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Press fit connection, PRESS7K1

: Problem description: Consider a press fit connection consisting of a shaft and a nave. Let the radii r₂=2r₁=1m. The inner radius of the nave is less than the one of the shaft by the interference $\Delta r_{1}$ . Determine the contact pressure developed between the two parts.

$\begin{figure} \centering\hspace{0pt}\rotate{ \epsfclipon\epsfxsize=2cm\epsffile{press7k1.ps}} \end{figure}$

Mesh: Ten quadrilaterals--see appendix A.4.

Material properties: $E=2\times 10^5$ MPa, $\nu=0.3$ .

Support: Axisymmetric-plane stress.


v=0 nodes: 1  3  5  7  9 11 13 15 17 19 21 23 26 29 32 35 38 42 45 48 51 54
Specification of contact surfaces.
Contact surface A  element face:	 5 S2
Contact surface B  element face: 	 6 S4

Loading: $\Delta r_{1}=0.6667\times 10^{-3}$ m modeled by the overlap of two FE meshes.

Solution: In the absence of external forces we have no definite tolerance for the residual vector criterion which, therefore, cannot be used directly for this and similar self-equilibrium problems. We may, however, control the magnitude of the out-of-balance vector in the OL file manually until it reduces to a ``reasonable small'' value. To this end we first execute the solver with default tolerance values on the RP line which will cause the program to stop after NITER iterations have been performed. When satisfied, we re-execute the solver with the convergence criteria disabled by setting RTOL = XTOL = -1 and the solution is obtained in next iteration step.

The relation between the contact pressure p_c and the interference $\Delta r_{1}$ can be expressed by

$\begin{displaymath}p_{C}=E\frac{\Delta r_{1}} {r_{1} \left(1+\displaystyle\frac... ...style\frac{1+0,5^{2}} {1-0,5^{2}} \right)} = 100\mbox{\,MPa} \end{displaymath}$

The computed distribution of radial and hoop stresses in the shaft and nave with penalty parametr set to $\xi=10^{15}{\rm [N/m^3]}$ is shown in figure. The analytical solution is plotted by the full line.

$\begin{figure} \centering\hspace{0pt}\rotate{ \epsfclipon\epsfxsize=8cm\epsffile{pres7k1.ps}} \end{figure}$

Execute from prompt:
>rmd2 press7k1.I1
>rpd2 press7k1.I2
>srh2 press7k1.I3
>fefs press7k1.I4
>hpp2 press7k1.IP
>hpls press7k1.IL1
>hpls press7k1.IL2
>str2 press7k1.I5

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