How to Calculate Cutting Force

When slicing through things, you want to make sure your knife makes the cut. Using knives to cut through material like metal can be difficult if you don't know how strong your knife needs to be. You can use the cutting force equation to figure out how much blades use when manufacturing materials like foil or metal while learning about the underlying physics involved in cutting. This can give you an idea of the force required to cut a wire or other material.

Blade Cutting Force Calculation

The shearing process that produces metals that manufacturing plants use involve a sheet metal cutting force that ensures metals are cut properly. The process is called blanking, in which a machine known as a die exerts a cutting force, which engineers call a "punch," on the plate material to be manufactured.

The word "die" can also be used to refer to the part of the machine that receives the actual punch or the plate of the shape to be punched out. During blanking, you can calculate the cutting force of this punch using the equation

F=l\times t\times s

for the cutting force ​F​, length of the sheet to be cut ​l​ in millimeters, sheet thickness ​t​ in millimeters and shear strength ​s​ in N/mm2. You can find a table of shear strength values for various materials like brass or copper on the Austek Design website here.

Engineers often use shear strength as a percentage of a material's tensile strength, the resistance of a material to fracture when under pressure. Shear strength as 80 percent of the tensile strength is good for general use of the cutting force equation to work, but aluminum is often used with 50 percent, cold roll steel with 80 percent and stainless steel, 90 percent. During blanking, the material punched through the metal sheet is called a "blank."

Determining a Cutting Force Equation 

Examining cutting force for these materials can let scientists and engineers come up with more detailed, complicated equations to determine cutting strength under different conditions and in different contexts. The cutting force of a blade would depend on the angle between the blade and the surface, the frictional force between the blade and the machine and the elastic-recoil force the machine material itself exerts in response to being bent and deformed.

Understanding this force alongside how the material forms a "chip" that the material separates from the blank can give you a better idea of these more complicated equations. This depends on how the teeth of the blade interacts with the feed of the blanking material itself.

These forces obey Newton's third law of motion: Every action has an equal and opposite reaction. The elastic-recoil and chip-formation forces are both reactions of the blanking machinery to a blade striking the surface. The shear force balances the chip-formation forces, and the elastic-recoil is in response to the pressure of the blanking force. Studying these forces, engineers can manufacture foil, metal, paper, textile, plastic film and wire through the cutting force of their machines.

Cutting Force of Scissors

You don't need a blanking machine in your living room to study cutting force. Scissors, made of a blade, fulcrum and a handle, exert a cutting force the same way a lever would. The fulcrum, where the two hands of the scissors are joined, lets you distribute weight through the handles letting you cutting materials like paper or wire. When the shear stress is greater than the materials' shear strength, the scissors cut.

But even the simple cutting force of scissors can present the potential for scientific discovery. Biomedical engineers produce models of forces that scissors exert when cutting biological materials for use in surgical simulation. These models describe the contact and fracture mechanics when scissors cut to study the deformation and fracture of scissors. They can then test these models in experimental settings by cutting paper, plastic, cloth and other materials.