Metric Units US Units    Text   
Steel Aluminum Low Composite Med. Composite High Composite
Dead Shaft Live Shaft     Cantilever Roll
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Definition of Angles
Angles are defined with 0 at the top. Gravity is assumed to act at 180° and is shown with a black arrow. For the other 2 effects the angle is defined in terms of the physical location of the force.

So if the web is specified at 90° and 270° they are (as shown by the arrow heads) pointing downwards, providing a net force in the 180° direction. No attempt is made to sort out strange wraps - if things look wrong, they are wrong and you need to fix them.

If the Nip is specified at 0° then it is pushing down from the top with a net force in the 180° direction. These forces might act with or against each other so the overall deflection and the angle in which it is deflected is the vector sum of the three components. The angle of this vector is given and is shown in red. If the overall deflection is straight down then the angle is 180° and so forth.

Summary of Inputs and Outputs
Inputs
Web LoadLoad (Tension) of the web (kg or lb). This is doubled because of the incoming/outgoing webs
Nip LoadLoad applied by the Nip (kg or lb)
Web Direction in which the web is pulling the roller
Nip AngleAngle from which the nip is pushing the roller
Roller ODOuter diameter of the roller shell (mm or in)
Roller IDInner diameter of the roller shell (mm or in). If accidentally entered as larger than OD, a shell of 1mm thickness is used in the calculation.
FaceFace width of the roller (mm or in). The Loads are divided by this value - i.e. the web is assumed to cover the full Face width of the roller
Brg-BrgTotal width of the roller including bearings (for Live rollers). If this is less than Face then the Dead Shaft calculation is used
Steel, Al, Low, Med, Hi CompositeChoice of material for roller shell. The moduli used are respectively: 200GPa, 69GPa, 100GPa, 165GPa, 270GPa. Although the composites are comparable to steel in modulus, they are ~5x less dense so bend far less under their own weight. Al is much less strong but 3x less dense than steel so the trade-off is more marginal.
DeadA Dead Shaft roller so the deflection applies only to the Face Width
LiveA Live Shaft roller so the deflection applies to the Brg-Brg width
Outputs
DeltaDeflection of the roller (µm or mil)
D/F ClassDeflection/Face width x 1E6 plus the Class
AngleDirection in which net force is acting
React.Reaction on bearings, i.e. Resultant/2 of the combination of loads
Vectors
ForcesDirections colour coded to match text
Cantilivers
If the Cantilever option is selected then two extra variables appear and Roll load can take on a new meaning:
Shaft LengthLength of the (steel) shaft supporting the cantilever roll
Shaft ODOD of the (solid steel) shaft supporting the cantilever
RollWhen selected the Nip load is the weight of a real roll, Angle is set to 0
Dead/LiveThese are disabled, only the Face length is used in the calculation
D/F Class
According to Dr Roisum in The Mechanics of Rollers, the ratio of Deflection over Face Length (D/F) can be used to define a Class of rollers. For ease of viewing, D/F is multiplied by 1E6 and the Class is defined as:
D/FClassMeaning
<80APrecision or nipped applications
<150BGeneral purpose rollers
<300CTissues, nonwovens and thick materials
<600DConveyer belts, spreaders, cores...
HigherXMay be unsuitable for web applications