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Appendix 1 : Shear and Strain Explanation
Shear Control
The Base window of the stage is rotated using a 1.8° stepper motor that has 200 steps per revolution
(360°/1.8°). Using a technique called “micro stepping” these 200 steps may be divided up into even smaller
steps for better positioning and lower resonance. Each motor step is broken up into 256 steps giving a resolu-
tion of 256x200 = 51200 micro steps per revolution
The shear motor drives the window carrier through a toothed belt to give a 4:1 velocity ratio so that for a win-
dow carrier velocity of 1 revs/sec the motor has to turn at 4revs/sec. This also means that the highest resolu-
tion in micro steps of the window carrier is 51200x4 = 204800.
The shear rates and strain values are defined below. Most Rheology systems use these.
Shear Rate
The shear rate is related to the rotary velocity at the centre of the heater aperture where the transmitted light
passes. It is defined as rw/d where w is the angular velocity in rads/sec, d is the gap setting in mm and r is the
observation radius (see below).
The shear rate is used to
specify the velocity for the
step and the steady modes and is limited to the range 0.001 to 10rads/sec. This velocity range will also affect
the range of values available in the oscillatory mode, as it is the frequency and amplitude that dictate the angu-
lar velocity.
Strain (Shear) value
The strain is related to d and the observation radius r and is entered as a percentage value from 0.1 to 40000%.
For a given gap setting d the angular displacement x gives the Strain or Shear = x/d = rØ/d. When entering the
Strain value, d and r are known, so Ø may be calculated and converted to an angular movement in motor steps.
Therefore the strain sets the angular distance in the step mode and the amplitude in the oscillatory mode.
E.g. In step mode a strain value of 1 at a gap setting of 500mm gives an angular distance of:
1x500/7500 = 0.066rads or 3.8°
This angular distance is then converted to a number of motor steps. In the oscillatory mode there is a limit of 2
rads for the Strain value.
Observation Radius
The radius from the centre of the bottom window to the centre of the hole in the heater block (aperture) is
7.5mm. The aperture diameter is 2.8mm.
At the observation radius r (7.5mm) the angular rotation Ø gives the displacement x = rØ. The gap setting is d
and is specified in mm, Ø is in rads.
