|
|
| |
| Praveen Holani (MS, September 2002) |
| FEA of the Head Disk Interface in a Hard Disk Drive with an Adaptive Mesh |
|
The numerical modeling of the pivoted slider bearing involves the simultaneous solution of the 2-D compressible
Reynolds Equation with slip flow effects for the air bearing and the equilibrium equations for the slider.
The 2-D compressible Reynolds equation is a non - linear partial differential equation that is used for calculating
the air bearing pressure as a function of the slider/disk interface. Since the analytical solution of the Reynolds
equation is not possible for a generic slider, a numerical solution is desired.
The finite difference method has been widely used for the solution of the Reynolds equation over number of years as
seen in the literature. However the finite element methods are better suited to adapt to the minute details of the complicated
slider geometries. One of the challenging problems with these numerical methods in the representation of the given domain by a
set of finite elements (i.e. discretization or mesh generation).The choice of element type, number of elements, and density of
elements depends on the geometry of the domain, the problem to be analyzed, and the degree of accuracy desired. The finite element
method improve upon the finite difference schemes in that the mesh can be adaptively refined locally to help resolve minute geometric
details and assure convergence while requiring a minimum number of elements. However the finite difference schemes are computationally
more efficient especially when used in conjunction with the Factored Implicit scheme as described by White, but suffer from a
drawback of requiring rectangular grid which in case of complicated slider geometries may require huge number of nodes for
the same degree of accuracy.
|
In this work the following tasks were undertaken:
- The Reynolds equation and slider equilibrium equations were solved simulataneously at steady state
- The Reynolds equation was solved on a rectangular mesh and an adaptive mesh algorithm was implemented
- Computationally efficient storage of the global stiffness matrix was used
In the course of this work the h-refinement is used, in particular the element subdivision (enrichment) method of the available
h-refinement methods. Here if the elements show too much error, they are simply divided into smaller ones keeping the original
element boundaries intact. This approach ordinarily leaves many dangling nodes where an element
with mid-side nodes is joined to a linear element with no such nodes. On such occasions it is necessary to provide local constraints
at the dangling nodes or use some algorithm to clean up the mesh of such abnormalities. In this work, an admissible function algorithm
is implemented to prevent such dangling nodes, which in turn subdivides a few adjacent elements apart from the master element to be divided.
A bandwidth reduction algorithm has been applied in order to keep the bandwidth of the system as small as possible for efficient memory
management and minimizing computational time.
|
|
Click here for a PowerPoint presentation demonstrating the mesh adaptation.
|
