Kuvvet kapalı yürek mekanizmalarında ayrılma olayının incelenmesi
Başlık çevirisi mevcut değil.
- Tez No: 55896
- Danışmanlar: PROF.DR. FUAT PASİN
- Tez Türü: Doktora
- Konular: Makine Mühendisliği, Mechanical Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1996
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 107
Özet
ÖZET Bu çalışmada içten yanmalı motorlarda kullanılan supap tahrik mekanizma sının titreşimlerinden dolayı ortaya çıkan ayrılma olayları incelenmiştir. Ayrılma, mekanizmanın kuvvet iletimi bakımından birlikte çalışan uzuvları arasında temasın kesilmesidir. Bu da sırası ile yürek ile tabla arasında, tabla ile itici çubuğu arasında, itici çubuğu ile külbütör arasında, külbütör ile supap yayı tutucusu arasında, supap yayı tutucusu ile supap yayı arasında ve supap yayı ile gövde arasında olmak üzere 6 ayrı yerde gerçekleşebilir. Yukarıda ifade edilen yerlerdeki ayrılma olaylarım incelemek için çeşitli modeller oluşturulabilir. Bu çalışmada 5 değişik model ile ayrılma olayı incelenmiştir. Bunlardan en gerçekçi olan birincisinde hem supap yayı hem de itici çubuğu sürekli ortam olarak modellenmiştir. İkinci modelde ise supap yayı yine sürekli ortam olarak, itici çubuğu ise basit kütle-yay sistemi olarak modellenmiştir. Üçüncü modelde ise bu defa tam tersi olarak itici çubuğu sürekli ortam, supap yayı ise basit kütle-yay sistemi alınmıştır. Dördüncü modelde de supap yayı yine sürekli ortam, itici çubuğu da rijid alınmıştır. En basit ve sonuncu model olan beşinci modelde ise hem itici çubuğu hemde supap yayı basit kütle-yay sistemi olarak modellenmiştir. Oluşturulan bu modeller vasıtası ile basit harmonik hareket veren yürek için ayrılma şartlan elde edilmiş ve dizayn açısından supap yayma verilmesi gereken ön sıkıştırmanın hesabında hangi ayrılmama şartının veya şartlarının geçerli olduğu incelenmiştir. Ayrıca ayrılmama şartlan bakımından modeller kendi aralarında karşılaştırılmıştır. Birinci model, kullanılarak değişik sistem parametrelerinin ayrılma olayına etkisi araştırılmıştır. Ayrıca bu modelle çeşitli yürek hareket kanunlan için yüreğin verdiği hareket s=s(t), Fourier serisine açılarak ayrılma olayı incelenmiştir.
Özet (Çeviri)
SUMMARY SEPARATION PHENOMENA JN FORCE CLOSED CAM MECHANISMS INTRODUCTION In force closed cam mechanisms the contact between the members of the mechanism is established by the force induced through the valve spring. This contact must be continuous, otherwise one cannot expect proper operation of the mechanism. Therefore, the physical parameters of the valve spring and the amount of preset which must be given to the valve spring in the cam assembly should be determined accurately. In order to choose a proper value of the preset, especially when high speed operation is considered, exact dynamic analysis of the system must be performed. If this analysis is not complete, jump phenomenon, i.e. separation phenomenon (the separation of the members of a cam mechanism) may occur. In a cam-follower mechanism, in addition to the separation of the tappet from the cam, separation of the other members of the mechanism which are kept in contact through the valve spring force must also be investigated. The separation phenomenon between pushrod and rocker arm, rocker arm and spring retainer, spring retainer and valve spring, valve spring and body has not been investigated previously, therefore one of the main contribution of this thesis is the formulation of separation criteria for these coupled members. For this purpose, an automobile engine's cam mechanism is taken into consideration and the amount of preset which must be given to the valve spring to prevent the separation is investigated using five different models. In the first step, simple harmonic cam motion is considered. Using this cam motion, separation criteria for all models are obtained and afterwards these models are compared with each other. Separation curves are obtained for different system parameters using the first model which is the most accurate one. Calculations for a general cam profile are carried out by expanding the cam profile function in to Fourier series. In this case also the first model is used.MODELS AND SEPARATION CONDITIONS 1. Continuous Pushrod and Valve Spring Model. In this model both pushrod and valve spring are modeled as continuous elements. Differential eqns. in this case are : krL d2v d\ 34.2 ? =0 \i dX' dt 2 d2u _ d2u d2s C dx2 ~ dt2 ~ dt2 The boundary conditions are formulated as v(0,t) = 0 u(0,t) = 0 s(t) +u(^,t) +80 + v(L,t) = 0 M a2v A2 J + r ^ X=L \cU X=L Mm) = EA X=L du. Solutions of the differential eqns. given above are u(x, t) = (-a cos qx + B2 sin qx + a) cosrat + (b4 sin qx) sin cot + kux v(X, t) = ( A2 sin pXj coseot + ( A4 sin pXJ sincot + kvX where K and kv are given as a + 5“ EA k”=- ^kr+EA L £kr+EA r and the coefficients B2, B4, A2 and A4 are to be determined from the boundary conditions. The separation conditions for this model areAı : Separation of the cam from the tappet A>A1=[ı+^(b2pVÂr“-nt^2)2+(b4pV^y)2 -ı A2 : Separation of the tappet from the pushrod : A>A”=U + T, Py/kYyjbJ+bJ-l A3 : Separation of the pushrod from the rocker arm : A> A3 Jl + -JpV^V(sinP^ + b2cosP^)2+(b4cosP^)2 -1 A4 : Separation of the rocker arm from the spring retainer A>A4 = (1 ^~fr 1+Tj PJ I vXPa2sinP-N/n + -v/Xy( sinP^ty +b2 cospVÂ/y) ^Xa4sin3^/ri + vA.pa4sinp.>/rt + Xy b4 cosP-v/^T +£Aa2 sinP^q A5 : Separation of the spring retainer from the valve spring A > A5 = (X + 1) PV^cosP^/tÎ U(a22+a42)- 1 A6 : Separation of the valve spring from the body A>A6=(X + l)p^(a22+a42)-l 2. Lumped Parameter Pushrod - Continuous Valve Spring Model. In this model the pushrod is assumed to be massless and valve spring is modeled as a continuous element. Therefore system mass is M* = M + m;. Differential eqn. in this case becomes : krL a2v a2v 2 ^2 u ax^ at = 0 XIThe boundary conditions are formulated as : v(0,t) = 0 c2v(L,t) fdv'] fdv] r, The solution of the differential eqn. given above is v(X,t) = (A2 coscot + A4 sincat)sinpX+kvX where A2 and A4 are to be determined from the boundary conditions. Separation conditions for this model are as follows : The first separation condition Ai will not be given from now on since it is independent of the other system parameters and should be investigated separately. A2 : Separation of the tappet from the pushrod : A>A2 =-j^- ^(l-a-aSİnP^/rf) +(-a4sin3>/rî) - 1 A3 : Separation of the pushrod from the rocker arm : A > A3 =. X + l J (typ2-l)a2 sinpV^l + (tyP2-l)a4 sinp^ - A4 : Separation of the rocker arm from the spring retainer : I r 12 A>A4=(^+ln| p2(v-l)a4sinP-^-^2Pa2sinPA/îl + P-v/na4cosPA/TÎ + - P2(v-l)a2sinP^+^2Pa4sinPA/ri + PA/T{a2cosPA/:n I 12 ^\ V2 -1 A5 : Separation of the spring retainer from the valve spring This condition is the same as in the first model. Ag : Separation of the valve spring from the body : This condition is also the same as in the first model. xu3. Continuous Pushrod - Lumped Parameter Valve Spring Model. For this case the valve spring is massless and the system mass is therefore M**=M+my/3. The differential eqn. for this model is : 2 d2u _ tfu d2s 8x2~ dt2~ dt2 The boundary conditions are formulated as u(0,t) = 0“ S2(s + u(x,t)x,) öt* (da) t \ c(s + u(x,t)x.) x=^ The solution of the differential eqn. given above is u(x, t) = (-a cosqx + B2 sin qx + a) coscot + (B4 sin qx) sin (at + kux where B2 and B4 are to be determined from the boundary conditions. The separation conditions for this model are as follows : A2 : Separation of the tappet from the pushrod : This condition is the same as the A2 condition of the first model. A3 : Separation of the pushrod from the rocker arm : This condition is also the same as the A3 condition of the first model. A4 : Separation of the rocker arm from the spring retainer : A>A4=' (1 + X)vp2[cospVÂT - b2 sinpV^r] + 1 + ^[pV^ysin pVty + b2pV^rcospV^r] (l + ^pfb^inpV^) (l+X)vp2[-b4sinpVty] +(l + X)[b4pV^ycospVty] + (l + X)^p [cos pV^y - b2 sin pV^] 2 I 1/2 -1 XH1A5 : Separation of the spring retainer from the valve spring : A > A5 = (1 + X){[j32(cos(3V^Y - b, sin pVty) + pJ^-fsinpVty + b, cosfijkf ) + ^PbdsinpV^r ]2-[ p2(-b4sinpv^) + p^(b4cospVty) + çp(cospV^r-b2sinpV^y) ]2 jV2 - 1 Aö : Separation of the valve spring from the body : A>A6=(l + X){ (-cospV^ + b2sinp^)2 + (b4sinpVty)2 }'/2-l 4. Rigid Pushrod and Continuous Valve Spring Model. In this model the pushrod is considered as rigid and valve spring is modeled as a continuous element. The differential eqn. of the valve spring is again krL 32v 8\ li dX2 dt2 The boundary conditions are formulated as v(0,t) = 0 v(L,t) = -50-s(t) The solution of the differential eqn. given above is v(X, t) = - -2-: - X + - - - sin pX cosoot L smpL, The separation conditions for this model are A2 : Separation of the tappet from the pushrod : If r-cosP^/q A>A2 = p ^i-^V-(i+y)p K sınPVîl + ? -1 A3 : Separation of the pushrod from the rocker arm : XIV”if,-cosBJîı i, A4 : Separation of the rocker arm from the spring retainer A>A4 = B^^£-(l-v)B2 cos i sin P^fi +fep)2 - 1 A5 : Separation of the spring retainer from the valve spring a > a5 = p^/n cost inp^/n sin -1 Aö : Separation of the valve spring from the body : A>A6=- P>M inpV^l -1 5. Lumped Parameter Pushrod and Valve Spring Model. In this model both pushrod and valve spring are considered as ideal massless springs. The system mass therefore is M*** = m; + Mı + M2 + my/3. The differential eqn. in this case is M***x = -rx~kr(x+50) + k(s-x) Solution of this differential eqn. is x = A coscot + B sincDt + C where A, B, C are X = ± =, l + --p2(l + y + T!/3) 1 T l + --(32(l + y + îi/3)j +(gp)a _ B B = - = -cp/x 1 + ^-P2(1 + Y + ti/3) ~\2 +&r XV_ C 1-AA a 1 + A. The separation conditions for this model are A2 : Separation of the tappet from the pushrod A >A2 =(! + -£) V(A + 1)2+B: -1 A3 : Separation of the pushrod from the rocker arm : X+l A>A3 = ^[i+a(i-p2xy)]2+[b(i-p2xt)]2 - 1 A4 : Separation of the rocker arm from the spring retainer _i2 A>A4=^{ [l + A[l-f^y + v)]+^XB + 2 \V2 [-a^p^+b[i-p2x(y+v)]] }' -1 A5 : Separation of the spring retainer from the valve spring A> A5 =(l + A.)1 xgpvi Ul sl2 +IB vSpV -1>0 A« : Separation of the valve spring from the body : a>a6={x+i)Va2-b2 -1 GENERAL CAM PROFILE FORMULATION If the periodic cam profile function s=s(t) is expanded using Fourier series s(t) = -f-+ zl[a.n cosnrot + bn sin not) Âl n=l is obtained. XVIIn analyzing the general profile cam curve excited mechanism, the first model is used. Solutions u(x,t) and v(x,t) of this model are formulated in the following manner : SO u(x,t) = 2u,n(x)cosncût + U:,n(x)sinnat + U0(x) n=l v(X,t) = Ivin (X) cos not + V,n (X) sin not + V0 (X) n=l The separation criteria are slightly different from those given for the simple harmonic excitation of Model 1. The integrations which must be calculated in determining the Fourier coefficients are manipulated by using the program Mathematica. Separation curves for cyclical motions, harmonic motions, constant velocity motion and parabolic cam motion are obtained. CONCLUSION Five different models are used to investigate the separation phenomenon in force closed cam mechanisms. Besides the separation of the cam from the tappet other separation conditions are also formulated. Comparison of these conditions for the case of simple harmonic motion leads to a conclusion that 2nd (separation of the pushrod from the tappet) and 6th (separation of the valve spring from the body) separation conditions are important in design stage. On the other hand comparison of the models shows that even the simplest model yields meaningful results. Except for the first one, all models depending on the separation criteria and the model, give results that are not satisfactory from the design point of view. Therefore if there are difficulties in using the first model, especially in general cam motion cases, the critical separation criteria must be determined and then suitable model that satisfies this criteria must be chosen. XVU
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