Abstract:Structural analysis is an essential tool fordesign engineers. Mesh generation is the basic step in any simulation. Inpractice of finite-element stress analysis, the engineer first needs to know ifkey stresses are converging, and second if they have converged to a reasonablelevel of accuracy.
In order to achieve results that are reliable when using thefinite element method one has to use an acceptable mesh with respect to theshape and size of the elements. Mesh quality and Mesh density are linked withthe solution accuracy. This paper presents a mesh convergence study on the hubwhich is most challenging part in the automotive clutch disc assembly. Introduction: Nowadays,Finite Element Analysis (FEA) is widely used in analysis since it has manyadvantages compared to analytical method. Also Finite Element Analysis (FEA)problems like that cannot solve by analytical methods. FEA is used forreduction of the cost as well as faster designing of any component.
It givesthe two-way solution “if any change is design is made then what?” FiniteElement Analysis (FEA) is numerical technique to find the approximate solutionof Partial Differential Equations (PDE) due to impact of Force, Vibration andHeat etc.Finite Element Analysis (FEA) is extensively used in manydepartments one of which is automobile industry. In automobile industry mainlyFinite Element Analysis (FEA) is used in Power Transmission systems, the mainobjective of Power Transmission system is to transfer efficient amount of powerto the wheels from engine, thus researchers are concentrating on optimal designof the Power Transmission system. Hub is used as Power Transmitting partpresent in the clutch disc assembly. Frictional pads which actually transmitsthe Power from the flywheel to hub in the clutch plate and from there to outputshaft.
Hub also acts as a torque absorption unit, it absorbs the torque at timeof engagement and disengagement of clutch disc with the help of springs locatedin drive plate. The aim of this study is to perform a Mesh Convergencestudy on hub. This paper tries to achieve acceptance of the specific solutionby considering the Mesh Discretization error.
“If I set everything right, load,Boundary conditions, material properties, element size then how do I know thatI arrived with fine mesh to capture the results?” Mesh Discretization Error: Displacement is the unknown variable in any Finite ElementAnalysis (FEA), displacement is calculated at every node in the model. Everyelement in the Finite Element Analysis (FEA) has its own shape functionassociated with the same. The stress are obtained by first derivative ofdisplacement field, that can be obtained from equation 1, (1)The stress values from the ANSYS are average of stressesfrom all elements attached to that node. This introduces the error in magnitudeof the stress value which is referred as the mesh discretization error.Phenomenon of mesh discretization error is shown in Fig 1. As mesh is coarsedifference is more between stress values of the adjacent elements.
?x ?x, ?y, ?xy = 171.25, 81.25, 25 Fig1 Mesh Discretization Error Nodal stress and Elemental stress value become close if themesh density increased as well as the solution accuracy increases but at thesame time required for the simulation also increases, but at certain pointthere is no change in stress value even after the refinement in mesh. For thisreason analyst should required to check the discretization errors in FEsolution. ANSYS Error Estimation:1) Percentage ErrorEnergy Norm (SEPC): SEPC is rough estimate ofthe stress error over the entire set of selected elements.
(Obtained from PRERRcommand in ANSYS APDL) 2) Element StressDeviations (SDSG): SDSG is measure amountbetween elemental and nodal stress. The difference between averaged andunaveraged stress gives an idea about mesh density. (Obtained from PRESOL andPRNSOL command in ANSYS APDL) 3) Element Energy Error(SERR): SERR is the energy associated with thestress mismatches all the nodes of the element. (Obtained from PRESOL andPRNSOL command in ANSYS APDL) 4) Maximum and MinimumStress Bounds (SMXB, SMNB): The stress boundsare used to determine the effect of mesh discretization error on the maximumstress. (Obtained from stress plots PLNSOL command in ANSYS APDL) FE solution will converge towards the exact solution withincreasing number of elements or with increasing order of polynomial in theelement. If the following requirements are fulfilled, then the solution isconverged.1. The element must beable to represent constant strain which is possible where small elements areused.
Small elements have strains are close to constant over the element.2. In order to avoid thegaps, adjutant elements must be compatible i.
e. the connecting nodes have thesame possibility to move as concerned element nodes. Finite Element Accuracy Criteria:Four types used as a study of mesh discretization erroranalysis, this calculated Global as well as Local mesh discretization errors. 1) Type 1A (SEPC_Model):The error norm of the entire model must be less than 15%. 2) Type 1B (SEPC_Local):3 layers of elements are selected as local area at high stress, the error normof the local area of high stress must be less than 10%.
3) Type 2 (Coefficient of variation): In local area of high stress, the average stress value oflocal elements have coefficient of variation stress less than 7%. COV (Coefficientof variation) is calculated as ratio of nodal stress to the mean stress value. 4) Type 3 (%Error): Thedifference between the stress component and stress considering thediscretization in local area of high stress must be less than 7%. (2) (Calculated byANSYS APDL)SMX = max stress value inselected set of element. 5) Type 4A (RMS_Model):This type uses the absolute value of SDSG (maximum variation of nodalcomponent) to Seqv (Von-mises stress) at that element and RMS(Root meansquare) is calculated from that values and it should be less than 15%.
6) Type 4B (RMS_Local): (SDSG/Seqv) RMS value of local area having high stress should be lessthan 10%.