 0 50 100 150 200 250 0 100 200 300 percent deviation relative dielectric constant (k) -100 5h 5a temperature (c) -100 -50 0 50 100 150 200 250 25 0 50 75 -25 percent deviation d 31 5a 5h temperature (c) -100 -50 0 50 100 150 200 250 -50 0 50 100 percent deviation mechanical q -100 5a 5h temperature (c) -100 -50 0 50 100 150 200 250 -40 -20 0 percent deviation g 31 -60 5a 5h p iezo s ystems ,i nc . 52 catalog #3, 1998 |
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