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Bend Functions Precision Sheet Metal Workshop

If it’s not Black Magic, and it’s not the old guy keeping the tricks of the trade to himself.

Then where do we begin?

Rosetta Stone

With a common language!

•Bend Deductions or K-factors?

•X-factor or Outside Setback?

•Z-factor or Inside through the material?

•What’s a Bend Allowance?

First, let’s look at Bend Deduction charts...

Are they valid?

What are they?

Do they work?

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As a bend is made the material elongates!

The flat measurement is always less than the sum total of the outside dimensions of that part.

Standard Bend Deduction Charts

Air form radius

Bottoming radius

Material thickness

Bend deduction

Chart .032 radius in .062 material

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Five charts found at random. 1/32 Radius in .062 material 5 different answers; what’s up with that?

Chart .062 radius in .062 material

Five charts found at random. And again… different answers!

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1/32 single

Charts, bend deductions, and single bend parts

1/16 single

Multi-bend parts

1/32 Radius in .060 material

1/16 Radius in .060 material

For 1/16 radius the total difference was .090

For 1/32 radius the total difference was .117

So which is right?

All of them Dude!

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As a general rule the customer may call a 1/32 radius, but, a 1/16 radius will pass if that’s how it works out… right?

Yeah, its no big deal… Right?

•Increasing production

•Decreasing the inherent errors

•Increasing Engineering's part in the ease of manufacture

Even if the customer doesn’t care

we should, why? Here’s just a few of the reasons:

What is the operators ability to produce the part?

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Tooling… What do I have? What do I need? What will the results be?

What about the type of bend?

Sharp

Radius and

Profound radius bends.

Air, bottom or coin

Bending methods effect it

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With air forming, the radius is derived as a percentage

of the V-die width.

For example:

Another source of error…. Inconsistent V-die width selection.

Different widths, different radii

.100 material thickness

Die used = .685

.100 inside radius

Bend deduction = .172

Example 1

Die width effects

.100 material thickness

Die used = 1.000

.150 inside radius

Bend deduction = .272

Example 2

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Air form radius

Bottoming radius

Remember this Bend Deduction Chart?

Too much material removed… part will be short. Don’t remove enough, part will be long..

Regardless of method “A is A”

In a speech by John Gault from Atlas Shrugged he states: “A is A” and can only be “A”…

1/32 is 1/32….

And that concept applies to sheet metal too…

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Just as with mathematics, we need to say the same thing, in the same way, with the same meaning!

So… how do we get there from here?

With a common language and common mathematics

K - factor (Lockheed- Martin) is the same as a Bend Deduction (BD)

The K - factor works with the neutral axis and is .446 in Cold Rolled Steel

X - factor is the same as OutSide SetBack (OSSB)

Bend Allowance (BA) = Bend Allowance (BA)

Compression of material on the inside of the bend

Expansion of material on the outside of the bend

Neutral axis, where no change occurs

Neutral axis

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Compression and Expansion… The root cause of Springback

The length of the bend as measured along the neutral axis of the material.

What are .017453 and .0078?

/ 180’ = .017453

( / 180’ ) x K = .0078

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Bend Allowance is always calculated using the complementary bend angle

The Neutral Axis does not change its length… It simply movers closer to the inside surface.

Causing the bend to “gain” length

K-Factor and Machinery’s handbook

If you really need to know where the neutral axis is located by material type this is the place.

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Outside setback: Where the radius begins to the apex of the bend.

OSSB = (Tangent ( / 2)) * (Mt + Rp)

The Bend Deduction is difference between twice the outside setback and the bend allowance.

Inside through the material (ISTM) The distance between the outside apex and the inside

apex

ISTM = (Tangent ( / 2)) * Mt

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Inside OffSet The distance between the inside apex and the center of the radius

Outside offset The measurement from the surface of the outside radius to the apex.

Included angle

OSOS = ((Rp + Mt) / (tangent ( / 2)) - (Rp + Mt)

The leg…any flat area, between bends or edge to bend.

leg

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Multi-breakage The leading radius prevalent

in large radius bends!

We’ll talk about this one later...

There are three distinct types of bends...

Sharp bends with radii less than 63% of the material thickness

Radius bends from 63% to 10 times the material thickness

Profound radius bends with bend radii greater than 10 times the material thickness

A sharp bend is a function of the material and not the radius of the punch tip.

A bend radius turns sharp at 63% of the material thickness.

Sharp = Mt * .63

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How it all fits together

Sharp = Material thickness x .63

BA = Bend Allowance OSSB = OutSide SetBack BD = Bend Deduction

Mt = Material Thickness Rp = Radius of punch or inside radius

They’re in the back of your book

Mt = .036 Rp = .032 Bend Angle = 90°

Bend Functions - Work problem #1

Where it turns sharp: Is it sharp?

Bend Allowance (BA) =

Outside setback (OSSB) =

Bend Deduction (BD) =

No

Actual usable radius =

.022

.032

.075

.068

.060

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Bend Functions - Work problem #2

Mt = .062 Rp = .032 Bend Angle = 90°

Bend Allowance (BA) =

Outside setback (OSSB) =

Bend Deduction (BD) =

Yes

Actual usable radius =

.039

.039

.104

.101

.097

Where it turns sharp: Is it sharp?

Bend Functions - Work problem #3

Mt = .062 Rp = .032 Bend Angle = 45°

Bend Allowance (BA) =

Outside setback (OSSB) =

Bend Deduction (BD) =

Yes

Actual usable radius =

.039

.039

.052

.041

.031

Where it turns sharp: Is it sharp?

Bend Functions - Work problem #4

Mt = .062 Rp = .015 Bend Angle = 110°

Bend Allowance (BA) =

Outside setback (OSSB) =

Bend Deduction (BD) =

Yes

Actual usable radius =

.039

.039

.128

.146

.163

Working from Complementary Angles

Where it turns sharp: Is it sharp?

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Bend Functions - Work problem #4 included

Mt = .063 Rp = .015 Bend Angle = 70° (110 °)

Bend Allowance (BA) =

Outside setback (OSSB) =

Bend Deduction (BD) =

Yes

Actual usable radius =

.039

.039

.128

.071

.012

Where it turns sharp: Is it sharp?

Past 90-degree bends Working Included angles

(BD) .012 @ 70

2) Leg (1.000) + OSSB (.071) = 1.071 x 2 = 2.142 BD - .012

flat = 2.130

1) Leg + leg + BA = 2.128

3) Leg (1.000) + OSSB (.145) x 2 = 2.290 BD - .163

flat = 2.127

Leg = 1.000 @ 110* comp.

Material .063 Bend radius inside = .039 Bend angle 110 complementary

(OSSB) .145 @ 110

(BA) .128

(OSSB) .071 @ 70

(BD) .163 @ 110

(BA) .128

Material .250 Bend radius inside = .250 Bend angle 135 complementary Bend Allowance (BA) = [(.017453 x Rp) + (.0078 x Mt)] x degree of bend angle (complementary) [(.017453 x .25) + (.0078 x .25)] x 135 [ .00436325 + .00195] x 135 .00631325 x 135 = (BA) .852 Outside setback (OSSB) = [ Tan(degree of angle/2)] x (Mt + Rp) (angle is included) [Tan (45/2)] x .5 [Tan 22.5] x .5 .4142 x .5 = (OSSB) .207 Bend Deduction = (OSSB x2) – BA (.207 x 2) – .852

.414 – .852 = -.438 Bend Deduction (note: negative value, add to flat) 1.207 x 2 = 2.414 edge to apex [(1.000 + OSSB of .207) x 2] + .438 Bend Deduction 2.852 Calculated Flat blank

Bend Deductions can also be a negative value when working with the included angle

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[Tangent (/2)] x (material thickness + Inside radius)

(Material thickness + Inside radius) / [Tangent (/2)]

written using the included angle of the bend .

So which is right?

Different formulas, same answer!

.124 / .577 = .214

Material (Mt) + Inside radius (Rp) = .124

[Tangent (/2)] x (material thickness + Inside radius)

(Material thickness + Inside radius) / [Tangent (/2)]

1.732 x .124 = .214

[Tangent (120/2)] = 1.732 [Cotangent (60/2)] = .577 Mt + Ir = .124

•[Tangent (c/2)] x (material thickness + Inside radius) 1.732 x .124 = .214 •[Cotangent (i/2)] x (material thickness + Inside radius) 1.732 x .124 = .214 •(Material thickness + Inside radius) x [Tangent (c/2)] .124 x 1.732 = .214 •(Material thickness + Inside radius) x [Cotangent (i/2)] .124 x 1.732 = .214 •(Material thickness + Inside radius) / [Tangent (i/2)] .124 / .577 = .214 •(Material thickness + Inside radius) / [Cotangent (c/2)] .124 / .577 = .214

Multiple Formulas

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For bend angles greater than 90-degree the original formula may also be written using the included bend angle.

BD = (OSSB x 2) – BA = BD where the BA equals .187 (.071 x 2) - .187 .142 - .187 = -.045-in

Using the same numerical values we’ve been working with.

Flat dimension: Leg 1.000 + OSSB .071 + Leg 1.000 + OSSB .071 + .045 = 2.187-in.

OSSB = [Tangent (i/2)] x (Mt+ Rp) .577 x .124 = .071

This Bend Deduction is negative, add value to the flat

Metric vs.

Imperial when bottoming

Imperial radius = .032 BD = .060

Metric radius = .030 BD = .059

Note: Metric values are given as their imperial decimal equivalent

Imperial radius = .125 BD = .100

Metric radius = .118 BD = .097

.003 different

Metric vs.

Imperial when bottoming

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Conclusions:

If you can define the inside radius...

And … If you can achieve that radius...

“You can calculate valid bend deductions (BD’s),

you can create valid flat patterns!”

We can do this!