雙立柱堆垛機(jī)設(shè)計(jì)【三維SW模型】【全套含12張CAD圖紙】,三維SW模型,全套含12張CAD圖紙,立柱,堆垛,設(shè)計(jì),三維,SW,模型,全套,12,CAD,圖紙 Aileron?Design Chapter?12 Design?of?Control?Surfaces From:?Aircraft?Design:?A?Systems?Engineering?Approach Mohammad?Sadraey 792?pages September?2012,?Hardcover Wiley?Publications 12.4.1.?Introduction The?primary?function?of?an?aileron?is?the?lateral?(i.e.?roll)?control?of?an?aircraft;?however, it?also?affects?the?directional?control.?Due?to?this?reason,?the?aileron?and?the?rudder?are usually?designed?concurrently.?Lateral?control?is?governed?primarily?through?a?roll?rate (P).?Aileron?is?structurally?part?of?the?wing,?and?has?two?pieces;?each?located?on?the trailing?edge?of?the?outer?portion?of?the?wing?left?and?right?sections.?Both?ailerons?are often?used?symmetrically,?hence?their?geometries?are?identical.?Aileron?effectiveness?is?a measure?of?how?good?the?deflected?aileron?is?producing?the?desired?rolling?moment.?The generated?rolling?moment?is?a?function?of?aileron?size,?aileron?deflection,?and?its?distance from?the?aircraft?fuselage?centerline.?Unlike?rudder?and?elevator?which?are?displacement control,?the?aileron?is?a?rate?control.?Any?change?in?the?aileron?geometry?or?deflection will?change?the?roll?rate;?which?subsequently?varies?constantly?the?roll?angle. The??deflection??of??any??control??surface??including??the??aileron??involves??a??hinge moment.?The?hinge?moments?are?the?aerodynamic?moments?that?must?be?overcome?to deflect?the?control?surfaces.?The?hinge?moment?governs?the?magnitude?of?augmented pilot?force?required?to?move?the?corresponding?actuator?to?deflect?the?control?surface.?To minimize??the??size??and??thus??the??cost??of??the??actuation??system,??the??ailerons??should??be designed?so?that?the?control?forces?are?as?low?as?possible. In?the?design?process?of?an?aileron,?four?parameters?need?to?be?determined.?They are:?1.?aileron?planform?area?(Sa);?2.?aileron?chord/span?(Ca/ba);?3.?maximum?up?and down?aileron?deflection?(?±?dAmax);?and?4.?location?of?inner?edge?of?the?aileron?along?the wing?span?(bai).?Figure?12.10?shows?the?aileron?geometry.?As?a?general?guidance,?the typical?values?for?these?parameters?are?as?follows:?Sa/S?=?0.05?to?0.1,?ba/b?=?0.2-0.3,?Ca/C =?0.15-0.25,?bai/b?=?0.6-0.8,?and?dAmax?=?±?30?degrees.?Based?on?this?statistics,?about?5?to 10?percent?of?the?wing?area?is?devoted?to?the?aileron,?the?aileron-to-wing-chord?ratio?is about?15?to?25?percent,?aileron-to-wing-span?ratio?is?about?20-30?percent,?and?the?inboard aileron??span??is??about??60??to??80??percent??of??the??wing??span.??Table??12.17??illustrates??the characteristics?of?aileron?of?several?aircraft. 1 b A ba/2  Ca Sa/2  bai/2  A a.???Top-view?of?the?wing?and?aileron dAup dAdown b.???Side-view?of?the?wing?and?aileron?(Section?AA) Figure?12.1.?Geometry?of?aileron Factors?affecting?the?design?of?the?aileron?are:?1.?the?required?hinge?moment,?2. the?aileron?effectiveness,?3.?aerodynamic?and?mass?balancing,?4.?flap?geometry,?5.?the aircraft?structure,?and?6.?cost.?Aileron?effectiveness?is?a?measure?of?how?effective?the aileron?deflection?is?in?producing?the?desired?rolling?moment.?Aileron?effectiveness?is?a function?of?its?size?and?its?distance?to?aircraft?center?of?gravity.?Hinge?moments?are?also important?because?they?are?the?aerodynamic?moments?that?must?be?overcome?to?rotate?the aileron.?The?hinge?moments?governs?the?magnitude?of?force?required?of?the?pilot?to?move the?aileron.?Therefore,?great?care?must?be?used?in?designing?the?aileron?so?that?the?control forces??are??within??acceptable??limits??for??the??pilots.??Finally,??aerodynamic??and??mass balancing?deals?with?techniques?to?vary?the?hinge?moments?so?that?the?stick?force?stays within?an?acceptable?range.?Handling?qualities?discussed?in?the?previous?section?govern these?factors.?In?this?section,?principals?of?aileron?design,?design?procedure,?governing equations,?constraints,?and?design?steps?as?well?as?a?fully?solved?example?are?presented. 12.4.2.?Principles?of?Aileron?Design A??basic??item??in??the?list??of??aircraft??performance??requirements??is??the??maneuverability. Aircraft?maneuverability?is?a?function?of?engine?thrust,?aircraft?mass?moment?of?inertia, and?control?power.?One?of?the?primary?control?surfaces?which?cause?the?aircraft?to?be steered?along?its?three-dimensional?flight?path?(i.e.?maneuver)?to?its?specified?destination is?aileron.?Ailerons?are?like?plain?flaps?placed?at?outboard?of?the?trailing?edge?of?the?wing. Right?aileron?and?left?aileron?are?deflected?differentially?and?simultaneously?to?produce?a 2 No Aircraft Type mTO (kg) b (m) CA/C Span?ratio dAmax?(deg) bi/b/2 bo/b/2 up down 1 Cessna?182 Light?GA 1,406 11 0.2 0.46 0.95 20 14 2 Cessna?Citation III Business jet 9,979 16.31 0.3 0.56 0.89 12. 5 12.5 3 Air?Tractor?AT- 802 Agriculture 7,257 18 0.36 0.4 0.95 17 13 4 Gulfstream?200 Business jet 16,080 17.7 0.22 0.6 0.86 15 15 5 Fokker?100A Airliner 44,450 28.08 0.24 0.6 0.94 25 20 6 Boeing?777-200 Airliner 247,200 60.9 0.22 0.321 0.762 30 10 7 Airbus?340-600 Airliner 368,000 63.45 0.3 0.64 0.92 25 20 8 Airbus?A340- 600 Airliner 368,000 63.45 0.25 0.67 0.92 25 25 rolling??moment??about??x-axis.??Therefore,??the??main??role??of??aileron??is??the??roll??control; however?it?will?affect?yaw?control?as?well.?Roll?control?is?the?fundamental?basis?for?the design?of?aileron. Table?12.1.?Characteristics?of?aileron?for?several?aircraft Table???12.12???(lateral???directional???handling???qualities???requirements)???provides significant?criteria?to?design?the?aileron.?This?table?specifies?required?time?to?bank?an aircraft?at??a?specified??bank??angle.??Since?the?effectiveness??of?control??surfaces??are??the lowest?in?the?slower?speed,?the?roll?control?in?a?take-off?or?landing?operations?is?the?flight phase?at?which?the?aileron?is?sized.?Thus,?in?designing?the?aileron?one?must?consider?only level?1?and?most?critical?phases?of?flight?that?is?usually?phase?B. Based?on?the?Newton’s?second?law?for?a?rotational?motion,?the?summation?of?all applied?moments?is?equal?to?the?time?rate?of?change?of?angular?momentum.?If?the?mass and?the?geometry?of?the?objet?(i.e.?vehicle)?are?fixed,?the?law?is?reduced?to?a?simpler version:?The?summation?of?all?moments?is?equal?to?the?mass?moment?of?inertia?time?of the?object?about?the?axis?or?rotation?multiplied?by?the?rate?of?change?of?angular?velocity. In?the?case?of?a?rolling?motion,?the?summation?of?all?rolling?moments?(including?the aircraft?aerodynamic?moment)?is?equal?to?the?aircraft?mass?moment?of?inertia?about?x-axis multiplied?by?the?time?rate?of?change?(?/?t)?of?roll?rate?(P). Inboard?aileron??1 Outboard?aileron???2 3 ??L  cg  =?I?xx  ?P ?t  (12.7) or · P?=  ??L I?xx  cg  (12.8) Generally?speaking,?there?are?two?forces?involved?in?generating?the?rolling?moment:?1. An?incremental?change?in?wing?lift?due?to?a?change?in?aileron?angle,?2.?Aircraft?rolling drag?force?in?the?yz?plane.?Figure?12.11?illustrates?the?front-view?of?an?aircraft?where incremental?change?in?the?lift?due?to?aileron?deflection?(DL)?and?incremental?drag?due?to the?rolling?speed?are?shown. The?aircraft?in?Figure?12.11?is?planning?to?have?a?positive?roll,?so?the?right?aileron is?deflected?up?and?left?aileron?down?(i.e.?+dA).?The?total?aerodynamic?rolling?moment?in a?rolling?motion?is: ??M  cgx  =?2DL?×?y?A??-?DD?×?yD  (12.9) The?factor?2?has?been?introduced?in?the?moment?due?to?lift?to?account?for?both?left and?right?ailerons.?The?factor?2?is?not?considered?for?the?rolling?moment?due?to?rolling drag?calculation,?since?the?average?rolling?drag?will?be?computed?later.?The?parameter?yL is?the?average?distance?between?each?aileron?and?the?x-axis?(i.e.?aircraft?center?of?gravity). The?parameter?yD?is?the?average?distance?between?rolling?drag?center?and?the?x-axis?(i.e. aircraft?center?of?gravity).?A?typical?location?for?this?distance?is?about?40%?of?the?wing semispan?from?root?chord. +dA  DDright  DLleft DLright  dy  y yo  yi  cg?????????????????????????????DDleft z yD  yA  +dA Front?view Figure?12.2.?Incremental?change?in?lift?and?drag?in?generating?a?rolling?motion 4 In??an??aircraft??with??short??wingspan??and??large??aileron??(e.g.??fighter??such??as??General Dynamics?F-16?Fighting?Falcon?(Figure?3.12))?the?drag?does?not?considerably?influence on?the?rolling?speed.?However,?in?an?aircraft?with?a?long?wingspan?and?small?aileron; such?as?bomber?Boeing?B-52?(Figures?8.20?and?9.4);?the?rolling?induced?drag?force?has?a significant?effect?on?the?rolling?speed.?For?instance,?the?B-52?takes?about?10?seconds?to have?a?bank?angle?of?45?degrees?at?low?speeds,?while?for?the?case?of?a?fighter?such?as?F- 16;?it?takes?only?a?fraction?of?a?second?for?such?roll. Owing?to?the?fact?that?ailerons?are?located?at?some?distance?from?the?center?of?gravity?of the?aircraft,?incremental??lift?force?generated??by?ailerons??deflected?up/down,??creates?a rolling?moment. LA?=?2DL?×?yA (12.10) However,?the?aerodynamic?rolling?moment?is?generally?modeled?as?a?function?of?wing area?(S),?wing?span?(b),?dynamic?pressure?(q)?as: LA?=?qSClb where?Cl?is?the?rolling?moment?coefficient?and?the?dynamic?pressure?is:  (12.11) q?= 1 2 rVT2 (12.12) where?r?is?the?air?density?and?VT?is?the?aircraft?true?airspeed.?The?parameter?Cl?is?a function?of?aircraft?configuration,?sideslip?angle,?rudder?deflection?and?aileron?deflection. In??a??symmetric??aircraft??with??no??sideslip??and??no??rudder??deflection,??this??coefficient??is linearly?modeled?as: Cl?=?CldA?d?A  (12.13) The??parameter??Cld  A  is??referred??to??as??the??aircraft??rolling??moment-coefficient-due-to- aileron-deflection?derivative?and?is?also?called?the?aileron?roll?control?power.?The?aircraft rolling?drag?induced?by?the?rolling?speed?may?be?modeled?as: DR?=?DDleft?+?DDright?= 1 2 rVR2?StotCDR  (12.14) where??aircraft??average??CDR??is??the??aircraft??drag??coefficient??in??rolling??motion.??This coefficient?is?about?0.7?–?1.2?which?includes?the?drag?contribution?of?the?fuselage.?The parameter?Stot?is?the?summation?of?wing?planform?area,?horizontal?tail?planform?area,?and vertical?tail?planform?area. Stot?=?Sw?+?Sht?+?Svt  5  (12.15) The?parameter?VR?is?the?rolling?linear?speed?in?a?rolling?motion?and?is?equal?to?roll?rate (P)?multiplied?by?average?distance?between?rolling?drag?center?(See?Figure?12.11)?along y-axis?and?the?aircraft?center?of?gravity: VR?=?P?×?yD  (12.16) Since?all?three?lifting?surfaces?(wing,?horizontal?tail,?and?vertical?tail)?are?contributing?to the??rolling??drag,??the??yD??is??in??fact,??the??average??of??three??average??distances.??The??non- dimensional?control?derivative?Cld?A?is?a?measure?of?the?roll?control?power?of?the?aileron;?it represents?the?change?in?rolling?moment?per?unit?change?of?aileron?deflection.?The?larger the??Cld?A?,?the?more?effective?the?aileron?is?at?creating?a?rolling?moment.?This?control derivative?may?be?calculated?using?method?introduced?in?[19].?However,?an?estimate?of the?roll?control?power?for?an?aileron?is?presented?in?this?Section?based?on?a?simple?strip integration?method.?The?aerodynamic?rolling?moment?due?to?the?lift?distribution?may?be written?in?coefficient?form?as: DCl?=  DLA qSb  =  qCLA?Ca?y?Ady qSb  =  CLA?Ca?y?Ady Sb  (12.17) The?section?lift?coefficient?CLA??on?the?sections?containing?the?aileron?may?be?written?as CLA?=?CLa?a?=?CLa  da dd?A  d?A?=?CLa?t?a?×?d?A  (12.18) where?ta?is?the?aileron?effectiveness?parameter?and?is?obtained?from?Figure?12.12,?given the?ratio?between?aileron-chord?and?wing-chord.?Figure?12.12?is?a?general?representative of?the?control?surface?effectiveness;?it?may?be?applied?to?aileron?(ta),?elevator?(te),?and rudder?(tr).?Thus,?in?Figure?12.12,?the?subscript?of?parameter?t?is?dropped?to?indicate?the generality. òy?Cydy 2CLaw?td??A yo Integrating?over?the?region?containing?the?aileron?yields Cl?= Sb i  (12.19) where??CLaw??has?been?corrected?for?three-dimensional?flow?and?the?factor?2?is?added?to account?for?the?two?ailerons.?For?the?calculation?in?this?technique,?the?wing?sectional?lift curve?slope?is?assumed?to?be?constant?over?the?wing?span.?Therefore,?the?aileron?sectional lift??curve??slope??is??equaled??to??the??wing??sectional??lift??curve??slope.??The??parameter??yi represents?the?inboard?position?of?aileron?with?respect?to?the?fuselage?centerline,?and?yo the?outboard?position?of?aileron?with?respect?to?the?fuselage?centerline?(See?Figure?12.11). 6 The?aileron?roll?control?derivative?can?be?obtained?by?taking?the?derivative?with?respect?to òy?Cydy dA: Cld?A??=  2CLaw?t??yo Sb i  (12.20) t 0.8 0.6 0.4 0.2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Control-surface-to-lifting-surface-chord?ratio Figure?12.3.?Control?surface?angle?of?attack?effectiveness?parameter The?wing?chord?(C)?as?a?function?of?y?(along?span)?for?a?tapered?wing?can?be?expressed by?the?following?relationship: C??=?Cr?ê1?+?2? ÷?yú é ??l?-1???ù ? è???b???????  (12.21) where?Cr?denotes?the?wing?root?chord,?and?l?is?the?wing?taper?ratio.?Substituting?this relationship?back?into?the?expression?for?Cld?A?(Equ.?12.20)?yields: ê1?+?2? b ÷?yú?ydy Cld?A??= 2CLaw?t Sb yo ò?C yi  r é?????????l?-1???ù ????????è?????????????  (12.22) or ???2 2???l?-1? 3?ù Cld?A  = 2CLaw?tCr?é?y?2 ê Sb  +?????????????÷?y??ú 3?è???b??????????yi yo  (12.23) This?equation?can?be?employed?to?estimate?roll?control?derivative??Cld?A?using?the?aileron geometry?and?estimating?t?from?Figure?12.12.?Getting?back?to?equation?12.12,?there?are two?pieces?of?ailerons;?each?at?one?left?and?right?sections?of?the?wing.?These?two?pieces may?have?a?similar?magnitude?of?deflections?or?slightly?different?deflections,?due?to?the adverse?yaw.?At?any?rate,?only?one?value?will?enter?to?the?calculation?of?rolling?moment. Thus,?an?average?value?of?aileron?deflection?will?be?calculated?as?follows: 7 [ ] d??A??= d??Aleft +?d??Aright 1 (12.24) 2 The?sign?of?this?dA?will?later?be?determined?based?on?the?convention?introduced?earlier;?a positive??dA??will??generate??a??positive??rolling??moment.??Substituting??equation??12.9??into equation?12.7?yields: · LA?+?DD?×?yD?=?I?xx?P · As?the?name?implies,?P??is?the?time?rate?of?change?of?roll?rate: (12.25) · P?= d dt P (12.26) On?the?other?hand,?the?angular?velocity?about?x-axis?(P)?is?defined?as?the?time?rate?of change?of?bank?angle: P?= d dt F (12.27) Combining?equations?12.26?and?12.27?and?removing?dt?from?both?sides,?results?in: · P?dF?=?PdP (12.28) Assuming?that?the?aircraft?is?initially?at?a?level?cruising?flight?(i.e.?Po?=?0,?fo?=?0),?both sides?may?be?integrated?as: f??· ò?P?dF?= 0 Pss ò?PdP 0  (12.29) Thus,?the?bank?angle?due?to?a?rolling?motion?is?obtained?as: F?=?ò ·??dP P P · where?P??is?obtained?from?equation?12.25.?Thus: (12.30) Pss F?=?ò 0 I?xx?P LA?+?DD?×?yD  dP  (12.31) Both?aerodynamic?rolling?moment?and?aircraft?drag?due?to?rolling?motion?are?functions?of roll?rate.?Plugging?these?two?moments?into?equation?12.31?yields: r(P?×?yD?)?(Sw??+?Sht??+?Svt?)CDR??×?yD F1?=  Pss ò 0?qSCl?b?+  1 2  I?xx?P 2  dP  (12.32) The?aircraft?rate?of?roll?rate?response?to?the?aileron?deflection?has?two?distinct?states:?1.?A transient?state,?2.?A?steady?state?(See?Figure?12.13).?The?integral?limit?for?the?roll?rate?(P) in?equation?12.32?is?from?an?initial?trim?point?of?no?roll?rate?(i.e.?wing?level?and?Po?=?0)?to a?steady-state?value?of?roll?rate?(Pss).?Since?the?aileron?is?featured?as?a?rate?control,?the deflection?of?aileron?will?eventually?result?in?a?steady-state?roll?rate?(Figure?12.13).?Thus, unless?the?ailerons?are?returned?to?the?initial?zero?deflection,?the?aircraft?will?not?stop?at?a specific?bank?angle.?Table?12.12?defines?the?roll?rate?requirements?in?terms?of?the?desired 8 bank?angle?(F2)?for?the?duration?of?t?seconds.?The?equation?12.32?has?a?closed-form solution?and?can?be?solved?to?determine?the?bank?angle?(F1)?when?the?roll?rate?reaches?its steady-state?value. Roll?rate (deg/sec) Pss tss t2  Time?(sec) Figure?12.4.?Aircraft?roll?rate?response?to?an?aileron?deflection Bank angle (deg) F2 F1 t1  t2  Time?(sec) Figure?12.5.?Aircraft?bank?angle?response?to?an?aileron?deflection When?the?aircraft?has?a?steady-state?(Pss)?roll?rate,?the?new?bank?angle?(Figure?12.14)?after Dt?seconds?(i.e.?t2-tss)?is?readily?obtained?by?the?following?linear?relationship: F2?=?Pss?×?(t2?-?tss?)?+?F1  (12.33) Due??to??the??fact??that??the??aircraft??drag??due??to??roll??rate??is??not??constant??and??is increased?with?an?increase?to?the?roll?rate;?the?rolling?motion?is?not?linear.?This?implies 9 that?the?variation?of?the?roll?rate?is?not?linear;?and?there?is?an?angular?rotation?about?x- axis.??However,??until??the??resisting??moment??against??the??rolling??motion??is??equal??to??the aileron?generated?aerodynamic?rolling?moment;?the?aircraft?will?experience?an?angular acceleration?about?x-axis.?Soon?after?the?two?rolling?moments?are?equal,?the?aircraft?will continue?to?roll?with?a?constant?roll?rate?(Pss).?The?steady-state?value?for?roll?rate?(Pss)?is obtained?by?considering?that?the?fact?that?when?the?aircraft?is?rolling?with?a?constant?roll rate,?the?aileron?generated?aerodynamic?rolling?moment?is?equal?to?the?moment?of?aircraft drag?in?the?rolling?motion. LA?=?DDR?×?yD  (12.34) Combining?equations?12.14,?12.15,?and?12.16,?the?aircraft?drag?due?to?the?rolling?motion is?obtained?as: DR?= 1 2 r(P?×?yD?)2?(Sw?+?Sht?+?Svt?)CDR (12.35) Inserting?the?equation?12.35?into?equation?12.34?yields: LA?=  1 2  r(P?×?yD?)2?(Sw?+?Sht?+?Svt?)CDR?×?yD  (12.36) Solving?for?the?steady-state?roll?rate?(Pss)?results?in: Pss??=  2?×?LA r(Sw??+?Sht??+?Svt?)CDR??×?yD3  (12.37) On?the?other?hand,?the?equation?12.32?is?simply?a?definite?mathematical?integration.?This integration?may?be?modeled?as?the?following?general?integration?problem: y??=?k?ò 2 xdx x???+?a?2 According?to?[20],?there?is?a?closed?form?solution?to?such?integration?as?follows:  (12.38) y?=?k 1 2 ln(x?2?+?a?2?) (12.39) The?parameters?k?and?a?are?obtained?by?comparing?equation?12.38?with?equation?12.32. ry??(Sw??+?Sht??+?Svt?)CDR k??=  3 D  2I?xx  (12.40) a?2??= (12.41) (Sw??+?Sht??+?Svt?)CD yD V?2?SCl?b 3 R Hence,?the?solution?to?the?integration?in?equation?12.32?is?determined?as: 11 ln??P?2??+ è ?ù 3?÷÷ú é F1??=?ê ê?  I?xx ryD3?(Sw??+?Sht??+?Svt?)CDR  ? ?  Pss V?2?SCl?b (Sw??+?Sht??+?Svt?)CDR?yD?????ú??0  (12.42) Applying?the?limits?(from?0?to?Pss)?to?the?solution?results?in: ry??(Sw??+?Sht??+?Svt?)CDR F1??=  3 D  I?xx  2 ln(Pss?)  (12.43) Recall?that?we?are?looking?to?determine?aileron?roll?control?power.?In?another?word,?it?is desired?to?obtain?how?long?it?takes?(t2)?to?bank?to?a?desired?bank?angle?when?ailerons?are deflected.?This?duration?tends?to?have?two?parts:?1.?The?duration?(tss