Fig. 2 Shear stress distribution in the contact area between
ball and raceway. (a) Two-dimensional model of ball and raceway. (b)
Nephogram of shear stress distribution in the contact area. (c) Maximum
orthogonal shear stress and maximum shear stress on the subsurface under
contact load.
According to the classical Hertz contact theory, the rolling contact
between ball and raceway can be simplified to ideal line contact under
2D conditions (shown in Fig. 3). p(x) represents the contact load
distribution and \(p_{\max}\) represents the maximum contact load which
is specified \(p_{\max}\) = 2000 MPa. p(x) is calculated by the
following formula:
\begin{equation}
{{p\left(d\right)=p}_{\max}\left[1-\left(d/w\right)^{2}\right]}^{1/2}\nonumber \\
\end{equation}Where w represents the half-width of the contact area and is
specified w = 0.25 mm, and d represents
distance from the maximum load
point. The computational domain is chosen to be 12w length and
5w depth with 0.01w distance between each node
horizontally or vertically (shown in Fig. 3a and b). p(x) is set
to move uniformly along the x -axis by the DLoad subroutine
implemented in ABAQUS, aiming to replace the rolling contact process
between ball and raceway. Fig. 3b presents the selected point P1 on the
subsurface of the model. Fig. 3c shows the shear stress at point P1 as a
function of loading time. The result is that shear stress at a certain
point on the subsurface changes alternately with the motion of contact
load. Considering the similarity between Fig. 3c and sine curve, the
alternating shear stress is replaced by the stress with
sinusoidal regularity in the interest of computational simplicity in the
following sections.