TWI250254B - The present invention relates to a new-designed hybrid air journal bearing with best stability - Google Patents

The present invention relates to a new-designed hybrid air journal bearing with best stability Download PDF

Info

Publication number
TWI250254B
TWI250254B TW93137582A TW93137582A TWI250254B TW I250254 B TWI250254 B TW I250254B TW 93137582 A TW93137582 A TW 93137582A TW 93137582 A TW93137582 A TW 93137582A TW I250254 B TWI250254 B TW I250254B
Authority
TW
Taiwan
Prior art keywords
bearing
coordinate coordinate
orifice
parameter
porous
Prior art date
Application number
TW93137582A
Other languages
Chinese (zh)
Other versions
TW200619525A (en
Inventor
Chi-Tsung Su
Kun-Nien Lai
Original Assignee
Chi-Tsung Su
Kun-Nien Lai
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Chi-Tsung Su, Kun-Nien Lai filed Critical Chi-Tsung Su
Priority to TW93137582A priority Critical patent/TWI250254B/en
Application granted granted Critical
Publication of TWI250254B publication Critical patent/TWI250254B/en
Publication of TW200619525A publication Critical patent/TW200619525A/en

Links

Abstract

The present invention relates to a new-designed hybrid air journal bearing with best stability. The rows of orifices are spaced equally on the axial sections and arrayed from the center section to both sides of bearing symmetrically, with 1, 2, 3, 4 or 5 circumferential rows. The number of orifices in each circumference has to be no less than 8. The said orifice could be stepped hole with a thin needle throttle hole, which can discharge pressurized air into bearing gaps to form a lubricating film. The 5-row orifice feeding bearing has the higher threshold load capacity of rotor mass than the porous bearing when small rotor whirl occurs for a moderate rotation speed (Lambda ≈ 0.5)and a lower feeding parameter(lambdao < 10<-4>) accordingly. The above said shows that the 5-row orifice feeding bearing is more stable than the porous bearing.

Description

1250254 九、發明說明: 【發明所屬之技術領域】 ▲本發明係有關於一種最佳穩定性混合氣體軸承設 計,尤其是指一種能令該軸承之轉子於轉動時具有更 =:r合氣壓空一新設計者。 混合氣麗空氣熟承由於湘空制滑具備 潔度與低摩擦之優點,使得目前已經成為高速 鐘叙配件但是該思合氣壓空氣頸轴承之轉子 易ί生榥動不穩核,為了克服此-問題,學 探討尋t文之剛性和阻尼係數來 成為年代,動錢體14承之轉料穩定性已 成為研'者之研究主題;例如利用Galerkins以及 動不穩疋性之最小質量與轉速,已參 提高轴承之剛性和阻尼係數來:善 瓣傾斜墊和㈣氣體轴承之轉1250254 IX. Description of the invention: [Technical field to which the invention pertains] ▲ The present invention relates to an optimum stability mixed gas bearing design, and more particularly to a method in which the rotor of the bearing has a more =: r-pressure air pressure when rotating A new designer. Due to the advantages of cleanliness and low friction, Xiangqi Air Slip has become a high-speed clock-synthesis accessory, but the rotor of the air-pressure air-neck bearing is easy to sway and unstable. In order to overcome this - The problem, the study explores the rigidity and damping coefficient of t-text to become the age, and the stability of the transfer material has become the research theme of the researcher; for example, the use of Galerkins and the minimum mass and speed of dynamic instability , has been to improve the rigidity and damping coefficient of the bearing: good flap tilting pad and (four) gas bearing turn

Leonard and R0We 以實驗來 ]= 不穩定性轉動 ^ 因為具有㈣的阻尼特性,所以- 直也疋研究者的焦點所在 ㈣所乂 質抽承所產生…與 ha:er);隨後之參考文獻以不現象=: 分析不同節流方式之靜壓空氣轴承;近== 1250254 研究報告,分別對液體潤滑軸承與空氣潤滑軸承作進 一步之探討。 然,上述諸多對混合氣壓空氣頸轴承之轉子轉動 不穩定性探討及分析,卻仍尚不足以對此複雜之機構 作有系統之結論,其皆未針對混合氣壓空氣頸軸承於 多排孔口節流之不同排數的設計,而會對轉子榥動不 穩定性之效應所產生的影響加以分析比較,因而並無 法得知何種排數之節流孔具有最佳之穩定性者。 【發明内容】 本發明之最佳穩定性混合氣體轴承設計,其主要 係分別設有數排節流孔,對稱於轴承中央,等距離配 置於軸向之截面上,每排節流孔數目不得少於8孔, :均分佈於圓周上,節流孔之形狀可為分段孔,多孔 f袖承之材料可由燒結金屬製造,而於5排孔口節流 ,承在中等轉速下(Λ% G.5),並且在低進氣量時 &lt; )在轉子晃動之狀態,其穩 【實施方式】 方式首ί別設嗜有參閱第:圖所示,本發明多排孔口節流 中繼抽承⑴ 數目不得少於8孔^均^面上,每排節流孔(11) 分析模擬邊界時,可:=於_上,如此在數值 準確性,節流孔(11) ’、、、、線狀進氣源,而不失其 由最小針孔注入薄膜潤J狀他 月々,而如第二圖所示,多孔 1250254 質軸承(2)之材料可由燒結金屬製造,其孔隙率 (porosity)低於ΗΓ” cm2,空氣壓經由多孔質材料進 入薄膜潤滑層,假設軸承内為薄膜潤滑,並考慮空氣 為可壓縮性,而多孔質軸承(2)之進氣流動為達西流 場(Darcy flow) 〇 一、數學分析 由以上假設,可推導出下列無因次雷諾方程式 (A)孔口節流轴承Leonard and R0We by experiment] = unstable rotation ^ Because of the damping characteristics of (4), so - the focus of the researcher is (4) the quality of the pumping is produced... and ha:er); the subsequent references are not Phenomenon =: Analysis of static air bearing with different throttling modes; near == 1250254 Research report, further discussion on liquid lubricated bearings and air lubricated bearings. However, the above discussion and analysis of the rotor instability of the mixed air pressure air neck bearing is still not enough to systematically conclude this complex mechanism, which is not aimed at the mixed air pressure neck bearing in the multi-row orifice. The design of the different rows of throttling will analyze and compare the effects of the effect of rotor turbulence instability, so it is impossible to know which troughs of the number of rows have the best stability. SUMMARY OF THE INVENTION The optimal stability mixed gas bearing design of the present invention is mainly provided with several rows of orifices respectively, symmetrically to the center of the bearing, and equidistantly disposed on the axial section, and the number of orifices per row is not small. In 8 holes, : are distributed on the circumference, the shape of the orifice can be segmented holes, the material of the porous f sleeve can be made of sintered metal, and the tube is throttled at 5 rows of holes, at medium speed (Λ% G.5), and at a low intake air amount &lt;) in the state of the rotor sway, it is stable [Embodiment] The first method is not described. Referring to: Figure, the multi-row orifice of the present invention is throttled After the number of draws (1) is not less than 8 holes ^ uniform surface, each row of orifices (11) when analyzing the simulated boundary, can be: = on _, so in the numerical accuracy, the orifice (11) ', ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, (porosity) is lower than ΗΓ" cm2, air pressure enters the film lubrication layer through the porous material, assuming the axis The inside is film lubrication, and considering the air as compressibility, and the inlet flow of the porous bearing (2) is the Darcy flow. The mathematical analysis is based on the above assumptions, and the following dimensionless Renault can be derived. Equation (A) orifice throttle bearing

d W Η3d W Η3

dP d n w y (B$多孔質軸承dP d n w y (B$ porous bearing

d W H3d W H3

dP2 W +Φ Η3dP2 W +Φ Η3

dP H3 dP2 1 :2Λ d(PH) ιΑγΚ d(PH) ⑴ c3 or ⑵ 其中方程式(2)比方程式(1)多出一項,是由徑向達西 流動速度(Darcy flow velocity) Γρ所產生的。 如果轉轴在穩定狀態下,轴承偏心率 (eccentricity ratio)為在。,傾斜角(attitude angle) 為九,當產生一微擾動量$和六,則產生一新的狀態: 左=石〇+气,φ = φ〇+ φχ (3) 在此微擾動量5和4是屬於諧振形式(harmonic motion),可以數學表示成:dP H3 dP2 1 : 2Λ d(PH) ιΑγΚ d(PH) (1) c3 or (2) where equation (2) is one more than equation (1) and is generated by the radial Darcy flow velocity Γρ of. If the shaft is in a steady state, the bearing eccentricity ratio is at . The angle of attack is nine. When a perturbation momentum of $ and six is generated, a new state is generated: left = sarcophagus + gas, φ = φ 〇 + φ χ (3) where the perturbation momentum is 5 and 4 is a harmonic motion, which can be expressed mathematically as:

Re{ l^il erb Φγ Re{ 1^1 e^} (4) 在擾動狀態下,所產生之無因次薄膜厚度以及薄膜 壓力可以數學表示成: (5) // =气一气 cos0。+ 石。戎 sin% 1250254 P = P〇+ + ε〇φχΡ2 (6) 其中么為穩定狀態之無因次薄膜厚度可以表示成· Κ- 1 + ^〇〇〇8^〇 (?)β 將擾動量之式子(4-6)代入雷諾方程式2),可推導 出擾動狀態下控制方程式 (A)孔口節流轴承 d2P2、Re{ l^il erb Φγ Re{ 1^1 e^} (4) In the disturbed state, the resulting dimensionless film thickness and film pressure can be mathematically expressed as: (5) // = gas-gas cos0. + stone.戎sin% 1250254 P = P〇+ + ε〇φχΡ2 (6) where the dimensionless film thickness of the steady state can be expressed as · Κ - 1 + ^ 〇〇〇 8 ^ 〇 (?) β Equation (4-6) is substituted into Reynolds equation 2), and the governing equation (A) orifice throttle bearing d2P2 can be derived under disturbance state.

Po 盖+ '嘴+ 2淼§ + φ、+ + 2紮為 +3(、sm0Q+ ssin^f Mcos^)(去 + Α〇〇吟碧如% ji + + Ρ〇|§) + + Ρ〇^) ^τήβ + + 2§f + p〇p + 2s,m^ + 2§§ + ρφ =2八+ 鉢—3¾ 决 Sin0n \3 V — V — ’ (^bsin^Po + h〇^) + ^(sin^〇P0- cos6&gt;〇|| + ^sin^ + + e^(cos0oPo + sin^〇^ + ^〇sin^〇P2 + /¾ 胃) 御皆 -£χ^θ〇 一 3 °^4 -) 广Acos⑹ + 捕 WGsin缽)] (A1) (l-SoCOsOo) 其中凡=片是穩定狀態之壓力的平方;而九 是無因次穩態轴承間隙。 (B)多孔質轴承 1250254 ^ + 2ει(φ + 2§§ + φ) + 2sAiP^ + 2§§ + P〇^) w + 2£i^PlW + Ρ〇^ + 1ε^ρ^Β + P〇w\ ㈣營+ 2,(皆響+嘴+ W發+ 2體+嚼) =2A(— + ^^cos^q — 3^sin^〇xPo cover + 'mouth + 2淼§ + φ, + + 2 tied to +3 (, sm0Q+ ssin^f Mcos^) (go + Α〇〇吟碧如% ji + + Ρ〇|§) + + Ρ〇 ^) ^τήβ + + 2§f + p〇p + 2s,m^ + 2§§ + ρφ =2八+ 钵—33⁄4 决 Sin0n \3 V — V — ' (^bsin^Po + h〇^) + ^(sin^〇P0- cos6&gt;〇|| + ^sin^ + + e^(cos0oPo + sin^〇^ + ^〇sin^〇P2 + /3⁄4 stomach) 御皆-£χ^θ〇一3 °^4 -) Wide Acos(6) + catch WGsin钵)] (A1) (l-SoCOsOo) where the = piece is the square of the steady state pressure; and nine is the dimensionless bearing gap. (B) Porous bearing 1250254 ^ + 2ει(φ + 2§§ + φ) + 2sAiP^ + 2§§ + P〇^) w + 2£i^PlW + Ρ〇^ + 1ε^ρ^Β + P 〇w\ (4) Camp + 2, (all ring + mouth + W hair + 2 body + chew) = 2A (- + ^^cos^q — 3^sin^〇x

一 W V — V (sosm0oPo + h^) + ^i(sin^〇P〇- cos^〇|^- + ^〇sin^ + h^) + ^〇φ[(^〇^〇Ρ〇 + sin^〇·^^- + sin^)/2 ^ 夂菩)2崎+ [肌+2句牌,2) -挪+咖圳 · + /4Λ^(^ + -气S4_) [^(^-Pocos^o) + e〇MkP2+P〇sm0Q)] (Bl) 其中七=1^是多孔質軸承進氣參數。 在(Α1)與(Β1)式子之推導過程中,兩階以上之微擾 量3和^之乘積可忽略不計。 為了求解壓力之微擾量/^和八,對方程式(Α1)與(Β1) 分別對擾動量6和Μ作偏微分,分別可以得到 耶繇+ 2§器+學(ι 4⑽Θ。溫 + + P0§) + 2φ(Ρι^ + 2§§ + φ) =夢⑽邮月+ /%碧;)+登sin0o(h^^十1}/&gt;0 +普⑺城錄+ Z ^ ’(〜乃-❽喊) (A2) 9 1250254 o/p 52P〇 ^ ^dP〇 dP2 ^ p d2P2\ ^ /3cos^〇 3sQsm20o ^dF〇 + 2观孤 + 尸〇 厭J + --——— + p0sm民(尸2語+尸。霖)+ 2(妾)2(尸2装+ 2證签+尸❶袋} =M (s0sm&amp;0P2 + h〇^) + ^ (c〇s^〇 - 啟)P0 -|Δδίη^〇 + / ^ {h〇P2 + P〇sin0〇) (A3) + + p〇l^) + ^(1 + %^)d4 -^osin^o^^ + φ + 2(^(P^ + 2§§ + P〇P)A WV — V (sosm0oPo + h^) + ^i(sin^〇P〇- cos^〇|^- + ^〇sin^ + h^) + ^〇φ[(^〇^〇Ρ〇+ sin^ 〇·^^- + sin^)/2 ^ 夂 )) 2 崎 + [muscle + 2 sentence cards, 2) - 诺+咖圳· + /4Λ^(^ + - gas S4_) [^(^-Pocos ^o) + e〇MkP2+P〇sm0Q)] (Bl) where seven=1^ is the porous bearing intake parameter. In the derivation of the (Α1) and (Β1) equations, the product of the two-order perturbation quantities 3 and ^ is negligible. In order to solve the pressure perturbation amount /^ and VIII, the other program (Α1) and (Β1) respectively differentiate the disturbance amount 6 and Μ, respectively, and get 繇 繇 + 2 § + + + (ι 4(10) Θ. temp + + P0§) + 2φ(Ρι^ + 2§§ + φ) = dream (10) postal month + /% bi;) + sin0o (h^^10 1}/&gt; 0 + general (7) city record + Z ^ '( ~乃-❽叫) (A2) 9 1250254 o/p 52P〇^ ^dP〇dP2 ^ p d2P2\ ^ /3cos^〇3sQsm20o ^dF〇+ 2 孤孤+ 尸〇厌J + --———— + P0smmin (corpse 2 words + corpse. Lin) + 2 (妾) 2 (corpse 2 loaded + 2 badge + corpse bag) =M (s0sm&amp;0P2 + h〇^) + ^ (c〇s^〇-启)P0 -|Δδίη^〇+ / ^ {h〇P2 + P〇sin0〇) (A3) + + p〇l^) + ^(1 + %^)d4 -^osin^o^^ + φ + 2(^(P^ + 2§§ + P〇P)

=碧⑽ίηθ〇/5 + 私爵)+ ^sm0〇(3^s0〇 +!)/&gt;〇 “神(豈+ 3cos0〇Po) 一尸(丑 + 3cos^〇Pq^ + 斧1COS你錄 + ’ 普 r (/^ - PGCOS0。) (B2) 2^^ + 2§|1 + /,〇^) + ^-^^)§ + ^〇sin0〇(P2§ + /&gt; §) + 2(^(p^ + 2§§ + p〇^} =^ (sosm0oP2 + /%||) + M (ccs^o - )p〇 +岭2卜(跫--哺- -^sin^〇 ^ + / M r (^ρ2 + P0sin^〇) (B3) 求解所需之三個共通之邊界條件可表示如^: (8) (9) (10) i^(^Z=l) = Ρ2(θ9Ζ=ΐ) = ο /;(^Ζ) = Ρλφ+2π,Ζ\ Ρ2φ,Ζ) = Ρ2φ^1π,Ζ) ^ (θ, Ζ) = ^ + 2^, Ζ), (^5 Ζ) = (^+2^τ? Ζ) 10 Ϊ250254 要求解擾動方程式(A2)與(A3)式、(B2)與(B3)式, 各需要4個邊界條件。對孔口節錄承之擾動方程式 (A2)與(A3)式,第4個邊界條件是在節流孔位置之連 續方程式。其可以下式表示: (11) 其中厂。為空氣經由節流孔注入轴承潤滑層之速度。擾 動狀態下之連續方程式(11)可推導成如 城祭+ 2語語4^ (1 + f-θ。溫 + + Ρ0§) + 2φ{Ρ^ Η- 2§§ + Ρ0^) ^ 2Α (^sin^ + /¾¾) + ^ίηθ0(^ψ^ + 1)Ρ〇 + 普cosA|| + ί 普…乃-P0COS你)=碧(10)ίηθ〇/5 + 私爵)+ ^sm0〇(3^s0〇+!)/&gt;〇"God (岂+ 3cos0〇Po) One corpse (ugly + 3cos^〇Pq^ + Axe 1COS you recorded + ' 普r (/^ - PGCOS0.) (B2) 2^^ + 2§|1 + /,〇^) + ^-^^)§ + ^〇sin0〇(P2§ + /&gt; §) + 2(^(p^ + 2§§ + p〇^} =^ (sosm0oP2 + /%||) + M (ccs^o - )p〇+岭2卜(跫--哺- -^sin^〇 ^ + / M r (^ρ2 + P0sin^〇) (B3) The three common boundary conditions required for solving can be expressed as ^: (8) (9) (10) i^(^Z=l) = Ρ2 (θ9Ζ=ΐ) = ο /;(^Ζ) = Ρλφ+2π,Ζ\ Ρ2φ,Ζ) = Ρ2φ^1π,Ζ) ^ (θ, Ζ) = ^ + 2^, Ζ), (^5 Ζ ) = (^+2^τ? Ζ) 10 Ϊ250254 Resolve the equations (A2) and (A3), (B2) and (B3), each requires four boundary conditions. The perturbation equation for the orifice excerpt (A2) and (A3), the fourth boundary condition is a continuous equation at the orifice position. It can be expressed as: (11) where the plant is the velocity at which the air is injected into the bearing lubrication layer via the orifice. The continuous equation (11) in the state can be derived as a city sacrifice + 2 language 4^ (1 + f-θ. temperature + + Ρ0§) + 2φ{Ρ^ Η- 2§§ + Ρ0^) ^ 2Α (^sin^ + /3⁄43⁄4) + ^ίηθ0(^ψ^ + 1)Ρ〇 + 普cosA|| + ί 普...乃-P0COS you)

(最+ 3气,.)卜_2(吳)· Η脊叫2 r 「 (A4) 11 1250254 〇iD S2p〇 ^ 0^0 ^p2 D ^ip2\ ^ /3cos&lt;9〇 _ 3^〇sin2^〇 ^dF〇 + ιτυτυ + ^qwt) + &quot; -v~~ + hsm0(P2 築 + P。器)+ 2(妾⑽袋 + 2签善 + PQ·)(most + 3 gas,.) Bu_2(吴)·Η脊叫2 r "(A4) 11 1250254 〇iD S2p〇^ 0^0 ^p2 D ^ip2\ ^ /3cos&lt;9〇_ 3^〇 Sin2^〇^dF〇+ ιτυτυ + ^qwt) + &quot; -v~~ + hsm0(P2 build + P.) + 2 (妾(10) bag + 2 sign good + PQ·)

=登(_ηθ。户2 + /%器)+ 替(cos0。- 3s〇sj^2^〇 )PQ -Msin^〇 + / M r (/¾^ + P〇sin^〇) - Α^φ(ξ} (辨哨1f『+!(¥)(钟f2卜(料f) (A5) 其中 24//^(2^^)2是孔口節流進氣參數;而= Deng (_ηθ. Household 2 + /%) + For (cos0. - 3s〇sj^2^〇) PQ -Msin^〇+ / M r (/3⁄4^ + P〇sin^〇) - Α^φ (ξ) (Discrimination whistle 1f "+! (¥) (clock f2 Bu (material f) (A5) where 24 / / ^ (2 ^ ^) 2 is the orifice throttle intake parameters; and

PalPaiC^ /w = 是轴向Z方向差分節點數。 對於多孔質軸承,第4個邊界條件是在轴承中央位 置之對稱性。其可以下式表示: 築似=〇)=签(θ,ζ = ο)=ο (12)❿ 二、擾動方程式之數值分析解 本發明以有限差分法和電腦數值分析求解:孔口節 流軸承之擾動方程式(Α2)與(A3)與其4個邊界條件方 程式(8)-(10)、(Α4)和(Α5),同時求解:多孔質轴承 之擾動方程式(B2)與(B3)與其4個邊界條件方程式 (8)-(10)和(12),穩定狀態下之壓力值户。必須在固定 12 1250254 條件和參數下先求出,然後將户。值代入擾動方程式求 2在相同條件下之擾動壓力值乃和八,而必須特別注 思的疋,在電腦程式中,擾動壓力值乃和乃之變數必 須設定為雙倍精度(double precision)以改善數值分 析之收斂性,其收斂標準設定為··每次計算前後之誤 差總和相對於變數值本身之總和要小於1(Γ5。 、 三、計算剛性和阻尼係數 在擾動狀態下’軸承之支#力沿著軸與轴 =向之分力尸R與切線方向之分力a可由下列式子表 W + Z#水^ (13)^ ^ ^ (14) 其中/L與/τ。分別是穩定狀態下支撐力分息 _ 运》’甘-言+曾 可參考文獻[21]。而上式中擾動支撐力係數/八 積分式子計算·· 可由下列2i: J;^iPalPaiC^ /w = is the number of differential nodes in the axial Z direction. For porous bearings, the fourth boundary condition is the symmetry at the center of the bearing. It can be expressed as follows: Build like = 〇) = sign (θ, ζ = ο) = ο (12) ❿ Second, the numerical analysis of the disturbance equation The solution is solved by the finite difference method and computer numerical analysis: orifice throttling The bearing disturbance equations (Α2) and (A3) and its four boundary condition equations (8)-(10), (Α4) and (Α5) are simultaneously solved: the perturbation equations (B2) and (B3) of the porous bearing Four boundary condition equations (8)-(10) and (12), the pressure value in steady state. It must be found under the fixed 12 1250254 conditions and parameters, and then the household. The value is substituted into the perturbation equation to find that the disturbance pressure value under the same conditions is equal to eight, and must be specially considered. In the computer program, the disturbance pressure value and the variable must be set to double precision (double precision). To improve the convergence of numerical analysis, the convergence criterion is set to be · · The sum of the error before and after each calculation is less than 1 with respect to the sum of the variable values themselves (Γ5. 3. Calculate the stiffness and damping coefficient in the disturbed state. #力 along the axis and the axis = the component of the force R and the tangential direction a can be expressed by the following formula W + Z# water ^ (13) ^ ^ ^ (14) where /L and /τ are respectively Supporting the spread of power under steady state _ Yun" 'Gan-yan+ was once referenced [21]. In the above formula, the perturbation support force coefficient / eight integral formula sub-calculation can be obtained by the following 2i: J; ^i

^RR ^TR^RR ^TR

^TT cosO sinO cos叫 sin^^TT cosO sinO cos called sin^

dOdZ 2Π、1 «Ιο Jo 2 ; 擾動支撑力係數在X與γ轴之方向分量dOdZ 2Π, 1 «Ιο Jo 2 ; Disturbing support force coefficient in the direction of the X and γ axes

dOdZ (15)(16) 可由下列 矩陣轉換求得: 2jcr ^χγ ^JRR ^TR sin 么-cos戎 sin厶-cos式 Zyx Ζγγ Zpj, Ζ,γρ cos么sin也 匕 « cos也sin么 在此擾動支撐力係數是為複數,可以把實數今 13 (17) 1250254 分分開表示如下: ^χγ S\\ Su + 7· Ζγχ Ζγγ Six S22 丁 ί βΐΐ Bi2 (18) 上式中,义2,尻與没2是為轴承剛性係數;而及 及2,也與及2是為軸承阻尼係數。 1 五、榥動不穩定性分析 轉轴之轉子質量貪在榥動情況下,位移^之運 程式,可由下列線性微分方程式表示: 方 M〇' ^ q ► + Al Βχΐ LI , 丄 susu r 1 0 0 Af B2\ B22 Π ^21 ^22 q 0 (19) 上式中位移g疋一維向量··包含X分量^與γ分量 在決定引發榥動不穩定性之最小轉子質量 (threshold rotor mass)可採取羅斯判定準則 (此uth’s criterion),轉子重量可視為轴承之全部^ 荷(F= ife·),而且由軸承支撐力Λ。與凡所平衡。、 由羅斯準則,引發榥動不穩定性之最小轉子質量, 可由運動方程式(19)推導出: M+^+Sn Bn+Su qx fo] M+B22m^S22 k] ί〇ί (20) 中性穩定(neutral stability)之標準為:(2〇)式存在 非零解,所以係數矩陣之行列式必須等於零,如下所 不二 14 (21) =0 1250254 為求得滿足(21)式之最大轉子質量分,需使用重覆 計算之疊代程式(iteration procedure)與牛頓-雷福 筌(Newton-Raphson)修正法,藉由修正改變軸榥動頻 率對旋轉頻率之比值參數7,而其他操作參數固定不 變’電腦程式計算直到行列式(21)之值小於1(Γ5之收 敛標準。 六、符號說明 a 節流孔半徑 radius of orifice 無因次阻尼係數 dimensionless damping coefficient = ^ 4 阻尼係數 damping coefficient C 同心轴承間隙 concentric bearing clearance for ε= 0dOdZ (15)(16) can be obtained by the following matrix transformation: 2jcr ^χγ ^JRR ^TR sin 么-cos戎sin厶-cos type Zyx Ζγγ Zpj, Ζ,γρ cos sin also 匕« cos also sin what is here The perturbation support force coefficient is a complex number, which can be divided into 13 (17) 1250254 points as follows: ^χγ S\\ Su + 7· Ζγχ Ζγγ Six S22 丁ί βΐΐ Bi2 (18) In the above formula, meaning 2, 尻And no 2 is the bearing stiffness coefficient; and 2, also and 2 is the bearing damping coefficient. 1 V. Instability instability analysis of the rotor quality of the rotating shaft. In the case of turbulence, the displacement equation can be expressed by the following linear differential equation: square M〇' ^ q ► + Al Βχΐ LI , 丄susu r 1 0 0 Af B2\ B22 Π ^21 ^22 q 0 (19) The displacement g疋 one-dimensional vector in the above equation·· contains the X component ^ and γ components in determining the minimum rotor mass that causes turbulence instability (threshold rotor mass The Ross criterion can be adopted (this uth's criterion), the rotor weight can be regarded as the total load of the bearing (F = ife ·), and the bearing support force Λ. Balance with everything. By Ross's criterion, the minimum rotor mass that causes turbulence instability can be derived from the equation of motion (19): M+^+Sn Bn+Su qx fo] M+B22m^S22 k] ί〇ί (20) Neutral The standard of neutral stability is: (2〇) has a non-zero solution, so the determinant of the coefficient matrix must be equal to zero, as follows: 14 (21) =0 1250254 to find the largest rotor that satisfies the formula (21) The mass fraction requires the use of repeated calculations of the iteration procedure and the Newton-Raphson correction method, by modifying the ratio of the shaft yaw frequency to the rotation frequency parameter 7, while other operating parameters The fixed computer program is calculated until the value of the determinant (21) is less than 1 (the convergence criterion of Γ5. VI. Symbol description a throttle radius radius of orifice dimensionless damping coefficient = ^ 4 damping coefficient damping coefficient C Concentric bearing clearance for ε= 0

Cd 喷流孔喷流係數orifice discharge coefficientCd jet orifice coefficient

Cp 等壓比熱 specific heat of constant pressure of airSpecific heat of constant pressure of air

Cv 等容比熱 specif ic heat of constant volume of air D 轉轴直徑 diameter of journal e 偏心量 eccentricity F 壓力變數 variable of pressure / =户2 g 重力加速度 specific gravity h 轴承間隙 bearing clearance = (1- ε cos0 ) h〇 無因次穩態轴承間隙dimensionless equilibrium bearing clearance = (1- ε〇 cos^〇) 15 1250254 Η 無因次軸承間隙 dimensionless bearing clearance =Λ/61 = (1- ε cos0 )Cv isometric heat of the diameter of the air diameter of the diameter of the diameter of the eccentricity F pressure variable variable of pressure / = household 2 g gravity acceleration specific gravity h bearing clearance bearing clearance = (1- ε cos0 ) H〇 dimensionless bearing clearance dimensionless equilibrium bearing clearance = (1- ε〇cos^〇) 15 1250254 Η dimensionless bearing clearance dimensionless bearing clearance =Λ/61 = (1- ε cos0 )

Hw 多孔質轴承徑向厚度porous wall thickness i 虛數 imaginary number = k 比熱比值 specif ic heat ratio of air = (G / G ) K 多孔質軸承滲透率permeability of porous bearing L 轴承長度 bearing length M 單一軸承之無因次轉子質量dimensionless threshold rotor mass supported per bearing = = M 單一轴承之無因次轉子質量threshold rotor mass supported per bearingHw Porous bearing radial thickness thickness imaginary number = k specific heat ratio specif ic heat ratio of air = (G / G ) K porous bearing permeability probability of porous bearing L bearing length bearing length M single bearing no Dimensionless threshold rotor mass supported per bearing = = M dimensionless rotor mass of a single bearing threshold rotor mass supported per bearing

m Z 方向差分節點數 mesh number in z direction L &quot;ISz N 每排節流孔數目number of orifices in a circumferential row n 單位圓周節流孔數目number of orifices per unit circumferential length =N/{2nR) p 轴承壓力pressure P 無因次轴承壓力 dimensionless pressure = / /¾m Z direction difference node number mesh number in z direction L &quot;ISz N number of orifices per row number of orifices in a peripheral row n number of orifices per unit circumferential number of orifices per unit circumferential length =N/{2nR) p Bearing pressure pressure P dimensionless bearing pressure dimensionless pressure = / /3⁄4

Pa 大氣壓力 ambient pressure p〇 穩態轴承壓力 equilibrium pressure P〇 無因次穩態轴承壓力dimensionless equilibrium 16 1250254 pressure - p〇/ paPa atmospheric pressure ambient pressure p〇 steady-state bearing pressure equilibrium pressure P〇 dimensionless steady bearing pressure dimensionless equilibrium 16 1250254 pressure - p〇/ pa

Pi 無因次微擾動轴承壓力dimensionless perturbed disturbance pressure - pi/ pa P2 無因次微擾動轴承壓力dimensionless perturbed disturbance pressure = a A 供應壓力 supply pressurePi dimensionless perturbation bearing pressure dimensionless perturbed disturbance pressure - pi/ pa P2 dimensionless perturbation bearing pressure dimensionless perturbed disturbance pressure = a A supply pressure supply pressure

Ps 無因次供應壓力 dimensionless supply pressure = ps / Pa 办,少無因次轴承榥動X、Y位移dimensionless φ displacements of journal center of X and Y coordinates =吾居 么,t 轴承榥動 X、Y 位移 displacements of journal center of X and Y coordinates {q} 軸承榥動 X、Y 位移向量 vector of displacements ofPs dimensionless supply pressure dimensionless supply pressure = ps / Pa, less dimensionless bearing swaying X, Y displacement dimensionless φ displacements of journal center of X and Y coordinates = my home, t bearing turbulent X, Y displacement Displacement of journal center of X and Y coordinates {q} bearing yaw X, Y displacement vector vector of displacements of

journal center of X and Y coordinates = dq di d2q dr1 轉動轴半徑radius of journal Su 無因次袖承剛性 dimensionless stiffness ΊπΕΠζ 轴承岡!I性 stiffness coefficient coefficient = t 時間變數time 17 1250254 U 轴轉動速度 journal rotation velocity V〇 孔口節流速度 orifice inlet velocity VP 徑向達西流場速度Darcy velocity in radial κ direction w 轴承轉子負荷能力threshold load capacity of rotor mass =Mg W 無因次軸承轉子負荷能力dimensionless threshold load capacity of rotor mass = iv / {2π RLpa)Journal center of X and Y coordinates = dq di d2q dr1 radius of journal radius of journal Su dimensionless sleeves rigid dimensionless stiffness ΊπΕΠζ bearing gang! I-stiffness coefficient coefficient = t time variable time 17 1250254 U-axis rotational speed journaling velocity V〇 orifice throttle speed orifice inlet velocity VP radial Darcy velocity field radial wave in radial κ direction w bearing rotor load capacity threshold load capacity of rotor mass =Mg W dimensionless bearing rotor load capacity dimensionless threshold load capacity of Rotor mass = iv / {2π RLpa)

x X Y z Z 圓周方向座標 circumferential coordinate X 方向座標 coordinate of X direction Y 方向座標 coordinate of Y direction 轉轴方向座標 axial coordinate of bearing 無因次轉轴方向座標dimensionless axial coordinate of bearing = ^ /(Z/2) P β ε θ Φ Λ ❿ 流體密度fluid density 流體黏度 fluid viscosity 偏心率 eccentricity ratio = e / C 角度座標 angular coordinate = z / 及 傾斜角 attitude angle 軸承參數 bearing number Λ = 入。 節流孔進氣參數orifice feeding parameterx XY z Z circumferential coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate coordinate P β ε θ Φ Λ 流体 fluid density fluid density eccentricity ratio = e / C angle coordinate angular coordinate = z / and inclination angle attitude angle bearing parameter bearing number Λ = in. Throttle intake parameter

k } FTk } FT

24 购 Q[2g. pJpaiC 18 1250254 λρ 多孔質進氣參數 porous feeding parameter ._ 12K ΤΉΖ ω 軸旋轉頻率 rotation frequency of journal =鮮 υ 轴榥動頻率 whirl frequency of journal 7 軸榥動對旋轉頻率比值whirl to rotation frequency ratio - υ /ω τ 虛時間變數 imaginary time = /y ί 同厂小 W 一忻爹閱笫三、 轉子重量 F(threshold load capacity of rotor mass) 相對於軸承參數Λ (bearing number)之變化。其進氣 參數分別為;I。= 1(Γ4和2xl(T4。可見在Λ= 〇· j和八= 〇·5之下都存在轉子重量F之極小值和極大值 。由此 可見空氣軸承在低轉速(八&lt;01)或中轉速(Λ^ 〇 5 =’可以承受較重的轉子重量卜承受較重的轉子 =罝也意味著容許較大_錢 rc孔轴承在較小之進氣參=: 10 ),可以承受較重的轉子重 在較大之進氣參數下α。= 2二4第四:可見, ^ f\ ),部只能承受較輕 別代表進氣參數n-7 ίο之夕孔質抽承。由第= 在較大之進氣參數下(Λ :;二圖可見多孔質抽承 0.1)’可以承受較重的轉;二)在/㈣速(Λ&lt; 二S。)’在較高轉速(心可以承受較重 19 1250254 數Λ請οΤΛ閱!五'六圖所示,其係分物承參 數Λ-0.1和Λ=0·5之下,最大轉 口節流進氣參數Λ。和多孔質轴承錢參數/目^ 圖=第五圖可見,5排節流孔轴承在較小之轉速= 見,.Hr承受較重的轉子重量。㈤時在第六圖可 受較重的承在較*之轉速(λ=g·5) ’可以承 =的轉子重ρ同時可以魏,對於每—不同形 j之轴f’存在—最佳進氣參數值λ。或;U,在此出現 :承轉子重I f之極大值。亦就是可以容許較大 、軸承偏心率e ,而不產生榥動不穩定性。 研一併參閱第七〜十四圖所示,其係表示在轴承 多數Λ= 〇·5之下,軸承之剛性&amp; (stiffness)和阻 ,係數方&quot;(damping coefficient)相對於孔口節流進 =參數λ。和多孔質軸承進氣參數;U之變化。一般而 5,較大的剛性&amp;值可以產生較大的負荷能力;較大 的阻尼係數見·可以產生較穩定之情況。由第七、十圖 可見’ 5排節流孔軸承和多孔質麵承產生較大負值的 對角線剛性係數和没2 (diagonal stiffness),如 此了以產生較大的負荷能力。但是由第十一圖中可 見 對角線阻尼係數屈1 (diagonal damping e〇efficient)隨著進氣參數λ。和λρ之增加而由負 值變成正值。阻尼係數及!由負變正,使得在第六圖 中’轴承可承受最大轉子重量F隨著進氣參數λ。和 λρ之增加而由極大值急速下降。同時可以發現,5排 節流孔轴承可以產生最大正值之阻尼係數,這使得 20 1250254 軸承可承受最大轉子重量F急速下降,β 定性跟著惡化。同時也可以發現,多 小正虎值,以及負及2值,可以在第」袖承產生較 質軸承可以承受較大的轉子重臺Χ可見,多孔 第十五圖表示在軸承參數Λ= 〇·5之τ 受之最大榥動頻率對旋轉頻率 #軸承J承 二T=Vhirl frequency rati°)相對於孔口節 k進氣參數;I。和多孔質軸承進氣參數八之變化。可 見5排節流孔軸承和多孔質軸承之最大頻率比γ隨著 進氣參數λ。和λρ^增加而增加;但是丨排節流孔轴 承之最大鮮比情著進氣參數λ。之増加而變小。同 時在第六圖中可以發現’較高的最大頻率h相對的 可承受之最大轉子重量比較小。在第七、十圖中可以 發現,較高的最大頻率比r產生較大之負义和免值; 並且在第十-圖中可以發現,較高的最大頻率比^使 得阻尼係數及1值由負急速變正。以上剛性係數义和 没2和阻尼係數氬之變化均不利於軸承之穩定性,使得 轴承可承受最大轉子重量1急速下降,如第六圖所示。 第十六圖表示在孔U節流進氣參數λ。= 1〇-4和多 孔質軸承進氣參數λρ = 1〇-7和1〇-8之下,最大頻率比 7相對於軸承參數Λ之變化。在Λ= 〇1時,出現一 最大頻率比r之極大值。由第三圖可見,此極大值正 好對應於可承党最大轉子重量之極小值。同時可以發 現,多孔質轴承之最大頻率比r隨著軸承參數Λ之增 加而減小。同時由第三圖可見,在Λ&lt;〇.丨之區域, 1250254 c:在較高的最大頻率比 子重里。由此結果可知··多 了承又取大轉 較良好的穩定性。同時由第!^承在低轉速下有比 流孔轴承在中轉速下(Λ% 以發現,5排節 經過比較多排節流孔办夕孔質轴承穩定。 獲致下列幾點關於混人氣:二轴承與多孔質轴承, 結論: 空氣難錢佳化設計之 1·多孔質轴承在低轉逮下( 動有較高的穩定性。因而可承受較 :::的最大頻率比”這可由第三=; 2.5在=^:°,5)和低進氣參數“。=約, 較高的穩定性。轴承對於轉轴轉子视動有 3·滿合氣壓空氣顯料中可以得知。 大轉子重量F存在極,連增加,軸承可承受最 0.5)。是為其特性之^值(Λ=⑶和極大值(心 得知。 這可由第三、四圖中可以 最广轉子重量,剛開始隨著孔 加而增加,而達到hl質軸承進氣參數又。之增 繼續增加,可承受==值。然後始隨著進氣參數 此之變化是因為大轉子重量疋急速下降。有如 Ρ之增加而增加;作;^之剛性隨著進氣參數又。和又 λ。和;U之增加=轴承之阻尼係數隨著進氣參數 钱小。因此在軸承之剛性與阻尼 22 125025424 purchase Q [2g. pJpaiC 18 1250254 λρ porous intake parameter porous feeding parameter ._ 12K ΤΉΖ ω axis rotation frequency rotation frequency of journal = fresh υ axis 榥 frequency whirl frequency of journal 7 axis 对 对 vs. rotation frequency ratio whirl To rotation frequency ratio - υ /ω τ virtual time variable imaginary time = /y ί same factory small W Variety. The intake parameters are respectively; = 1 (Γ4 and 2xl (T4. It can be seen that there are minimum and maximum values of rotor weight F under Λ=〇·j and 八=〇·5. It can be seen that the air bearing is at low speed (eight &lt;01) Or medium speed (Λ^ 〇5 = ' can withstand heavier rotor weights to bear the heavier rotor = 罝 also means to allow larger _ money rc hole bearings in the smaller intake gin == 10), can withstand The heavier rotor weighs under the larger intake parameter α.= 2 2 4 4: visible, ^ f\ ), the part can only bear lighter than the air intake parameter n-7 ίο By the = under the larger intake parameters (Λ:; two figures can be seen in the porous pumping 0.1) can withstand heavier turn; b) at / (four) speed (Λ &lt; two S.) 'at higher Rotating speed (the heart can bear the heavier 19 1250254 number Λ ΤΛ ! ! 五 五 五 五 五 五 五 五 五 五 五 五 五 五 五 五 五 五 五 五 五 五 五 五 五 五 五 五 五 五 五 五 五 五 五 五 五 五Porous bearing money parameters / mesh ^ Figure = the fifth figure can be seen, the 5 rows of orifice bearings at a small speed = see, .Hr bears a heavier rotor weight. (5) in the sixth picture can be heavier bearing At a speed of * (λ = g · 5) ' The rotor weight ρ of the bearing = can be Wei at the same time, for each axis j' of different shape j exists - the optimal intake parameter value λ. Or; U, appears here: the maximum value of the bearing rotor I f. It is possible to tolerate a large, bearing eccentricity e without causing turbulence instability. As shown in the seventh to fourteenth drawings, it is shown that under the majority of bearings Λ = 〇 · 5, the rigidity of the bearing & (stiffness) and resistance, coefficient square (damping coefficient) relative to the orifice throttle = parameter λ. and porous bearing intake parameters; U changes. Generally 5, a larger stiffness &amp; value can be generated Larger load capacity; a larger damping coefficient can be seen to produce a more stable situation. From the seventh and tenth figures, it can be seen that the '5-row orifice bearing and the porous surface bearing produce a large negative diagonal stiffness coefficient. And diagonal stiffness, so as to produce a large load capacity. However, it can be seen from the eleventh figure that the diagonal damping coefficient 11 (diagonal damping e〇efficient) with the intake parameters λ and λρ Increase and change from negative to positive. Damping coefficient and ! In the sixth figure, the bearing can withstand the maximum rotor weight F with the increase of the intake parameter λ. and λρ by the maximum value, and it can be found that the 5 rows of orifice bearings can produce the maximum positive damping coefficient. This makes the 20 1250254 bearing can withstand the maximum rotor weight F sharply decreasing, β qualitatively deteriorates. It can also be found that the small and positive value of the tiger, as well as the negative and the 2 value, can produce a better bearing in the first sleeve. The large rotor is visible in the turret, and the fifteenth figure shows the maximum turbulent frequency versus the rotational frequency of the bearing parameter Λ = 〇 · 5 τ. The bearing J Cheng II T = Vhirl frequency rati °) relative to the orifice section k intake parameter; I. And the change in the intake parameters of the porous bearing eight. The maximum frequency ratio γ of the 5 rows of orifice bearings and the porous bearing can be seen along with the intake parameter λ. And λρ^ increases and increases; but the maximum freshness of the orifice orifice is better than the intake parameter λ. It becomes smaller and smaller. At the same time, it can be found in the sixth figure that the higher maximum frequency h is relatively less than the maximum acceptable rotor weight. It can be found in the seventh and tenth figures that the higher maximum frequency ratio r produces a larger negative and exempt value; and in the tenth-graph, it can be found that the higher maximum frequency ratio makes the damping coefficient and the value 1 Change from negative to rapid. The above stiffness coefficient and the change of the damping coefficient argon are not conducive to the stability of the bearing, so that the bearing can withstand the maximum rotor weight 1 sharp drop, as shown in the sixth figure. Figure 16 shows the intake air parameter λ at the orifice U. = 1〇-4 and multi-porous bearing intake parameters λρ = 1〇-7 and 1〇-8, the maximum frequency ratio 7 is relative to the bearing parameter Λ. When Λ = 〇1, a maximum value of the maximum frequency ratio r occurs. As can be seen from the third figure, this maximum value corresponds exactly to the minimum value of the maximum rotor weight of the party. At the same time, it can be found that the maximum frequency ratio r of the porous bearing decreases as the bearing parameter Λ increases. At the same time, it can be seen from the third figure that in the area of Λ&lt;〇.丨, 1250254 c: in the higher maximum frequency ratio. From this result, it is known that many of them have a good turn and a good stability. At the same time, by the first! ^ at low speed, there are more than the flow hole bearing at the middle speed (Λ% to find that 5 rows of sections have been stabilized by more rows of orifices. The following points are about the mixed popularity: Two bearings and porous bearings, Conclusion: The air is difficult to design. The porous bearing is under low rotation (the movement has a high stability. Therefore, it can withstand the maximum frequency ratio of :::: Three =; 2.5 in =^: °, 5) and low intake parameters ". = about, higher stability. The bearing can be known for the 3D full-pressure air air intake for the rotor of the rotating shaft. The weight of the rotor F is extremely high, and the bearing can withstand up to 0.5). Is the value of its characteristics (Λ = (3) and the maximum value (the heart is known. This can be the largest rotor weight in the third and fourth figures, just beginning to increase with the hole, and reach the hl mass bearing intake parameters again The increase continues to increase and can withstand == value. Then the change with the intake parameter is due to the rapid decrease of the weight of the greater trochanter. It increases as the enthalpy increases; And λ. And; U increase = bearing damping coefficient with the intake parameter is small. Therefore, the rigidity and damping of the bearing 22 1250254

係,之=互作用τ,產生—最佳進氣參數值又。或A P 出現—可承受轉子重量F之極大值。超越此 一最佳進氣參數值’财承受最大轉子重量F急速 下降。 &gt;犯合亂&gt;1空氣頸軸承之優點是··在低轉速時有較 尚的轴承雜。本文探雜承轉子齡不歡性,有 助於設計者瞭解其特性,而針_承之㈣,獲致最 佳化設計。 綜上所述,本發明實施例確能達到所預期之使用 功效’又其所揭露之具體構造’不僅未曾見諸於同類 產品中,亦未曾公開於申請前,誠已完全符合專利法 之規定與要求,爰依法提出發明專利之申請,懇請惠 予審查,並賜准專利,則實感德便。 月^ 23 1250254 【圖式簡單說明】 第一圖·本發明多排節流孔轴承徑向轴承之示意圖 ,二圖:多孔質軸承徑向軸承之示意圖 第二圖:本發明最大轉子重量f (threshold load capacity of rotor mass)相對於軸承參數Λ (bearing number)之變化(孔口節流進氣參 數 λ 〇 = 1〇·4) 第四圖:本發明最大轉子重量F (threshold load capacity of rotor mass)相對於軸承參數Λ φ (bearing number)之變化(孔口節流進氣參 數 λ 〇 = 2&gt;&lt;1(Γ4) 第五圖:本發明大轉子重量y相對於孔口節流進氣參 數又。和多孔質轴承進氣參數λ ρ之變化圖形 (軸承參數Λ= 0· 1) 第六圖:本發明最大轉子重量F相對於孔口節流進氣 參數λ。和多孔質軸承進氣參數λ ρ之變化圖 形(軸承參數Λ= 0.5) _ 第七圖·本發明轴承之剛性5\i (stiffness)相對於孔 口節流進氣參數λ。和多孔質軸承進氣參數 又ρ之變化(抽承參數Λ = 0· 5 ) 第八圖:本發明轴承之剛性A (stiffness)相對於孔 口節流進氣參數;I。和多孔質軸承進氣參數 λΡ之變化(轴承參數Λ= 0·5) 第九圖:本發明轴承之剛性免(stiffness)相對於孔 口節流進氣參數λ。和多孔質轴承進氣參數 24 1250254 入p之變化(轴承參數Λ= 0·5) 第十圖:本發明轴承之剛性没2 (stiffness)相對於孔 口節流進氣參數;I。和多孔質轴承進氣參數 ;U之變化(轴承參數Λ= 0/5) 第Η--圖:本發明轴承之阻尼係數屈1 (damping coefficient)相對於孔口節流進氣參數λ 。和多孔質軸承進氣參數λ ρ之變化(軸承 參數Λ = 0 · 5 ) 第十二圖:本發明韩承之阻尼係數及2 (damping φ coefficient)相對於孔口節流進氣參數λ 。和多孔質韩承進氣參數λΡ之變化(柏承 參數Λ= 0· 5) 第十三圖··本發明轴承之阻尼係數及1 (damping coefficient)相對於孔口節流進氣參數λ 。和多孔質轴承進氣參數λ Ρ之變化(軸承 參數Λ = 0· 5 ) 第十四圖:本發明轴承之阻尼係數万22 (damping φ coefficient)相對於孔口節流進氣參數λ 。和多孔質軸承進氣參數λ ρ之變化(轴承 參數Λ = 0· 5 ) 第十五圖:本發明軸承可承受之最大榥動頻率對旋轉 頻率之比值參數7 (threshold whirl frequency ratio)相對於孔口節流進氣 參數λ。和多孔質軸承進氣參數;U之變化 (轴承參數Λ= 0· ) 5 25 1250254 第十六圖:本發明最大頻率比r相對於轴承參數Λ之 變化(孔口節流進氣參數;I。= 1(Γ4和多孔 質轴承進氣參數;U = 1〇—7和1〇_8) 【主要元件符號說明】 (1) 轴承 (11) 節流孔 (2) 多孔質轴承System, which = interaction τ, produces - the optimal intake parameter value again. Or A P appears - can withstand the maximum value of the rotor weight F. Beyond this, the optimal intake parameter value is succumbing to the maximum rotor weight F. &gt; confusing &gt; 1 air neck bearing has the advantage that there are better bearing miscellaneous at low speed. This article explores the age of the rotor, which helps the designer to understand its characteristics, and the needle_承之(4) is the best design. In summary, the embodiments of the present invention can achieve the expected use efficiency 'and the specific structure disclosed therein' has not been seen in similar products, nor has it been disclosed before the application, and has fully complied with the provisions of the Patent Law. And the request, the application for the invention of a patent in accordance with the law, please forgive the review, and grant the patent, it is really sensible.月^ 23 1250254 [Simple description of the drawing] First figure · Schematic diagram of the radial bearing of the multi-row orifice bearing of the present invention, FIG. 2: Schematic diagram of the radial bearing of the porous bearing. Second figure: The maximum rotor weight f of the present invention ( Threshold load capacity of rotor mass) relative to the bearing parameter Λ (bearing number) (orifice throttle intake parameter λ 〇 = 1〇·4) Fourth: the maximum rotor weight F of the invention (threshold load capacity of rotor Mass) relative to the bearing parameter Λ φ (bearing number) change (orifice throttle intake parameter λ 〇 = 2 &gt; 1 (Γ 4) fifth figure: the greater rotor weight y of the present invention relative to the orifice throttle Gas parameter and the change pattern of the porous bearing intake parameter λ ρ (bearing parameter Λ = 0·1). Fig. 6: The maximum rotor weight F of the present invention is relative to the orifice throttled intake parameter λ. and the porous bearing The change pattern of the intake parameter λ ρ (bearing parameter Λ = 0.5) _ The seventh figure · The rigidity of the bearing of the invention 5\i (stiffness) relative to the orifice throttle intake parameter λ. And the porous bearing intake parameters ρ change (sucking parameter Λ = 0· 5 ) : The stiffness A of the bearing of the present invention is relative to the orifice throttle intake parameter; I. and the change of the porous bearing intake parameter λ ( (bearing parameter Λ = 0·5) ninth: the rigidity of the bearing of the present invention Stiffness relative to the orifice throttle intake parameter λ. and porous bearing intake parameter 24 1250254 into p change (bearing parameter Λ = 0·5) Tenth: the rigidity of the bearing of the invention is not 2 (stiffness The throttle parameter is compared with the orifice; I. and the porous bearing intake parameter; the change of U (bearing parameter Λ = 0/5) Η--Figure: Damping coefficient of the bearing of the present invention The change in the intake air parameter λ relative to the orifice and the change in the intake parameter λ ρ of the porous bearing (bearing parameter Λ = 0 · 5) Fig. 12: The damping coefficient of the invention and the damping coefficient of 2 (damping φ coefficient) The inlet throttle parameter λ and the change of the porous Hancheng intake parameter λΡ (Baicheng parameter Λ = 0·5) The thirteenth figure · The damping coefficient of the bearing of the invention and the damping coefficient of the bearing relative to the hole The mouth throttle intake parameter λ. and the porous bearing intake parameter λ Ρ change (Bearing parameters Λ = 0 · 5) FIG XIV: Wan damping bearing of the present invention 22 (damping φ coefficient) with respect to the intake orifice restrictor parameter λ. And the change of the intake parameter λ ρ of the porous bearing (bearing parameter Λ = 0· 5). Figure 15: The ratio of the maximum turbulent frequency to the rotational frequency of the bearing of the present invention (threshold whirl frequency ratio) is relative to The orifice throttles the intake parameter λ. And porous bearing intake parameters; U changes (bearing parameters Λ = 0 · ) 5 25 1250254 Figure 16: The maximum frequency ratio r of the invention is relative to the bearing parameter Λ (orificate throttle intake parameters; I = 1 (Γ4 and porous bearing intake parameters; U = 1〇-7 and 1〇_8) [Main component symbol description] (1) Bearing (11) Throttle (2) Porous bearing

2626

Claims (1)

1250254 十、申請專利範圍: 一種最佳穩定性混合氣體轴承設計,其主要係於 轴承中央,等距離於轴向之截面上,對稱配置設有五 排節流孔,每排節流孔數目不得少於8孔,平均分佈 於圓周上,節流孔之形狀可為分段孔,而在中等轉速 下(0.4&lt;八&lt;0.8),並且在低進氣量時(;1。=1〇-4),其 穩定性最高,以能獲得最佳之穩定性者。1250254 X. Patent application scope: An optimal stability mixed gas bearing design, mainly in the center of the bearing, equidistant from the axial section, symmetrically arranged with five rows of orifices, the number of orifices per row shall not be Less than 8 holes, evenly distributed on the circumference, the shape of the orifice can be a segmented hole, at medium speed (0.4 &lt; eight &lt; 0.8), and at low intake air (1. = 1 〇-4), the highest stability, in order to get the best stability. 2727
TW93137582A 2004-12-06 2004-12-06 The present invention relates to a new-designed hybrid air journal bearing with best stability TWI250254B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
TW93137582A TWI250254B (en) 2004-12-06 2004-12-06 The present invention relates to a new-designed hybrid air journal bearing with best stability

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
TW93137582A TWI250254B (en) 2004-12-06 2004-12-06 The present invention relates to a new-designed hybrid air journal bearing with best stability

Publications (2)

Publication Number Publication Date
TWI250254B true TWI250254B (en) 2006-03-01
TW200619525A TW200619525A (en) 2006-06-16

Family

ID=37432973

Family Applications (1)

Application Number Title Priority Date Filing Date
TW93137582A TWI250254B (en) 2004-12-06 2004-12-06 The present invention relates to a new-designed hybrid air journal bearing with best stability

Country Status (1)

Country Link
TW (1) TWI250254B (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US8485729B2 (en) 2010-12-03 2013-07-16 Industrial Technology Research Institute Self-compensating hydrostatic journal bearing

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US8485729B2 (en) 2010-12-03 2013-07-16 Industrial Technology Research Institute Self-compensating hydrostatic journal bearing

Also Published As

Publication number Publication date
TW200619525A (en) 2006-06-16

Similar Documents

Publication Publication Date Title
Ruhl et al. A finite element model for distributed parameter turborotor systems
Chen et al. The comparison in stability of rotor-aerostatic bearing system compensated by orifices and inherences
Kirillov Destabilization paradox due to breaking the Hamiltonian and reversible symmetry
Zhang et al. Comparison of the characteristics of aerostatic journal bearings considering misalignment under pure-static and hybrid condition
Shi et al. Effect of angular misalignment on the static characteristics of rotating externally pressurized air journal bearing
Ehyaei et al. Dynamic response and stability analysis of an unbalanced flexible rotating shaft equipped with n automatic ball-balancers
Wang et al. Numerical calculation of rotation effects on hybrid air journal bearings
Zhang et al. Comparison study of misalignment effect along two perpendicular directions on the stability of rigid rotor-aerostatic journal bearing system
TWI250254B (en) The present invention relates to a new-designed hybrid air journal bearing with best stability
Bi et al. On the dynamic behaviors of freely falling annular disks at different Reynolds numbers
Su et al. Rotor dynamic instability analysis on hybrid air journal bearings
Zheng et al. Improving the stiffness of the aerostatic thrust bearing by using a restrictor with multi-orifice series
Feng et al. Dynamic analysis of water-lubricated motorized spindle considering tilting effect of thrust bearing
Chen et al. Analysis of aerostatic spindle radial vibration error based on microscale nonlinear dynamic characteristics
Chen et al. Static performance of the aerostatic journal bearing with grooves
Zha et al. Influence of microscale effect on the radial rotation error of aerostatic spindle
Dal et al. Performance characteristics of an aerostatic journal bearing with partially blocked orifices
Huang et al. A theoretical and experimental study on the stiffness of aerostatic thrust bearings with vacuum preloading
Wang et al. Dynamic stability analysis of a flexible rotor filled with liquid based on three-dimensional flow
Dwivedi et al. Effects of turbulence on dynamic performance of accelerated/decelerated hydrodynamic journal bearing system
Li et al. Drag and wake structure of a quasi-dandelion pappus model at low and moderate Reynolds numbers: The effects of filament width
Kataoka et al. Numerical simulations of the behaviour of a drop in a square pipe flow using the two-phase lattice Boltzmann method
Yang et al. Dynamic characteristics of spiral-grooved opposed-hemisphere gas bearings
Dal et al. Dynamics of externally pressurized air bearing with high values of clearance
Fang et al. Investigations of the static and dynamic characteristics of the precision hydrostatic spindle with mid-thrust bearing under different loads

Legal Events

Date Code Title Description
MM4A Annulment or lapse of patent due to non-payment of fees