bend allowance formulas

UP

BEND ALLOWANCE FORUMLAS

By Ronald W. Leigh, Ph.D.

December 5, 2008Copyright 1994, 2006 Ronald W. Leigh

This paper explains the formulas used by the Bend Allowance Calculator.

Drawings of sheet metal parts usually show the part in its finished (bent) state. However, the designershould supply information about the layout of the flat sheet stock before it is bent, which requires thecalculation of the amount of material used at each bend. This amount of material at each bend is referredto as the bend "allowance." The individual bend allowances are shown in a developed (flat) view of thepart which can thus include overall dimensions and the locations of key features prior to bending.

A. The Formulas

The bend allowance for any bend is the length of the neutral arc, as shown below. This neutral arc can becalculated from the material thickness (T), inside radius (R), and the angle through which the material isbent (A).

The neutral arc, in a side view of the bend, represents the theoretical cylindrical plane of material that isneither stretched nor compressed. The material on the outside of this plane is stretched, while the materialon the inside of this plane is compressed. But the length of this arc is the same before and after bending.

This plane occurs a certain fraction of the material thickness into the material measured from the insidesurface. This fraction ranges between 1/4 and 1/2, but is never greater than 1/2. For rough calculations,some designers use a fixed fraction for all bends (such as .3, or .333, or .4). However, the fraction actuallyvaries from one bend to the next because the fraction depends on the ratio between the size of the insideradius and the thickness of the material. The fraction is closer to 1/4 when the the bend is "profound" or"tight," that is, the inside radius is relatively small and the material is relatively thick. The fraction movesfrom 1/4 toward 1/2 as the radius gets larger or the material gets thinner.

The first formula below provides a fraction (K) that is based on experimental results with soft steel asreported in various reference manuals.

Bend Allowance Formulas http://ronleigh.com/ivytech/_ref-ba.htm

1 of 4 10/10/2012 7:09 AM

FIRST FORUMLA (applies to soft steel)

K = ((R/T)/16) + .25 (K never greater than .5)

The above formula applies to "medium hard" materials such as soft steel and aluminum. For softermaterials such as soft copper and soft brass replace the .25 with .21. For harder materials such as hardcopper, bronze, CRS, and spring steel, replace the .25 with .28.

After K is determined, a second formula is used to calculate the bend allowance.

SECOND FORUMLA

Bend allowance for any angle = A (R + KT) / 180 Thus, the bend allowance for a 90 angle = (R + KT) / 2

These formulas can be used whether you are working in inches or millimeters. The derivation of bothformulas is explained at the end of this article.

B. Print Reading Pitfalls

Four cautions are necessary when working with sheet metal drawings and calculating bend allowances.

Thickness: Because of the variety of sheet metal gages used in the past, use the actual decimalthickness, which should appear on the drawing along with the gage.Straight sections: Straight sections are measured only up to the center of the bend radius (not themiddle or "center" of the actual bend). Any dimensions on straight sections which go beyond thecenter of the bend will have to be adjusted by subtracting the inside radius and perhaps the materialthickness.Radius: Since the designer is free to dimension sheet metal bends either on the inside or the outside,remember that both formulas above require the inside radius.Angle: Be careful how you interpret angular dimensions on a sheet metal drawing. The angleneeded for the second formula above is the angle the material actually bends through, which may notbe the same as the angle dimensioned on the drawing. For example, in the following drawing, thedimensions are correct in the sense that they define the bends. However, none of the numbersshould be used for A in the second formula.

For the angle on the left, don't use 20. Instead use 90 - 20, that is, 70For the angle on the right, don't use 30. Instead use 90 + 30, that is, 120For the angle on the right, don't use 60. Instead use 180 - 60, that is, 120

C. Inaccurate Tables in Machinery's Handbook


2 of 4 10/10/2012 7:09 AM

The three bend allowance tables in the Machinery's Handbook (Industrial Press) are based on threedifferent formulas which use a constant fraction K for each different material.

For soft materials such as soft copper and soft brass, K is always .350.For medium-hard materials such as soft steel, K is always .408.For hard materials such as bronze, CRS, and spring steel, K is always .452.

The fact that these tables do not recognize variations in K (as the radius and the thickness change) makesthem unacceptably inaccurate. The use of a different K for different radius bends (determined by the firstformula above) yields much more accurate results.

D. Other Sources of Inaccuracy

Even when using the more accurate fraction K from the first formula above, we must keep in mind that anyformula based on experience is still only a theoretical approximation. In the case of sheet metal bends, theabove formulas do not take into account several facts.

The thickness of the material changes slightly at the bend.The center of the neutral arc is not exactly coincident with the center of the inside radius.Material deformation (stretching and compressing) is not entirely limited to the theoreticalboundaries of the bend.The neutral plane does not form a perfect cylinder, but "bells out" at its edges (this effects bends invery narrow strips more than wide strips).

Even so, the error introduced by these factors is far less than the error introduced by the assumption of aconstant K.

However, there are many production factors which can affect the actual amount of material used in a givenbend.

True material thickness may vary from the specification.Certain production methods will stretch the material more than others.Forming tools may not bottom completely, producing inaccurate bends.Multiple bends done in one operation may trap panels and thus increase elongation.Temperature and direction of grain affect the bend allowance.

Since the designer usually cannot control these factors, he/she must offer the best general estimate possibleand expect those who fabricate the part to know how to compensate for these factors as needed. See thefollowing articles:

S. M. Adams, Bend Allowance OverviewOlaf Diegel, Bend Works: The fine-art of Sheet Metal Bending

E. Derivation of the Formulas

First formula

The first formula is based on experience rather than purely on mathematics. By plotting experimental datawe can construct a suitable formula. Here is the data reported by Pollack and Ostergaard.


3 of 4 10/10/2012 7:09 AM

Herman Pollack,Tool Design, 2nd ed.,Prentice Hall, 1988,

page 465

If R < T then K = 1/4If T

bend allowance formulas

Documents