in this video I will show you how to derive an equation that can determine
the theoretically optimal V size given material thickness inside radius and
bending with so many variables to consider sheet metal air bending is
sometimes considered in art as this video will show however that is not
usually the case one key variable is die opening or v-size it affects the
radius of the bend, which in turn affects the event deduction, which in turn
affects the accuracy the flange lengths, and ultimately the quality of the
finished part. for this reason it is important to have a standardized method
for V size selection many are guided by rules of thumb travel knowledge or
gut feelings as we know these can be dangerous in that they may produce
inaccurate or more importantly varying results from operator to operator
luckily there is a way to determine the optimal visa is given a few key
parameters so as I said there are a number of rules of thumb out there which
guide the selection of veto size common ones that I've heard are six seven or
eight times of material thickness I've even heard all the way up to 10 or 12
times material thickness so this right there tells us that these rules of thumb
are open to guessing their variation or difference of opinion again this is
important because changing the V size directly affects the bend it is one of
the key variables especially in area another issue is these rules of thumb do
not work for radius bends where the radius is greater than one maybe two
times material thickness for example what if you need to use a quarter inch
radius in .060"? material how would you determine the
correct die opening to use if you tried taking eight times the material thickness you
would select the die opening around .480" this would
result in a very tight fit requiring a lot of tonnage and the contact points be
very high and the die walls where the die is weakest. Before I get into the
mathematical solution I want to give credit to Steve Benson's fabricator
article where I learned this method which I'll link up in the description so
check that article out and check out anything else by Steve Benson he if is a
sheet metal forming expert and puts out a lot of great information on these
topics so definitely go and check out his work as well all right since rules
of thumb don't always work how do we determine the optimal V size well the
optimal V size would be when the outside setback (OSSB) of the bend is equal to
1/2 of the V wall [Length] in other words the tangent point of the outside radius is
exactly at this halfway point in the die. this point is optimal for a few reasons
without going into too much detail if we think about the forces going into the
bend the smaller the die the more force is required to bend the material because
the moment (leverage) in the middle of the material decreases making it harder to bend if we
go too big in a sense we are under utilizing the strength of the die and
we'll end up using a diet that's unnecessarily large for the required
Bend using this method also yields good Bend geometry and helps avoid sharp or
parabolic Bend geometries caused by excessive force and you can read about
those types of bends or those phenomenon and Steve Benson's writing lastly using
this method standardizes the relationship between punch die opening
and material thickness this means that the K factors theoretically will remain
more consistent between varying setups so now that we know why this point is
optimal we can just use some basic trig to derive an equation that will give us
the numbers we're looking for as with many trig problems there is more than
one way to go about this but I'll show you the way that I prefer first let's
look at a simple 90 degree Bend the starting point and first triangle we
will need to use to solve this problem looks like this where we know what the
length of this leg is the inside radius plus the thickness then we can use this
triangle to solve for this larger triangle whose hypotenuse is equal to
the optimal V size opening or die opening first we should recognize that
since this is a 90 degree Bend these are 45-45-90 triangles meaning the two legs
are equal this means that both legs of this triangle are equal to the inside
radius plus the thickness again because these are 45-45-90 triangles we can see
that this leg is half the length of the larger leg so the length of the larger
triangle is two times the inside radius plus the thickness once we know this
it's just a matter of using the Pythagorean theorem to solve for the
hypotenuse which is again what we're after so if we plug in our variables to
the Pythagorean theorem and do a little bit of algebra we get the simplified
equation for solving for the optimal die opening size of a 90 degree bend
but what if the Bend is not 90 degrees notice here we have an over bend. The cool
thing about this method is that I have found it works very well for bends of
any angle with the right math even with acute or obtuse bends, this method still
works and you may be thinking if I wanted to over bend a piece of material
to a 60 degree inside angle I probably would use a 30 degree die to do it and
you're correct many over bend dies are 30 degrees but this method still works
because even though the die is 30 degrees in material will be floated to whatever
the desired Bend angle is since we were talking about air bending here so it's
almost like we can pretend the die would be the same as the bend angle its
kinda hard to explain but I promise this method does work for bends of any angle
so with an acute or obtuse Bend we will still use the same halfway point on the
die wall as a reference for the optimal die opening the only difference is the
trig is a little bit trickier since we aren't using a 45-45-90 triangle I'll be
using an acute angle Bend [as an example ] to derive this equation even though again it works for
bends of any angle in order to solve for the V or die opening size first let's
start again with what we know starting with the smaller inside triangle we know
the short leg is equal to the inside radius plus the material thickness we
also know that one angle of the smaller inside triangle will be one half the [inside]
bend angle with the larger triangle we know, W, the hypotenuse will be twice the
long leg of the inside triangle and the short leg of this larger triangle will
be half of V the die opening size we're looking for once we know these things we
can just use some basic trig functions to solve for V going back to the
pneumonic from high-school sohcahtoa it can solve for W by setting the tangent
of our triangle equal to the opposite over the adjacent leg in our case we
would set the tangent of half the bend angle equal to the inside radius plus
material thickness over one half of W what's some algebra this can be
simplified to this equation where we solve for W now that we have an equation
for W we want to solve for V by setting the sin of our angle equal to the
opposite leg over the hypotenuse which is W in our case we would set sin of
one-half the bend angle equal to 1/2 of V or the
die opening over W again using some algebra magic we can simplify this to a
more easily digestible equation and this would be the final equation we can use
to solve for the optimal die opening giving any combination of thickness
radius and bend angle so hopefully this gives you a good standardized method of
die size opening selection in the next video on this topic we'll show you how
to implement this in Excel and create a reference matrix sheet that can be
distributed to shopfloor whoever needs this information again this is something
that I use in practice since learning about this method we have implemented it
at my company and have seen pretty good results as long as this method is
followed I'm curious to hear how your company does things and if you think
this is overkill this is something that should be standardized or should be left
up to operators to make these decisions how could designers utilize this
information to get a better understanding of how other parts will be
made let me know in the comments below and if you're new to the engineering
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check it out and as always thank you so much for watching and we'll see you next
time