Finite Element Analysis

4.4.1 Component Geometry And Material Properties

Due to the c o m p l e x i t y of the c o m p o n e n t g e o m e t r y in p a r t i c u l a r the b l e n d r a d i i a r o u n d the b o s s e s , the generation of a three dimensional finite element model was necessary. There were however, considerable constructional difficulties in undertaking such a task. Restrictions on element geometry presented the largest problem. W i t h i n s u c h a c o m p l e x m e s h it w a s d i f f i c u l t to a v o i d the generation of elements which violated the basic elemental r u l e s .

Distorted elements even far removed from the r e g i o n of immediate interest can lead to the introduction of quite considerable inaccuracies.

The biggest problems encountered were at the changes of section around the bosses, where the adjacent angles were o u t s i d e the a c c e p t a b l e limit. To m i n i m i s e t h e a b o v e difficulties some geometric modifications were necessary. These will be described in the next section.

The material properties used for input to PAFEC data file w e r e : -

Y o u n g 's Modulus, E 214800 MPa

Poisson's ratio, v 0.3

4.4.2 Development Of The Finite Element Model

Initially the full component was modelled. To overcome the d i f f i c u l t i e s p o s e d by t h e c o m p l e x g e o m e t r y of t h e component the geometric model in Medusa was modified in o r d e r to s i m p l i f y the f i n i t e e l e m e n t d i s c r e t i s a t i o n process. The diameter of the bosses were made the same (40 mm), this increased the blend radii around the bosses from 25mm to 25.73mm.

The component was split into several suitable blocks [82] and the boundary co-ordinates were entered using a global axis set. PIGS was used to fill these blocks w i t h 892 individual elements.

The elements used were standard twenty noded isoparametric brick elements (37110) and fifteen noded isoparamet ric p r i s m e l e m e n t s (37210) as shown in f i g u r e 4.3 [82]. These elements have three degrees of freedom at each node and the stress/strain varies linearly in each direction. This also has the advantage that the d i s p l acement and boundary shapes are .quadratic in nature. The midside nodes allow curved boundaries to be represented accurately if necessary.

A point load of 20 kN was applied to the area XY in figure 4.4. Since the stress/strain varies linearly, unit load may be applied. This value of load was chosen to obtain reasonable stress values for comparison with strain gauge r es u l t s .

The l o w e r s u r f a c e s AB and GH of the c o m p o n e n t w e r e restrained in the Z direction. The end AC was fully restrained in the X direction. The upper surface CD and EF were subjected to a uniform pressure of 87 MPa in Z direction representing fastening bolt pressure in both the rig and the real location. This value was derived using the following method:-

T h e c l a m p i n g f o r c e of b o l t a n d w a s h e r = 2 ay 3

w h e r e :-

ay = yield stress of the bolt * 640 MPa

Clamping force of the bolt •= 2/3 x 640 = 427 MPa bolts diameter = 18mm

Area of bolt = n r2 = 254.54 mm2 Load = F = a.A

Load = 108.6 x 103 N

Diameter of the washer = 40 mm Area of the washer = 1256 mm2

P r e s s u r e = a = F_ = 8 6 . 5 « 87 M P a

• A

The dat a file was. c r e a t e d in PIG S and the m a t e r i a l properties were entered via the keyboard.

The basic output from the computer was in digital form. For every node or element in the structure the print out gave the values of stress and displacement in X, Y and Z directions. The computer also calculated the principal stresses and their directions. Whilst the printed output was required for detailed analysis, a clear picture of the state of stress was given on the graphics terminal. The

results were also plotted as stress contours, to highlight the highly stressed regions as shown in figure 4.5.

Close examination of the stress contours and stress data file r e v e a l e d t hat the c o m p o n e n t does not c a r r y any appreciable load between A-A and B-B. Hence, this part was discarded and the component was restrained in the X direction at the section of cut to enable a finer mesh to be produced at the critical location.

Again the blend radii were increased from 25 mm to 25.73 mm to enable the element geometry to be within acceptable l i mits of PAFEC. At this point the r e m a i n d e r of the •component was r e m o d e l l e d . A p o i n t load of 20 KN was

applied to the kingpin, area XY shown in figure 4.6.

To ensure the accuracy of the solution a finer mesh was defined at the section of the component which exhibited high stress gradients, identified by the previous model. The new model resulted in a total of 600 elements and 3156 nodes.

The lower surface of the component, AB, was restrained in the Z direction as shown in figures 4.6. The section of cut, AC, was clamped in the X direction. The upper surface, CD, was subjected to a uniform pressure of 87 MPa to represent the fastening pressure exerted by the bolt. The data file was created in PIGS and material properties were input via the keyboard.