IE 337: Materials and Manufacturing Processes Lab # 3

1 January 14, 2010

Orthogonal Machining

Introduction: Machining can be defined as the process of removing material from a workpiece in the form of chips by a sharp cutting to leave the desired part shape. The predominant cutting action in machining involves shear deformation of the work-piece to form a chip; as the chip is removed, a new surface is exposed. A typical machining process is illustrated in Figure 3.1.

Figure 3.1. (a) Cross-sectional view of a typical machining process, and (b) a cutting tool with positive rake angle.

A cutting tool has one or more sharp cutting edges and is made of a material harder than that

of work material. It usually achieves their motion relative to workpiece by rotating. The cutting edge serves to separate a chip from the workpiece. There are two surfaces connected to the cutting edge: the rake face and the flank. The rake face, which directs the flow of chips, is oriented at a certain angle called the rake angle, α. The rake angle can be positive or negative. The flank of the tool provides a clearance between the tool and the newly generated work surface, thus protecting the surface from abrasion. The rake face and flank are shown in Figure 3.2.

Figure 3.2. A single-point tool showing rake face and flank.

The orthogonal Cutting Model

The machining process is a complex 3D operation. A simplified 2D model of machining is available that neglects many of geometric complexities, yet describes the process quite well. Orthogonal cutting uses a wedge-shaped tool in which the cutting edge is perpendicular to the cutting direction. As the tool is forced into the material, the chip is formed by shear deformation along shear

IE 337: Materials and Manufacturing Processes Lab # 3

2 January 14, 2010

Orthogonal Machining

plane oriented at an angle φ (shear angle) with the surface of the workpiece. Along the shear plane, plastic deformation of work material occurs. The tool in orthogonal cutting has only two elements of geometry: (1) rake angle and (2) clearance angle. The rake angle α determines the direction of chip flow as it is formed; and the clearance angle provides a small clearance between tool flank and newly generated work surface. During cutting, the cutting edge of the tool is positioned at a certain distance below the original work surface. This corresponds to the chip thickness prior to chip formation, to. As the chip is formed along the shear plane, its thickness increases to tc. The ratio of to to tc is called chip ratio thickness is called the chip ratio, rc and is always less than 1.

𝑟𝑟𝑐𝑐 =𝑡𝑡0

𝑡𝑡𝑐𝑐

The governing equations in a machining process are provided below: Shear angle: Shear strain:

Force Relationships Several forces act during the cutting process. A normalized force diagram is shown in Figure 3.3.

Figure 3.3. Forces in orthogonal cutting: (a) Forces acting on the chip, and (b) forces on the tool. Merchant Equation: Cutting force:

𝜏𝜏𝑠𝑠 = 𝐹𝐹𝑐𝑐 cos ∅−𝐹𝐹𝑡𝑡 sin ∅(𝑡𝑡0𝑤𝑤/𝑠𝑠𝑠𝑠𝑠𝑠∅)

𝐹𝐹𝑐𝑐 = 3∗𝐸𝐸∗𝐼𝐼∗𝛿𝛿𝐿𝐿3

Other related equations and related terms are: MRR=(𝑡𝑡0 ∗ 𝑑𝑑)𝑉𝑉

IE 337: Materials and Manufacturing Processes Lab # 3

3 January 14, 2010

Orthogonal Machining

Objective:

1. Understand the basic mechanics of chip formation. 2. Study the effect of rake angle, material system and the depth of cut on the process.

Equipment & Materials: 1. Vertical milling machine 2. Tool deflection gauge 3. Cutting tools with different rake angles (10°, 20°, 30°) 4. Workpiece: 6061 Aluminum, Brass 5. Dial calipers, protractor

Procedure: 1. Mount the aluminum work piece in the vise and the 10° cutting tool in the fixture. (The

rake angle is α in the calculation section). 2. Measure the distance from the bottom of the tool fixture to the point where the dial

indicator touches the tool. (This is the length L in the calculation section). 3. Adjust the X-axis feed rate (fr) to 4 inches per minute using the settings on the feed motor. 4. Turn on the CCD camera and monitor. With the cutting tool resting on the work piece,

adjust the camera so that the work piece fills approximately the bottom third of the screen and the cutting tool appears on the right side of the screen. (*Note, focus the camera on the work piece material, only a visible outline of the tool is needed).

5. Touch off on the top of the work piece then set the depth of cut to .003”. (This is to in the calculation section).

6. Feed the tool into the work piece. Take an average reading from the tool deflection dial indicator. Using a protractor, measure the shear angle on the screen. (These are δ and φ in the calculations).

7. Collect the chip and measure the thickness with the dial calipers. (This is tc in the calculations).

8. Repeat steps 1-7 at a depth of .006”. 9. Repeat steps 1-8 for the 20° rake angle tool. 10. Repeat steps 1-8 for the 30° rake angle tool. 11. Repeat steps 1-10 for brass.

rc Chip thickness ratio w Width of work piece material (in)

φ Shear angle b Thickness of cutting tool (in) α Tool rake angle d Width of cutting tool (in) MRR Material Removal Rate (in3/min) E Modulus of Elasticity (Young’s Modulus) I Moment of Inertia (in4) δ Deflection of tool (in)

L Tool length (measured from tool fixture to tip of dial indicator) (in) V Linear cutting speed of cutting tool relative to work

piece (in/min) Fc Cutting force (lbf) hpc Cutting horsepower (hp) R Resultant force hpu Specific (Unit) horsepower (hp/in3/min)

tc Chip thickness (in) γ Shear strain

to Undeformed chip thickness (in) τs Shear Stress (psi)

IE 337: Materials and Manufacturing Processes Lab # 3

4 January 14, 2010

Orthogonal Machining

Lab Deliverables: 1. Prepare a report detailing the lab activity, observations, results and difficulties faced

(follow the lab report instructions). 2. Compare calculated shear angle with the values obtained in lab. Explain your findings. 3. Calculate cutting forces based on:

a. Deflection of the tool b. Specific energy of the material c. Shear strength of the material How do they compare? Which of these you think are most representative of the actual cutting force?

4. Describe the different types of chips formed for each experiment? How does chip type affect the cutting forces?

5. What is the relationship between the shear angle and cutting force? Shear strain and cutting force? Do these relationships make sense?

6. Why is the shear angle important in machining? 7. What factors control the shear angle in cutting? 8. How does the un-deformed chip thickness (depth of cut), tool rake angle, and work

piece material influence: a) cutting force, b) shear angle, and c) chip type

References:

1. M.P. Groover, “Fundamentals of modern manufacturing,” 3rd edition, (2007). 2. F. Jones, H. Ryffel, E. Oberg, C. McCauley, and R. Heald, “Machinary’s handbook,” 26th

edition, Industrial Press, (2000). 3. You can see the chip formation for different conditions at

http://machine-tools.netfirms.com/Assets/FlashMovies/chip-formation-animation-2.htm http://machine-tools.netfirms.com/Assets/FlashMovies/chip-formation-no-rake-angle.htm

Orthogonal Machining Experiment Data Sheet

Aluminum

Rake Angle

Depth of cut

Tool Deflection

Shear Angle

Chip Thickness

Chip Type

10° .003” .006”

20° .003” .006”

30° .003” .006”

Brass

Rake Angle

Depth of cut

Tool Deflection

Shear Angle

Chip Thickness

Chip Type

10° .003” .006”

20° .003” .006”

30° .003” .006”

Tool width Material width

Aluminum Brass

10° 20° 30°