# Form milling cutters design with multiple inserts

Form milling cutters with multiple inserted cutter blades are widely used in roughing screw rotors. This paper proposes a mathematical method for finding the distribution of cutter body inserts that will result in an equal wear rate for their cutting edges. First, commercially available standard inserts are selected and positioned in the form milling cutter axial section to satisfy profile geometry tolerance.

Next, the insert tool life in every position is estimated based on its cutting material volume and corresponding wear rates. To even the insert wear rate and increase tool life, multiple inserts can be used at the same insertion position. Once the numbers of insert positions and inserts at each position have been explicitly defined, the inserts can be distributed on the cutter body periphery in a spiral form.

Not only is the operational cost of such form milling cutters far less than that of cutters using special order blades, but the fact that all inserts are chosen from standard blades and can be replaced when the cutting edge becomes dull makes geometric precision easier to maintain.

Form milling cutters with multiple inserts are widely used to cut the tooth profiles of threaded cylindrical workpieces like the rotors in twin-screw compressors. However, because the rotor profile geometry depends on the application and every new rotor design requires new form milling cutters, the cutter blade geometry and positional arrangement of inserts on the form milling cutters body vary significantly.

Moreover, because the form milling cutters usually requires special inserts, it is relatively expensive. Therefore, a mathematical method is needed to design form milling cutters with multiple standard inserts.

Earlier research has proposed various models for calculating grinding wheel profiles, wear rates, and tool life. For example, Litvin [1,2] proposed a mathematical model to calculate grinding wheel profiles using the axes of meshing, while Xing calculated them by deriving an equation of the contact line.

You et al. then proposed a model that profiles the CBN shape of a grinding wheel using the geometric properties of the contact points.

Stosic, who used the envelope theory of gearing to calculate the relative motion between every point of the form tool and rotor during the cutting process, outlined a model that could produce a grinding wheel profile with uniform wear rate for any given stock allowance. To determine the wear rate equation,

Wang et al. investigated the wear conditions of grinding stock curves and form grinding wheels in which special inserts form the blade profiles.

Engin et al. proposed a generalized mathematical model of inserted form milling cutters that orients rectangular and convex triangular inserts around the cutter bodies. Chu [10] then formulated an equation for the life of a turning tool insert by investigating the manufacturing parameters. Subsequently, many other researchers have calculated tool life using different insert materials.

This paper proposes a mathematical method for finding the distribution of inserts on the cutter body that results in their cutting edges having an equal wear rate on form milling cutters.

First, the envelop theory of gearing is used to calculate the standard grinding wheel profile for a given rotor tooth profile. The grinding stock allowance curve that produces equal wear on the grinding wheel is then derived using the wear rate equation and superimposed on the rotor profile to be used as a basis for calculating the form milling cutters body profile.

Next, commercially available standard inserts are selected from a database and positioned in the axial section of the form milling cutters to satisfy the profile geometry tolerance. The tool life of the insert in every position is estimated based on their cutting material volume and the corresponding wear rates. To even the wear rate of every insert and to increase the tool life, multiple inserts can be used in the same position. Once the number of insert positions and the number of inserts at each position has been explicitly defined, the inserts can be distributed on the periphery of the cutter body in spiral form.

The operational cost of such form milling cutters is far lower than that of one using special order blades, and it is easier to maintain geometric precision because all inserts are chosen from mass-produced standard blades and can be replaced as their cutting edges become dull.