雙模態耦合的三角形超音波馬達

୯ ҥ Ҭ ೯ ε Ꮲ

ᐒఓπำᏢسᅺγ੤

ᅺ γ ፕ Ў

ᚈኳᄊጠӝޑΟف׎ຬॣݢଭၲ

Dual-Mode Coupled Triangular Ultrasonic Motors

ࣴ ز ғ Ǻ ጰቼޱ

ࡰᏤ௲௤ Ǻ ϑቼύ റγ

ᚈኳᄊጠӝޑΟف׎ຬॣݢଭၲ

Dual-Mode Coupled Triangular Ultrasonic Motors

ࣴ ز ғǺጰቼޱ StudentǺChing-Fang Tsai

ࡰᏤ௲௤Ǻϑቼύ റγ AdvisorǺDr. Ching-Chung Yin

୯ ҥ Ҭ ೯ ε Ꮲ ᐒఓπำᏢسᅺγ੤

ᅺ γ ፕ Ў

A Thesis

Submitted to Department of Mechanical Engineering College of Engineering

National Chiao Tung University in Partial Fulfillment of the Requirements

for the Degree of Master of Science

in

Mechanical Engineering July 2011

Hsinchu, Taiwan, Republic of China

ᚈኳᄊጠӝޑΟف׎ຬॣݢଭၲ

ࣴزғǺጰቼޱ ࡰᏤ௲௤Ǻϑቼύ റγ ୯ҥҬ೯εᏢᐒఓπำᏢسᅺγ੤

ᄔा

ҁࣴزගр΋ᅿ჻ཥ೛ीϐᚈኳᄊጠӝ០୏ޑຬॣݢଭၲǴЬा੝ ቻࢂӧΟف׎ۓηޑୁᜐ܈فᆄೀբНѳ໒ኲǴ෧১ۓηޑᕵӛখ܄Ǵ ٬ۓηޑᕵӛᆶסᙯӅਁᓎ౗ख़ӝǶۓηޑӚᜐᗹຠБ׎ᓸႝഏౠ׷ ਑Ǵႝཱུ೽ҽϩപࣁ AǵB ࣬ٿ༧୔ୱǴࡼуٿಔ࣬Տৡ 90 ࡋޑҬࢬႝ ᓸܭႝཱུǴёᐟวۓηޑᕵӛᆶסᙯӅਁኳᄊǴ٬ளۓηௗ᝻ᗺँଆբ ᐍ༝׎ॉၞၮ୏Ǵۓηᆶᙯη໔ޑነᔔΚ០٬ᙯη௽ᙯǶϪඤ࣬Տޑሦ ӃᆶပࡕǴё௓ڋᙯηޑ௽ᙯБӛǶҁࣴزаԖज़ϡનϩ݋௖૸Οف׎ ۓηޑଯࡋǵࠆࡋǵНѳ໒ኲߏࡋϷՏ࿼฻൳ՖЁκჹۓη੝ۓኳᄊԾ ฅᓎ౗ޑቹៜǴၲԋᓬ౦ޑኳᄊ႖ᚆǴ٠௖૸ۓηᆶᙯηޑௗ᝻ΚᏢՉ ࣁǴ՗ᆉຬॣݢଭၲᙯೲᆶסંޑ܄ૈԔጕǶҁࣴزᇙբϷෳ၂Οঁଭ ၲচࠠᐒǴۓηޑ׷፦ࣁ᎑ӝߎǴᙯηࣁόឌᒳǶځύന٫೛ीޑᏹբ ᓎ౗ࣁ 19.59kHzǴচࠠᐒΟޑനεᙯೲࣁ 142rpmǴനεסં 3.17N-cmǶ ऩஒচ᎑ӝߎۓηޑँଆׯࣁᒳౚǴௗ᝻୔ୱҗጕௗ᝻ᡂࣁᗺௗ᝻Ǵଭ ၲޑനεסંගϲԿ 4.239N-cmǴԖਏගϲଭၲޑᒡр܄ૈǶҁࣴز೛ ीǵᇙբޑଭၲڀեᙯೲǵଯסંǵᛙۓᒡрϷᓉॣޑ੝܄Ƕ ᜢᗖӷǺຬॣݢଭၲǵᚈኳᄊӅਁǵௗ᝻ΚᏢǵסંᙯೲԔጕ

Dual-Mode Coupled Triangular Ultrasonic Motors

Student: Ching-Fang Tsai Advisor: Dr. Ching-Chung Yin

Department of Mechanical Engineering National Chiao Tung University

ABSTRACT

This thesis presents a novel design of dual mode coupled ultrasonic motor, which is driven by the fundamental longitudinal mode and torsional mode of the stator. The triangular tube-like stator is machined with horizontal slot in each side or at each corner to form a flexible structure with appropriate weakness in its axial stiffness. It results that the longitudinal mode has reduced resonant frequency very close to that of the desired torsional mode. The PZT4 element with two segmented electrodes is adhered to each peripheral surface of the stator. Two ac signals with 90 degree phase difference are applied to the electrodes to excite both vibration modes. Every contact point undergoes an elliptical trajectory in response to a harmonic excitation of the coupled modes, which are used to drive the ultrasonic motor via frictional force between both rotor and stator. The revolution direction of the rotor can be controlled by switching phase lag or lead. Excellent modal separation was achieved by modifying the geometric parameters, such as height, thickness of the triangular stator and length, location of the slots, according to the calculated natural frequencies of the stator by using finite-element analysis. The contact mechanics between both rotor and stator are explored and is used to estimate the T-N curves of the present ultrasonic

motor.

Three prototypes of the presented ultrasonic motor were fabricated and tested. The stator and rotor are made of aluminum alloy and steel, respectively. In the best design, the operating frequency is 19.59 kHz. The maximum revolution speed is 142 rpm without payload, and the maximum measured torque is 3.17 N-cm. To reduce the wear, an embedded steel ball is used to replace the line contact bump on the stator and to form a point-like contact. It follows that the output torque promotes to 4.239 N-cm. The presented ultrasonic motor has advantages of high torque at low speed, stable output and quiet performance.

Keywords: ultrasonic motor, dual-mode resonance, contact mechanics, T-N curves

ᇞ ᖴ

ӧԜགᖴךޑࡰᏤ௲௤ ϑቼύറγǴӧךൺᏢޑ೭ࢤය໔Ǵ๏ϒቼ ޱനεޑޭۓᆶ௲ᏤǴӧࣴزޑၸำύόᘐӦගឫᆶࡰ҅Ǵӆԛҗ૱ޑ གᖴாǶӕਔགᖴ׵ӼᖰᆶᎄݫܿԴৣኘϧᏼҺα၂ہ঩Ǵ๏ϒࡰ௲ᆶ ࡌ᝼Ǵ٬ፕЎૈ׳ֹ᏾ޑև౜ǴჹԜుགᖴཀǶགᖴᏢߏෞੀکǵЦӭ ᆪǵ೚Шܴǵྕηົǵቅػ๔ǵᝄ܍ߠǵᗛख़Ӏǵ໳நণǵᎄറኾǵᒘ ՙԃǵᏢۆ஭ຽ఼ǵֆࢅዠගٮᏢಞ΢ޑᝊ຦ཀـϷғࢲ΢ޑ࿶ᡍǴག ᖴӕᏢЦျϼǵֆৎӹǵ໳࠻ᆢǵ෯γ݇ǵᎄඵᇻǵጰ᫢ଈܭঅፐᆶࣴ ز΢ޑڐշᆶฒᑃǴᡣךॺ۶Ԝ໔׳уԋߏᆶᇡ᛽ǴаϷᏢ׌ۂǴֆ᫢ অǵ׵ᥰᇻǵఉ֡ԁǵᵊЈችǵ׵࢙Ꮜǵ໳ҸѳǴӧ೭อኩ࣬ೀύޑᔅ շᆶϩ٦Ǵჴᡍ࠻္ޑཥғڮΚΨӢգॺݨฅԶғǴᝩុஒ೭ҽཥғڮ Κ໺ሀΠѐփ!ӧԜΨઔᅽգॺፕЎ໩ճǶ നࡕǴቼޱाע೭ҽЈ௃ᆶག୏᝘๏ךനལངޑР҆ᒃǴаϷᒃང ޑঢঢǴӢࣁգॺޑҔЈᆶЍ࡭Ǵᡣቼޱૈడคࡕ៝ϐኁޑ໩ճֹԋᏢ ཰Ǵགᖴ΋ၡഉՔޑζ϶໳໡޹Ǵӧךന༽ർคշਔǴᕴࢂ๏ϒᆒઓ΢ ޑኃᙖᆶႴᓰǴՔך෠ၸǶ ໻аԜፕЎ ᝘๏Р҆ǵৎΓаϷ܌ԖᜢངךޑΓ

Ҟᒵ

ύЎᄔा ...i मЎᄔा ...ii ᇞᖴ ...iv Ҟᒵ ...v ߄Ҟᒵ ... viii კҞᒵ ...ix ಃ΋ക ᆣፕ ...1 1.1 ߻ق ... 1 1.2 ࣴزङඳ... 2 1.3 Ў᝘ӣ៝... 4 1.3.1 ਁ୏ጠӝࠠຬॣݢଭၲ... 4 1.3.2 ຬॣݢଭၲϐௗ᝻ϩ݋... 6 1.4 ࣴزҞޑ... 7 1.5 ϣ৒ᙁॊ... 8 ಃΒക ౛ፕϩ݋...9 2.1 ᓸႝচ౛... 9 2.1.1 ᓸႝਏᔈ... 9 2.1.2 ᓸႝ׷਑ޑᅿᜪ... 10 2.1.3 ᓸႝ׷਑ޑҁᄬБำԄ... 11 2.1.4 ᓸႝ่ᄬޑ୏ᄊБำԄ... 13 2.2 ኳᄊϩ݋... 14 2.3 ኩᄊϩ݋... 14 2.4 ௗ᝻ΚᏢϩ݋... 16

2.4.1 ߚጕ܄؃ှࢬำ... 16 2.4.2 ௗ᝻Κᄽᆉݤ... 17 2.4.3 ነᔔᐒڋ... 17 2.5 ຬॣݢଭၲठ୏চ౛... 18 ಃΟക ኧॶኳᔕϩ݋ᆶ่݀...20 3.1 ΟᆢԖज़ϡનϐᆛ਱ᆶϡનࠠᄊ... 20 3.2 ኳᄊϩ݋่݀... 21 3.2.1 Ծฅኳᄊᒣձ... 21 3.2.2 ൳ՖЁκჹܭ੝ۓኳᄊԾฅᓎ౗ޑቹៜ... 21 3.2.3 ኳᄊ႖ᚆᆶኳᄊጠӝ... 24 3.3 ۓηޑਔᒋϩ݋่݀... 25 3.4 ۓηޑኩᄊៜᔈϩ݋่݀... 26 3.5 ۓηᆶᙯηޑௗ᝻ΚᏢϩ݋... 28 3.5.1 ௗ᝻ϡનޑᒧҔ... 28 3.5.2 ჴதኧᆶᜢᗖᒧ໨೛ۓ... 29 3.5.3 ଭၲᙯೲᆶסંीᆉ... 31 ಃѤക ჴᡍໆෳᆶ่݀૸ፕ...33 4.1 ຬॣݢଭၲᇙբ... 33 4.2 Ӆਁᓎ౗ໆෳ... 33 4.3 ჴᡍໆෳࢎᄬ... 35 4.4 ຬॣݢଭၲ܄ૈໆෳ... 35 4.4.1 ቹៜᙯೲޑӢન... 35 4.4.2 ቹៜסંޑӢન... 37 4.4.3 סંᆶᙯೲޑ܄ૈԔጕ... 38 4.4.4 ᙯೲᆶסં܄ૈԔጕϐኳᔕᆶໆෳ่݀Кၨ ... 39

ಃϖക ่ፕᆶ҂ٰ৖ఈ...41 5.1 ่ፕ ... 41 5.1.1 ኧॶϩ݋่݀૸ፕ... 41 5.1.2 ჴᡍໆෳ่݀૸ፕ... 42 5.2 ҂ٰ৖ఈ... 43 ୖԵЎ᝘ ...44 ߕ߄ ...47 ߕკ ...51

߄Ҟᒵ

߄ 1 ᎑ӝߎ T-6061 ޑ׷਑߯ኧ ... 47 ߄ 2 ᓸႝഏౠ PZT-4 ޑ׷਑߯ኧ[25] ... 47 ߄ 3 ֹ᏾Οف׎่ᄬϐ߻ 20 ಔኳᄊਁ׎ǴL=30mmǵH=20mmǵt=2mm ... 48 ߄ 4 Οف׎ۓηܭόӕНѳ໒ኲՏ࿼Π୷ҁᕵӛኳᄊᆶಃΒסᙯኳᄊ ਁ׎ǴL=30mmǴH=15mmǴLa=15mmǴt=2mm ... 49 ߄ 5 Οف׎ۓηᚈጠӝኳᄊϐԾฅᓎ౗ᆶኳᄊ႖ᚆ௃׎... 50 ߄ 6 ௗ᝻ჹϐჴதኧ೛ۓ... 50

კҞᒵ

კ 1.1 Barth ගрޑຬॣݢଭၲ[1] ... 51 კ 1.2 Sashida ගрϐᎫݢԄຬॣݢଭၲ[4]... 51 კ 1.3 ᎫݢԄຬॣݢଭၲ០୏চ౛ᆶᄬ೷[6] ... 52 კ 1.4 ՉݢԄຬॣݢଭၲ០୏চ౛ᆶᄬ೷[5] ... 52 კ 1.5 Kumada ගрޑ΋ᅿຬॣݢଭၲ[7] ... 53 კ 1.6 Nakamura et al ගрޑ΋ᅿຬॣݢଭၲ[8] ... 53 კ 1.7 Toyoda ᆶ Murano ගрϐຬॣݢଭၲ[9] ... 54 კ 1.8 Li and Zhao ගрޑጕ܄ຬॣݢଭၲ[10] ... 54 კ 1.9 Hemsel ᆶ Wallaschek ගрޑጕ܄ຬॣݢଭၲ[11] ... 55 კ 1.10 Vyshnevskyy ᆶ Kovalev ගрޑຬॣݢଭၲ[12] ... 55 კ 1.11 Vyshnevskyy ᆶ Kovalev ගрޑጕ܄ຬॣݢଭၲ[13] ... 56 კ 1.12 ҁࣴزගрϐຬॣݢଭၲۓη่ᄬ΋... 56 კ 1.13 ҁࣴزගрϐຬॣݢଭၲۓη่ᄬΒ... 57 კ 1.14 ҁࣴزගрϐຬॣݢଭၲۓη่ᄬΟ... 57 კ 2.1 ҅ᓸႝਏᔈ... 58 კ 2.2 ଍ᓸႝਏᔈ... 58 კ 2.3 ФႥ-܎ᅽහ᠄жำׇ ... 59 კ 2.4 Ԗज़ϡનኳࠠϐ(a)ௗ᝻߻Ǵ(b)ௗ᝻ࡕҢཀკ ... 59 კ 2.5 Οف׎ۓη่ᄬ΋ᆶႝཱུଛ࿼... 60 კ 2.6 ຬॣݢଭၲۓη่ᄬ΋ϐբ୏БԄ... 60 კ 2.7 Οف׎ۓη่ᄬΒᆶႝཱུଛ࿼... 61 კ 2.8 ຬॣݢଭၲۓη่ᄬΒϐբ୏БԄ... 61 კ 2.9 Οف׎ۓη่ᄬΟᆶႝཱུଛ࿼... 62

კ 2.10 ୖԵᗺϐНѳᆶႉࠟՏ౽ਁ൯࣬฻Ǵ࣬Տৡჹܭၮ୏ॉၞޑቹ ៜ ... 62 კ 3.1 Οف׎ۓη่ᄬ΋Ңཀკ... 63 კ 3.2 Οف׎ۓη่ᄬΒҢཀკ... 63 კ 3.3 Οف׎ۓη่ᄬΟҢཀკ... 64 კ 3.4 Οف׎ۓη่ᄬ΋ޑԖज़ϡનᆛ਱... 64 კ 3.5 Οف׎ۓη่ᄬΒޑԖज़ϡનᆛ਱... 65 კ 3.6 Οف׎ۓη่ᄬΟޑԖज़ϡનᆛ਱... 65 კ 3.7 ֹ ᏾ Ο ف ׎ ۓ η ่ ᄬ ΋ ܭ ό ӕ ଯ ࡋ Π ޑ Ծ ฅ ᓎ ౗ ϩ թ Ǵ L=30mmǴt=2mm ... 66 კ 3.8 ֹ ᏾ Ο ف ׎ ۓ η ่ ᄬ ΋ ܭ ό ӕ ࠆ ࡋ Π ޑ Ծ ฅ ᓎ ౗ ϩ թ Ǵ L=30mmǴH=15mm... 67 კ 3.9 Οف׎ۓη่ᄬ΋ܭόӕНѳ໒ኲߏࡋΠޑԾฅᓎ౗ϩթǴ L=30mmǴH=15mmǴt=2mm... 68 კ 3.10 Οف׎ۓη่ᄬ΋ܭόӕНѳ໒ኲՏ࿼ΠޑԾฅᓎ౗ϩթǴ L=30mmǴH=15mmǴLa=15mmǴt=2mm ... 69 კ 3.11 Οف׎ۓη่ᄬ΋ܭόӕࠟޔ໒ኲߏࡋΠޑԾฅᓎ౗ϩթǴ໒ ኲՏ࿼ǺۓηୁᜐύጕೀǴL=30mmǴH=15mmǴt=2mm... 70 კ 3.12 Οف׎ۓη่ᄬ΋ܭόӕࠟޔ໒ኲߏࡋΠޑԾฅᓎ౗ϩթǴ໒ ኲՏ࿼Ǻۓηୁᜐύጕೀޑٿ਒ǴL=30mmǴH=15mmǴt=2mm ... 71 კ 3.13 Οف׎ۓη่ᄬΟܭόӕ໒ኲుࡋΠޑԾฅᓎ౗ϩթǴ໒ኲՏ ࿼ ຯ ᚆ ۭ ᆄ 10.5mm Ǵ L=41mm Ǵ H=14mm Ǵ t=1.6mm Ǵ RI=RO=4.5mm... 72 კ 3.14 Οف׎ۓη่ᄬΟܭόӕНѳ໒ኲՏ࿼ΠޑԾฅᓎ౗ϩթǴ

L=41mmǴH=14mmǴt=1.6mmǴRI=RO=4.5mmǴCL=13.28mm 73 კ 3.15 Οف׎ۓη่ᄬΟܭόӕϣᏤفΠޑԾฅᓎ౗ϩթǴ໒ኲՏ࿼ ຯᚆۭᆄ 10.5mmǴL=41mmǴH=14mmǴt=1.6mmǴRO=3.5mmǴ CL=13.28mm ... 74 კ 3.16 Οف׎ۓη่ᄬΟܭόӕѦᏤفΠޑԾฅᓎ౗ϩթǴ໒ኲՏ࿼ ຯᚆۭᆄ 10.5mmǴL=41mmǴH=14mmǴt=1.6mmǴRI=4.5mmǴ CL=13.28mm ... 75 კ 3.17 Οف׎ۓη่ᄬ΋ܭόӕНѳ໒ኲߏࡋΠޑԾฅᓎ౗ϩթǴ໒ ኲՏ࿼Ǻຯᚆۭᆄ 2mmǴL=30mmǴH=15mmǴt=2mm ... 76 კ 3.18 Οف׎ۓη่ᄬ΋ܭόӕНѳ໒ኲߏࡋΠޑԾฅᓎ౗ϩթǴ໒ ኲՏ࿼Ǻຯᚆۭᆄ 2mmǴL=30mmǴH=17mmǴt=2mm ... 77 კ 3.19 Οف׎ۓη่ᄬ΋ܭόӕНѳ໒ኲߏࡋΠޑԾฅᓎ౗ϩթǴ໒ ኲՏ࿼Ǻຯᚆۭᆄ 2mmǴL=30mmǴH=19mmǴt=2mm ... 78 კ 3.20 Οف׎ۓη่ᄬ΋ϐᚈኳᄊጠӝკǴ(a)ಃΒסᙯኳᄊǴ(b)୷ҁ ᕵӛኳᄊ... 79 კ 3.21 Οف׎ۓη่ᄬΟϐᚈኳᄊጠӝკǴ(a)ಃ΋סᙯኳᄊǴ(b)୷ҁ ᕵӛኳᄊ... 79 კ 3.22 Οف׎ۓη่ᄬΟܭόӕϡનኧໆϐԾฅᓎ౗ϩթǴ໒ኲՏ࿼ ຯ ᚆ ഗ ᆄ 2.5mm Ǵ L=41mm Ǵ H=14mm Ǵ t=1.6mm Ǵ RI=RO=4.5mmǴCL=13.28mm... 80 კ 3.23 ۓη่ᄬ΋(a)ँଆᗺޑਁ൯ᆶᓎ౗ៜᔈ ... 81 კ 3.24 ۓη่ᄬ΋(b)ँଆᗺޑਁ൯ᆶᓎ౗ៜᔈ ... 81 კ 3.25 ۓη่ᄬ΋(c)ँଆᗺޑਁ൯ᆶᓎ౗ៜᔈ ... 82 კ 3.26 ۓη่ᄬ΋(d)ँଆᗺޑਁ൯ᆶᓎ౗ៜᔈ ... 82 კ 3.27 ۓη่ᄬΒँଆᗺޑਁ൯ᆶᓎ౗ៜᔈ... 83

კ 3.28 ۓη่ᄬΟँଆᗺޑਁ൯ᆶᓎ౗ៜᔈ... 83 კ 3.29 ႝᓸ០୏ 250 ຼයࡕۓη่ᄬ΋ँଆᗺޑՏ౽ៜᔈǴ(a) X Бӛ Տ౽ៜǴ(b) Y БӛՏ౽ៜᔈǴ(c) Z БӛՏ౽ៜᔈ ... 84 კ 3.30 ۓη่ᄬ΋ँଆᗺϐୖԵ০኱Ϸၮ୏ॉၞ... 85 კ 3.31 ႝᓸ០୏ 250 ຼයࡕۓη่ᄬΒँଆᗺޑՏ౽ៜᔈǴ(a) X Бӛ Տ౽ៜǴ(b) Y БӛՏ౽ៜᔈǴ(c) Z БӛՏ౽ៜᔈ ... 86 კ 3.32 ۓη่ᄬΒँଆᗺϐୖԵ০኱Ϸၮ୏ॉၞ... 87 კ 3.33 ႝᓸ០୏ 230 ຼයࡕۓη่ᄬΟँଆᗺޑՏ౽ៜᔈǴ(a) X Бӛ Տ౽ៜǴ(b) Y БӛՏ౽ៜᔈǴ(c) Z БӛՏ౽ៜᔈ ... 88 კ 3.34 ۓη่ᄬΟँଆᗺϐୖԵ০኱Ϸၮ୏ॉၞ... 89 კ 3.35 ۓη่ᄬΟᆶᙯηϐԖज़ϡનኳࠠ... 90 კ 3.36 ௗ᝻ჹϡન০኱ϐݤӛໆҢཀკ... 90 კ 3.37 ۓη่ᄬΟ០୏ 150 ຼයࡕǴᙯηޑኩᄊՏ౽ៜᔈ... 91 კ 3.38 ۓη่ᄬΟ០୏ 150 ຼයࡕǴᙯηޑኩᄊೲࡋៜᔈ... 91 კ 3.39 ႣᓸΚ 0.98N ᆶ 4.116N բҔΠǴᙯೲᆶסંޑᜢ߯Ԕጕ... 92 კ 4.1 Б׎ᓸႝഏౠ... 92 კ 4.2 ჴᡍᇶշπڀ(a)ᓸႝТᗹຠᇶշᏔǴ(b)ᓸլΚ֨ڀ ... 93 კ 4.3 ຬॣݢଭၲۓη่ᄬ΋চࠠ... 93 კ 4.4 ຬॣݢଭၲۓη่ᄬΒচࠠ... 94 კ 4.5 ຬॣݢଭၲۓη่ᄬΟচࠠǴௗ᝻ᗺࣁۓηഗᗺँଆ ... 94 კ 4.6 ຬॣݢଭၲۓη่ᄬΟচࠠǴௗ᝻ᗺࣁᒳౚ... 95 კ 4.7 ᆛၡϩ݋ሺໆෳଭၲۓηӅਁᓎ౗Ңཀკ... 95 კ 4.8 ჴᡍໆෳຬॣݢଭၲۓη่ᄬ΋ޑߔלᆶ࣬Տᓎ᛼... 96 კ 4.9 ჴᡍໆෳຬॣݢଭၲۓη่ᄬΒޑߔלᆶ࣬Տᓎ᛼... 96 კ 4.10 ჴᡍໆෳຬॣݢଭၲۓη่ᄬΟޑߔלᆶ࣬Տᓎ᛼Ǵௗ᝻ᗺࣁ

ۓηഗᗺँଆ... 97 კ 4.11 ჴᡍໆෳຬॣݢଭၲۓη่ᄬΟޑߔלᆶ࣬Տᓎ᛼Ǵௗ᝻ᗺࣁ ᒳౚ ... 97 კ 4.12 ႜ৔೿Νୌෳਁሺໆෳଭၲۓη่ᄬΟӅਁᓎ౗ҢཀკǴௗ᝻ ᗺࣁᒳౚ... 98 კ 4.13 LDV ໆෳଭၲۓη่ᄬΟୖԵᗺ a ޑਁ൯ᓎ౗ៜᔈԔጕǴௗ᝻ ᗺࣁᒳౚ... 99 კ 4.14 LDV ໆෳଭၲۓη่ᄬΟୖԵᗺ b ޑਁ൯ᓎ౗ៜᔈԔጕǴௗ᝻ ᗺࣁᒳౚ... 99 კ 4.15 ຬॣݢଭၲϐסંᆶᙯೲ܄ૈໆෳǴჴᡍࢎᄬҢཀკ ... 100 კ 4.16 ຬॣݢଭၲচࠠᐒΟϐ០୏ᓎ౗ᆶᙯೲԔጕǴௗ᝻ᗺࣁۓηഗ ᗺँଆ ... 101 კ 4.17 ຬॣݢଭၲচࠠᐒΟϐ០୏ᓎ౗ᆶᙯೲԔጕǴௗ᝻ᗺࣁᒳౚ . 101 კ 4.18 ຬॣݢଭၲচࠠᐒΟϐ០୏ႝᓸᆶᙯೲԔጕǴௗ᝻ᗺࣁۓηഗ ᗺँଆ ... 102 კ 4.19 ຬॣݢଭၲচࠠᐒΟϐ០୏ႝᓸᆶᙯೲԔጕǴௗ᝻ᗺࣁᒳౚ . 102 კ 4.20 ຬॣݢଭၲচࠠᐒΟϐ០୏ႝᓸᆶסંԔጕǴௗ᝻ᗺࣁۓηഗ ᗺँଆ ... 103 კ 4.21 ຬॣݢଭၲচࠠᐒΟϐ០୏ႝᓸᆶסંԔጕǴௗ᝻ᗺࣁᒳౚ . 103 კ 4.22 ຬॣݢଭၲচࠠᐒΟϐႣᓸΚᆶסંԔጕǴௗ᝻ᗺࣁۓηഗᗺ ँଆ ... 104 კ 4.23 ຬॣݢଭၲচࠠᐒΟϐႣᓸΚᆶסંԔጕǴௗ᝻ᗺࣁᒳౚ ... 104 კ 4.24 ຬॣݢଭၲচࠠᐒΟϐסંᆶᙯೲԔጕǴௗ᝻ᗺࣁۓηഗᗺँ ଆ ... 105 კ 4.25 ຬॣݢଭၲচࠠᐒΟϐסંᆶᙯೲԔጕǴௗ᝻ᗺࣁᒳౚ ... 105

კ 4.26 ႣᓸΚ 0.98N բҔΠǴຬॣݢଭၲচࠠᐒΟϐᙯೲᆶסં܄ૈ Ԕጕޑኳᔕᆶໆෳ่݀КၨǴௗ᝻ᗺࣁᒳౚ... 106 კ 4.27 ႣᓸΚ 4.116N բҔΠǴຬॣݢଭၲচࠠᐒΟϐᙯೲᆶסં܄ૈ

ಃ΋ക ᆣፕ

1.1

߻ق

ᒿ๱ࣽמౢ཰מೌޑว৖Ǵᐒႝ᏾ӝςԋࣁ୯ৎౢ཰ᆶᏢೌ௲ػว ৖ख़ᗺϐ΋Ǵଭၲࢂനڂࠠޑᐒႝ᏾ӝჴٯǴคፕӧπ཰ǵ҇ғǵᙴᕍǵ ႝတၗૻ܈ै٣ૐޜ฻ሦୱǴࣣࢂόё܈લϐး࿼Ǵଭၲ٬Ҕ௃ݩΨϸ ࢀр୯ৎჹࣽמౢ཰ว৖ޑ׫ΕǶ ໺಍ႝᅶଭၲ(electromagnetic motor)ว৖ԿϞςԖ΋ԭӭԃޑᐕ ўǴႝᅶଭၲϝฅӸӧ೚ӭᜤаլܺޑୢᚒǴٯӵǺѦӧᅶ൑υᘋǵᡏ ᑈ༾ࠠϯࡕਏ౗ୃեǵեᙯೲᏤठคݤၲډଯᙯંϷᏓॣ฻લᗺǶԶຬ ॣݢଭၲ(ultrasonic motor)ૈׯ๓ႝᅶଭၲ೭٤લᗺǶ ຬॣݢଭၲΞᆀࣁᓸႝଭၲ(piezoelectric motor)Ǵஒᓸႝഏౠ׷਑ᗹ ຠܭቸ܄ᡏ่ᄬǴճҔᓸႝ׷਑ޑ଍ᓸႝਏᔈǴаଯᓎҬࢬႝᓸᐟว੝ ۓኳᄊޑ่ᄬਁ୏Ƕቸ܄ᡏ่ᄬ߄य़ޑಈηൻᐍ༝ॉၞբຼයၮ୏Ǵᙖ ๱ነᔔΚ០୏ଭၲᙯη௽ᙯ܈ྖ০ޔጕၮ୏Ƕຬॣݢଭၲޑਁ୏ᓎ౗ଯ ܭΓᜪ᠋ΚጄൎǴ፾ӝᔈҔܭሡाӼᓉޑ൑܌ǴЪਁ൯Տ౽ໆλǴૈ୺ ՉଯᆒࡋޑۓՏ௓ڋǶ ຬॣݢଭၲڀഢեᙯೲଯᙯંǵᛙۓᒡр௓ڋϷᆒஏۓՏǴόڙᅶ ൑υᘋǵуπ৒ܰǵΞόሡམଛ෧ೲᐒᄬޑ୏Κ੝܄Ǵ٬ளຬॣݢଭၲ ӧࢌ٤ᔈҔሦୱёаڗж໺಍ޑႝᅶଭၲǴٯӵǺѸ໪ᗉխᅶ൑υᘋϐ ᙴᕍᏔ׷ǴਡᅶӅਁ௟ඔሺ MRIǶຬॣݢଭၲ೸ၸነᔔޑБԄၮᙯǴௗ ᝻୔ୱ༈Ѹ཮ౢғᑃ઻ǴߏΦΠٰነᔔय़೴ᅌӀྖǴᏤठଭၲסં܄ૈ फ़եǶᗨฅԖ೚ӭ෧Ͽᑃ઻ޑ೛ीϷ٬Ҕऐᑃ܄٫ޑ׷਑೏ᔈҔӧຬॣ ݢଭၲ΢Ǵ࣬ၨܭႝᅶଭၲǴຬॣݢଭၲޑ٬ҔტڮၨอǴࢂځલᗺǶ ߈ԃٰǴຬॣݢଭၲςቶݱᔈҔܭ࣬ᐒǵЋᒮǵᙴᕍ೛ഢǵૐϼπ

཰ǵᆒஏۓՏ೛ഢϷᐒᏔΓ฻ᐒஏᐒఓǶຬॣݢଭၲᡏᑈλǵख़ໆᇸϷ ่ᄬᙁൂǴ࣬ၨܭӕЁκޑႝᅶଭၲૈᕇளၨεޑסંǶӢԜǴ߈ԃٰ ຬॣݢଭၲޑࣴزᆶว৖೴ᅌڙᏢޣख़ຎǶ

1.2

ࣴزङඳ

ຬॣݢଭၲޑว৖ёଓྉԿ 1973 ԃǴBarth [1]ගрᎫݢԄຬॣݢଭ ၲǴځଭၲᄬ೷ӵკ 1.1 ܌ҢǴճҔᓸႝਁᕏηޑືӛᡂ׎௢୏ᙯηൂӛ ௽ᙯǴऩᒧ᏷០୏ޑਁᕏηǴջё௓ڋଭၲᙯӛǴԜठ୏ᐒڋᛖܭᑃ઻ (wear)ǵኚ຋(tear)Ϸྕࡋ΢ϲࡕᜤаᆢ࡭ᛙۓၮᙯ฻લᗺǴؒԖбፏჴሞ ᔈҔǶ Lavrinenko et al [2]ܭ 1796 ԃǴගрӭᅿόӕ่ᄬޑຬॣݢଭၲǴᘜ યрଭၲڀԖ่ᄬᙁൂǵଯסંǵեᙯೲǵଯᒡрф౗ϷᆒஏۓՏ฻ᓬ ᗺǶVasiliev et al [3]ܭ 1979 ԃǴճҔᙔ݇Ў(Langevin)ਁᕏηޑຬॣݢඤ ૈᏔౢғᕵӛਁ୏Ǵ០୏ᙯη௽ᙯǴҗܭคݤᆢ࡭ڰۓਁ൯аϷྕࡋǵ ᑃ઻฻ୢᚒǴҭคёᔈҔޑ൑ӝǶ Sashida [4]ܭ 1982 ԃǴගр΋ᅿᎫݢԄຬॣݢଭၲǴӵკ 1.2 ܌ҢǴ аᙔ݇Ўਁᕏηբࣁ០୏ྍǴගଯਁᕏηޑՏ౽ໆǴਁᕏηޑུ׎Ӿᆄ аᐍ༝ॉၞၮ୏Ǵ໔ྂ܄௢୏ᙯη௽ᙯǴԖਏӦׯ๓Ӣྖ୏೷ԋޑૈໆ ཞ઻Ƕڀഢեᙯೲଯסંǵଯਏ౗฻੝ՅǴՠ٬ҔტڮϝคݤගଯǶӕ ԃǴSashida ᆶ Kenjo [5]ว৖΋ᅿՉݢԄᕉࠠຬॣݢଭၲǶஒڀԖٿಔཱུ ϯБӛ࣬ϸޑᓸႝ༝ᕉǴᗹຠܭ΋ڀԖ਩Ꮑރܫεᐒᄬޑߎឦ༝ᕉΠ БǴϩձᒡΕٿಔ࣬ӕᓎ౗ǵਁ൯࣬฻ǵڀ 90 ࡋ࣬Տৡϐ۰ݢႝᓸǴᐟ วൂБӛᙯ୏ޑՉ຾ݢǶஒᙯηܫ࿼ܭߎឦ༝ᕉ΢БǴᙖ๱ٿޣ໔ޑነ ᔔΚ០୏ᙯηǴׯᡂ࣬Տৡё௓ڋଭၲᙯӛǶ٠ගрӧᙯηᆶۓηϐ໔ ᗹຠ΋ቫऐᑃ׷਑Ǵёε൯ׯ๓ᑃ઻ޑୢᚒǶԜ΋ଭၲ२ӃᔈҔӧྣ࣬

ᐒޑԾ୏ჹขس಍ύǴࢂಃ΋ঁၲډ୘཰ᔈҔሽॶޑຬॣݢଭၲǴϐࡕǴ ֎ЇΑ೚ӭᏢޣ׫ΕࣴزǶ Ҟ߻ςԖ೚ӭຬॣݢଭၲഌុ೏ගрǴਥᏵᙯηᆶۓηޑௗ᝻ࠠԄ ܈ۓη೏ᐟวޑݢԄǴёϩࣁٿᜪǺᎫݢ(standing wave)ԄϷՉݢ(traveling wave)ԄຬॣݢଭၲǶᎫݢԄຬॣݢଭၲۓηаϸᙟБԄਁ୏Ǵۓηᆶᙯ η଺໔ྂԄޑௗ᝻Ǵۓηޑௗ᝻ᗺբ΋ᐍ༝ॉၞၮ୏ǴᙖҗነᔔΚ௢୏ ᙯηǶკ 1.3 ܌Ңࣁ Ueha ᆶ Tomikawa[6]܌ගрϐ΋ᅿᎫݢԄ༝ࢊࠠຬ ॣݢଭၲǴӧ໘ࢤ(1)ਔǴסᙯՏ౽ࣁ႟ǵೲࡋӛѓǴᕵӛਁ୏Տ౽ࣁന ε҅ॶǴ٬ۓη่ᄬ՜ߏᆶᙯηௗ᝻Ǵ٠ஒϪጕБӛਁ୏໺Կᙯη٬ځ ௽ᙯǶӧ໘ࢤ(2)ਔǴᕵӛਁ୏Տ౽ࣁ႟Ǵᙯηᆶۓηϩ໒ǴԜਔϪጕБ ӛਁ୏Տ౽ࣁനεॶǴೲࡋࣁ႟Ƕӧ໘ࢤ(3)ਔǴۓηືӛߏࡋᕭอǴᕵ ӛਁ୏Տ౽ࣁനεॄॶǴϪጕБӛਁ୏Տ౽ࣁ႟ǴסᙯೲࡋӛѰ٠໒ۈ ϸӣډচᗺǶӧ໘ࢤ(4)ਔǴᕵӛਁ୏Տ౽ࣁ႟ǴϪጕБӛਁ୏Տ౽ࣁന εॄॶǴೲࡋࣁ႟ǴԜਔ༝ࢊᡏۓηסᙯǴՠߥ࡭চٰᡏᑈǴ҂ᆶᙯη ௗ᝻ǶӵԜຼԶൺۈǴߡૈ០୏ଭၲբൂ΋Бӛ௽ᙯၮ୏Ǵ೭ᅿբ୏Б Ԅᆀࣁᚈኳᄊጠӝਁ୏ޑຬॣݢଭၲǶ΋૓ԶقǴᎫݢԄຬॣݢଭၲޑ ԋҁեǴѝሡ΋ঁਁ୏ྍǴਏ౗ଯǴ౛ፕ΢ёၲ 98%Ǵଭၲޑ೛ीၨ൤ ቸ܄ЪӭኬϯǶ Չݢ(traveling wave)Ԅຬॣݢଭၲޑ០୏ᐒڋӵკ 1.4 ܌ҢǴӧᓸႝ ᡏ΢೛࿼ٿಔႝཱུǴႝཱུౢғޑႝ൑ᆶᓸႝᡏޑཱུϯБӛ࣬ӕ܈ϸӛǴ ᄬԋٿಔඤૈᏔǴаٿಔᓎ౗ᆶਁ൯࣬฻ޑ҅۰ݢૻဦ០୏ඤૈᏔǴٿ ಔૻဦޑ࣬Տৡࣁ 90 ࡋǴٿಔඤૈᏔᐟਁрޑӅਁኳᄊυੋԋࣁ΋Չ຾ ݢǶۓηᆶᙯηߥ࡭ௗ᝻Ǵௗ᝻ᗺޑၮ୏ॉၞև౜΋ᐍ༝Ǵᙖ๱ነᔔΚ ០୏ᙯη௽ᙯǶᆶᎫݢԄଭၲόӕϐೀӧܭۓηޑௗ᝻ᗺߚڰۓǴᙯη ၮ୏ޑБӛᆶՉ຾ݢಈηၮ୏Бӛ࣬ӕǶՉݢԄຬॣݢଭၲޑᙯӛ௓ڋ

৒ܰǵௗ᝻ᑃ઻λ฻ᓬᗺǴՠՉ຾ݢբ୏ਔؒԖ࿯ᗺӸӧǴۓηڰ๱Б Ԅ٬ளௗ᝻ᗺՏ౽λǴᏤठၮᙯਏ౗फ़եǶ

1.3

Ў᝘ӣ៝

1.3.1 ਁ୏ጠӝࠠຬॣݢଭၲ 1985 ԃ Ǵ Kumada[7] ೛ ी ΋ ੝ ਸ ่ ᄬ ϐ ס ᙯ ጠ ӝ η (torsional coupler)Ǵӵკ 1.5 ܌ҢǴճҔᙔ݇Ўਁᕏ୏ηࣁਁ୏ྍǴ྽ਁ୏η΢Π ਁ୏ਔǴӕਔᐟว่ᄬᡏޑ៻ԔኳᄊᆶסᙯኳᄊǴ٬ளጠӝηޑᆄय़ౢ ғᐍ༝׎ॉၞၮ୏Ǵ௢୏ᙯηݮൂ΋Бӛᙯ୏Ƕ࿶ന٫ϯ೛ीࡕଭၲਏ ౗ёၲ 80%Ǵቚ຾ຬॣݢଭၲޑჴҔ܄Ƕ ࣁΑ٬ᙯηڀԖ҅ϸӛ௽ᙯޑૈΚǴNakamura et al [8]೛ी΋סᙯ ࠠᙔ݇ЎᙯඤᏔ(torsional Langevin transducer)Ǵӵკ 1.6 ܌ҢǶаסᙯठ ୏Ꮤ(torsional actuator)่ӝᕵӛठ୏Ꮤ(longitudinal actuator)Ǵӧۓηௗ᝻ ᗺೀౢғᕵӛᆶᐉӛՏ౽Ǵ่ӝԋᐍ༝׎ၮ୏ॉၞǶଭၲޑ០୏БԄӵ კ 1.3 Ѥঁठ୏໘ࢤǴסᙯठ୏Ꮤᆶᕵӛठ୏ᏔޑᒡΕႝᓸ࣬Տৡࣁ 90 ࡋǴ௓ڋ࣬ՏޑሦӃᆶပࡕ،ۓᙯηޑ௽ᙯБӛǴԜ០୏БԄࣁڂࠠޑ ጠӝࠠਁ୏ηǶ 1991ԃǴToyoda ᆶ Murano[9]೛ीӵკ 1.7 ܌Ңޑຬॣݢଭၲ೛ीǴ ӧ΋ঁٿᆄڰۓޑఉΠБᗹຠᓸႝ׷਑Ǵᐟਁఉޑ៻ԔኳᄊǴ٬ளఉޑ ٿଫۯ՜ဌ଺ࠟޔБӛޑၮ୏Ƕٿဌ໔Ԗ΋ᑈቫԄᓸႝ׷਑(multilayer piezoelectric material)௓ڋٿဌբНѳБӛޑਁ୏Ƕ྽ࠟޔБӛᆶНѳБ ӛϐਁ୏࣬Տৡࣁ 90 ࡋਔǴٿဌӾᆄևᐍ༝׎ॉၞၮ୏Ƕ 1998 ԃǴLi ᆶ Zhao[10]ගрӵკ 1.8 ܌ҢޑຬॣݢଭၲǴа࣬ӕޑ Ӆਁᓎ౗Ϸ࣬Տৡ 90 ࡋޑႝᓸᐟਁٿಔᓸႝТǴ่ӝᕵӛኳᄊᆶಃΟ៻ Ԕኳᄊӧਁ୏ηᆄᗺբᐍ༝׎ॉၞၮ୏Ǵ٠ᙖ࣬ՏޑሦӃᆶပࡕ௓ڋྖ

୏ѳѠޑၮ୏БӛǶ

2000 ԃǴቺ୯ۦቺ࢙ৱεᏢ(University of Paderborn)ޑ Hemsel ᆶ Wallaschek [11]೛ी΋ጕ܄ຬॣݢଭၲǴӵკ 1.9 ܌ҢǴஒ่݈ᄬϐᕵӛ ਁ୏ᆶ៻Ԕਁ୏ޑኳᄊጠӝǴ٬ௗ᝻ᆄᗺբᐍ༝׎ॉၞၮ୏Ƕ٠ஒЍኖ ᗺ೛ीӧਁ୏ηޑ࿯ᗺ΢ǴаϷᚈӛᒡрޑ೛ीǴගଯଭၲޑ௢Κᆶਏ ౗ǴЪ෧ϿႣᓸΚ܌೷ԋޑቹៜǶҗܭਁ୏ηޑၮ୏БԄᜪ՟ӊ኶ (rowing)ǴӢԜڮӜࣁۦቺ࢙ৱӊ኶ଭၲ(Paderborn rowing motor)Ƕ

2005ԃǴቺ୯ Physik Instrumente Ϧљޑπำৣ Vyshnevskyy et al [12] аᓸႝ༝ᆅࣁۓηǴӵკ 1.10 ܌ҢǴ០୏༝ᆅౢғືӛᆶᐉӛޑጠӝኳ ᄊǴ༝ᆅૉጔޑ፦ᗺբᐍ༝׎ॉၞၮ୏ǶԜ០୏БԄёҗൂ࣬ठ୏Ꮤᐟ วǴឦᎫݢԄຬॣݢଭၲǹќ΋ී߾җΟ࣬ठ୏ᏔǴ࣬Տৡϩձࣁ 0 ࡋǵ 120 ࡋϷ 360 ࡋ܌ठ୏ǴឦՉݢԄຬॣݢଭၲǶԜଭၲϐ០୏ႝᓸ໻ሡ 15 Vrmsջૈᕇளଯਏ౗ޑᒡр܄ૈǶӕԃǴΞว߄ൂ΋ኳᄊ០୏ޑጕ܄ ຬॣݢଭၲ[13]Ǵӵკ 1.11 ܌ҢǴठ୏Ꮤࣁ߄य़ϩപԋٿ༧ႝཱུϐᓸႝഏ ౠǴൂ࣬ᐟਁϸჹᆀӅਁኳᄊǴ٬ठ୏Ꮤ΢ᆄௗ᝻ᗺݮ΋௹ጕٰӣਁ୏Ƕ ऩሡׯᡂѳѠޑྖ୏БӛǴᒧ᏷ќ΋ႝཱུ୔༧ठ୏ջёǶଭၲ࿶ന٫ϯ ೛ीࡕǴഌុ໒วрӭීόӕೕ਱ޑ୘ࠔ΢ѱǶ 2011 ԃǴShi ᆶ Zhao [14]ගр΋ᎫݢԄϐጕ܄ຬॣݢଭၲǴۓη೽ ϩࣁ΋อఉ่ᄬᆶอఉ΢ୁޑΟف׎่ᄬ܌ಔԋǴఉޑΠୁᗹຠٿТᓸ ႝ׷਑ǴӧᓸႝТϐ߄य़ႝཱུࡼуٿಔ࣬Տৡ 90 ࡋޑҬࢬႝᓸǴᐟวอ ఉ่ᄬޑٿಔय़ϣӅਁኳᄊǴ٬ளಃ΋ᕵӛኳᄊᆶಃΒ៻ԔኳᄊጠӝǴ Οف׎ޑഗᗺբᐍ༝׎ॉၞၮ୏ǴᙖҗነᔔΚ஥୏ྖ০ၮ୏Ƕ٠аᚈጠ ӝኳᄊޑനλᓎ౗ৡࣁҞ኱ڄኧǴ࿶җന٫ϯ೛ी،ۓۓηޑ൳Ֆୖ ኧǴኳᔕΟف׎่ᄬϐۭففࡋჹௗ᝻ᗺ X ᆶ Y БӛՏ౽ޑቹៜǴЪჴ ᡍ᛾ჴǴӧόӕΟف׎่ᄬϐۭففࡋǴௗ᝻ᗺ X БӛޑՏ౽ελױᜢ

ܭᙯೲޑଯեǴY БӛޑՏ౽ελױᜢܭסંޑελǶჴᡍໆෳۭفࣁ 20ࡋޑΟف׎่ᄬǴଭၲ܄ૈന٫ǴคॄၩΠޑᙯೲࣁ 98mm/sǴനε܎ Κࣁ 3.2NǶ 1.3.2 ຬॣݢଭၲϐௗ᝻ϩ݋ 1992ԃǴMaeno et al [15]аԖज़ϡનݤϩ݋ଭၲۓηޑਁ୏ኳᄊǴ ीᆉۓη߄य़сᏁޑᐍ༝ၮ୏ॉၞǴᆶჴᡍ่݀Ԗؼӳޑ΋ठ܄Ƕ٠ܭ ௗ᝻ϩ݋ύયΕᚵᆦڄኧݤ(penalty function formulation*Ǵኳᔕۓηᆶᙯ ηޑ୏ᄊௗ᝻ՉࣁǴ؃рۓηᆶᙯηޑՏ౽ǵೲࡋǵᗹᅉ୔ୱᆶྖ୏୔ ୱޑϩթय़ᑈϷௗ᝻य़΢ޑ҅ӛΚᆶነᔔΚϩթǴ٠ीᆉଭၲᒡрޑΚ ંᆶᙯೲԔጕǵଭၲਏ౗ᆶཞѨૈໆǶ 1993ԃǴHirata ᆶ Ueha [16]ගр΋঺ीᆉՉݢԄຬॣݢଭၲॄ಻੝ ܄ޑБݤǴа฻ਏႝၡኳࠠ՗ෳଭၲޑ܄ૈǴҗܭขᗺࣁਁ୏ηޑӅਁ ᓎ౗Ǵ଑ၡύ۹ౣ฻ਏ፦ໆᆶখࡋޑᜢ߯ԄǶஒᙯηᆶਁ୏η໔ޑௗ᝻ ୔ୱຎࣁΒᆢቸ܄ᡏௗ᝻ǴճҔΒᆢቸ܄ᡏௗ᝻౛ፕीᆉрᙯηᆶਁ୏ η໔ޑௗ᝻ᓸΚǴᘜય؃ှࢬำǴኳᔕ่݀ᆶჴᡍໆෳ่݀࣬՟Ƕ 1995 ԃǴHagood ᆶ McFarland[17]ஒᔈᡂᆶႝՏӕਔԵቾયΕس಍ ޑ୏ᄊБำԄǴճҔႜճ(Reyleigh-Ritz)ኳᄊଷ೛ݤளډ୏ᄊኳᔕޑ߈՟ ှǶຎۓηࣁখᡏǴᙯηࣁ΋ጕ܄ቸᘽǴۓηᆶᙯηख़᠄୔ୱۓကࣁ΋ ᓸᕭޑቸᘽس಍ǴӧᛙᄊਔǴ۹ౣᙯηᄍ܄ΚޑቹៜǴ๏ۓຬॣݢၲޑ ០୏ႝᓸǵືӛႣᓸΚϷଭၲޑѦуסંࣁᒡΕୖኧǴջёीᆉଭၲޑ ᛙᄊᙯೲǵᒡрф౗Ϸਏ౗Ƕ٠ܭۓηޑ߄य़ࡌҥсᏁރ่ᄬǴ૸ፕԖ คсᏁϷᏁଯჹଭၲ܄ૈޑቹៜǶ 2001ԃǴStorck et al [18][19]ᇥܴቹៜଭၲۓηᆶᙯηܭᗹᅉᆶྖ୏ ၸำύǴЬाᜢᗖӧܭነᔔቫ׷਑ޑቸ܄܄፦Ǵஒነᔔቫຎࣁᗹቸ܄׷ ਑ǴӧືӛᆶϪጕБӛࡌҥቸᘽߔѭޑௗ᝻س಍ǴճҔነᔔቫύൂ΋፦

ໆϡનޑၮ୏БำԄǴ௢Ꮴ҅ӛΚᆶነᔔΚǴ٠уΕᄍ܄ΚޑቹៜǴҗ ฻ਏቸᘽᆶߔѭ،ۓଭၲޑᒡрסંǵᙯೲϷਏ౗ǴᇥܴΑۓηᆶᙯη ࣁᗹᅉ(stick)ነᔔਔǴଭၲޑਏ౗ཞѨനλǶ 2007ԃǴVasiljev et al [20]аԖज़ϡન ANSYS ኳᔕຬॣݢଭၲޑ୏ ᄊௗ᝻ୢᚒǴԵቾۓηᆶྖ০ޑௗ᝻ՉࣁǴܭྖ০ௗ᝻य़у΢΋ቫነᔔ ቫǴ٬Ҕय़ჹय़ௗ᝻ϡનǴஒҞ኱ϡન TARGE170 ߕ๱ܭྖ০߄य़Ǵௗ ᝻ϡન CONTA174 ߕ๱ܭۓη߄य़Ǵ٠ӧۓηᆶነᔔቫǵነᔔቫᆶྖ০ ϐ໔Ӛࡌҥٿಔόӕޑௗ᝻ჹୖኧǴӧ۹ౣߔѭ௃ݩΠǴኳᔕྖ০ӧ߻ Οঁ០୏ຼයϣǴۓηௗ᝻ᗺӧ X ᆶ Y Бӛ΢ޑՏ౽-ਔ໔ԔጕǴ၀ᗺޑ ၮ୏ॉၞᆶਔᒋϩ݋่݀࣬՟Ƕჴᡍ௦Ҕႜ৔ෳਁሺໆෳௗ᝻ᗺޑਁ ൯Ǵᆶኧॶኳᔕ่݀ᇤৡӧ 5~8%ϐ໔Ƕ

1.4

ࣴزҞޑ

ҁࣴزගрΟᅿᚈኳᄊጠӝࠠຬॣݢଭၲǴۓηҗ᎑ӝߎ܌ᇙԋǴ Οف׎Ӛᜐύᗺޑ΢ᆄ܈Οف׎ഗᗺ೛ी΋ँଆǴϩձӧΟف׎ޑୁᜐ ᆶفᆄೀϪപНѳϾᕳǴӵკ 1.12~კ 1.14 ܌ҢǶۓηޑΟᜐᗹຠБ׎ᓸ ႝഏౠǴႝཱུ೽ϩϩപԋٿ༧୔ୱǴࡼу΋࣬Տৡࣁ 90 ࡋޑٿಔҬࢬႝ ᓸǴа࣬ӕπբᓎ౗ठਁۓη࣬ϕ҅Ҭޑ୷ҁᕵӛኳᄊᆶסᙯኳᄊǴ٬ ځጠӝਁ୏Ƕۓηँଆᗺևᐍ༝׎ॉၞၮ୏Ǵᙖۓηᆶᙯη໔ޑነᔔΚ ០٬ᙯη௽ᙯǴፓ᏾ᒡΕႝᓸ࣬ՏৡޑሦӃᆶပࡕǴё௓ڋᙯηޑᙯ୏ БӛǶᒧ᏷Οف׎่ᄬޑЬाӢનࢂа۳ۓη௦Ҕ༝ᆅ׎่ᄬǴᓸႝ׷ ਑٬Ҕᓸႝ༝ᆅǴӧᇙբਔܰวғᐨ่ᆶཱུϯό֡฻ୢᚒǴۓηᆶᓸႝ ༝ᆅௗӝਔ৒ܰౢғୃЈޑᇤৡǴቹៜଭၲ᏾ᡏ܄ૈǴԶБ׎ᓸႝТڀ ׷਑܄፦ᛙۓǵ୯ϣڗள৒ܰǵܰܭуπǵԋҁե༹ϷБߡᗹຠ฻ᓬᗺǶ ҁࣴزගٮ΋೛ीБݤϩ݋ۓηኳᄊጠӝ่ᄬǴҗኳᄊϩ݋௖૸ܭ

Οف׎ୁᜐϪപಒߏޑНѳϾᕳǴԖਏӦ෧১ۓηޑᕵӛখ܄Ǵ٬୷ҁ ᕵӛኳᄊϐԾฅᓎ౗ᗊफ़Ǵᖿ߈ܭסᙯኳᄊޑԾฅᓎ౗ǴᢀჸӚኳᄊ໔ ᓎ౗ϩթǴפрଭၲۓηന٫ኳᄊ႖ᚆϐ൳ՖୖኧǴ෧Ͽ୷ҁᕵӛኳᄊ ᆶסᙯኳᄊጠӝਔڙډځѬኳᄊυᘋǶനࡕǴ຾Չຬॣݢଭၲޑኩᄊៜ ᔈϩ݋Ǵᡍ᛾ኳᄊ႖ᚆϐਏ݀Ϸᢀჸँଆᗺϐၮ୏ॉၞǶ ҁࣴزӧຬॣݢଭၲচࠠᐒޑჴᡍໆෳύǴ௦ҔႝᅶགᔈБԄǴ௓ ڋႝࢬޑελࡼϒᙯηႣᔈΚǴڗж໺಍ࡼуઆዸ৒ܰᏤठᙯηᙯ୏ᄍ ໆၸεǴΨ௭కܫ࿼ᓸᕭቸᘽ೷ԋᙯηڙΚંό֡Ǵᗉխቹៜଭၲ܄ૈǶ ӧόӕႣᔈΚǵႝᓸϷᓎ౗ΠǴໆෳຬॣݢଭၲޑᛙᄊᙯೲᆶסંǶ ٩Ᏽຬॣݢଭၲচࠠᐒϐჴሞ០୏БԄǴаԖज़ϡન঺း೬ᡏ ANSYSǴࡌҥۓηᆶᙯηޑኳࠠǴኳᔕۓηᆶᙯη໔ޑኩᄊௗ᝻ΚᏢՉ ࣁǴ๏ۓჴሞރݩޑՏ౽ᆶѦΚᜐࣚచҹǴа፾྽ޑௗ᝻ୖኧǴෳ၂౛ གྷޑԏᔙှᆶӝ౛ޑीᆉ่݀Ǵ՗ෳଭၲޑᙯೲᆶסં܄ૈԔጕǶ

1.5

ϣ৒ᙁॊ

ҁЎӅϩԋϖകǴಃ΋കϟಏࣴزङඳᆶ୏ᐒǵЎ᝘ӣ៝ϷፕЎࢎ ᄬǶಃΒകࣁ౛ፕϩ݋Ǵϟಏᓸႝਏᔈǵᓸႝ׷਑ޑΚᏢǵႝ܄ՉࣁϷ ҁࣴز࣬ᜢޑຬॣݢଭၲπբচ౛ǶಃΟകᇥܴຬॣݢଭၲޑኳᄊϩ݋ ᆶኩᄊϩ݋ǴаΟف׎ۓηޑଯࡋǵࠆࡋϷНѳ໒ኲߏࡋࣁ೛ीୖኧǴ ௖૸ۓη୷ҁᕵӛኳᄊᆶסᙯኳᄊጠӝޑᓎ౗ᡂϯϷኳᄊ႖ᚆޑന٫ ϯǴीᆉۓηӧँଆᗺϐՏ౽ៜᔈǴᢀჸ၀፦ᗺޑၮ୏ॉၞǶࡌҥۓη ᆶᙯηޑௗ᝻ኳࠠǴኳᔕଭၲբ୏ਔۓηᆶᙯη໔ޑௗ᝻ΚᏢՉࣁǶಃ Ѥക௶ॊ٩ᏵಃΟക܌ᕇளޑۓηୖኧǴᇙբຬॣݢଭၲচࠠᐒǴ຾Չ ଭၲ܄ૈໆෳǴ௦ҔႝᅶགᔈБԄࡼϒᙯηႣᓸΚǴໆෳຬॣݢଭၲᒡ рᙯೲᆶסંޑ߄౜Ƕಃϖകࣁҁࣴزޑ่ፕϷ҂ٰ৖ఈǶ

ಃΒക ౛ፕϩ݋

ҁകϟಏᓸႝਏᔈޑΚᏢՉࣁᆶᓸႝ׷਑ޑႝ܄੝܄Ǵ٠ᇥܴኳᄊ ϩ݋ᆶኩᄊϩ݋ޑኧॶ౛ፕǴϟಏ ANSYS ঺း೬ᡏܭኩᄊϩ݋ύ܌௦Ҕ ޑફଭլ(Newmark)ᑈϩᆶ؃ှߚጕ܄ୢᚒਔ௦ҔޑФႥ܎ᅽහ᠄ж ݤǴനࡕᇥܴҁࣴزຬॣݢଭၲၮᙯϐπբচ౛Ƕ

2.1

ᓸႝচ౛

2.1.1 ᓸႝਏᔈ Ջϡ 1880 ԃ໔Ǵۚٚл׌ӧҡम඲ᡏ΢ว౜ᓸႝਏᔈ(piezoelectric effect)Ǵ׷਑ڀԖᐒఓૈᆶႝૈϕඤޑ౜ຝǶᓸႝਏᔈޑౢғࢂӢࣁ඲਱ ϣচη໔ޑ੝ਸ௨ӈБԄǴ٬׷਑ޑᔈΚ൑ᆶႝ൑ϕ࣬ጠӝǶ

ᓸႝਏᔈх֖҅ᓸႝਏᔈ(direct piezoelectric effect)ᆶ଍ᓸႝਏᔈ (converse piezoelectric effect)Ƕ྽ᓸႝ׷਑܍ڙ҅ӛᓸΚਔǴࣁܢלႝጠ ཱུંڙډᓸᕭԶᡂอϐᖿ༈Ǵౢғႝᓸלᑽаᆢ࡭চރǶୖԵკ 2.1 ܌ ҢǴ྽΋ᐒఓᔈΚբҔܭᓸႝ׷਑ਔǴ׷਑ᡏٿᆄౢғ΋ಔᆶᔈΚελ ԋ҅Кٯޑႝ಻ໆǴ྽ᔈΚޑБӛ࣬ϸਔǴႝᓸޑཱུ܄Ψᒿϐ࣬ϸǴᆀ ࣁᐒఓૈᙯඤࣁႝૈޑ҅ᓸႝਏᔈǴёᔈҔܭགෳᏔǴӵуೲೕϷᓸΚ གෳᏔ฻Ƕӵკ 2.2 ܌ҢǴࡼуޔࢬႝ൑ܭᓸႝ׷਑ཱུϯБӛޑٿᆄਔǴ ׷਑ޑᡂ׎཮ᒿ๱ႝ൑ޑελԶׯᡂǴ྽ႝ൑ޑБӛ࣬ϸਔǴᓸႝ׷਑ ޑᡂ׎БӛҭᒿϐϸӛǹऩׯаࡼуҬࢬႝᓸǴ׷਑ޑᡂ׎཮ᒿ๱ᒡΕ ႝᓸޑᓎ౗ౢғຼය܄ਁᕏǴԜջႝૈᙯඤࣁᐒఓૈޑ଍ᓸႝਏᔈǴѱ ൑΢೚ӭᓸႝठ୏Ꮤ(piezoelectric actuator)ճҔԜᅿਏᔈᇙԋǴӵᓸႝီ ሳᏔϷຬॣݢଭၲ฻Ƕ

2.1.2 ᓸႝ׷਑ޑᅿᜪ

ڀԖᓸႝᓸਏᔈޑ׷਑εठ΢ёϩࣁϖεᜪǴಃ΋ᜪࣁൂ඲ᜪ(single crystalline)ǴٯӵǺҡमǵᛥቺᡶǵႝ਻ҡǵ✔ለ᎖(lithium niobateǴ LiNbO3)ǵ✗ለ᎖(lithium tantalateǴLiTaO3)฻ǶಃΒᜪࣁᖓጢᜪ(thin film)Ǵ

ٯӵǺ਼ϯᎋ(ZnO*ǵේϯ᎑(AlN)฻ǶಃΟᜪࣁଯϩηᆫӝނ(polymer)Ǵ

ٯӵǺPVDF ฻ǶಃѤᜪࣁഏౠ(ceramics)ǴٯӵǺ⑲ለ᎕(BaTiO3)ǵ⯗⑲

ለ ႉ (lead zirconate titanate Ǵ PZT) ฻ Ƕ ಃ ϖ ᜪ ࣁ ፄ ӝ ׷ ਑ (composite materials)ǴٯӵǺAFC(active fiber composites)฻Ƕ

Ӛᅿᓸႝ׷਑೿ԖᓬલᗺǴٯӵൂ඲ᜪԖؼӳޑྕࡋ੝܄Ǵՠᇙ೷ ֚ᜤǴሡһᒘ੝ਸޑ඲ᡏԋߏ(crystal growth)מೌǴ੝܄ڙϪय़ቹៜǴЪ ৒ܰڙډޜ਻ޑᔸࡋԶዊှǴӢԜѨѐᓸႝ܄ǴٯӵǺႝ਻ҡǵᛥቺᡶ ฻Ƕᖓጢᜪᓸႝ׷਑ޑᇙ೷ሡा੿ޜמೌǴόӕ੿ޜచҹ཮ౢғόӕޑ ׷਑੝܄Ƕଯϩηᜪ܄፦ࢋ೬Ǵёа଺ԋߚதᖓޑϡҹǴՠᓸႝୖኧλǴ ሡࣗଯޑཱུϯႝ൑ǴٯӵǺPVDF ӧ࠻ྕਔϐཱུϯႝ൑ሡଯၲ 4MV/mmǶ ഏౠᜪᓸႝ׷਑ࢲ܄(piezoelectric activity)ӼۓǴऐለᡵǴёᇙԋҺՖ׎ ރǴۚٚྕࡋଯǴᆶଯϩηᆫӝނǵፄӝ׷਑΋ኬǴӧᇙ೷ၸำύሡा ଯᓸཱུϯೀ౛Ǵՠࢂཱུϯႝ൑மࡋၨଯϩηᆫӝނᆶᓸႝፄӝ׷਑եࣗ ӭǴٯӵǺPZT ޑཱུϯႝ൑ѝԖ 3kV/mm ѰѓǶ ᓸႝഏౠڀԖπբྕࡋଯǵᐒఓமࡋεǵܰܭуπЪԋҁե༹฻ᓬ ᗺǴࢂҞ߻π཰ᔈҔനቶݱЪჴҔ܄നଯޑᓸႝ׷਑Ƕ⑲ለ᎕ࣁᓸႝഏ ౠޑж߄ǴڀԖᓬ౦ޑϟႝதኧϷᐒႝጠӝதኧǴϯᏢ܄፦ᛙۓǴᏹբ ྕࡋጄൎεЪᇙ೷৒ܰǴ٠ёᇙԋҺՖ׎ރǴӢԜԋࣁᓸႝ׷਑ᔈҔޑ २ᒧǶҁЎջ௦Ҕᓸႝഏౠ׷਑ PZT-4 բࣁຬॣݢଭၲठ୏ᏔǶ

2.1.3 ᓸႝ׷਑ޑҁᄬБำԄ ᓸႝഏౠࣁᐒఓૈᆶႝૈϕ࣬ጠӝޑ׷਑ǴҁᄬБำԄ(constitutive equation)хࡴᐒఓ੝܄ᆶႝ਻੝܄Ƕᓸႝഏౠࣁߚ฻ӛ܄׷਑ǴҁᄬБำ ԄሡԵቾӚБӛϩໆޑጠӝǴၨ΋૓ޑᐒఓ׷਑ፄᚇǶჹߚᓸႝ׷਑Զ قǴᐒఓᔈΚ  ࡼϒ׷਑ᡏ཮ౢғᐒఓᔈᡂS ǴځᔈΚᔈᡂޑᜢ߯ࣁ S = s T T = c S (2.1)

ԜೀǴ s ࣁቸ܄ࢋࡋંତ(matrix of elastic compliance)Ǵ c ࣁቸ܄খࡋંତ (matrix of elastic stiffness)Ƕ

ჹϟႝ܄׷਑ԶقǴܭ׷਑ٿᆄуΕႝ൑ E Ǵ׷਑ϣ೽཮ౢғႝՏ ౽ D Ǵႝ൑ᆶႝՏ౽ޑᜢ߯ࣁ

D  E

E  D (2.2)

ԜೀǴ  ࣁϟႝதኧંତ(matrix of dielectric constant)܈ᆀᇨႝதኧંତ (matrix of permeability)Ǵ ࣁϸᇨႝதኧંତ(matrix of impermeability)Ƕ

ᓸႝഏౠᆶ΋૓ᐒఓ܈ϟႝ׷਑όӕೀǴᓸႝ׷਑όѝൂᐱӸӧᔈ Κǵᔈᡂᜢ߯Ǵӕਔڀഢႝ൑ᆶႝՏ౽ޑᜢ߯Ǵ٠Ъϕ࣬ጠӝǶᓸႝ׷ ਑ޑҁᄬБำԄᜢ߯όऩ(2.1)ǵ(2.2)ԄᙁൂǴѸ໪ӕਔԵቾቸ܄߯ኧǵᓸ ႝ߯ኧǵϟႝ߯ኧΟ೽ϩǶᓸႝ׷਑ޑҁᄬБำԄੋϷޑᡂኧԖѤಔǴ ځύٿಔࣁᐒఓ൑ᡂኧǴջᔈΚ  ᆶᔈᡂSǴќѦٿಔࣁႝ܄൑ᡂ൑Ǵջ ႝ൑ E ᆶႝՏ౽ D ܈ᆀႝ೯ໆஏࡋǶ٩܌ᒧ᏷ޑԾᡂኧϷӢᡂኧޑό ӕǴᓸႝБำԄёϩԋ dǵgǵe Ϸ h ѤᅿόӕޑࠠᄊǴҁЎᒧҔ e ࠠᄊ ંତԄ߄Ңᓸႝ׷਑ޑҁᄬБำԄǴ E T S  T = c S e E D = e S +  E (2.3)

ځύǴǵS ࣁᔈΚ஭ໆᆶᔈᡂ஭ໆંତǴ E

c ࢂڰۓႝ൑చҹΠޑቸ܄খ

ࡋંତ(matrix of elastic stiffness)Ǵe ࢂᓸႝதኧંତ(matrix of piezoelectric constants)Ǵ T

e ࣁᓸႝதኧંତޑᙯ࿼ંତ(transport matrix)Ǵ D ࣁႝՏ౽

ӛໆંତǴE ࣁႝ൑ӛໆǴ S

 ࣁڰۓᔈᡂ(constant strain)చҹΠޑϟႝத ኧ ં ତ (matrix of dielectric constants) Ƕ ٩ Ᏽ IEEE Standard on Piezoelectricity[21^Ǵᓸႝ׷਑ڙႝ൑܈ᐒఓΚբҔޑҁᄬБำԄ߄Ңӵ ΠǺ 1 11 12 13 14 15 16 11 21 31 2 21 22 23 24 25 26 12 22 32 3 31 32 33 34 35 36 13 23 33 4 41 42 43 44 45 46 14 24 34 5 51 52 53 54 55 56 15 25 35 6 61 1 2 3 T C C C C C C e e e T C C C C C C e e e T C C C C C C e e e T C C C C C C e e e T C C C C C C e e e T C D D D    ª º « » _{  } « »    « » « » _{  } « » « »    « » « » « » « » « » « » ¬ ¼ 1 2 3 4 5 62 63 64 65 66 16 26 36 6 11 12 13 14 15 16 11 12 13 1 21 22 23 24 25 26 21 22 23 2 31 32 33 34 35 36 31 32 33 3 S S S S S C C C C C e e e S e e e e e e E e e e e e e E e e e e e e E ª º ª º « » « » « » « » « » « » « » « » « » « » « » « » « _{  } » « » « » « » « _{H H H} » « » « » « » H H H « » « » « _{H H H} » « » ¬ ¼ ¬ ¼ (2.4) ҁࣴزኧॶϩ݋௦Ҕޑᓸႝഏౠ׷਑ࣁ PZT-4ǴឦܭϤБ(hexdgonal crystal)඲سǴऩځཱུϯБӛѳՉܭ z (x3)ືǴᓸႝഏౠ׷਑ޑቸ܄খࡋં ତࣁ 11 12 13 12 11 13 13 13 33 44 44 66 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 E C C C C C C C C C C C C ª º « » « » « » « » « » « » « » ¬ ¼ c (2.5) ᓸႝதኧંତࣁ

15 15 31 31 33 0 0 0 0 0 0 0 0 0 0 0 0 0 e e e e e ª º « » « » « » ¬ ¼ e (2.6) ڰۓᔈᡂϐϟႝதኧંତࣁ 11 11 33 0 0 0 0 0 0 S S S S

H

H

H

ª º « » « » « » ¬ ¼  (2.7) ᆕӝ΢ॊǴPZT-4 ޑҁᄬБำԄ߄ҢӵΠǺ 1 11 12 13 31 2 21 22 23 31 3 31 32 33 33 4 44 15 5 44 15 6 66 1 15 11 2 15 11 3 31 31 33 33 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 T C C C e T C C C e T C C C e T C e T C e T C D e D e D e e e

H

H

H

 ª º ª º « » « _ » « » «  « » « « » « _ « » « « » «  « » « « » « « » « « » « « » « « » « ¬ ¼ ¬ ¼ 1 2 3 4 5 6 1 2 3 S S S S S S E E E ª º « » » « » » « » » « » » « » » « » » « » » « » » « » » « » » « » » « »_{¬ ¼} (2.8) 2.1.4 ᓸႝ่ᄬޑ୏ᄊБำԄ ຬॣݢଭၲۓη่ᄬх֖ᓸႝഏౠᆶߎឦቸ܄ᡏǴஒϐᚆණԋԖज़ ኧҞޑϡનǴҁ࿯ޑϩ݋όԵቾۓηᆶᙯη໔ޑௗ᝻҅ӛΚᆶϪጕΚբ ҔǶਥᏵᅇᔆႥচ౛(Hamilton’s principle)Ǵऩӧ΋ঁຼයޑᓐ׀ǴՏ౽ ᆶႝՏޑ΋ԛᡂϩࣁ႟Ǵ߾س಍ᕴ༈ૈޑ΋ԛᡂϩࣁ႟ǶஒӚ࿯ᗺՏ౽ ϷႝՏಔԋ΋ঁࡑۓޑӛໆǴёᕇள᏾ঁس಍ޑ୏ᄊБำԄǴ߄ҢӵΠǺ 0 0 0 0 0 uu u u M M MM ­ ½ ª º ­ ½ ­ ½ ª _{º ° ° } ® ¾ « »® ¾ ® ¾ « _{» ° ° ¯ ¿} ¬ ¼¯ ¿ ¬ ¼¯ ¿   M U U       (2.9) ځύǴ  ࣁႝՏǴ M ࣁଭၲۓηޑᕴ፦ໆંତ(mass matrix)Ǵk_uuࣁᆶᐒ

ఓՏ౽ԖᜢޑଭၲۓηখࡋંତǴ፦ໆંତ M ǵখࡋંତk_uuǵk_MM֡ࣁ ჹᆀޑჴኧંତǴԜѦǴk_Mu kT_uMǶऩԵቾଭၲۓηڙډߔѭϷѦΚբ ҔΠǴёஒ(2.9)Ԅׯቪԋ 0 0 0 0 0 0 uu u u M M MM ­ ½ ­ ½ ª º ­ ½ ­ ½ ª º° °_ª º° °_ ® ¾ ® ¾ « »® ¾ ® ¾ « »_{° °} « »_{° ° ¯ ¿} ¬ ¼¯ ¿ ¬ ¼¯ ¿ ¬ ¼¯ ¿   M U C U U F    Q      (2.10) ځύǴஒߔѭંତ೛ࣁКٯߔѭ(proportional damping)ǴC =

D

M + K

E

_uuǴ Fࣁଭၲۓηᆶᙯη໔ޑௗ᝻҅ӛΚᆶϪጕΚǴQࣁѦуႝ൑բҔܭᓸႝ ׷਑ޑᕴႝ಻ໆǶ

2.2

ኳᄊϩ݋

ଷ೛ଭၲۓηس಍คߔѭǴЪคѦΚբҔΠǴऩ࿯ᗺޑՏ౽ϷႝՏ ڀԖਔᒋӢηei tZ ǴзU U*ei tZ ǵU 

Z

2U*ei tZ ǵ *ei tZ Ǵϩձ жΕ(2.9)ԄǴёᕇள΋ಔሸ܄БำԄ(homogeneous equations)Ǵ * 2 0 0 0 0 uu u u M M MM

Z

§ª º_ ª º· ­ ½ ¨« » « »¸ ® ¾ ¨_{¬ ¼ ¬ ¼ ¯ ¿}¸ © ¹   M U   _ (2.11) Ԝࣁ੝ቻॶୢᚒǴࣁ؃ளߚ႟ှ(non-trivial solution)ԋҥޑкϩచҹࣁ 2 0 det 0 0 0 uu u u M M MM

Z

§ª º_ ª º· ¨_{« » « »}¸ ¨_{¬ ¼ ¬ ¼}¸ © ¹   M   (2.12) ΢Ԅջࣁ੝ቻॶՉӈԄǴ(2.12)Ԅޑ n ঁ੝ቻॶ

Z

ǴջࣁԾฅᓎ౗(natural frequency)Ƕ

2.3

ኩᄊϩ݋

ҁЎ௦Ҕ ANSYS ঺း೬ᡏीᆉ่ᄬޑ୏ᄊៜᔈǴϩ݋ۓηँଆᗺޑ ၮ୏ॉၞǴ٠௖૸ۓηँଆᗺᆶᙯηޑௗ᝻ՉࣁǶANSYS ঺း೬ᡏϐኩ ᄊϩ݋௦Ҕફଭլᑈϩݤ[22]ǴаΠϟಏځ౛ፕǶ

Եቾ΋ᚆණϯޑӭԾҗࡋس಍Ǵځၮ୏БำԄ߄ҢӵΠ   Mu Cu Ku F _(2.13) ځύ MǵCǵK ϩձࣁس಍ϐ፦ໆǵߔѭϷখ܄ંତǴu ࣁ߄Տ౽ӛໆǴ F߾ж߄բҔӧس಍ޑѦΚӛໆǶ ફଭլᑈϩݤϐኧॶϩ݋ࣁஒਔ໔ᚆණԋኧঁᑈϩ؁ᡯǴஒ߻΋؁ ᡯޑှ೛ࣁ߃ۈచҹǴжΕΠ΋؁ᡯǴ೴ԛᑈϩࡕǴ؃ளനࡕޑኩᄊៜ ᔈǶځ᠄жᜢ߯ӵаΠΒԄǺ! 1 [(1 ) 1] n n  

G

n 

G

n 't u u u u (2.14) 2 1 1 1 [( ) ] 2 n n  ' n t 

D

n 

D

n 't u u u u u (2.15) ځύu_nж߄ӧਔ໔t_nޑ࿯ᗺՏ౽ӛໆǴਔ໔ቚໆ' t tn1tnǴ

D

ᆶ

G

ࢂ ફଭլᑈϩޑୖኧǴਥᏵᑈϩᆒࡋϷᛙۓ܄җ،ۓ

D

0.25Ǵ

G

0.5[23]Ƕ ӧҁࣴزޑϩ݋ύǴ௦Ҕጕ܄уೲࡋݤ຾ՉीᆉǶҗ(2.15)Ԅள 1 ₂ 1 1 1 1 ( ) 1 2 n n n n n t t

D

D

D

 _'    _' §¨  ·¸ © ¹ u u u u u    (2.16) Եቾਔ໔tn1Ǵ่ᄬޑ୏ᄊѳᑽБำԄࣁ 1 1 1 1 n  n  n Fn Mu Cu Ku (2.17) ஒ(2.16)ԄжΕ(2.14)Ԅᕇளu_n1ޑ่݀Ǵӆᆶ(2.16)Ԅϐu_n1жΕ(2.17) ԄǴள 1 1 2 1 1 1 1 2 1 1 2 n n n n n n n n t t t t

D

D

D

G

G

G

D

D

D

   ª« _'  _' §¨  ·¸ º» © ¹ ¬ ¼ ª § · § · º  _« _¨  _¸ _¨  '_{¸ »} ' © ¹ © ¹ ¬ ¼ F M u u u u K K C u u u K     (2.18) ځύǴ 1 ₂ t t

G

D

D

  ' ' K K M CǴਥᏵ(2.18)ԄǴёճҔਔ໔ᗺ t ޑ่݀؃ ڗun1ޑ Տ ౽ Ƕ ફ ଭ լ ਔ ໔ ᑈ ϩ ݤ ឦ ܭ ค చ ҹ ᛙ ۓ (unconditionally stable)Ǵёڗၨεޑਔ໔ቚໆ t' Ǵՠ t' ໪ى୼λǴωૈԏᔙԿ׳ᆒዴޑ

่݀Ƕ

2.4

ௗ᝻ΚᏢϩ݋

2.4.1 ߚጕ܄؃ှࢬำ ௗ᝻ϩ݋ࣁٿނᡏ܈ӭঁނᡏǴᜐࣚ࣬ϕௗ᝻ЇଆޑΚᏢୢᚒǴӧ Ԗज़ϡનϩ݋ύǴௗ᝻ϩ݋ࢂឦܭߚጕ܄ୢᚒǶANSYS ঺း೬ᡏӧ؃ှ ߚጕ܄ୢᚒਔǴаФႥ-܎ᅽහݤ(Newton-Raphson method)Ǵ᠄ж؃ှߚ ጕ܄БำԄޑਥǶ! ऩ΋่ᄬڙ΋ѦΚբҔǴځѦΚᆶՏ౽ᜢ߯ࣁߚጕ܄ਔǴ࿯ᗺޑѦ ΚϷჹᔈޑϡનϣΚό࣬฻Ǵٿޣ໔Ӹӧ΋ৡॶǴ߄ҢӵΠǺ ! Rn1Fn1 'R (2.19) ځύRn1ǵFn1ϩձ߄Ңӧਔ໔tn1(tn1  ' )ਔǴ࿯ᗺޑѦΚϷჹᔈtn t ޑϡનϣΚǴ'R ࣁٿޣޑৡॶǴ྽ 'R εܭ೛ۓޑԏᔙ኱ྗǴёຎ 'R ࣁ ΋ཥޑѦΚॶǴճҔϪጕখࡋંତKT؃р'R ܌অ҅ޑՏ౽ቚໆ 'u 1 (KT) ' 'R u (2.20) ཥޑՏ౽un1೛ࣁ߃ۈՏ౽unᆶঅ҅Տ౽ቚໆ'u ޑک!! ! u_n1 u_n  'u (2.21) ӆҗu_n1ीᆉр࣬ჹᔈޑϡનϣΚF_n1Ƕ࡭ុঅ҅ৡॶ'R Ǵޔډ 'R ฻ ܭ܈λܭԏᔙ኱ྗRcriǴԜਔಃi ԛ᠄жޑՏ౽un i Ǵջࣁߚጕ܄БำԄ ޑ߈՟ှǶ᠄жၸำୖԵკ 2.3 ܌ҢǴკύޑԔጕ߄Ң่ᄬϐڙΚᆶՏ౽ ᜢ߯Ǵևߚጕ܄ᡂϯǶF_nᆶu_nϩձ߄Ңਔ໔ࣁt_nਔޑϡનϣΚᆶՏ౽Ǵ ФႥ܎ᅽහݤޑၳ߈ݤ२ӃаP₀ࣁଆۈᗺǴբಃ΋ԛ᠄жǴ଺΋Ϫጕ(௹ ౗ࣁ 1 T K )ᆶࠟޔጕࡕёளډᗺP1Ǵ྽ѦΚᆶϣΚޑৡॶ R' εܭԏᔙ኱ ྗǴ߾ᝩុΠ΋ঁ᠄жǶаӕኬБݤ࿶i ԛ᠄жਔǴё؃ளᗺP_iǴჹᔈޑ Տ౽ࣁu_{n i} ǴϡનϣΚࣁF_{n i} ǴऩԜਔ R' λܭԏᔙ኱ྗǴ߾ჹᔈޑՏ౽

n i

u Ǵջࣁ܌؃ޑ߈՟ှǴ᠄жၮᆉ่݀ԏᔙǶԜѦǴऩԔጕϼፄᚇǴ܈

๏ۓޑଆۈᗺP₀ϐॶό࡞྽Ǵ߾᠄жၸำύёૈᏤठ؃ှวණǶ!

2.4.2 ௗ᝻Κᄽᆉݤ

ӧ ANSYS ঺း೬ᡏޑௗ᝻ϩ݋ύǴኳᔕٿނᡏޑௗ᝻௃׎ǴளӃӧ ٿނᡏޑௗ᝻य़΢ࡌҥௗ᝻ჹ(contact pair)ǴхࡴҞ኱य़(target surface)ᆶ ௗ᝻य़(contact surface)ǴҞ኱य़ᆶௗ᝻य़ϩձҗҞ኱ϡન(target elements) ௗ᝻ϡન(contact elements)܌ᄬԋǶीᆉٿޣ໔ޑೣऀໆǴ؃ளϩթӧϡ નᆶ࿯ᗺ΢ޑௗ᝻ΚελǴ٠җ 2.4.1 ࿯܌ϟಏޑߚጕ܄؃ှࢬำǴीᆉ р࿯ᗺՏ౽ޑ߈՟ှǶ ANSYS঺း೬ᡏӧय़ჹय़ޑௗ᝻ϩ݋ύගٮΑѤᅿௗ᝻ᄽᆉݤǴҁ ࣴز௦Ҕᚵᆦڄኧݤ(penalty method)Ǵҗ৤উነᔔۓࡓޑௗ᝻Κ߄ҢԄ normal normal p F k x ! ! ! ! ! ! ! ! ! ! ! (2.22)!

ௗ᝻ΚF_normalࣁௗ᝻খࡋk_normal(contact stiffness)ᆶऀ೸ໆx_pޑ४ᑈǶٿނ ᡏϐԖज़ϡનኳࠠޑௗ᝻௃׎ӵკ 2.4 ܌ҢǴٿޣ໔Ԗ΋ௗ᝻ቸᘽ(contact spring)Ǵځቸᘽதኧ(spring constant)ջࣁௗ᝻খࡋǴፓ᏾ௗ᝻খࡋёෳ၂ р፾྽ޑԏᔙރݩᆶӝ౛ޑीᆉ่݀Ƕऩௗ᝻খࡋཇεǴ߾ٿނᡏϐ໔ ޑऀ೸ໆ൩ཇλǴຎჴሞௗ᝻খࡋԶۓǴՠࢂௗ᝻খࡋගଯǴ཮٬ளФ Ⴅ-܎ᅽහݤޑीᆉ֚ᜤࡋቚуǴᏤठߚጕ܄ޑ؃ှၸำКၨᜤԏᔙǶ! 2.4.3 ነᔔᐒڋ ANSYS ঺ း ೬ ᡏ ޑ ܭ ௗ ᝻ ነ ᔔ ϩ ݋ а ৤ উ ነ ᔔ ኳ ࠠ (Coulomb friction model)ኳᔕௗ᝻ነᔔ౜ຝǶ΋૓ԶقǴ྽ٿނᡏࣁᗹᅉ(stick)ነᔔ ਔǴٿޣܭௗ᝻୔ޑ࣬ჹೲࡋࣁ႟ǴԜਔࣁᓉነᔔՉࣁǴነᔔ߯ኧࣁ

P

_sǶ ྽ٿނᡏࣁྖ୏(sliding)ነᔔਔǴٿޣܭௗ᝻୔ޑ࣬ჹೲࡋόࣁ႟ǴԜਔ ࣁ୏ነᔔՉࣁǴነᔔ߯ኧࣁ

P

_dǶฅԶǴANSYS ঺း೬ᡏޑௗ᝻ነᔔϩ݋

ஒᓉǵ୏ነᔔ߯ኧٿޣᜢ߯ۓကࣁ

P

_s FACT u

P

_dǴځύ FACT ࣁᓉነᔔ ᆶ୏ነᔔ߯ኧޑКॶǶ! !!!!ࣁΑᗉխௗ᝻୊ᔈΚၸεᏤठόӝ౛ޑ่݀Ǵё೸ၸ೛ۓነᔔय़ޑ നε୊ᔈΚॶှ،೭ঁୢᚒǴऩٿނᡏௗ᝻ਔǴነᔔय़୊ᔈΚၲԜॶਔǴ ྖ୏วғǴځነᔔय़୊ᔈΚޑ΢ज़ॶਥᏵ[24]೛ۓࣁ

W

_max 0 3 ǴځύS_y y

S ࣁ׷਑ޑ܎՜फ़ҷமࡋǴ୊ᔈΚޑ΢ज़ॶ

W

maxջࣁ von Mises ᔈΚǶ!

2.5

ຬॣݢଭၲठ୏চ౛

ҁࣴز೛ीޑΟᅿᚈኳᄊጠӝຬॣݢଭၲࢂаڰۓޑᓎ౗ᐟว่ᄬ ጠӝϐٿঁኳᄊਁ୏Ǵಃ΋ᅿଭၲ่ᄬϐᚈኳᄊጠӝࢂҗΟف׎ۓηޑ ୷ҁᕵӛኳᄊᆶಃΒסᙯኳᄊጠӝǴӧΟف׎ۓηޑΟᜐӚᗹຠ΋Тࠆ ࡋБӛཱུϯϐБ׎ᓸႝഏౠǴӵკ 2.5 ܌ҢǴஒഏౠ߄य़ႝཱུϩപԋٿ༧ ୔ୱǴаٿಔᓎ౗ᆶਁ൯࣬฻ޑ҅۰ݢૻဦ០୏ A ࣬ᆶ B ࣬ඤૈᏔǴٿ ಔૻဦϐ࣬Տৡࣁ 90 ࡋǴӕਔᐟวۓηϐ୷ҁᕵӛኳᄊᆶಃΒסᙯኳ ᄊǶᚈ࣬ᐟวٿಔӅਁኳᄊǴ٬ளΟف׎ۓηӚᜐύᗺ΢ᆄޑँଆᗺբ ᐍ༝׎ॉၞၮ୏Ǵբ୏ޑҢཀკӵკ 2.6 ܌ҢǶಃΒᅿଭၲ่ᄬࢂӧΟف ׎ۓηޑΟᜐӚᗹຠٿТБ׎ᓸႝഏౠǴँଆᗺ೛࿼ܭΟف׎ۓηޑഗ ᗺ΢ᆄೀǴӵკ 2.7 ܌ҢǴ០୏БԄᆶ่ᄬ΋࣬ӕǴᐟวۓηϐ୷ҁᕵӛ ኳᄊᆶಃΒסᙯኳᄊǴ٬ளΟف׎ۓηޑӚँଆᗺբᐍ༝ॉၞၮ୏Ǵբ ୏ޑҢཀკӵკ 2.8 ܌ҢǶಃΟᅿ่ᄬޑ០୏БԄᆶಃΒᅿ่ᄬ࣬՟Ǵோ ഗᗺߕ߈ޑϪኲՏ࿼ୃӛۓη΢БǴӵკ 2.9 ܌ҢǴᐟวۓη่ᄬϐ୷ҁ ᕵӛኳᄊᆶಃ΋סᙯኳᄊǶ ऩаಃΟᅿ่ᄬϐΟف׎ۓηځύޑ΢ഗفँଆᗺբࣁୖԵᗺǴୖ ԵᗺՏܭ Y ື೯ၸύЈጕೀǴ٠ଷ೛ Y БӛޑՏ౽ᡂϯࡐλǴୖԵᗺਁ ୏ޑՏ౽ϩձаuxᆶuz߄ҢǴ

0 sin( ) x x u u

Z

t (2.23) 0 sin( ) z z u u

Z I

t (2.24) ځύǴu_{0 x}ࣁኳᄊጠӝϐ X Бӛޑਁ୏Տ౽Ǵu_{0 z}ࣁ Z Бӛޑਁ୏Տ౽Ǵ

Z

ࣁ០୏ႝᓸޑᓎ౗Ǵ྽ٿಔඤૈᏔᒡΕႝᓸޑ࣬Տৡࣁ

I

ਔǴୖԵᗺݮ X-Z ѳय़բᐍ༝׎ॉၞၮ୏Ƕӧ࣬ӕޑ០୏ᓎ౗ᆶਁ൯ΠǴऩu0x u0zǴ ୖԵკ 2.10 ܌ҢǴٿಔඤૈᏔޑႝᓸ࣬Տৡ

I

ࣁ 0 ࡋǵ45 ࡋϷ 90 ࡋޑୖ Եᗺၮ୏ॉၞࣁ௹ጕǵ௹ᐍ༝Ϸ҅༝ǶҁࣴزஒٿಔඤૈᏔޑႝᓸ࣬Տ ৡ೛ۓࣁ 90 ࡋǴ߾(2.24)Ԅׯቪࣁ 0 cos( ) z z u u

Z

t (2.25) ԜਔǴ᏾౛(2.23)Ԅᆶ(2.25)Ԅёள 2 2 0 0 1 x z x z u u u u § · §_ · ¨ ¸ ¨ ¸ © ¹ © ¹ (2.26) (2.26)Ԅࣁᐍ༝׎ޑၮ୏ॉၞǴԜࣁΟف׎ۓηܭᚈኳᄊጠӝЪٿಔඤૈ Ꮤႝᓸ࣬Տৡࣁ 90 ࡋਔޑୖԵᗺၮ୏ॉၞǶ

ಃΟക ኧॶኳᔕϩ݋ᆶ่݀

ҁࣴزаԖज़ϡનϩ݋ኳᔕຬॣݢଭၲۓηޑ୏ᄊՉࣁǴҁࣴزа Ԗज़ϡનݤ຾Չኧॶϩ݋Ǵ௦Ҕ ANSYS ঺း೬ᡏբࣁϩ݋πڀǴၮҔ่ ᄬኳᄊϩ݋(modal analysis)Ϸኩᄊϩ݋(transient analysis)ኳಔ຾Չϩ݋Ƕ ҁകӅϩࣁΟ೽ҽǴಃ΋೽ϩ௖૸ۓη่ᄬ΋ϐ൳ՖЁκჹ੝ۓኳᄊϐ Ծฅᓎ౗ޑቹៜǴፓ᏾ۓη൳Ֆୖኧၲډኳᄊ႖ᚆޑਏ݀Ǵ٠٩Ᏽྗ߾ ೛ीۓη่ᄬΒᆶ่ᄬΟǹಃΒ೽ϩаኩᄊϩ݋ኳᔕۓηँଆᗺޑՏ౽ ៜᔈᆶၮ୏ॉၞǹಃΟ೽ҽीᆉۓη่ᄬΟᆶᙯηޑኩᄊௗ᝻ΚᏢՉࣁǶ

3.1

ΟᆢԖज़ϡનϐᆛ਱ᆶϡનࠠᄊ

ANSYS Ԗज़ϡનϩ݋೬ᡏޑ่ᄬ୏ᄊϩ݋ำׇЬाϩԋ߻ೀ౛ (pre-processor)ǵ؃ှ(solver)ᆶࡕೀ౛(post-processor)Οঁ೽ҽǶၮҔ߻ೀ ౛೽ҽࡌҥଭၲۓηኳࠠǴځ൳ՖЁκӵკ 3.1~კ 3.3 ܌ҢǴаΟف׎ۓ ηޑࠆࡋ tǵଯࡋ H ϷНѳ໒ኲߏࡋ La ϷځՏ࿼բࣁ೛ीޑᡂ୏ୖኧǴ ׷਑ᒧҔ᎑ӝߎ T-6061Ǵ׷਑ୖኧӈܭ߄ 1ǶۓηޑӚᜐᗹຠߏ 20mmǵ ቨ 10mmǵࠆࡋ 0.72mm ܈ߏ 16mmǵቨ 12mmǵࠆࡋ 0.72mm ޑБ׎ᓸ ႝഏౠ PZT-4ǴЪஒႝཱུϩപࣁ AǵB ٿ೽ҽǴ߄ 2 ܌ӈࣁኳᔕीᆉϐ PZT-4 ׷ ਑ ߯ ኧ [25] Ƕ ᓸ ႝ ׷ ਑ ٬ Ҕ 8 ࿯ ᗺ ϐ Ο ᆢ ጠ ӝ ϡ ન (3-D coupled-field solid element) SOLID5Ǵ؂ঁ࿯ᗺڀԖ xǵyǵz ΟঁБӛޑ Տ౽ԾҗࡋϷ΋ঁႝՏԾҗࡋǶ᎑ӝߎޑϡનࠠᄊ௦Ҕ SOLID45 ϡનǴ Ԝϡનӕࣁ 8 ࿯ᗺϐΟᆢϡનǴ؂ঁ࿯ᗺ໻Ԗ xǵyǵz ΟঁБӛޑՏ౽ ԾҗࡋǴа፾྽ޑϡનኧໆஒۓη่ᄬ΋ᆛ਱ϯ(mesh)Ǵӵკ 3.4 ܌ҢǴ ϡનኧҞӅ 23552Ƕۓη่ᄬΒᆶ่ᄬΟ߾а 6 ࿯ᗺޑ SOLID45 Οᆢϡ નᆛ਱߈՟Ǵӵკ 3.5ǵკ 3.6 ܌ҢǴϡનኧҞӅ 46080 Ϸ 43366 ঁǶӧ ᜐࣚచҹ೛ۓ΢Ǵஒۓηۭ೽ڰۓᜐޑϡન࿯ᗺՏ౽೛ۓࣁ႟Ƕ؃ှᏔ

ஒ؃ှԖज़ϡનϩ݋ࡌҥޑس಍ᖄҥБำԄǴࡕೀ౛߾ஒ؃ှᏔޑϩ݋ ၗૻǴ଺ኧᏵᘜયϷࡕុკ׎ϯೀ౛Ƕ

3.2

ኳᄊϩ݋่݀

3.2.1 Ծฅኳᄊᒣձ ӧ೛ीଭၲۓηϐ߻Ǵ२Ӄ୔ձΟف׎่ᄬޑԾฅኳᄊǴ߄ 3 ࣁ΋ ֹ᏾Οف׎่ᄬޑ߻ 20 ಔԾฅኳᄊǴёϩࣁᕵӛኳᄊ(longitudinal mode)ǵסᙯኳᄊ(torsional mode)ϷኙԔኳᄊ(flexural mode)ǶਥᏵа۳Ў ᝘૶ၩǴऩۓη่ᄬࣁ༝ᅷࠠޑຬॣݢଭၲǴځኙԔኳᄊёа᏾ኧ(m, n) ඔॊǴm ж߄ᅷࠠۓηޑ৩ӛኳᄊኧǴn ж߄ᅷࠠۓηޑڬӛኳᄊኧǶऩ аԜۓကΟف׎ۓηޑኙԔኳᄊǴଯ໘ޑኙԔኳᄊځਁ׎ӧϩᒣ΢ϝԖ ࡑ୘ᄮǴҁࣴزύࣁБߡ୔ձኙԔኳᄊޑਁ׎ǴኩаȨځѬኳᄊȩ(other mode)๱ᆀǶᕵӛኳᄊ߾٩Οف׎ືӛߏࡋޑᡂϯ௃׎ղᘐǴёୖԵ߄ 3 ጓဦಃ 14 ಔޑኳᄊਁ׎Ǵסᙯኳᄊ߾٩ڬӛ௽ᙯޑᡂϯ௃׎ղᘐǴ߄ 3 ጓဦಃ 4ǵ10ǵ13 ಔޑኳᄊਁ׎ឦϐǶΟف׎่ᄬᕵӛኳᄊϐԾฅᓎ౗ ࣁ 61.641kHzǴಃΒסᙯኳᄊࣁ 43.015kHzǴٿޣৡຯ߈ 20kHzǴऩाӕ ਔᐟวа΢ٿಔኳᄊǴ༈Ѹሡाፓफ़ᕵӛኳᄊޑԾฅᓎ౗܈ፓϲಃΒס ᙯኳᄊޑԾฅᓎ౗Ǵ٬ٿޣᓎ౗ᖿ߈ܭ΋ۓॶǴωૈӕਔᐟวٿಔኳᄊ ਁ୏Ƕ 3.2.2 ൳ՖЁκჹܭ੝ۓኳᄊԾฅᓎ౗ޑቹៜ ҁࣴز܌ගᚈኳᄊጠӝ០୏ϐຬॣݢଭၲջፓ᏾ᕵӛኳᄊᆶಃΒס ᙯኳᄊޑԾฅᓎ౗Ǵ٬ள࣬ӕ០୏ᓎ౗ΠǴӕਔठਁۓη࣬ϕ҅Ҭޑᕵ ӛኳᄊᆶಃΒסᙯኳᄊǶҗ 3.2.1 ࿯ϟಏֹ᏾ޑΟف׎่ᄬϐኳᄊϩ݋ள ޕǴᕵӛኳᄊޑԾฅᓎ౗ᇻଯܭಃΒסᙯኳᄊǴӧ่ᄬ҂ᗹຠᓸႝТϷ уπׯᡂ่ᄬҁᡏ߻ǴஒΟف׎ۓη่ᄬ΋ޑᜐߏ L ೛ࣁ 30mmǴ२Ӄ

ፓ᏾ۓηޑଯࡋ HǴ௖૸ H ჹӚኳᄊԾฅᓎ౗ޑቹៜǶӵკ 3.7 ܌ҢǴ ྽ H=15mm ਔǴᕵӛᆶಃΒסᙯኳᄊޑԾฅᓎ౗ৡऊ 27kHzǴ྽ H=30mm ਔǴٿಔኳᄊޑԾฅᓎ౗ৡᕭλԿ 5kHzǴЪٿޣԾฅᓎ౗֡ᒿ๱ଯࡋޑ ቚуԶफ़եǴΞаᕵӛኳᄊޑԾฅᓎ౗Πफ़൯ࡋၨεǴऩाஒٿಔኳᄊ ጠӝ༈ѸӆቚуଯࡋǴՠၸߏޑଯࡋஒᏤठჴᡏۓηуπ֚ᜤǴቚу׳ ᚳεޑԋҁ઻຤Ƕ ۓηࠆࡋ t ჹӚኳᄊԾฅᓎ౗ޑቹៜӵკ 3.8 ܌ҢǴ྽ࠆࡋҗ 1.4mm ቚуԿ 2.4mmǴᕵӛኳᄊᆶಃΒסᙯኳᄊϐԾฅᓎ౗֡٤༾΢ϲǴϩձ ΢ϲ 7kHz ᆶ 6kH{ǴٿಔኳᄊޑԾฅᓎ౗คௗ߈ޑᖿ༈Ǵࠆࡋჹܭᚈኳ ᄊጠӝޑ่ᄬ೛ीคܴᡉբҔǶ ӧόԵቾуπׯᡂҁᡏ่ᄬޑ߻ගΠǴፓ᏾ଯࡋᆶࠆࡋޑୖኧࡕǴ ่݀ϝคݤԖਏᄬԋᚈኳᄊጠӝޑ่ᄬ೛ीǴനಖ༈ѸᙖᐒఓуπǴ෧ ཞ่ᄬҁᡏϐᕵӛখ܄ǴаၲႣය่݀ǶҁࣴزୖԵኙ܄ᖄືᏔޑ೛ीǴ ӧᖄືᏔޑڬӛբ໔ᘐޑϪኲǴ෧Ͽ໺୏ਔҗӧື΢໺ሀޑፂᔐ܄ॄ ၩǴԖਏӦፓ᏾Ϸׯ๓௽ᙯϡҹޑਁ୏੝܄ǶᔈҔԜཷۺܭΟف׎ۓη ޑୁᜐϪപН໒ኲǴ໒ኲޑቨࡋࣁ 1mmǴНѳ໒ኲߏࡋჹۓη่ᄬখ܄ ޑቹៜӵკ 3.9 ܌ҢǶ྽Нѳ໒ኲߏࡋεܭ 4mmǴᕵӛኳᄊޑԾฅᓎ౗ ࡚ቃΠफ़ǴϸᢀǴಃΒסᙯኳᄊޑԾฅᓎ౗໻٤༾Πफ़Ǵ྽໒ኲߏࡋၲ 14mm ਔǴٿޣᓎ౗໻ৡຯ 4.8kHzǴҗԜёޕǴΟف׎ۓηୁᜐޑНѳ ໒ኲǴૈ୼ԖਏӦ෧১่ᄬޑᕵӛখ܄ǶԜѦǴόӕޑ໒ኲՏ࿼Ψ཮ቹ ៜኳᄊԾฅᓎ౗ޑϩթǴӵკ 3.10 ܌ҢǴӧΟف׎ۓηޑୁᜐҗ΢ԿΠ ӅჄϩΐೀՏ࿼Ǵ྽໒ኲՏ࿼ӧύΠᆄೀǴ୷ҁᕵӛኳᄊޑԾฅᓎ౗ௗ ߈ಃΒסᙯኳᄊޑԾฅᓎ౗Ƕ߄ 4 ܌ӈࣁՏ࿼ 1 ԿՏ࿼ 9 ୷ҁᕵӛኳᄊ ᆶಃΒסᙯኳᄊޑኳᄊਁ׎ϷԾฅᓎ౗ǶҗܭჴᡍԵໆᓸႝТޑᗹຠՏ ࿼ǴஒНѳ໒ኲ೛ीܭΟف׎ۓηୁᜐޑۭᆄೀǴନΑԖਏ෧১ۓηޑ

ᕵӛখ܄ǴΨճܭᓸႝТޑᗹຠǶ ନΑНѳ໒ኲǴࣴزၸำύΨ჋၂ࠟޔ໒ኲǴϩ݋่݀ӵკ 3.11 ᆶ კ 3.12 ܌ҢǴϩձܭΟف׎ۓηୁᜐύጕೀϪപ΋ၰࠟޔ໒ኲǴ܈ӧύ ጕೀޑٿ਒Ϫപٿၰࠟޔ໒ኲǴٿᅿࠟޔ໒ኲޑБԄǴ֡٬ள୷ҁᕵӛ ኳᄊᆶಃΒסᙯኳᄊޑԾฅᓎ౗ᒿ๱໒ኲߏࡋ Ha ޑቚуԶफ़եǴฅԶٿ ޣኳᄊ໔ޑԾฅᓎ౗٠คܴᡉௗ߈ޑᖿ༈ǶНѳ໒ኲᆶࠟޔ໒ኲޑБԄ ֡Ꮴठ่ᄬޑᕵӛখ܄ڙډቹៜǴНѳ໒ኲБԄၨૈၲԋᚈኳᄊጠӝޑ ೛ीཷۺǶϐࡕǴΟف׎ۓηޑ೛ी֡௦ҔНѳ໒ኲޑБԄǴբࣁ෧১ Οف׎ۓηᕵӛখ܄ޑ٩ᏵǶ ่ᄬ΋ᆶ่ᄬΒϐጠӝኳᄊࣣࣁ୷ҁᕵӛኳᄊᆶಃΒסᙯኳᄊޑጠ ӝǴ่ᄬΟ߾ׯа୷ҁᕵӛኳᄊᆶಃ΋סᙯኳᄊޑጠӝǴฅԶǴಃ΋ס ᙯኳᄊϐԾฅᓎ౗ၨեǴ٬ள୷ҁᕵӛኳᄊᆶಃ΋סᙯኳᄊϐԾฅᓎ౗ ޑৡຯ׳εǴऩाε൯ፓफ़୷ҁᕵӛኳᄊϐԾฅᓎ౗Ǵሡჹۓηޑ൳Ֆ Ёκբ׳຾΋؁ΑှǶୖԵკ 3.3 ܌ҢǴCL ೛ࣁНѳ໒ኲϐϪαೀຯᚆ Οف׎൳ՖύЈᗺޑຯᚆǶკ 3.13 ܌ҢࣁНѳ໒ኲుࡋ CL ჹۓη่ᄬ ΟӚኳᄊԾฅᓎ౗ޑቹៜǴკύ໻୷ҁᕵӛኳᄊϐԾฅᓎ౗ᒿ CL ෧ϿԶ Πफ़ǴځᎩኳᄊϐԾฅᓎ౗߾คܴᡉৡ౦Ƕკ 3.14 ܌Ң߾ࣁНѳ໒ኲՏ ࿼ OD ჹۓη่ᄬΟӚኳᄊԾฅᓎ౗ޑቹៜǴOD ೛ࣁНѳ໒ኲೀԿۓη ۭ೽ޑຯᚆǴOD ޑᡂϯጄൎҗ 3mm Կ 10.5mmǴ྽ OD ཇεਔǴཇૈԖ ਏӦफ़ե୷ҁᕵӛኳᄊϐԾฅᓎ౗ǴԶಃ΋סᙯኳᄊϐԾฅᓎ౗߾ౣ༾ ΢ϲǴ٬ளٿޣኳᄊ׳৒ܰጠӝǶკ 3.15 ܌ҢࣁόӕޑϣᏤفჹۓηӚ ኳᄊԾฅᓎ౗ޑቹៜǴϣᏤف RI ޑᡂϯጄൎҗ 2.5mm Կ 5.5mmǴ୷ҁᕵ ӛኳᄊϐԾฅᓎ౗ౣ༾Πफ़Ǵಃ΋סᙯኳᄊϐԾฅᓎ౗߾٤༾΢ϲǶό ӕޑѦᏤفჹۓηӚኳᄊԾฅᓎ౗೷ԋޑቹៜӵკ 3.16 ܌ҢǴѦᏤف RO ޑᡂϯጄൎҗ 1.5mm Կ 5.5mmǴ྽ѦᏤفεܭ 2.5mm ਔǴ໻୷ҁᕵӛኳ

ᄊϐԾฅᓎ౗ε൯΢ϲǴಃ΋סᙯኳᄊϐԾฅᓎ౗߾คܴᡉᡂϯǶ! 3.2.3 ኳᄊ႖ᚆᆶኳᄊጠӝ ᚈኳᄊ០୏ޑຬॣݢଭၲࢂаޑӅਁᓎ౗ᐟวۓη่ᄬբਁ୏Ǵࣁ Αᗉխᐟวрᎃ߈ޑӅਁኳᄊǴቹៜۓηޑਁ׎ᆶਁ൯ǴࣗԿफ़եଭၲ ޑ܄ૈᆶ௓ڋ܄Ǵ௦Ҕኳᄊ႖ᚆ(modal separation)ޑཷۺǴፓ᏾ۓηޑ൳ ՖୖኧǴᢀჸӚኳᄊ໔Ծฅᓎ౗ޑᡂϯ௃׎Ǵ٬ᚈጠӝኳᄊޑ០୏ᓎ౗ ᆶ߻ࡕ࣬ᎃኳᄊϐӅਁᓎ౗႖ᚆၨᇻǴᗉխቹៜຬॣݢଭၲ௴୏ᕓ໔ᆶ ଶЗਔޑኩᄊៜᔈǶ ௖૸ֹ൳ՖЁκჹܭ੝ۓኳᄊޑቹៜǴ٩ᏵԜ೛ीྗ߾Ǵ೛ीᚈኳ ᄊጠӝޑຬॣݢଭၲۓηǴ่ᄬ΋ஒँଆᗺ೛࿼ܭΟف׎ۓηӚᜐޑ΢ ጔύᗺǴ٠ஒᗹຠϐᓸႝ׷਑યΕۓη่ᄬǴ຾Չኳᄊϩ݋Ƕკ 3.17~3.19 ܌ҢࣁНѳ໒ኲߏࡋ La ჹۓηӚኳᄊԾฅᓎ౗ޑቹៜǴځύǴL=30mǵ t=2mmǵ໒ኲՏ࿼ຯᚆۭ೽ 2mmǴۓηޑଯࡋϩձࣁ 15ǵ17ǵ19mmǶ ୷ҁᕵӛኳᄊᆶಃΒסᙯኳᄊϐԾฅᓎ౗Ԕጕӧ໒ኲߏࡋࣁ 14mm Կ 16mmਔҬ཮ǴٿޣҬ཮ਔǴж߄Οف׎ۓηӧ೭൳ՖЁκϐΠǴ୷ҁᕵ ӛኳᄊᆶಃΒסᙯኳᄊጠӝǴጠӝኳᄊਁ׎ӵკ 3.20 ܌ҢǴٿಔኳᄊ֡ Քᒿסᙯၮ୏ᆶᕵӛၮ୏Ƕ೸ၸ༾ፓЁκࡕǴӅ᏾౛рѤಔጠӝኳᄊޑ Ծฅᓎ౗Ϸኳᄊ႖ᚆำࡋǴӈܭ߄ 5Ǵۓη่ᄬ΋ϐѤಔ୷ҁᕵӛኳᄊᆶ ಃΒסᙯኳᄊޑԾฅᓎ౗ৡຯ֡ӧ 5Hz аϣǴጠӝำࡋ࣬྽ᓬϯǴኳᄊ ႖ᚆำࡋΞаۓηଯࡋࣁ 17mm ޑٿಔЀ٫Ƕ ҁࣴز຾΋؁೛ीۓη่ᄬΒǴ٠ஒँଆᗺׯ೛ܭΟف׎ۓηޑӚ ഗᗺ΢ᆄೀǴНѳ໒ኲϐՏ࿼ܭΟف׎ۓηޑӚفᆄޑΠጔೀǴຯᚆۭ ೽ 2mm ೀǴᜐߏࣁ 56mmǵଯࡋࣁ 16.51mmǵࠆࡋࣁ 2mmǴጠӝኳᄊӕ ࣁ୷ҁᕵӛኳᄊᆶಃΒסᙯኳᄊ܌ಔԋǴԾฅᓎ౗Ϸኳᄊ႖ᚆำࡋӈܭ ߄ 5Ƕ

ۓη่ᄬΟϐँଆᗺӕኬ೛࿼ܭΟف׎ۓηޑӚഗᗺ΢ᆄೀǴНѳ ໒ኲϐՏ࿼ՏܭΟف׎ۓηޑӚفᆄೀǴຯᚆۭ೽ 9.36mm ೀǴᜐߏࣁ 40mmǵଯࡋࣁ 14mmǵࠆࡋࣁ 1.8mmǴጠӝኳᄊࣁ୷ҁᕵӛኳᄊᆶಃ΋ סᙯኳᄊ܌ಔԋǴٿಔኳᄊጠӝϐኳᄊਁ׎ӵკ 3.21 ܌ҢǴᢀჸΟف׎ ۓηޑಃ΋סᙯኳᄊǴӧӚᜐ΢ጔޑύᗺԖ΋࿯ᗺӸӧǶᢀჸΟف׎ۓ ηޑ୷ҁᕵӛኳᄊǴӚᜐύᗺߕ߈ޑՏ౽ໆΨࣁ႟Ƕᕵӝ΢ॊٿᗺᢀჸǴ ӚᜐύᗺۗӵᝌᖉఉޑڰۓᆄǴѰѓٿ਒Ӛۯ՜΋ߏᖉǴӵӕ Hemsel ᆶ Wallaschek [11]ޑຬॣݢଭၲǴஒЍኖᗺ೛ीܭਁ୏ηޑ࿯ᗺ΢Ǵගଯଭ ၲޑ௢Κᆶਏ౗ǶᚈጠӝኳᄊޑԾฅᓎ౗Ϸኳᄊ႖ᚆำࡋΨӈܭ߄ 5Ǵځ ύԖ΋ኳᄊϐԾฅᓎ౗࣬྽᎞߈ጠӝኳᄊϐԾฅᓎ౗Ǵځኳᄊਁ׎ࣁߚ ჹᆀࠠԄǴऩΟف׎ۓηӧ AǵB ࣬ठ୏ᏔჹᆀޑᐟਁచҹΠǴё۹ౣ ၀ኳᄊ೏ᐟวޑёૈǶۓη่ᄬΟӚಔኳᄊޑԾฅᓎ౗ԏᔙ܄ϩ݋ᆶ௦ ҔޑϡનኧҞޑԏᔙ܄ϩ݋ӵკ 3.22 ܌ҢǴϡનኧҞҗ 2 ࿤Կ 21 ࿤ǴӚ ಔኳᄊޑԾฅᓎ౗ᛙۓԏᔙܭۓॶǶ

3.3

ۓηޑਔᒋϩ݋่݀

ҁࣴزၮҔਔᒋϩ݋ǴीᆉଭၲۓηڙډਔᒋѦΚΠँଆᗺޑਁ൯-ᓎ౗ៜᔈǶଷ೛ଭၲۓηޑߔѭ߯ኧࣁ

]

=0.2%Ǵаਁ൯ 400Vp-pҬࢬႝ ᓸࡼуܭ AǵB ࣬ठ୏Ꮤޑ߄य़ႝཱུǴٿಔႝᓸ࣬Տৡ 90 ࡋǶୖԵკ 2.5 ܌ҢǴ่ᄬ΋аΟف׎ۓηΠᜐޑँଆᗺբࣁୖԵᗺǴीᆉୖԵᗺޑᓎ ౗-Տ౽ៜᔈǶϩձୖԵკ 2.7 ᆶკ 2.9 ܌ҢǴ่ᄬΒᆶ่ᄬΟ߾аΟف׎ ۓηޑ΢ᆄഗᗺբࣁୖԵᗺǶ ྽ۓη೏ठ୏ਔǴۓηϐँଆᗺբᐍ༝׎ॉၞၮ୏ǴԶᐍ༝׎ॉၞ ࢂҗୖԵᗺ X (ᐉӛ)Бӛᆶ Z (ᕵӛ)БӛٿޣޑՏ౽᠄уԶԋǶUeha [6] මගрǴᐍ༝ॉၞύޑڬӛՏ౽ཇεǴ߾ଭၲޑ܄ૈཇӳǴ܌ගڬӛՏ

౽࣬྽ܭҁࣴزۓη่ᄬୖԵᗺޑ X БӛՏ౽ UXǴҁࣴز٩Ԝፕᗺᑔᒧ ኳࠠ൳ՖୖኧǴY Бӛ߾ࣁΟف׎ۓηޑ৩ӛБӛǶ߄ 5 ύۓη่ᄬ΋ ޑѤಔኳࠠ(aǵbǵcǵd)ୖԵᗺޑਁ൯ᆶᓎ౗ៜᔈӵკ 3.23~3.26 ܌ҢǴ നεਁ൯ೀჹᔈޑӅਁᓎ౗ᆶኳᄊϩ݋่݀࣬ӕǶ่ᄬ΋(a)ϩ݋่݀ࣁ Y БӛՏ౽ၨεǴX ᆶ Z БӛՏ౽ၨλǴଭၲ܄ૈёૈӢԜڙቹៜԶफ़ եǹ่ᄬ΋(b)ϩ݋่݀಄ӝ΢ॊ܌ගޑՏ౽೛ीྗ߾ǴUXεܭ UZЪ UY നλǴՠځኳᄊ႖ᚆਏ݀ό٫Զኩஒϐ௨ନǹ่ᄬ΋(c)ϩ݋่݀ᅈى΢

ॊՏ౽ྗ߾೛ीǴUXനεǵUZԛϐǵUYࣗλǴኳᄊ႖ᚆำࡋࣁ 3.8kHzǹ

่ᄬ΋(d)ϩ݋่݀ᗨ಄ӝ೛ीྗ߾Ǵՠځਁ൯ϝόӵಃΟಔϩ݋ޑ่݀ ٫Ƕ่ᄬΒᆶ่ᄬΟޑୖԵᗺਁ൯ᆶᓎ౗ៜᔈϩ݋่݀ӵკ 3.27 ᆶკ 3.28 ܌ҢǴୖԵᗺΟঁБӛޑՏ౽൳Я΋ठǴЪኳᄊ႖ᚆޑਏ݀٫Ǵᗨ Y Б ӛ(৩ӛ)ԖၨεޑՏ౽ǴՠۓηޑΟঁँଆᗺӕਔբ୏Ǵ৩ӛՏ౽ჹଭၲ ܄ૈޑቹៜόεǶ᏾౛Ѥಔۓη่ᄬޑਔᒋϩ݋่݀Ǵᒧ᏷ۓη่ᄬ΋ (c)ǵ่ᄬΒᆶ่ᄬΟ຾Չኩᄊៜᔈϩ݋Ǵኳᔕۓηँଆᗺӧ௴୏ᕓ໔ᆶ ᛙᄊਔޑՏ౽ᡂϯໆϷၮ୏ॉၞǶ

3.4

ۓηޑኩᄊៜᔈϩ݋่݀

ࣁኳᔕຬॣݢଭၲۓηँଆᗺϐၮ୏ॉၞǴҁࣴز௦Ҕ ANSYS ঺း ೬ᡏޑኩᄊϩ݋ኳಔϒаीᆉǶӧीᆉำׇύǴԵቾᒡΕႝᓸᒿਔ໔ׯ ᡂǴࡼу࣬Տৡ 90 ࡋޑٿಔҬࢬႝᓸԿ AǵB ࣬ᓸႝඤૈᏔǴ០୏ۓη ่ᄬਁ୏Ǵᢀჸଭၲۓηܭ௴୏ᕓ໔ᆶᛙᄊਔޑՏ౽ᡂϯໆǴ٠ஒ XǵZ БӛޑՏ౽ᛤԋॉၞǶ ANSYS঺း೬ᡏ௦Ҕફଭլᑈϩݤ຾Չኩᄊϩ݋Ǵஒ០୏ຼය฻ϩ ԋΜϤঁਔ໔ቚໆǴ؃ڗၨ٫ޑीᆉᆒࡋǴዴߥ܌؃ޑኩᄊှόѨ੿Ƕ ่ᄬߔѭޑ೛ۓࣁኳᔕޑख़ाୖኧϐ΋Ǵ᏾ᡏ่ᄬޑ׷਑ߔѭଷ೛ࣁႜ

ճߔѭ(Rayleigh damping)ǴߔѭંତC

D

M

E

KǴځύ

D

Mᆶ

E

Kϩձ

ж߄᏾ᡏޑ৤উነᔔߔѭᆶ่ᄬߔѭǴଷ೛ኳᄊߔѭК

]

=0.2%Ǵаጠӝ

ኳᄊᆶځၨଯᎃ߈ኳᄊϐԾฅᓎ౗Ǵ،ۓ

D

(alpha damping)ᆶ

E

(beta

damping)ॶǴਥᏵϦԄ[22] 2 2 i i i

D EZ



Z]

(3.1) ё؃ள

D

545.423Ǵ -9 7.315 10

E

u Ƕ җܭ߃ۈ೛ीޑۓη่ᄬ΋ϐϣᏤفϷНѳ໒ኲቨࡋၸλǴᏤठ่ ᄬуπ֚ᜤǴਥᏵуπቷ୘ࡌ᝼ǴஒϣᏤفъ৩җ 1.5mm ׯࣁ 2.5mmǴ ࿶༾ፓ่ᄬϐ൳ՖЁκǴख़ཥीᆉۓη่ᄬ΋ጠӝኳᄊޑԾฅᓎ౗ࣁ 41.303kHz ǵۓη่ᄬΒࣁ 24.643kHzǵۓη่ᄬΟࣁ 23.065kHzǴ٩ྣ ԜΟಔ០୏ᓎ౗ϩձ຾Չຬॣݢଭၲۓηޑኩᄊៜᔈϩ݋Ǵаٿಔ࣬Տ ৡ 90 ࡋЪਁ൯ࣁ 400Vp-pޑҬࢬႝϩձࡼуܭ AǵB ࣬ठ୏Ꮤޑ߄य़ႝ ཱུǴӅ០୏ 250 ঁຼයǶ ۓη่ᄬ΋Ǻ ஒΟف׎ۓηΠᜐύᗺ΢ᆄޑँଆᗺຎࣁୖԵᗺǴკ 3.29 ܌Ңϩձ ࣁ၀ᗺܭ XǵYǵZ БӛޑՏ౽ៜᔈǴۓη໒ۈᐟਁࡕǴXǵZ БӛՏ౽ ޑਁ൯೴ᅌሀቚǴޔډ 0.85 msec р౜നεॶǶϐࡕǴਁ൯և౜ݢ୏ރᄊ ቚу܈෧ϿǴऊԿ 5.6 msec ࡕǴΨ൩ࢂ 230 ຼයаࡕǴਁ൯և౜ᛙۓރ ᄊǶY БӛՏ౽໻ܭ໒ۈठ୏ࡕǴԖ༾λᘋ୏วғǴ࣬ၨܭ X Бӛᆶ Z БӛϐՏ౽ࣗλǶӕ΋ਔ໔ǴX ᆶ Z БӛՏ౽ϐӝԋॉၞӵკ 3.30(a)܌ ҢǴୖԵᗺҗύЈೀӛѦբᐍ༝׎ॉၞၮ୏ǴឦܭߏືѳՉܭ X Бӛޑ ᐉᐍ༝ǶX ᆶ Y БӛՏ౽ϐӝԋॉၞӵკ 3.30(b)܌ҢǴӢ Y БӛՏ౽ࣗ λǴև౜ޑၮ୏ॉၞࣁࡧᐍ༝Ǵჹଭၲ܄ૈޑቹៜၨόܴᡉǶ ۓη่ᄬΒǺ ஒΟف׎ۓη΢БޑഗᗺຎࣁୖԵᗺǴᘏڗځ࿯ᗺՏ౽ޑᡂϯໆǴ

კ 3.31 ܌Ңϩձࣁ၀ᗺܭ XǵYǵZ БӛޑՏ౽ៜᔈǴޔԿ 6.3 msecǴΨ ൩ࢂεऊၸΑಃ 155 ຼයǴਁ൯໒ۈᛙۓǶΟޣύа X БӛޑՏ౽ၨλǴ Yᆶ Z БӛޑՏ౽ᡂϯ൳Я΋ठǶஒ X ᆶ Z БӛޑՏ౽ǵX ᆶ Y БӛՏ ౽ϐӝԋॉၞӵკ 3.32 ܌ҢǴୖԵᗺӧ X-Z ѳय़ᆶ X-Y ѳय़և౜ޑၮ୏ ॉၞ֡ࣁอືѳՉܭ X Бӛޑޔҥᐍ༝Ƕ ۓη่ᄬΟǺ ຎΟف׎ۓη΢БޑഗᗺࣁୖԵᗺǴᘏڗځ࿯ᗺՏ౽ޑᡂϯໆǴკ 3.33܌Ңࣁ០୏ 230 ຼයୖԵᗺϐՏ౽ៜᔈǴXǵYǵZ БӛޑՏ౽ελ ൳Я΋ठǴऊԿ 8 msec ࡕǴՏ౽ៜᔈ೴ᅌᛙۓǶX ᆶ Z БӛޑՏ౽Ϸ X ᆶ Y БӛՏ౽ϐӝԋॉၞӵკ 3.34 ܌ҢǴୖԵᗺӧ X-Z ѳय़ᆶ X-Y ѳ य़և౜ޑၮ୏ॉၞ߈՟҅༝Ƕ җа΢Οಔۓη่ᄬޑኩᄊϩ݋ᆶਔᒋϩ݋่݀ว౜Ǵਔᒋϩ݋ᆶ ኩᄊϩ݋܌ᕇளޑՏ౽ελᖿ༈࣬߈ǴࡺёӃҗਔᒋϩ݋ᢀჸ XǵYǵZ ΟঁБӛޑՏ౽ᡂϯǴӆ຾Չሡ઻ਔၨΦޑኩᄊϩ݋Ƕ

3.5

ۓηᆶᙯηޑௗ᝻ΚᏢϩ݋

ҁ࿯ۯុ 3.4 ࿯ޑኩᄊៜᔈϩ݋Ǵीᆉଭၲۓηᆶᙯηޑௗ᝻ΚᏢՉ ࣁǴႣෳຬॣݢଭၲޑᙯೲᆶסંǶ୏ᄊௗ᝻ୢᚒӸӧ๱ଯࡋߚጕ܄Ǵ ᠄ж؃ှၸำࢂցԏᔙஒࢂ؃ள่݀ޑख़ाᜢᗖǶӢԜǴௗ᝻ϡનჴୖ ኧᆶᜢᗖᒧ໨ޑ೛ۓǴஒ،ۓ؃ှၸำޑ᠄жԛኧǵԏᔙᆶցϷीᆉ่ ݀ޑӝ౛Ƕ 3.5.1 ௗ᝻ϡનޑᒧҔ

ANSYS ঺း೬ᡏޑௗ᝻ϩ݋ࢂᔈҔௗ᝻ϡન(contact elements)ኳᔕ ٿނᡏௗ᝻य़ޑௗ᝻ՉࣁǴ΋ѿௗ᝻୔ୱޑௗ᝻ϡન೏ࡌҥǴ؃ှਔǴ ൩཮Եቾډٿޣޑௗ᝻చҹǶ؃ှ߻ǴѸ໪Եໆௗ᝻୔ୱޑ೛ۓጄൎࢂ

ց፾྽ǴऩۓကၸλǴёૈᏤठ҂ࡌҥޑௗ᝻୔ୱวғऀ೸౜ຝǴၸε ஒቚуس಍ၮᆉਔ໔Ƕҁࣴز௖૸ຬॣݢଭၲޑௗ᝻ΚᏢϩ݋໻ჴࡼܭ ۓη่ᄬΟᆶᙯηޑԖज़ϡનኳࠠǴۓηϐௗ᝻ᗺࣁᒳౚǴӵკ 3.35 ܌ ҢǴٿޣޑௗ᝻ୢᚒଷ೛ࣁখᡏჹቸ܄ᡏၮ୏Ǵᙯη׷਑ᒧҔόឌᒳ (SUS304)Ǵ٠ຎࣁখᡏǴᙯηᆶۓηϐϡનࠠᄊ௦ҔΟᆢଯ໘Μ࿯ᗺޑ SOLID92 Ѥय़ᡏϡનǶӧۓηޑँଆय़ᆶᙯηΠ߄य़ࡌҥ΋ಔௗ᝻ჹ

(contact pair)ǴۓηᆶᙯηܭΟᆢޜ໔ϣ଺य़ჹय़(surface to surface)ௗ ᝻ǴஒҞ኱ϡન TARGE170 ߕ๱ܭᙯηΠ߄य़Ǵௗ᝻ϡન CONTA174 ߕ ๱ܭᒳౚޑ΢߄य़Ƕௗ᝻ჹࡌҥֹԋࡕǴѸ໪ᔠࢗௗ᝻ϡનаϷҞ኱ϡ નϐϡન০኱س಍(element coordinate system, ESYS)Ǵӵკ 3.36 ܌ҢǴௗ ᝻ϡન ESYS ޑݤӛໆБӛࡰӛҞ኱ϡનǴҞ኱ϡન ESYS ޑݤӛໆБ ӛࡰӛௗ᝻ϡનǴӵԜس಍ωૈ٩ࡌҥޑௗ᝻ჹ຾ՉीᆉǶ 3.5.2 ჴதኧᆶᜢᗖᒧ໨೛ۓ ᜢܭௗ᝻ჹϐߚೣऀௗ᝻చҹǴࢂҗҞ኱ϡનکௗ᝻ϡનӅӕ٬Ҕ ޑჴதኧ(real constant)ٰ،ۓǴаΠଞჹගଯኳࠠԏᔙ܄ᆶჹϩ݋่݀Ԗ ܴᡉቹៜޑୖኧ଺຾΋؁ޑᇥܴǶ (1) ௗ᝻খࡋ(FKN)Ǻӧࡌҥय़ჹय़ௗ᝻ϡનਔǴѸ໪೛ۓϡનޑௗ᝻খ ࡋǴӵ݀ௗ᝻খࡋཇεǴଭၲۓηᆶᙯη໔ޑऀ೸ໆཇλǴཇௗ߈ჴሞ ރݩǶ٬ҔФႥ-܎ᅽහݤ؃ှਔǴ཮Ӣࣁௗ᝻খ܄ఊࡋගଯǴቚу؃ှ ޑ᠄жԛኧϷीᆉޑ֚ᜤࡋǴᏤठߚጕ܄ޑ؃ှၸำ׳ᜤԏᔙǶFKN ޑ ೛ۓॶёҗλԿε೛ۓௗ᝻খࡋǴӆղᘐ่݀ޑԏᔙ܄Ϸӝ౛܄Ƕ! (2) ೣऀϦৡ(FTOLN*Ǻӧௗ᝻य़ޑीᆉ΢ǴٿނᡏޑೣऀໆѸ໪λܭೣ ऀϦৡǴӧ᠄жीᆉޑၸำύǴऩೣऀໆεܭೣऀϦৡ߾߄Ңۘ҂ԏᔙǴ س಍཮ᝩុ຾Չ᠄жीᆉǴޔԿೣऀໆλܭೣऀϦৡǴωᆉԏᔙǶFTOLN ޑ೛ۓރݩᜪ՟ FKNǴ೛ۓཇλޑೣऀϦৡཇௗ߈ჴሞௗ᝻௃ݩǴѸ໪

޸׳ӭޑਔ໔ၮᆉǴ٠ёૈ೷ԋ่݀คݤԏᔙǶ!

(3) ௗ᝻ୀෳጄൎ(pinball region, PINB)Ǻᙖ๱๏ۓௗ᝻ϡનޑୀෳጄൎǴ ྽೛ۓޑጄൎϣԖҞ኱ϡનӸӧਔǴس಍ջ཮Եቾٿޣ໔ޑௗ᝻Κी ᆉǶ೛ۓϼλޑୀෳጄൎܰ٬س಍҂ୀෳډௗ᝻ޑวғԶр౜᝾֋Ǵϼ ε߾཮ቚу׳ӭޑཛྷ൨ၸำԶ෧ᄌ؃ှޑೲࡋǴӢԜ೛ۓਔሡຑ՗ჴሞ ޑௗ᝻ጄൎǴዴᇡ೛ۓޑጄൎىаୀෳډௗ᝻ޑวғջёǶ! (4) ୊ᔈΚ΢ज़ॶ(TAUMAX)Ǻ೸ၸ೛ۓነᔔय़ޑനε୊ᔈΚॶǴёᗉխ ௗ᝻҅ӛᔈΚၸεǴᏤठόӝ౛ޑ่݀Ǵነᔔय़୊ᔈΚޑ΢ज़ॶ೛ۓࣁ max Sy

W

/ 3 ǴځύSyࣁ׷਑ޑ܎՜फ़ҷமࡋǶ! (5) ነᔔ߯ኧǺᙯηᆶۓηޑነᔔၸำϩձࣁᗹᅉ(stick)ነᔔ܈ྖ୏ (sliding)ነᔔǴᓉነᔔᆶ୏ነᔔ߯ኧޑ೛ۓஒ཮ቹៜௗ᝻ϡનϐነᔔᔈ Κǵௗ᝻ჹྖ୏ޑጄൎϷଭၲޑᒡр܄ૈǶа΢܌٬Ҕޑჴதኧ೛ۓӵ ߄ 6 ܌ҢǶ ፓ᏾ௗ᝻ϡનᆶҞ኱ϡનޑᜢᗖᒧ໨(key options)೛ۓǴΨࢂ؃ှࢬ ำޑᜢᗖाᗺǴ٩ۓηᆶᙯη໔ޑௗ᝻ୢᚒϷ࿶ᡍݤ߾Ǵᒧ᏷፾྽ޑ೛ ۓǴ൳ঁख़ाᜢᗖᒧ໨ӵΠǺ (1) ௗ᝻ΚᄽᆉݤǺᒧҔޑᄽᆉݤࣁᚵᆦڄኧݤ(penalty method)Ǵ࣬ᜢϟ ಏୖԵ 2.6.2 ࿯ޑᇥܴǴANSYS ঺း೬ᡏޑௗ᝻ᄽᆉݤႣ೛ࣁۯ՜܎਱ ਟВ(augmented Largrangian method)ᄽᆉݤǴԜݤᗨૈ࿶җቚуѳᑽ᠄ж ԛኧᕇளၨଯޑᆒዴࡋǴՠΨӢᚐѦޑ᠄жၮᆉሡ઻຤׳ӭޑਔ໔ᆶޜ ໔ၮᆉǶ (2) ௗ᝻ϡનϐୀෳྗ߾Ǻௗ᝻ϡનୀෳҞ኱ϡનޑ୷ྗ༝Јё೛ۓࣁଯ ථᗺୀෳ܈࿯ᗺୀෳǶҗܭҁࣴزஒᙯηຎࣁখᡏǴௗ᝻ୀෳޑղᘐሡ ௦Ҕ࿯ᗺԶߚଯථᗺǴ࿯ᗺୀෳޑᓬᗺёᗉխௗ᝻ჹऀ೸Ƕ (3) ௗ᝻ՉࣁǺ೛ۓଭၲۓηᆶᙯηௗ᝻ਔࣁόёϩᚆރᄊǴջᙯη߄य़

ᆶۓη߄य़ۈಖόёϩᚆǴՠϢ೚ྖ୏วғǶ (4) ௗ᝻খࡋ׳ཥ௃׎Ǻ྽ଭၲۓηᆶᙯηௗ᝻ਔǴௗ᝻୔ୱόᘐޑᡂϯ ௃׎ǴஒᏤठس಍খࡋ࡭ុׯᡂǴ؂΋ԛ᠄жၸำύǴس಍Ծ୏׳ཥௗ ᝻খࡋᆶϪጕখࡋǴаගଯ؃ှޑԏᔙ܄Ƕ (5) ௗ᝻य़߃ۈ೛ۓǺӧނᡏۘ҂ௗ᝻߻Ǵջ٬ࢂ΋ࢤλλޑ໔ሜǴ۳۳ ӧௗ᝻ޑᕓ໔Ꮴठ؃ှԏᔙ֚ᜤǶӢԜǴӧԖज़ϡનኳࠠࡌҥࡕǴёܭ ߃ۈௗ᝻೽Տբ࣬ᜢ܄ޑ೛ۓǶٯӵǺѺ໒໔ሜഈӝᒧ໨Ǵ٬ளଭၲۓ ηᆶᙯη΋໒ۈ൩ߥ࡭ௗ᝻ރᄊǴ෧Ͽࡌኳᆶᆛ਱೷ԋޑ༾λᇤৡǶ 3.5.3 ଭၲᙯೲᆶסંीᆉ ҁࣴزᔈҔኩᄊϩ݋ीᆉଭၲۓηᆶᙯηௗ᝻ՉࣁǶӧۓη่ᄬΟ ϐௗ᝻ᗺ΢БǴௗ᝻ᗺࣁᒳౚǴࡌҥ༝ዬъ৩ࣁ 21mmǵື৩ࣁ 6mm ޑ ᙯηኳࠠǴܭ AǵB ࣬ठ୏Ꮤޑ߄य़ႝཱུࡼуਁ൯ 400Vp-pҬࢬႝᓸǴAǵ B࣬ठ୏Ꮤႝᓸ࣬Տৡ 90 ࡋǶᙯືۭ೽ࡼϒӛΠޑႣᓸΚǴ؃ှ߻ஒᙯ ηޑ০኱س಍җьМ০኱ׯࣁ༝ࢊ০኱ǴаБߡᘏڗᙯηኩᄊޑڬӛՏ ౽ϷڬӛೲࡋǴ྽ۓη೏ᐟਁਔᙖ๱ௗ᝻ޑነᔔΚ០୏ᙯηǴటளډᙯ ηޑᛙᄊՏ౽ᆶᛙᄊೲࡋሡԿϿ០୏ 150 ຼයǶᙯηޑኩᄊՏ౽ӵკ 3.37 ܌ҢǴНѳືࣁਔ໔ǴႉࠟືࣁՏ౽Ǵᙯηޑ৩ӛՏ౽ᖿ߈ܭ႟Ǵڬӛ Տ౽߾ᒿਔ໔ԶቚуǴҗԜёղᘐᙯηޑᙯ୏Ъ௽ᙯБӛࣁ଍ਔଞǶᙯ ηޑኩᄊೲࡋӵკ 3.38 ܌ҢǴНືࣁਔ໔ǴႉࠟືࣁᙯೲǴஒᙯηޑڬ ӛೲࡋV_T ඤᆉԋᙯೲǴ߄ҢӵΠ 60 2 rotor V RPM R T

S

u (3.2) ځύR_rotorࣁᙯηޑъ৩Ǵᙯηܭଆ୏ᕓ໔ೲࡋ࡚ೲ΢ϲǴऊԿ 6 msec ࣾ ࡕ໒ۈᛙۓǴԜਔޑᙯೲջࣁᛙᄊᙯೲǶ ӕਔᢀჸۓηᆶᙯηௗ᝻୔ୱޑௗ᝻ᓸΚᆶነᔔΚǴҗነᔔΚीᆉ

ᙯηޑነᔔסંǶHagood[17]මᇥܴຬॣݢଭၲܭᛙᄊၮᙯਔǴᙯηޑᄍ ܄໨ࣁ႟ǴନΑᓉЗסંѦǴ྽ᙯηᙯೲόࣁ႟ਔǴߔѭϝӸӧǴԜਔ ޑነᔔסંऊ฻ܭॄၩסંǶीᆉଭၲסંѸ໪ܭᙯηࡼуॄၩסંǴ ࡼуॄၩסંޑБӛᆶᙯηᙯ୏ޑБӛ࣬ϸǴ࡭ុቚуॄၩסંǴ٠૶ ᒵᙯηޑᙯೲᡂϯǴޔԿᙯηޑᙯೲࣁ႟ǴԜਔଭၲޑനεסંᆀࣁᓉ Зסં(stall torque)Ǵջֹԋᙯೲᆶסં܄ૈԔጕǴӵკ 3.39 ܌ҢǴϩձ ࣁᙯη܍ڙႣᓸΚ 0.98N ᆶ 4.116N բҔΠǴסંᆶᙯೲޑᜢ߯Ǵคॄၩ ޑ ᙯ ೲ ࣁ ϩ ձ ࣁ 50.5rpm ᆶ 40.2rpm Ǵ ന ε ס ં ϩ ձ ࣁ 2N-cm ᆶ 2.52N-cmǶӧၨεޑႣᓸΚբҔΠǴᙯηޑᙯೲफ़եǴᒡрޑסંගଯǶ ҁࣴزीᆉޑ܄ૈԔጕᖿ༈ᆶЎ᝘ޑຬॣݢଭၲ܄ૈԔጕ่݀΋ठǶ

ಃѤക ჴᡍໆෳᆶ่݀૸ፕ

ਥᏵಃΟകϐኧॶϩ݋่݀Ǵ،ۓଭၲۓη่ᄬϐ൳ՖЁκǴᇙբ ຬॣݢଭၲচࠠᐒǶჴᡍӃаᆛၡϩ݋ሺໆෳଭၲۓηচࠠޑӅਁᓎ ౗Ǵ٠ϟಏჴᡍ௦Ҕޑໆෳس಍Ϸଭၲޑᙯೲᆶסંໆෳ่݀Ƕ

4.1

ຬॣݢଭၲᇙբ

ຬॣݢଭၲޑ่ᄬЬाҗۓηᆶᙯηಔԋǴځύۓη่ᄬҗ᎑ӝߎ ׷਑ϷБ׎ᓸႝठ୏Ꮤ܌ಔԋǶᓸႝठ୏Ꮤ௦ҔᏣٍࣽמϦљᇙ೷ޑБ ׎ᓸႝഏౠ PZT-4ǴЁκӵკ 4.1 ܌ҢǴཱུϯБӛࣁࠆࡋБӛǶΟف׎ۓ ηࢂаሕ׉уπǴۓη่ᄬ΋ӧΟف׎Ӛᜐ΢ጔύᗺ೛࿼ँଆᗺǴНѳ ໒ኲՏܭୁᜐۭᆄೀǶۓη่ᄬΒᆶ่ᄬΟϐँଆᗺ೛࿼ܭΟف׎Ӛف ഗᗺޑ΢ጔǴНѳ໒ኲϩձՏܭӚفഗᗺޑΠБǶନۓη่ᄬΟѦǴ่ ᄬ΋ᆶ่ᄬΒϐߎឦ߄य़࿶໚ཱུೀ౛Ƕനࡕ௦ҔჇ਼ጤ Loctite No.648Ǵ ஒБ׎ᓸႝТᗹຠܭΟف׎ۓηӚᜐޑѦୁǶҁࣴزќѦᇙբᓸႝТᗹ ຠᇶշᏔϷᓸլΚ֨ڀǴӵკ 4.2 ܌ҢǴዴߥᓸႝТᗹຠՏ࿼ޑ΋ठ܄Ǵ ٠җᓸլΚ֨ڀ֨࡭ۓηǴගଯᓸႝТᆶΟف׎ۓηޑᗹ๱மࡋǶᇙբ ֹԋޑΟঁۓη่ᄬϩձӵკ 4.3~კ 4.6 ܌ҢǶ

4.2

Ӆਁᓎ౗ໆෳ

ຬॣݢଭၲޑӅਁᓎ౗ໆෳ௦Ҕᆛၡϩ݋ሺ HP-8751A (Agilent Technologies, Santa Clara, CA, USA)Ǵໆෳຬॣݢଭၲۓηޑߔל-ᓎ౗ៜ ᔈԔጕǴᕇளۓη่ᄬޑӅਁᓎ౗Ƕ܌ᒏߔל(impedance)൩ࢂࡑෳނ(܈ ΋֖ႝ৒ǵႝགϷႝߔޑႝၡ)ჹຼය܄ႝࢬ܈Ҭࢬ܄ႝࢬౢғϐלΚǶ ஒଭၲۓηڰۓӧෳ၂ѳѠ΢Ǵᜐࣚచҹᆶኧॶኳᔕރݩ΋ठǴໆෳࢎ ᄬӵკ 4.7 ܌ҢǴ೛ۓޑ௟ᓎጄൎࣁ 10~50kHzǶҗᆛၡϩ݋ሺගٮ΋۰