From time to time, we get a question wanting to compare the Machinery Handbook Bend Formula to the Solid Edge use of Neutral Factor and the PZL. Many designers are accustomed to consulting the Machinery Handbook to get bend allowances; others have their own allowance table defined by years of experience. In Solid Edge you calculate bend allowances either by using the standard PZL (Plastic Zone Length) formula or creating a table that defines the bend allowances for each thickness and radius combination.  We will not get into the creation of tables in this article, but we will discuss how to accurately define the Neutral Factor for the Solid Edge PZL formula for those accustomed to using the Machinery Handbook formulas and tables.

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The formula in the Machinery Handbook (MH for short) is the result of many years of experience in bending materials. The way it is presented is:

L = (0.55 x T) + (1.57 x R)   For 90 degrees bend, using soft brass or soft copper.

L =(0.64 x T) + (1.57 x R)     For 90 degrees bend, using half-hard copper and brass, soft steel and aluminum.

L =(0.71 x T) + (1.57 x R)     For 90 degrees bend, using bronze, hard copper, cold-rolled steel and spring steel.

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Where:

L - Bend allowance or bend length.  It is the length of the bend on the flat.

R - Bend Radius.

T - Thickness of the material.

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As you can see, there is a factor in the formula that changes depending on the material and defines how much bend allowance is going to be added to the mathematical length of the bend. We will call this factor, MHF, or Machinery Handbook Factor for the calculations we will make below.  If we use the MHF on the above formulas, they all could be written as:

L =(MHT x T) + (1.57 x R)     Where the material being used defines MHF.

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Now, looking at the Solid Edge PZL (Plastic Zone Length) formula below, one can see we do calculate the actual length of the bend at the neutral plane, which does not shrink or grow during bending. In this formula, a particular parameter defines where the neutral plane is located for each material and thickness. It is called Neutral Factor. Here you have to enter the Neutral Factor for the material based on your own experience to obtain the PZL or bend allowance. This method of calculation is widely used amongst CAD vendors.

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Or for 90-degree bends:

PZL= 1.57 x (R + (NF x T))

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Where:

PZL - Plastic Zone Length.  It is the length of the bend on the flat.

R - Bend Radius.

NF - Neutral Factor (value between 0 and 1, defines the neutral fiber for each material).

T - Thickness of the material.

BA - Bend angle, normally 90 degrees.

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New Sheetmetal CAD users tend to not have much experience with the term, Neutral Factor. In fact, seems that quite a number of them had never even heard the term before.

The following exercise will give users a way to calculate the Neutral Factor, using the Machinery Handbook values they are used to. This is not an exact procedure and will not totally make the values from the Machinery Handbook match the results in Solid Edge, but in most cases they are as close as 0.001 inch from each other. Most are generally a sufficient tolerance for sheet metal formed parts.

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If both formulas are calculating the length of the bend, we can assume they should be equal. Making the two equations equal we have:

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Solving this for NF, you will get to a very simple formula:

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This formula will assume different values for the different MHF set on the formulas in the beginning of the article.

For 90 degrees bend, using soft brass or soft copper.

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For 90 degrees bend, half-hard copper and brass, soft steel and aluminum.

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For 90 degrees bend, using bronze, hard copper, cold-rolled steel and spring steel.

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That is basically it. If you use this formula, you will get pretty close to the Neutral Factor you want to use in Solid Edge to get the results you were used to with the Machinery Handbook. Again, they might be a little off here and there, but should be within your manufacturing tolerances.

To wrap up, here is a small table with some values comparing the Machinery Handbook tables and the Solid Edge PZL formula, after calculating the Neutral Factor per above formula:

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Note: Taken from the GTAC website. Article written by Marcelo Martins.