There are a number of different broaching calculations which must be developed accurately, in order to conduct a successful broaching operation. In most cases, engineers will develop these calculations for your company, because they have the knowledge and the expertise to figure out exactly what’s called for.

Given the fact that broaching generally calls for extremely small tolerances and precise cuts, it is essential for such calculations to be performed with precision and accuracy.

Some of the most important types of calculations necessary for a standard broaching operation are described below. In order to avoid getting bogged down with technical jargon, these calculations are expressed in layman’s terms to the greatest extent possible, although it is necessary to inject some technical terms in order to properly convey the idea behind the calculations.

**Calculating the Necessary Broaching Forces **

One of the most important forces in play during a broaching operation is the maximum force required to conduct the operation. This will let you know just what type of equipment will be necessary for the operation, and it will also help explain why the force will vary throughout the machining operation. During a machining operation, the number of teeth which get cut (n) remains constant and can be expressed by the phrase

“n = L/p”

where L is equal to the length of the piece to be broached, and p represents the pitch of the teeth. If the calculation resulting from this formula is not a whole number, accepted practice calls for rounding it up to the next whole integer. When actually grinding, the maximum force can be calculated by using the formula,

“F****max[kg] = a{mm2]*re[kg/mm2]*n”

In this formula, a represents the area of material to be discarded, re represents the exact degree of resistance in cutting, and n represents the number of teeth involved in the cutting. As the teeth shape changes, so does the value of ‘a’, and that means the value of the Force will also vary with them.

### Let’s recap

This may seem a little fuzzy, so to clarify, we’ll use a real-world example and plug in some realistic values for the variables. Let’s say you need to broach a hole with eight slots, using a piece of steel that is 32 mm in thickness and has a specific cutting resistance of 315 kg/mm2. Your broach has a pitch of 12 mm, and step-forward thinning equal to .05 mm.

Your first step would be to calculate the number of teeth which are being simultaneously cut, represented by n.

n = L/p

n = 32/12 = 2.667

Rounding up, that would give us 3 teeth. Next, we’ll have to calculate the area of material that needs to be discarded during the operation (A).

A = 8 * (5 * 0.05)

A = 2 [mm2]

Now, we can calculate the actual maximum force to be used during the broaching operation, which is represented by Fmax.

Fmax = 2 * 315 * 3

Fmax = 1890 [kg]

Now we can proceed to the final step, which involves calculating the force necessary when the grinding operation begins. At this point, there is only a single tooth in contact with the workpiece, so we can accurately state the Force can be represented as F1 = 630 [kg]. Once a second tooth joins the operation, that expression would change to F2 = 1260 [kg].

As mentioned above, calculating the broaching forces necessary for a broaching operation is one of the most critical calculations done to ensure precision in the final broached product.

**Broaching Length and Machine Time **

The cutting cycle will always be determined by the length of a broach, and the broach itself must be usable by your broach machine in order to have a successful operation. In a case where the average amount of stock to be removed by each tooth is .075 mm, the tooth spacing is 12.5 mm, and the amount of material to be discarded is 3 mm, the effective length of the broach can be calculated by using this formula:

In this equation, E is equal to the effective length of the broach, Cd is the depth of the cut which you’ll be making, Ct represents the average cut for each tooth, and p represents the pitch of the broaching teeth. Obviously, the length of the broach will fluctuate in tandem with any changes made to the cut per tooth, and the pitch of the teeth.

The broach pitch will undergo variance with the length of any cut which is to be made. As an example, if you were to make a 2.5 cut, it would require a pitch of 1.5 mm, while a cut of 25 mm would necessitate a pitch of 7.5 mm.

**Broaching Parameters **

To calculate your broaching parameters, we can assume that cutting speed V would be the speed at which your broach would be pushed or pulled across the workpiece. The apparent engagement of the cutting edge b = the width of the particular broach.

That means the actual cutting edge engagement ba = b/cos θs

In this formula θS = the angle of tooth inclination with respect to the cutting velocity. The apparent thickness of the uncut chip f = difference in the heights between any two consecutive teeth. The effective thickness of the uncut chip fa = f cos θS

If we then state that the area of uncut chip = fb, and the removal rate per tooth = fbV, we can also represent machining time as = (lw + lb)/V.

That will leave us with the expression lw = length of workpiece and lb = length of broach, and that will determine the length of the broach to be used.

While all the variables used in these formulas can be a little overwhelming, it is necessary to perform precise calculations in order to have the level of precision which is usually required for any workpiece being operated on by a broaching tool.