ME 350 – Lecture 3 – Chapter 21

ME 350 – Lecture 3 – Chapter 21 THEORY OF METAL MACHINING: • Overview of Machining Technology • Theory of Chip Formation in Metal Machining • Force Relationships and the Merchant Equation • Power and Energy Relationships in Machining • Cutting Temperature

Machining As the chip is removed, a new surface is exposed α = rake angle

Machining Operations • Most important machining operations: • Turning • Drilling • Milling • Other machining operations: • Shaping and planing • Broaching • Sawing

1. Turning 2. Drilling Single point cutting tool removes material from a rotating workpiece to form a cylindrical shape Used to create a round hole, usually by means of a rotating tool (drill bit) with two cutting edges

3. Milling Rotating multiple-cutting-edge tool is moved across work to cut a plane or straight surface • Two forms: peripheral millingand face (or end) milling

Cutting Tool Classification • Single-Point Tools • Point is usually rounded to form a nose radius • Example: turning • Multiple Cutting Edge Tools • Motion relative to work achieved by rotating • Examples: drilling and milling

Cutting Conditions in Machining • Material removal rate can be computed as MRR = v f d where v = cutting speed; f = feed; d = depth of cut

Roughing vs. Finishing • Roughing - removes large amounts of material from starting workpart • Close to desired geometry (not to full depth) • Feeds and depths: large • Cutting speeds: slow • Finishing - completes part geometry • Final dimensions, tolerances, and finish • Feeds and depths: small • Cutting speeds: fast

Orthogonal Cutting Model – Chip Thickness Ratio where r = chip thickness ratio; to = thickness of the chip prior to chip formation; and tc = chip thickness after separation • Chip thickness after cut should always be greater than before, so chip ratio is always: less than 1

Determining Shear Plane Angle • Based on the geometric parameters of the orthogonal model, the shear plane angle  can be determined as: where r = chip ratio, and = rake angle

Shear Strain in Chip Formation ABD angle? 90 - Φ DBE angle? Φ E Strain: • = tan( - ) + cot  • where  = shear strain, = shear plane angle, and  = rake angle

Chip Formation More realistic view of chip formation, showing shear zone rather than shear plane. Also shown is the secondary shear zone resulting from tool‑chip friction.

Four Basic Types of Chip in Machining • Discontinuous chip • Continuous chip • Continuous chip with Built-up Edge (BUE) • Serrated chip

1. Discontinuous Chip 2. Continuous Chip • Work material: brittle • Cutting speed: slow • Feed & depth of cut: large • Tool‑chip friction: large • Work material: ductile • Cutting speed: fast • Feed & depth of cut: small • Tool‑chip friction: low • Sharp cutting edge

3. Cont. with BUE 4. Serrated Chip • Semicontinuous - saw-tooth appearance • Cyclical chip forms with alternating high shear strain then low shear strain • Associated with difficult-to-machine metals at high cutting speeds • Work material: ductile • Cutting speeds: low-medium • Tool‑chip friction: large, causing portions of chip to adhere to rake face • BUE means: built-up edge

Metal Cutting - Introduction Videos • Drilling – slow motion chips • Milling – slow motion chips • Turning – slow motion chips • Turning – large lathe • Complex Shapes, Mill-Turn: Dental Implant • Milling – pocket CNC milling

Forces Acting on Chip • Vector addition of F (friction) and N (normal) = R • Vector addition of Fs (shear) and Fn (normal shear) = R' • Relationship between R' & R: • equal in magnitude, opposite in direction, collinear

Coefficient of Friction & Shear Stress Coefficient of friction between tool and chip: whereβ is: the friction angle Shear stress acting along the shear plane: where S is: the shear strength where As is: the shear plane area • to is: cut depth • w is: cutting edge width, • Φ is: shear plane angle

Cutting Force and Thrust Force • F, N, Fs, and Fn cannot be directly measured • The only forces that can be measured are the forces acting on the: tool • Cutting force Fc • Thrust force Ft • F = Fc sin + Ft cos • N = Fc cos ‑ Ft sin • Fs = Fc cos ‑ Ft sin • Fn = Fc sin + Ft cos

The Merchant Equation • Of all the possible angles at which shear deformation can occur, the work material will select a shear plane angle  that minimizes energy, given by • Derived by Eugene Merchant • Based on orthogonal cutting, but approximate validity extends to 3-D machining • To increase shear plane angle (more efficient cutting) • Change to the rake angle: increase • Change to the friction angle (or coefficient of friction): reduce

Effect of Higher Shear Plane Angle • Larger shear plane angle means the shear plane will be: smaller • Which means the shear force, cutting forces, power, and temperature will all be: lower Effect of shear plane angle  : (a) higher  with a resulting lower shear plane area; (b) smaller  with a corresponding larger shear plane area. Note that the rake angle is larger in (a), which tends to increase shear angle according to the Merchant equation

Cutting Temperature • Approximate % of the energy in machining that is converted into heat: 98% • This can cause temperatures to be very high at the tool‑chip • The remaining energy is retained as elastic energy in the chip Note: Hottest point is in secondary shear zone, NOT the tooling point

Cutting Temperatures are Important High cutting temperatures • Reduces: tool life • Produce hot chips that pose safety hazards to the machine operator • Can cause inaccuracies in part dimensions due to work material: thermal expansion

Cutting Temperature • Derived by Nathan Cook from dimensional analysis using experimental data for various work materials where T = temperature rise at tool‑chip interface; U = specific energy (found on page 499); U = Fcv / RMR v = cutting speed; to = chip thickness before cut; C = volumetric specific heat of work material; K = thermal diffusivity of work material

ME 350 – Lecture 3 – Chapter 21