BILL MUNDY THEORY, EFFECTIVE RAKE ANGLE CUTTING TOOLS IN COPPER ALLOYS

Magazines like American Machinist and Manufacturing Engineering, have explained the Bill Mundy theory about the effective rake angle of cutting tools. These articles show the effective rake angle of cutting tools for carbon steel, steel, alloys, cast iron, aluminium and stainless steel. In the present work the theory is applied to cutting tools used in brass and bronze. The effective rake angle for these materials was obtained with the tensile stress test. The rake angles in the cutting tools were made in a Universal Grinding Machine Heiler. Finally, the power consumption was measured in a CNC Lathe. Tools with commercial rake angles from bibliography were compared with tools with the experimental effective rake angle obtained from the Bill Mundy Theory. The results show that the power consumption is about 10% lower for tools with the experimental effective rake angle.


INTRODUCTION
Copper is a soft material and when it is mechanized produces a plastic and continuous chip.The cutting tool must have a suitable geometry to obtain a good surface quality but the manufacturers offer cutting tools for materials group.The Bill Mundy theory said that each material needs the right rake angle tool when it is mechanized.He relates the rake angle of each material with the angle formed in the slipping plane of the rupture cone probe after the tensile strength test [1].
In this work, it was made the tensile strength test in brass and bronze probes.It was determined the experimental rake angle for these materials and some cutting tools were sharpened with these experimental effective rake angles.
Ingeniare.Revista chilena de ingeniería, vol.15 Nº 2, 2007 Brass and Bronze bars with 19 [mm], diameter, were turned in a Lathe with cutting tools recommended in the literature and by the manufacturers and cutting tools sharpened with the experimental effective rake angle.It was measured the power consumption for different feed and cutting velocities.The results indicate power consumption 10% lower for the tools with the experimental rake angle recommended by Bill Mundy.
Other work related with drilling and tapping tools sharpened with the experimental effective rake angle calculated from Bill Mundy theory showed similar decrease power consumption when compared with commercial drilling and tapping tools [2].

EXPERIMENTAL PROCEDURE
A Universal Hardness Machine SKF was used to measure the hardness of the alloys used in this work.Emission Spectroscopy Baird determined the chemical composition of the copper alloys.
The Tensile Stress Test was made in a Universal Testing Machine Kratos.
The samples were machined in a CNC Lathe Denford ORAC with 0,37 kW.The power consumption was measured with a Wattmeter.
A Universal Grinding Machine Heiler was used to make the experimental rake angles in the cutting tools.The angles were measured in a Tool Microscope Carl Zeiss.

Hardness
The hardness of the different samples are indicated in table 1

Tensile Stress
The tensile stress of each sample was made according to ASTM B55 M-79.The results are indicated in table 3.

Experimental effective rake angle
The effective rake angle ( ) was calculated measuring the initial length (L o ), final length (L 1 ) and the neck-down angle (B) obtained from the sample after the tensile stress test.
The value is calculated from the equation 2.1 [1].
= effective rake angle l i = probe long before tensile strength test l f …. = probe long after tensile strength test = angle in the rupture cone.

Cutting tool grinding
The HSS cutting tools were grinding without nose radius in a Universal grinding machine.For the brass samples the incidence angle was : 8º and the effective rake angle was : 40º.
The information from Larburu and Jütz, Scharkus and Lobert was used to prepare two standard tools.In both cases, incidence angle with 8º was used.

Power Test
The CNC lathe was used at constant speed 2.000 rpm, with four feeds, 0.1, 0.2, 0.

Power Consumption at constant speed
Three cutting tools were selected in each run for different bronze samples.They all have incidence angle : 8º.The effective rake angles were 12º and 14º according to literature [3,4] and 36º, 31º, 22º and 28º for samples S 1 S 2 , S 3 ; and S 4 according to Bill Mundy theory.The four runs indicate lower power consumption for the tool with rake angles made with the Bill Mundy theory.Figure 1 shows the run for sample S 1 with rake angle : 36º.Power consumption is lower for the cutting tool according to Bill Mundy theory.

Cutting tools with differents rake angles
For brass, three cutting tools were selected in each run.They have an incidence angle of : 8º and rake angle : 14º [4] and : 40º for sample B 1 Figure 2 shows the curves for sample B 1 .The cutting tool with the effective rake angle obtained from Bill Mundy theory ( : 40º) shows less power consumption.Cutting tools with differents rake angles.

Power Consumption with variable speed
A new set of experiments was made but now using the Manual of Sandvik Coromant [5] or high speed cutting tools with a rake angle : 14º.This manual recommends different cutting velocities or variable speed for each feed.The cutting velocity relates to speed through equation 3.1 [6].' Where Vc is the cutting velocity in [m/min], D the diameter of the bar (in this case 19 [mm]) and the speed in rpm.
Table 5 shows for brass and bronze, the feed (mm/rev) and the recommended cutting velocity according to Sandvik.It also included the corresponding speed for 19 mm diameter bars.

CONCLUSIONS
The cutting tools with effective rake angle recommended by Bill Mundy theory show lower power consumption for brass and bronze.
The less power consumption increased with cutting velocity of the tools with the effective rake angle obtained from Bill Mundy theory.
The lower power consumption of the experimental effective rake angle tools determined by Bill Mundy theory can be explained by the cutting edge working more freely.
3 and 0.4 [mm/rev].The cutting depth was 0,5 [mm].The external diameter sample bar is 19 [mm] and the cutting length was 30 [mm].where Vc is the cutting velocity in [m/min], D the diameter of the bar (in this case 19 mm) and the speed in rpm.

Figure 1 .
Figure 1.Power consumption versus feed for bronze S 1 .

Figure 2 .
Figure 2. Power consumption versus feed for brass B 1 .Cutting tools with differents rake angles.

Figure 4 .
Figure 4. Power consumption versus cutting velocity for brass B 1 .Cutting tools with differents rake angles

Table 2 .
Brass and Bronze chemical composition.

Table 4 .
Brass and Bronze effective rake angle.

Table 5 .
Brass and Bronze Cutting Data.