機(jī)械專業(yè)畢業(yè)論文中英文翻譯--在全接觸條件下，盤式制動器摩擦激發(fā)瞬態(tài)熱彈性不穩(wěn)定的研究

1、<p>　　Frictionally excited thermoelastic instability in disc brakes—Transient problem in the full contact regime</p><p><b>　　Abstract</b></p><p>　　Exceeding the critical sliding

2、 velocity in disc brakes can cause unwanted forming of hot spots, non-uniform distribution of contact pressure, vibration, and also, in many cases, permanent damage of the disc. Consequently, in the last decade, a great

3、deal of consideration has been given to modeling methods of thermo elastic instability (TEI), which leads to these effects. Models based on the finite element method are also being developed in addition to the analytical

4、 approach. The analytical mode</p><p>　　Keywords: Thermo elastic instability; TEI; Disc brake; Hot spots</p><p>　　1. Introduction</p><p>　　Formation of hot spots as well as non-unif

5、orm distribution of the contact pressure is an unwanted effect emerging in disc brakes in the course of braking or during engagement of a transmission clutch. If the sliding velocity is high enough, this effect can becom

6、e unstable and can result in disc material damage, frictional vibration, wear, etc. Therefore, a lot of experimental effort is being spent to understand better this effect (cf. Refs.) or to model it in the most feasible

7、fashion. Barber de</p><p>　　This paper is related to the work by Lee and Barber [7].Using an analytical approach, it treats the inception of TEI and the development of hot spots during the full contact regim

8、e in the disc brakes. The model proposed in Section 2 enables to cover finite thickness of both friction pads and the ribbed portion of the disc. Section 3 is devoted to the problems of modeling of partial disc surface c

9、ontact with the pads. Section 4 introduces the term of ‘‘thermal capacity of perturbation’’ emphasizi</p><p>　　2. Elaboration of Lee and Barber model</p><p>　　The brake disc is represented by th

10、ree layers. The middle one of thickness 2a3 stands for the ribbed portion of the disc with full sidewalls of thickness a2 connected to it. The pads are represented by layers of thickness a1, which are immovable and press

11、ed to each other by a uniform pressure p. The brake disc slips in between these pads at a constant velocity V.</p><p>　　We will investigate the conditions under which a spatially sinusoidal perturbation in t

12、he temperature and stress fields can grow exponentially with respect to the time in a similar manner to that adopted by Lee and Barber. It is evidenced in their work [7] that it is sufficient to handle only the antisymme

13、tric problem. The perturbations that are symmetric with respect to the midplane of the disc can grow at a velocity well above the sliding velocity V thus being made uninteresting.</p><p>　　Let us introduce a

14、 coordinate system （x1; y1）fixed to one of the pads (see Fig. 1) the points of contact surface between the pad and disc having y1 = 0. Furthermore, let a coordinate system （x2; y2） be fixed to the disc with y2=0 for the

15、points of the midplane. We suppose the perturbation to have a relative velocity ci with respect to the layer i, and the coordinate system （x; y）to move together with the perturbated field. Then we can write</p>&l

16、t;p>　　V = c1 -c2; c2 = c3; x = x1 -c1t = x2 -c2t,</p><p>　　x2 = x3; y = y2 =y3 =y1 + a2 + a3.</p><p>　　We will search the perturbation of the uniform temperature field in the form</p>

17、<p>　　and the perturbation of the contact pressure in the form</p><p>　　where t is the time, b denotes a growth rate, subscript I refers to a layer in the model, and j =-1½is the imaginary unit. Th

18、e parameter m=m（n）=2pin/cir =2pi/L, where n is the number of hot spots on the circumference of the disc cir and L is wavelength of perturbations. The symbols T0m and p0m in the above formulae denote the amplitudes of ini

19、tial non-uniformities (e.g. fluctuations). Both perturbations (2) and (3) will be searched as complex functions their real part describing the actual pertu</p><p>　　Obviously, if the growth rate b<0, the

20、initial fluctuations are damped. On the other hand, instability develops if</p><p><b>　　B〉0.</b></p><p>　　2.1. Temperature field perturbation</p><p>　　Heat flux in the d

21、irection of the x-axis is zero when the ribbed portion of the disc is considered. Next, let us denote ki = Ki/Qicpi coefficient of the layer i temperature diffusion. Parameters Ki, Qi, cpi are, respectively, the thermal

22、conductivity, density and specific heat of the material for i =1,2. They have been re-calculated to the entire volume of the layer (i = 3) when the ribbed portion of the disc is considered. The perturbation of the temper

23、ature field is the solution of the equatio</p><p>　　With and it will meet the following conditions:</p><p>　　1，The layers 1 and 2 will have the same temperature at the contact surface</p>

24、<p>　　2，The layers 2 and 3 will reach the same temperature and the same heat flux in the direction y</p><p><b>　　,</b></p><p>　　3，Antisymmetric condition at the midplane </p

25、><p>　　The perturbations will be zero at the external surface of a friction pad </p><p>　　(If, instead, zero heat flux through external surface has been specified, we obtain practically identical n

26、umerical solution for current pads).</p><p>　　If we write the temperature development in individual layers in a suitable form </p><p><b>　　we obtain</b></p><p><b>

27、　　where</b></p><p><b>　　and</b></p><p>　　2.2. Thermo elastic stresses and displacements</p><p>　　For the sake of simplicity, let us consider the ribbed portion of

28、the disc to be isotropic environment with corrected modulus of elasticity though, actually, the stiffness of this layer in the direction x differs from that in the direction y. Such simplification is, however, admissible

29、 as the yielding central layer 3 practically does not take effect on the disc flexural rigidity unlike full sidewalls (layer 2). Given a thermal field perturbation, we can express the stress state and displacements</p

30、><p>　　在全接觸條件下，盤式制動器摩擦激發(fā)瞬態(tài)熱彈性不穩(wěn)定的研究摘要超過臨界滑動盤式制動器速度可能會導(dǎo)致形成局部過熱，不統(tǒng)一的接觸壓力，振動分布，而且，在多數(shù)情況下，會造成盤式制動閘永久性損壞。因此，在過去十年，人們通過大量建模實(shí)驗(yàn)來研究盤式制動閘的摩擦熱彈性的不穩(wěn)定性的可能導(dǎo)致的影響。除了數(shù)學(xué)分析方法，基于模型有限元法也正在發(fā)展中。在李和鮑勃描述的摩擦熱彈性不穩(wěn)定性發(fā)展的分析模型已經(jīng)擴(kuò)大了在現(xiàn)今的工作[摩

31、擦熱彈性不穩(wěn)定興奮 國立交大摩擦學(xué) 1993; 115:607-14]。在他們模型修改中值得注意的是，有這樣一個事實(shí)：摩擦盤襯墊弧長比光盤的圓周少，，當(dāng)摩擦襯墊與光盤充分接觸時(shí)，可以在制動盤破壞早期開發(fā)溫度擾動振幅。一種方法建議如何兼顧兩者的摩擦盤表面最初的不平坦接觸和在制動過程中摩擦盤內(nèi)部擾動形狀的變化。關(guān)鍵詞：熱彈性不穩(wěn)定;TEI，盤式制動閘;受熱區(qū)域</p><p><b>　　1,介紹<

32、/b></p><p>　　在盤式制動器制動過程或者是在傳輸過程離合器的接觸過程中,過熱區(qū)域的形成以及非均勻接觸壓力分布是一種不希望出現(xiàn)的效果.如果滑動速度足夠高的話,這種效應(yīng)會變得極不穩(wěn)定,有可能會導(dǎo)致盤式制動器摩擦介質(zhì)受損,發(fā)出振動,導(dǎo)致磨損等.因此,許多試驗(yàn)都花費(fèi)在想更好了解這種效應(yīng)產(chǎn)生的原理或者用可行的建模方法來建模.鮑勃解釋這種現(xiàn)象的原因描述為熱彈性的不穩(wěn)定性.后來道先生和伯頓等人介紹一種數(shù)學(xué)模型

33、來,在兩個半平面熱彈性盤式制動盤相互接觸的地方建立不穩(wěn)定狀態(tài)下臨界滑動速度.李先生和鮑伯的工作將制動盤的厚度影響考慮進(jìn)去,他們認(rèn)為這種模型對盤式制動盤適用.李先生和鮑伯的模型是由兩個半平面摩擦材料在金屬層直接滑動.直到最近一種盤式制動閘的熱彈性穩(wěn)定性參數(shù)分析和多盤離合器和制動閘的熱彈性穩(wěn)定性模型已經(jīng)建立了起來.制動盤的熱點(diǎn)區(qū)域的振幅問題在塑性理論中得到了解決.通過使用分析方法或者考慮用間歇接觸效應(yīng).最后,有限元分析法也應(yīng)用到了熱彈性不穩(wěn)

34、定性的問題,在非線性的模式下,當(dāng)分離的接觸區(qū)域發(fā)生時(shí),即使完成了,在其他工程不穩(wěn)定的情況下,通過數(shù)學(xué)建模更準(zhǔn)確的預(yù)測往往值得懷疑.通過忽視各種缺陷和隨機(jī)波動或者有可能通過恰當(dāng)?shù)拿?lt;/p><p><b>　　專業(yè)術(shù)語：</b></p><p>　　本文與李先生和鮑伯研究工作有關(guān).通過分析,當(dāng)盤式制動閘充分接觸時(shí),主要研究熱彈性不穩(wěn)定性成立與否和過熱區(qū)域的發(fā)展.在第二部

35、分的模型認(rèn)為摩擦墊和制動盤肋板部分都能夠覆蓋有限厚度.在第三部分則專注研究部分制動盤表面通過墊片接觸的建模問題.第四節(jié)通過評價(jià)制動盤材料價(jià)值的增加或者是滑動速度的范圍來介紹激發(fā)擾動的原因.一種基于制動盤摩擦表面不平整和它最初擾動幅度的分析在第五節(jié)提出了.最后,第六部分提出了在上述制動過程最初制動盤的不平整會引起溫度擾動的發(fā)展模型.這個在這里使用的模型來源于一個差分方程,它涵蓋了再制動過程充分接觸激發(fā)能力的多變性.</p>

36、<p>　　2,李先生和鮑伯模型的發(fā)展</p><p>　　制動盤包括三層,中間那層的厚度為2a3代表制動盤的肋板部分與a2的厚度完全連接在一起。不能移動和受均勻壓力互相壓制的摩擦墊的厚度表示為a1,制動盤以恒定速度在這些摩擦墊之間滑動。</p><p>　　我們將探討在何種條件下的溫度和應(yīng)力場空間正弦擾動增長能夠呈現(xiàn)冪級數(shù)增長通過以類比的方式來套用李先生和鮑伯的研究。在摩擦激發(fā)

37、的熱彈性穩(wěn)定性研究工作表明只處理不對稱問題是足夠的。這種關(guān)于制動盤中平面對成的擾動可以在滑動速度之上繼續(xù)增長，因此研究這個是沒有意義。</p><p>　　讓我們引入一個坐標(biāo)系（x,y）固定圖一中的墊，在墊和盤之間的接觸點(diǎn)y1=0,此外，讓我餓每年引入關(guān)聯(lián)坐標(biāo)系(x2,y2)在中平面點(diǎn)y2=0處插入到盤中。我們假設(shè)擾動層在層i有一個相對速度ci，以及相關(guān)聯(lián)坐標(biāo)(x,y)與擾動區(qū)域移動到一起。</p>

38、<p>　　那么我們可以寫下下面的等式：</p><p>　　V=c1-c2;c2=c3;x=x1</p><p>　　x2 = x3; y = y2 =y3 =y1 + a2 + a3.</p><p>　　在閘內(nèi)我們將搜索均勻的溫度場激發(fā)。</p><p>　　與接觸壓力的形式擾動，，在公式里面，t代表時(shí)間，b代表增長率，定義

39、i指模型的層數(shù)，j=-1的開根號是虛數(shù)單元，參數(shù)m=m（n）=2pin/cir =2pi/L，n代表制動盤圓周上熱點(diǎn)區(qū)域的個數(shù)，L代表擾動波長。在上述公式的符號Tom和Pom表示非均勻性振幅(例如波動)，圖中2，和3描述溫度的實(shí)際擾動和壓力區(qū)域?qū)⒈划?dāng)作復(fù)雜功能被搜索。顯然,如果b<0,那么最初的增長率是有阻尼的，相反，不穩(wěn)定發(fā)展那么b>0.</p><p><b>　　2.1溫度場的擾動&l

40、t;/b></p><p>　　當(dāng)制動盤肋板部分被考慮時(shí)，在X軸方向上的熱流為0.接下來，讓我們研究ki = Ki/Qicpi，它表示層溫度擴(kuò)散系數(shù).參數(shù)Ki, Qi, cpi分別指代熱導(dǎo)率，密度和1到2種材料的比熱。當(dāng)整卷制動盤的肋板部分被考慮，他們就要重新計(jì)算層的全部體積。溫度場的擾動用如下方程來解決：</p><p>　　其中，§=1，i=1,2,3。它需要滿足下列條

41、件：</p><p>　　1，層數(shù)1和2在接觸的表面需要相同的溫度：</p><p>　　2，層數(shù)2和3需要達(dá)到相同的溫度，并且在Y方向上要有相同的熱流。</p><p>　　3，在中間平面對稱的條件是： </p><p>　　在摩擦片的外表面零件的擾動為0的條件是</p><p>　　相反，如果通過外表面指明了零熱通

42、量，在現(xiàn)有襯墊的情形下，我們可以得到幾乎相同的數(shù)值解。</p><p>　　如果我們在適合下式的形式下，記錄單層的溫度發(fā)展范圍：</p><p><b>　　我們可以得到</b></p><p><b>　　這些參數(shù)</b></p><p><b>　　和</b></p&

43、gt;<p>　　2.2熱彈性應(yīng)力和位移</p><p>　　為了簡單起見，讓我們考慮，帶肋要各向同性環(huán)境與光盤的一部分實(shí)際上，雖然，糾正彈性模量，剛度 x 不同于此層的方向中方向 y。 但是，這種簡化是獲接納為高產(chǎn)中央層 3 實(shí)際上并不會對與完全不同的光盤抗彎剛度的影響側(cè)壁 （圖層 2）。 給定一個熱場攝動我們可以表達(dá)引起的位移與應(yīng)力狀態(tài)此攝動的任何圖層中。熱彈性問題能解決的疊加對一般的等溫一個特