Table of Factors
and Terms For Bending Formulas 
B = degree of bend
E = feathered edge thickness
F_{b} = bend difficulty factor
F_{d} = "D" of bend
F_{w} = wall factor
K_{r} = constant for rigidity
K_{s} = constant for minimum clamp
length
K_{z} = constant for feathered
edge 
L_{c} = clamp length
L_{p} = pressure die length
M_{b} = mandrel ball diameter
M_{d} = mandrel nose diameter
M_{m} = mandrel body diameter
M_{r} = mandrel nose radius
P_{e} = percentage of elongation
at arc
P_{t} = percentage of
wallthinning
P_{w} = wall thickness after
thinning 
R = centerline radius
R_{i} = inside radius
R_{o} = outside radius
S = maximum setup depth
T = tube outside diameter
T_{i} = tube inside diameter
W = wall thickness
W_{i} = thickness of inside
lamination
W_{o} = thickness of outside
lamination 

Tube inside diameter:
T_{i}
= T  ( W x 2 )

Inside radius:
R_{i}
= R  ( T / 2 )

Outside radius:
R_{o}
= R + ( T / 2 )

Wall factor:
F_{w}
= T / W

"D" of bend:
F_{d}
= R / T

Bend difficulty rating (the higher the
value, the more difficult the bend is to make; rule of thumb only):
Where "K_{r}" = a constant for
material rigidity (assign the same value to "K_{r}" as you would
to calculate pressure die length; a value of 2 is suitable for most
applications; click here for more information) and "n_{1}"
through "n_{4}" are values to adjust the weight of each factor
in the equation (see below for our recommended weighting):
General formula:
F_{b} = [ ( n_{1} x K_{r} ) + ( n_{2}
x F_{w} ) + ( ( n_{3} x B ) / 180 ) ) ] / [ n_{4}
x F_{d} ]
Formula with recommended weighting:
F_{b} = [ 2K_{r} + .2F_{w}
+ ( B / 180 ) ] / [ F_{d} ]
Note: A bend difficulty rating (calculated
with our recommended weighting) of 7 or less indicates a bend that is
relatively simple to produce with the rotarydraw method. Factors in
excess of 7 typically require either additional precision in setup or
close attention during production in order to hold the setup
parameters.

Wallthinning of extrados at outside
radius after bending (rule of thumb only):
Where "P_{t}" = percentage of
wallthinning and "P_{w}" = targeted thickness of wall after
thinning out from bending:
P_{t} = ( R_{o} 
R ) / R_{o}
P_{w
}= W x ( 1  P_{t} )

Percentage of elongation at arc of the
bend (rule of thumb only):
P_{e}
= ( R_{o} / R )  1

Mandrel nose diameter
for singlewall tubing:
M_{d}
= T  ( W x 2.21 )

Mandrel nose diameter for doublewall
tubing:
Where "W_{o}" = wall thickness of
outside lamination and "W_{i}" = wall thickness of inside
lamination:
M_{d}
= ( T  ( W_{o} x 2 ) )  ( W_{i} x 2.21 )

Mandrel nose radius:
if F_{w}
< 50 then M_{r} = M_{d} x .1 else M_{r} = M_{d}
x .02

Mandrel body diameter:
M_{m}
= M_{d} x .995

Mandrel ball diameter:
M_{b}
= M_{d} x .998

Maximum
setup depth of mandrel nose relative to the
line of tangency, as measured from nose end (including nose radius):
S = [
( R + ( T / 2)  W )^{2}  ( R + ( M_{d} / 2 ) )^{2} ]^{1/2}
+ M_{r}

Wiper feathered edge thickness
(simplesweep geometry only):
Where "K_{z}" = a constant
approaching zero depending upon limitations of material and method of
manufacturing (with current technology, a value of .0025 is reasonable
for "K_{z}"):
if T x K_{z}
> .006* then E = T x K_{z} else E = .006*
* Inches. For metric applications,
substitute .15 millimeters.

Clamp length:
Where "K_{r}" = a constant for
material rigidity (assign a value of 2 to "K_{r}" for most
applications; click here for more information) and "K_{s}" = a
constant limiting the minimum clamp length depending upon the surface of
the cavity (assign to "K_{s}" the value of 2 for smooth cavities
and 1 for serrated cavities; click here for more information):
if ( T x (
K_{r} x 2.5) )  R < T x K_{s} then L_{c} = T x
K_{s} else L_{c} = ( T x ( K_{r} x 2.5) )  R

Pressure die length:
Where "K_{r}" = a constant for
material rigidity (assign a value of 2 to "K_{r}" for most
applications; click here for more information):
L_{p} = ( R x
3.14 x ( B /
180 ) ) + ( T x K_{r} )
Springback
and radial growth:
We are
frequently asked for formulas to calculate
springback and
radial growth. While there
are rules of thumb  e.g., a radius will increase 1% for every "D" of
bend  they are not effective, as a true formula would be, in
reducing the proveout needed to lock in the parameters of a machine
setup.
Unfortunately, effective formulas for springback and radial growth
have not been developed, because the factors involved include not only
tube and bend specifications but also machine settings  especially
the radial pressure and axial pressure applied by the pressure die to
the tube and the placement of the mandrel nose relative to the line of
tangency. How an operator sets these things on a particular make
and model of machine alters where the
neutral axis of a tube bend lies in
relationship to the centerline of the radius, and it is the location
of the neutral axis that determines how much springback and radial
growth there will be. Moreover, springback and radial growth are
the result of fundamentally nonlinear processes, which would make any
effective formula that does account for all these factors fairly
complex. Presently, finite element analysis (FEA) is the only
tool up to this task, and it is not yet practical for everyday use in
the bend shop.
Fortunately,
the trialanderror needed to adjust for springback and radial growth
does not have to be repeated for every setup of a tube bend. By
using the "FourStep SetUp Method" to
employ the "forward mandrel, low pressure" setup for rotarydraw
tubebending, the parameters of a successful setup can be recorded
and then duplicated with little or no trialanderror to prove out
future setups of the same or similar tube bends.
