# Tool unbalance vs. cutting forces.

In the July 2005 "Tooling Around" column, we looked at the calculation of balance as applied to rotating tool assemblies using the balance standard ISO 1940-1, and the amount of force that results from just a small amount of unbalance. (See the Archives link at Tooling & Production's website: www.toolingandproduction.com.) This month we'll look more closely at how the force from unbalance compares to what happens during the cutting process.

If we review our tool assembly: A balance quality grade of ISO G2.5 was selected. Our tool was a 1/4" diameter TiA1N-coated solid carbide endmill, held in a short length 40 Taper V-Flange hydraulic chuck--with a tool assembly weight of 0.85 kilos (1.87 lb). We plan to run this tool at a maximum of 14,000 RPM. Using ISO 1940-1, we calculate that the tool assembly must be balanced within 1.45 gram-millimeters. The unbalance of 1.45 g-mm can be calculated to result in 3.11 Newtons of unbalance force.

In most machine shops, trying to relate 3.11 Newtons of force into the workday can be a bit of a challenge. But you could think of that as roughly translated to be about the same amount of force you could exert with three sticks of butter. How does that small a force compare to the force generated when our 1/4" endmill goes into cut?

If we take one of the reliable shortcut methods of calculating cutting force, the formula is:

F = (Hp x 26,400) / SFM

Where: SFM = Cutting Speed in Surface Feet per Minute. Hp = Horsepower. 26,400 is a constant. F = Force in pounds.

In medium alloy steel, a four flute 1/4" endmill running at 915 SFM, edging at a 0.040" width of cut, cutting 3/4" deep, with a feed per tooth of 0.0016" results in running our endmill at 14,000 RPM and 90 inches per minute. This cut would consume right around 2.7 hp. Therefore, inserting 2.7 hp into our force calculation would look about like this: F = (2.7 x 26,400) / 915 or a Force of 77.9 pounds or 346 Newtons.

So, our small 0.040" wide cut with a 1/4" diameter endmill results in a cutting force over 100 times greater than the 3.11 Newtons of force from our unbalance of 1.45 g-mm. This means that as soon as our tool gets engaged in cut, the forces inherent in the cutting process so greatly exceed the precision balancing--that quite possibly we could have wasted quite a bit of time going to such an extreme grade of balance.

Does this mean that one should never balance their tools? In a word, no--there are many situations where tools must be balanced, and it is difficult to envision how balancing could ever be detrimental to the performance of a tool assembly. But it is very possible to spend considerable time, (and therefore money) balancing tool assemblies to overly restrictive grades of balance. Good principles to always follow would be:

a) When machining at elevated spindle speeds (>10,000 RPM), buy high quality tools and tool holders, preferably balanced by design and factory certified to a balance grade standard.

b) Keep tool assemblies as short as possible.

c) The heavier the tool assembly, the more likely the need for it to be balanced.

d) Tools that are inherently out of balance (e.g., hollow mills) should almost always be balanced.

e) Precision finishing tools (e.g., single point fine boring tools) will perform better if balanced.

By considering the above guidelines, investing a certain amount of time understanding the standards applied to balancing, and recognizing the actual forces that result during the cutting process and the amount of unbalance, most shops can more easily determine the right economics to apply for rotating tool balance situations.

All photos courtesy of Sandvik Coromant

Mark Stover provides sales and marketing services to manufacturers and distributors in the metalworking industry. He's had chips in the soles of his shoes for the last 25 years. This column appears in T&P every other month. Mark can be reached at mstover@strsolutions.com