2I2-04ϐΤκΞΫνϡΤʔλΛ༻͍ͨճస‫ػ‬ցʹ࡞༻͢Δ֎ྗ‫ܭ‬ଌ૷ஔͷͨΊͷ੍‫ܥޚ‬ઃ‫ܭ‬Development of Control System for Measurement of External
Forces Acting on a Rotating Machine Using a Piezo Actuator໊‫ݹ‬԰େֶʓᤵҪɹকଠɼӜɹ݈ଠ࿕ɼҪ্ɹ߶ࢤ* Shota Yabui, Kentaro UraɼTsuyoshi Inoue
Nagoya university
Abstract In this research, in order to accurately estimate the external force acting on a rotatingmachine, we applied a motion control technology and developed a measuring device using a piezo
actuator. From the experimental results, it was conﬁrmed that the proposed measuring device
can control the orbit of the rotating shaft in micro order. In this study, a mechanical seal wasinstalled in the plant part to measure the external force generated in the mechanical seal part. The
mechanical seals are parts that prevent ﬂuids handled by rotating machines from leaking outside
the machine. In the design of mechanical seals, the estimation of the force generated by coupling
the ﬂuid and structure in the machine is an important factor. We also conﬁrmed that the force
generated in the mechanical seal can be estimated in real time from the control signal.
Key Words: Controller design, Rotating machine, External force,1͸͡Ίʹ

Actuator partAC servo motorShaftϞʔγϣϯίϯτϩʔϧ͸༷ʑͳ࢈‫ۀ‬੡඼ͷ։ൃʹԠ༻͞Εɼ࢈‫ۀ‬෼໺ʹ͓͚Δॏཁͳཁૉٕज़Ͱ͋Δ [1]ɽճస‫ػ‬ցͷ։ൃʹ͓͍ͯɼߏ଄ͱྲྀମͷಈಛੑ͕૬‫ޓ‬࡞༻͢Δ֎ྗͷଌఆʹ͓͍ͯɼΞΫνϡΤʔλΛ༻͍ͨଌఆ૷ஔͷ։ൃ͕ਐΊΒΕ͍ͯΔ [2] [3]ɽճస‫ػ‬ցʹ࡞༻͢Δ֎ྗ͸ճస࣠ͷ‫ي‬ಓʹґଘ͢ΔͨΊɼଌఆ࣌ʹ͸࣮ࡍͷ࣠ͷ‫ي‬ಓΛߴਫ਼౓ʹ࠶‫͢ݱ‬Δ͜ͱ͕ॏཁ
Ͱ͋Δɽຊ‫Ͱڀݚ‬͸ɼճస‫ػ‬ցʹ࡞༻͢Δ֎ྗΛਫ਼౓ྑ͘ਪఆ͢ΔͨΊɼϞʔγϣϯίϯτϩʔϧͷ੍‫ٕޚ‬ज़ΛԠ༻͠ɼϐΤκΞΫνϡΤʔλΛ༻͍ͨଌఆ૷ஔ
Λ։ൃͨ͠ɽ࣮‫݁ݧ‬Ռ͔ΒఏҊ͢Δଌఆ૷ஔ͸ճస࣠

Ball bearingPlantCouplingͷ‫ي‬ಓΛϚΠΫϩΦʔμʔͰ੍‫͖Ͱޚ‬Δ͜ͱΛ֬ೝͨ͠ɽ·ͨɼຊ‫Ͱڀݚ‬͸ϝΧχΧϧγʔϧ෦ʹൃੜ͢ΔFig. 1: Overview of the proposed experimental system֎ྗΛଌఆ͢ΔͨΊɼϓϥϯτ෦ʹϝΧχΧϧγʔϧΛઃ͚ɼ֎ྗͷଌఆΛ࣮ࢪͨ͠ɽϝΧχΧϧγʔϧ͸ճస‫ػ‬ցͰऔΓѻΘΕΔྲྀମ͕ɼ‫ػ‬ցͷ֎෦΁࿙ΕΔ͜ͱΛ๷͙ύʔπͰ͋Δ [4]ɽྫ͑͹ɼϩέοτ༻λʔϘϙϯϓͰ͸೩ྉͷ࿙ΕΛ๷͙ͨΊʹ༻͍ΒΕɼճస‫ػ‬ցͷ҆શಈ࡞ʹ͓͍ͯॏཁͳύʔπͰ͋ΔɽͦͷϝΧχΧϧγʔϧ෦Ͱൃੜ͢ΔྗΛɼ੍‫ޚ‬৴߸͔ΒϦΞϧλΠϜͰਪఆͰ͖Δ͜ͱΛซͤͯ֬ೝͨ͠ɽ2ఏҊ͢Δଌఆ૷ஔస࣠ͷத৺ʹ͸ଌఆର৅Ͱ͋Δྲྀମͱߏ଄Λ֨ೲͨ͠ϓϥϯτ͕ઃஔ͞Ε͍ͯΔɽͦͯ͠ɼϘʔϧϕΞϦϯάΛ‫ݻ‬ఆ͢Δ୆࠲ʹ͸ੵ૚‫ܕ‬ϐΤκΞΫνϡΤʔλ͕औ෇ΒΕ͓ͯΓɼϘʔϧϕΞϦϯάΛհͯ͠ճస࣠ͷҐஔΛ੍‫͖Ͱޚ‬ΔɽFig.2 ʹΞΫνϡΤʔλͷ֦େਤΛࣔ͢ɽϐΤκΞΫνϡΤʔλ͸ 2 ͭऔ෇ΒΕ͓ͯΓɼx−yฏ໘্Ͱ೚ҙʹճస࣠Λ੍‫͖Ͱޚ‬Δɽ·ͨɼϐΤκΞΫνϡΤʔλʹ༩ѹʹΑΓൃੜྗͱൃੜมҐΛௐ੔͢ΔͨΊͷόω͕औΓ෇͚ΒΕ͍ͯΔɽ ͜ͷ࣮‫૷ݧ‬ஔͷ

Fig.1 ʹఏҊ͢Δଌఆ૷ஔΛࣔ͢ɽճస࣠͸Ұํ͕໛ࣜਤΛ Fig.3 ʹࣔ͢ɽຊ‫Ͱڀݚ‬͸ϝΧχΧϧγʔϧ෦ΧοϓϦϯάΛհͯ͠αʔϘϞʔλʹ઀ଓ͞Εɼଞํʹൃੜ͢Δ֎ྗΛଌఆ͢ΔͨΊɼϓϥϯτ෦ʹϝΧχ͸ϘʔϧϕΞϦϯάʹΑΓࢧ࣋͞Ε͍ͯΔɽ·ͨɼճΧϧγʔϧΛઃ͚͍ͯΔɽϝΧχΧϧγʔϧͰ෧ೖ͢

Piezo actuator
FtFrShaftȍxexyyBall bearing

SpringFig. 2: Close up the actuator part in the proposed
experimental system
Piezo actuator

Seal (target)

Coupling

Fig. 4: Relationship between the external force andthe orbit of the rotating shaft
RotateOrbit control

Motor

Piezo

Plant

Motor

DSP

SensorInverterFig. 5: Schematic diagram of the control system
Ball bearing Position sensor

Liquid (water)‫ي‬ಓͱप೾਺Λਖ਼֬ʹ࠶‫ͯ͠ݱ‬ଌఆ͢Δඞཁ͕͋Δɽ

Fig. 3: Schematic diagram of the proposed experimental system3ϐΤκΞΫνϡΤʔλʹ༻͍Δ੍‫ܥޚ‬ճస࣠Λ೚ҙͷ‫ي‬ಓɼप೾਺ͰৼΕճΒͤΔͨΊɼϐΔྲྀମ͸ਫͱͨ͠ɽճస͕࣠ಈ࡞ͨ͠ͱ͖ɼྲྀମͱߏΤκΞΫνϡΤʔλʹ༻͍Δ੍‫ܥޚ‬Λઃ‫ͨ͠ܭ‬ɽFig.5଄͕࿈੒ͯ͠ྗΛൃੜ͢Δ͕ɼ͜Ε͕γεςϜʹͱͬʹ੍‫ܥޚ‬ͷ֓ཁΛࣔ͢ɽճస࣠͸αʔϘϞʔλʹΑͬͯ֎ྗͱͳΓɼͦͯ͠ෆ҆ఆԽͤ͞Δ֎ྗͱͳΓಘΔɽͯࣗస͠ɼͦͷঢ়ଶͰϐΤκΞΫνϡΤʔλʹΑΓճFig.4 ʹࣔ͢Α͏ʹɼFr ͱ Ft ͸ͦΕͧΕ൒‫઀ͱ޲ํܘ‬స࣠ͷ‫ي‬ಓΛੜ੒͢ΔɽɼมҐηϯαʹΑΓऔಘͨ͠ઢํ޲ͷྗͰ͋Δɽe ͸ճస࣠ͷৼΕճΓ൒‫ܘ‬ɼΩ ͸ৼ࣠มҐΛ‫ʹݩ‬ɼ੍‫ޚ‬ΞϧΰϦζϜΛॻ͖ࠐΜͩ digitalΕճΓप೾਺ͱ͢ΔͱɼFr ͱ Ft ͱಈಛੑͷؔ࿈͸࣍signal processor (DSP) ͕ੜ੒੍ͨ͠‫ޚ‬৴߸͕ϐΤκࣜͰද‫͖Ͱݱ‬Δ [5]ɽΞΫνϡΤʔλ΁ͷೖྗ৴߸ͱͳΔɽϐΤκΞΫνϡ

Fr= M Ω2 − cΩ − Ke
Ft= −mΩ2 − CΩ + ke(1)(2)͜͜ͰɼM ͸௚઀࣭ྔ܎਺ɼC ͸௚઀‫ݮ‬ਰ܎਺ɼK ͸Τʔλ͸ xɼy ੍‫ ʹ͚޲ޚ‬2 ࣮ͭ૷͞Ε͓ͯΓɼͦΕͧΕʹ੍‫ܥޚ‬Λઃ‫͍ͯ͠ܭ‬Δ͕ɼ྆ํ޲Ͱಉ੍͡‫Ͱܥޚ‬͋ΔͨΊɼ͜͜Ͱ͸ x ํ޲ʹ஫໨ͯ͠ৄࡉΛ‫ه‬ड़͢Δɽ੍‫ܥޚ‬ͷϒϩοΫઢਤΛ Fig.6 ʹࣔ͢ɽ͜͜ͰɼC ͸ϝΠϯίϯτϩʔϥɼP ͸ϐΤκΞΫνϡΤʔλ͔Β௚઀߶ੑ܎਺ɼm ͸࿈੒࣭ྔ܎਺ɼc ͸࿈੒‫ݮ‬ਰ܎਺ɼճస࣠·Ͱͷಈಛੑɼrx ͸ x ํ޲ͷ໨ඪ‫ي‬ಓɼe ͸Ґͦͯ͠ k ͸࿈੒߶ੑ܎਺Ͱ͋Δɽࣜ (1)ɼ(2) ΑΓɼFrஔ‫ࠩޡ‬৴߸ɼx ͸࣠มҐɼͦͯ͠ d ͸֎ྗͰ͋Δɽຊͱ Ft ͸ճస࣠ͷৼΕճΓ‫ي‬ಓɼ͓Αͼप೾਺ʹґଘ͢ଌఆ૷ஔ͸ճస‫ػ‬ցͰ͋ΓɼϝΧχΧϧγʔϧͷ֎ྗ

Δ͜ͱ͕෼͔ΔɽͦͷͨΊɼӡసதͷճస‫ػ‬ցͰൃੜ͸ৼΕճΓप೾਺ʹಉ‫ͨ͠ظ‬प೾਺Ͱൃੜ͢Δɽ·ͨɼ͢Δ Fr ͱ Ft Λଌఆ͢ΔͨΊʹ͸ɼӡసதͷճస࣠ͷճసʹ൐͍ৼΕճΓप೾਺ͷ੔਺ഒʹಉ‫ʹͨ͠ظ‬ϥϯ

AFCTable 1: Angular frequency ωaf c−ifaf c−i [Hz]….

㽢iuafc-1䠇q1(k)sin(Ȧafc-1Tk)

㽢䠇

p1(k)
cos(Ȧafc-1Tk)

xy position [m]

䠇Cx

350

466.675100PxFig. 6: Block diagram of the feedback control system
in DSP for x direction

621.67-5

w/o control
w/ control
Target

2
䠇䠇

e(k)
䠉

102
33.33

d

䠇

rx(k) 䠇㽢uafc-6䠇q6(k)sin(Ȧafc-6Tk)

㽢3

䠇

p6(k)
cos(Ȧafc-6Tk)

1
16.67

10-1-2φ΢τ͕ൃੜ͢ΔՄೳੑ͕͋Δɽͦ͜Ͱɼ੍‫ޚ‬෦ʹ͸

-3adaptive feedforward cancellation (AFC) Λ࣮૷ͯ͠
͍ΔɽAFC ͸ϋʔυσΟεΫυϥΠϒɼޫσΟεΫɼͦ-20x position [m]210-5࣓ͯ͠‫࣠ؾ‬डΛ༻͍ͨճస‫ػ‬ցʹ͓͍ͯɼճసʹಉ‫ظ‬ͨ͠ৼಈิঈʹ༗ޮͳ੍‫͋Ͱࣜํޚ‬Δ [6][7][8]ɽAFCFig. 7: Experimental results: orbit of the shaftͷΞϧΰϦζϜ͸Լ‫Ͱه‬ද‫͞ݱ‬ΕΔɽui (k) = pi (k) sin(ωaf c−i T k)+qi (k) cos(ωaf c−i T k)(3)pi (k) = pi (k − 1)+λi e(k) sin(ωaf c−i T k + θi )(4)

qi (k) = qi (k − 1)+λi e(k) cos(ωaf c−i T k + θi )(5)

pi (k) ͱ qi (k) ͸ֶशύϥϝʔλɼωaf c−i ͸ AFC ग़ྗ uiͷ֯प೾਺ɼλi ͸ֶश཰ɼͦͯ͠ θi ͸Ґ૬Ͱ͋Δɽi ͸࣮૷͢Δ AFC ͷ਺Ͱ͋Δɽk ͸αϯϓϧ਺Ͱ͋ΓɼదԠΞϧΰϦζϜ͸ 1 αϯϓϧલ·Ͱͷֶश݁Ռ pi (k − 1)ɼ

qi (k − 1) ʹɼҐஔ‫ࠩޡ‬৴߸ e(k) ʹ λi ͱิঈ͢Δप೾਺ͷਖ਼‫ݭ‬೾ɼ༨‫ݭ‬೾Λ৐ࢉͨ݁͠ՌΛՃࢉ͠ɼߋ৽͍ͯ͘͠ɽAFC ͷదԠΞϧΰϦζϜ͕܎਺ pi (k)ɼqi (k)Λߋ৽͠ɼਪఆ͕‫ ྗ֎͖ͱͨྃ͠׬‬di ͷৼ෯͸࣍ࣜͰද‫͞ݱ‬ΕΔɻ

P|di (k)| =1 + PC
p2i (k) + qi2 (k)(6)Δɽ·ͨɼ֎ཚͷҐ૬͸࣍ࣜͱͳΔɻpi (k)qi (k)

ͨ͠ɽAFC ͷ਺͸ i = 6 Ͱ͋Γɼग़ྗ ui ͷप೾਺

faf c−i = ωaf c−i /2π Λ Table 1 ʹࣔ͢ɽi = 1 − 5 ͷAFC ͸ओʹࣗసप೾਺ʹԠͯ͡‫ݦ‬ஶʹൃੜͨ͠ϥϯφ΢τͷิঈͷͨΊʹ࣮૷ͨ͠ɽi = 6 ͸໨ඪ‫ي‬ಓʹ௥ै্ͤͨ͞Ͱɼp6 , q6 ͔ΒৼΕճΓৼಈʹԠͯ͡ϝΧχΧϧγʔϧ෦Ͱൃੜ͢Δ֎ྗΛਪఆ͢ΔͨΊʹ࣮૷ͨ͠ɽճస࣠ͷ‫ي‬ಓΛ Fig.7 ʹࣔ͢ɽϐΤκΞΫνϡΤʔλΛ༻͍ͯ࣠Λ੍‫͢ޚ‬Δ͜ͱͰ໨ඪ‫ي‬ಓʹԊͬͯৼΕճΓ͍ͯ͠Δ͜ͱ͕෼͔ΔɽҐஔ‫ࠩޡ‬৴߸ͷඪ४ภࠩ͸໿

1.5um Ͱ͋Γɼ໨ඪ‫ي‬ಓʹର͢Δ‫ࠩޡ‬͸໿ 7.5%Ͱ͋ͬ
ͨɽճస࣠ͷ x ํ޲ͷมҐͷৼ෯εϖΫτϧΛ Fig.8 ʹࣔ͢ɽ21.67Hz ͷৼ෯εϖΫτϧ͸໨ඪ‫ي‬ಓͷ൒‫Ͱܘ‬
͋Δ 0.02mm ʹ΄΅౳͘͠ɼfaf c−1 − faf c−5 ͷप೾਺͜͜Ͱɼdi ͸ ωaf c−i ͱҰக͢Δ֯प೾਺ͷ֎ྗͰ͋arg(di (k)) = arctanͷৼΕճΓ‫ي‬ಓΛϐΤκΞΫνϡΤʔλΛ༻͍ͯੜ੒

੒෼͸ϐʔΫ஋͕‫ݮ‬গ͍ͯ͠Δ͜ͱ͕෼͔Δɽͦͯ͠ɼ

p6 , q6 ͔Βࢉग़ͨ͠ x, y ํ޲ͷ֎ྗ͔Βճస࠲ඪ‫ʹܥ‬ม‫ࢉͯ͠׵‬ग़ͨ͠ Fr , Ft Λ Fig.9 ʹࣔ͢ɽFr , Ft ͷৼ෯஋͸‫֨ن‬Խ͍ͯ͠Δ͕ɼ΄΅Ұఆ஋ʹऩଋ͠ɼ࣌ؒ(7)೾‫͔ܗ‬Βͦͷ஋Λࢉग़ՄೳͰ͋Δ͜ͱ͕෼͔ΔɽҎ্ͷ݁Ռ͔ΒɼఏҊ͢Δ࣮‫૷ݧ‬ஔΛ༻͍ͯճస࣠Λ೚ҙҎ্ͷΑ͏ʹɼͦͷਪఆ݁Ռʹ‫ ͍ͯͮج‬AFC ͸֎ཚิͷৼΕճΓ‫ي‬ಓʹ੍‫Ͱ্ͨ͠ޚ‬ɼ੍‫ޚ‬৴߸͔Β֎ྗΛঈΛߦ͏͜ͱ͕Ͱ͖ΔɻਪఆՄೳͰ͋Δ͜ͱ͕֬ೝͰ͖ͨɽ

45࣮‫݁ݧ‬Ռ݁‫ݴ‬ఏҊ͢Δ࣮‫૷ݧ‬ஔΛ༻͍ͯ Fr ͱ Ft Λଌఆͨ͠ɽຊճస‫ػ‬ցʹ࡞༻͢Δ֎ྗΛਪఆ͢ΔͨΊʹɼϐΤκ࣮‫͍͓ͯʹݧ‬͸ɼ1000rpm(16.67Hz) Ͱࣗస͍ͯ͠Δճ

ΞΫνϡΤʔλΛ༻͍ͨଌఆ૷ஔΛఏҊͨ͠ɽճస‫ػ‬స࣠ʹର͠ɼ൒‫ ܘ‬0.02mmɼप೾਺ 1300rpm(21.67Hz)

ցʹ࡞༻͢Δ֎ྗ͸ճస࣠ͷৼΕճΓ‫ي‬ಓʹґଘ͢Δ

ࢀߟจ‫ݙ‬-5103w/o control
w/ control

y position [m]2.5[1] A. Alonso, Concheir, Real Time Digital Control Applications 1st Edition, Proceedings of theIFAC/IFIP Symposium, Guadalajara, Mexico,January 17-19, 656pages (1983).

21.5[2] M. Vance John, Rotordynamics of Turbomachinery, John Wiley & Sons, Inc., NY (1988).

10.5020406080100120[3] D. Childs, Turbomachinery Rotordynamics: Phenomena, Modeling, and Analysis, John Wiley &Sons, Inc., NY (1993).

Frequency [m][4] https://www.ekkeagle.com/jp/technology/mechanical/
Fig. 8: Experimental results: amplitude spectrum ofdisplacement in x direction

F41 ‫ר‬ɽୈ 10 ߸ɼpp. 41–48 (2013)

rnologies, Vol. 18, No. 9-10, pp 1703-1709 (2012).

Ft

0.8Force [-]༻͢ΔϩʔλμΠφϛοΫྲྀମྗʀλʔϘ‫ػ‬ցɽୈ

[6] S. Yabui, A. Okuyama, M. Kobayashi and T. Atsumi, Optimization of adaptive feedforward repeatable run-out cancellation for positioning control system of hard disk drives, Microsystem Tech-

1[7] J. J. Liu and Y. P. Yangt, Comparison ofAFC and FACT Method for Periodic Disturbance Suppression in Optical Disk Drives, Pro-0.6

ceedings of the IEEE Industrial Electronics Society(IECON 2004), Busan, November 2-6, pp.19871992 (2004).

0.4
0.20[5] ߂দɼ಺ւɼ௕ඌɼߐ‫ޱ‬ɿFloating Ring Seal ʹ࡞01000

2000

300040005000Time [s]Fig. 9: Experimental results: Fr and FtͨΊɼ࣮ࡍʹӡసதͷճస‫ػ‬ցͷঢ়ଶΛ࠶‫Ͱ্ͨ͠ݱ‬ଌఆ͢Δඞཁ͕͋ΔɽఏҊ͢Δ࣮‫૷ݧ‬ஔͰ͸ϐΤκΞΫνϡΤʔλΛ༻͍ͯճస࣠Λ೚ҙͷ‫ي‬ಓʹ੍‫ͨ͠ޚ‬্Ͱɼ੍‫ޚ‬৴߸͔Β֎ྗΛਪఆͰ͖Δɼຊ࿦จͰ͸ɼճస‫ػ‬ցͷॏཁͳ‫ػ‬ցཁૉͰ͋ΔϝΧχΧϧγʔϧΛର৅ͱͨ͠ଌఆ࣮‫ݧ‬Λ࣮ࢪͨ͠ɽ࣮‫݁ݧ‬Ռ͔ΒɼϐΤκΞΫνϡΤʔλΛ༻͍ͯճస࣠ͷ‫ي‬ಓΛ‫ ࠩޡ‬7.5%Ͱ੍
‫͠ޚ‬ɼಉ࣌ʹ੍‫ޚ‬৴߸͔Βճస࣠ʹ࡞༻͢Δ൒‫޲ํܘ‬ͱ઀ઢํ޲ʹ࡞༻͢ΔྗΛਪఆͰ͖Δ͜ͱΛ֬ೝͨ͠ɽ

[8] S. Yabui and T. Inoue, Development of a Measurement System for Analyzing External Forces Acting on Rotating Machineries, Journal of DynamicSystems Measurement and Control, Vol. 141, No.
10, 9pages (2019).