Upper Height Function Constants#

Upper Height Function Constants = {model_name} <floatlist>

Description / Usage#

This card takes the specification of the upper-height function for the confined channel lubrication capability, or the lub_p equation. This function specifies the height of the channel versus distance and time. Currently three models for {model_name} are permissible:

CONSTANT_SPEED

This model invokes a squeeze/separation velocity uniformly across the entire material region, viz. the two walls are brought together/apart at a constant rate. This option requires two floating point values

<float1> the separation velocity (rate) in units of length/time

<float2> the initial wall separation in units of length

<float3> An OPTIONAL parameter which scales the addition of an external field called “HEIGHT” which is read in using the External Field or External Pixel Field capabilities. If this field is present, the value of it is added to the height calculated with this model.

ROLL_ON

This model invokes a squeeze/separation velocity in a hinging-motion along one boundary. The model is best explained with the figure in the technical discussion section. The equation for the gap h as a function of time and the input parameters (floats) is as follows:

<float1> is x0 in units of length

<float2> is hlow in units of length

<float3> is h Δ, in units of length

<float4> is the verticle separation velocity (if negative then squeeze velocity) in units of length/time

<float5> is the length of the plate, L.

ROLL

This model is used for a roll coating geometry. This option requires 8 floats:

<float1> x-coordinate of origin, L.

<float2> y-coordinate of orgin, L.

<float3> z-coordinate of origin, L.

<float4> Direction angle 1 of rotation axis

<float5> Direction angle 2of rotation axis

<float6> Direction angle 3of rotation axis

<float7> rotation speed L/t.

FLAT_GRAD_FLAT

This model used two arctan functions to mimic a flat region, then a region of constant slope, then another flat region. The transitions between the two regions are curved by the arctan function. This currently on works for changes in the x direction. This option requires five floating point values

<float1> x location of the first transition (flat to grad)

<float2> height of the first flat region

<float3> x location of the second transition (grad to flat)

<float4> height of the second flat region

<float5> parameter controlling the curvature of the transitions

POLY_TIME

This time applies a time-dependent lubrication height in the form of a polynomial. It can take as many arguments as GOMA can handle, and the resulting height function is

<floati> value of Ci

JOURNAL

This model simulates a journal bearing. It is intended to be run on a cylindrical shell mesh aligned along the z axis and centered at (0,0). It could be extended to be more flexible, but this is all it is currently capable of. The height is defined by

h(θ ) = C(1+ε cos(0))

Where C is the mean lubrication height and is the eccentricity of the two cylinders, with the smallest gap in the –y direction.

<float1> C

<float2> ε

EXTERNAL_FIELD

Not recognized. Oddly, this model is invoked with the extra optional float on the CONSTANT_SPEED option.

External Field = HEIGHT Q1 name.exoII (see this card)

Examples#

Following is a sample card:

Upper Height Function Constants = CONSTANT_SPEED {v_sq = -0.001} {h_i=0.001}

This results in an upper wall speed of 0.001 in a direction which reduces the gap, which is initial 0.001.

Technical Discussion#

The material function model ROLL_ON prescribes the squeezing/separation motion of two non-parallel flate plates about a hinge point, as shown in the figure below.