Dişli çarklarda diş üzerinde ANSYS sonlu elemanlar paket programıyla gerilme analizi

Abstract

Bu çalışmada öncelikle dişlilerde, diş profllindeki gerilmelerin klasik yöntemlerle analizi verildi. Bu tip gerilme analizi problemlerinin çözümü için son zamanlarda geniş kullanım alanı bulan sonlu elemanlar yönteminin prensipleri verildi. Bu prensibe dayanan ANSYS sonlu elemanlar paket programı tanıtıldı. Örnek bir uygulama ile bir dişlinin diş profilinin modellenmesi ve diş profllindeki gerilmelerin ve gerilme dağılımlarının analizi gerçekleştirildi. Elde edilen değerler kontur diyagramları üzerinde gösterildi. örnek uygulamada bulunan maksimum gerilme değerleri ile ANSYS programıyla yapılan analizden alman gerilme dağılımı değerleri karşılaştırıldı ve aradaki farklar yorumlandı.The analytic analyses of irregular structures to which loads apply in various ways is very difficult, even in many cases impossible. Because of some recent advances in technology, this kind of analyses has become a real challenge in mechanical engineering. Finite elements method is a new and very effective way of solving these engineering problems. Nevertheless, it needs a great burden of matrix calculations. Therefore, computers and various software packets are very important tools for this method. Finite element packet programs enable us to perform the simulation of the structures loaded in various ways quickly and economically. Hence, possible product errors can be figured out before production. ANSYS computer packet program is the most recent and effective finite element software. By this program, very difficult engineering problems can be solved easily. Also solution time is short and Results are easy to visualize. Gears are one of the most common mechanical elements. They are designed according to maximum stress criteria so that they can endure in the most critical situations. There are two important critical situations for two gears rotating together : 1) When all load is applied to one cog of the gear 2) When two cogs are in contact and the forces applied on the top of the cogs produce the maximum moment on the cog causing stresses on the connection area between the cog and the gear body. In this study, a simulation for a gear in two dimensions is performed by ANSYS software. For two critical situaions, all stresses on a cog of the gear is calculated. Numeric and graphic (visiual) results are available. These results are also compared to classical hand calculations. The maximum stress value on the cogs can be analytically calculated by the following simplified formula : a = -.q<ö- (1) max 0,85.£.b.m 4 em W where Fu : Tangential force s : Coupling ratio b : Cogs width m : Modul value q : Shape factor The value calculated by the equation above is the maximum stress value. To solve this type of the problems by ANSYS, first the model geometry of the system is generated by the pre-processor module. The finite element model of the system is derived from the geometric model. The next step is ANSYS solving module. In this modules loading conditions and constraints are defined then the solution is performed by using SOLVE command. After this step, the results can be obtained numerically and seen visually by contour diagrams. First, ANSYS calculates strain values on the gear, then it derives stresses from these values by using the following equations.: The element integration point strains and stresses are computed by {^} = [B]{u}-{^} (2) where M = P]{«-} (3) {sel} : strains that cause stresses (output quantity EPEL) [B] : strain-displacement matrix evaluated at integration point {s} :nodal displacement vector XI {8th} :thermal strain vector {a} : stress vector (output quantity S) [D] : elasticity matrix nodal and centroidal stresses are available from the integration point stress. Combined Strains The principal strains are calculated from the strain components by the cubic equation: 1 i i i- 2 *jss n S= %x ~ *0 1 *1C» *X3 £p ~ S0 n ^J2 2 "= s. -s, (4) where So =principal strain (3 values) The three principal strains are labeled (output quantities 1, 2 and 3 with strain items such as EPEL).The principal strains are ordered so that Si is the most positive and S3 is the most negative. The strain intensity Si (output quantity INT) is the largest of the absolute values of ei - e2, s2 - 83, s3 - si That is: MAxfls, - s2\\s2 - s4k - «i| (5) The von Mises or equivalent strain se (output quantity EQV) is computed as: ^ = ^([h - *2r+ 1*2 -^r+k-sifi) (6) Xll Combined Stresses The principal stress are calculated from the strain components by the cubic equation: 0»-°o 'xy X2 lk>-c4K- CT-.D (8) The von Mises or equivalent stress ae (output quantity SEQV) is computed as: °d = j( h " 02'2 + 102 _ °f + 10* ? ai n ) (9) The equivalent stress is related to the equivalent strain through ae = 2 G se (10) where G : Shear module E : Young's module v : Poisson's ratio xni