Mechanical machining §

Chip formation. In a single-point cut (turning, milling), the workpiece material ahead of the tool is sheared along a plane at an angle $\phi$ to the cutting direction. The shear angle depends on the tool rake angle $\alpha$ and the friction at the tool–chip interface. A larger rake angle reduces the shear angle, lowering the cutting force but weakening the tool tip. The chip thickness $t_c$ is related to the feed by the shear ratio: $t_c = f \sin\phi / \cos(\phi - \alpha)$.

Cutting forces. The force on the tool resolves into three components: tangential (drives the spindle, dominates power), feed (resists the table or carriage), and radial (pushes the tool into the workpiece). The tangential force $F_t$ is the primary determinant of spindle power: $P = F_t \cdot v_c / 60000$ (W, with $F_t$ in N and $v_c$ in m/min).

Heat generation. Roughly 80 % of the cutting energy becomes heat. Most of it flows into the chip (≈ 60 %), some into the workpiece (≈ 20 %), and a small fraction into the tool (≈ 10 %). The tool–chip interface temperature can exceed 600 °C for carbide tools, which is why tool life is governed by thermal softening and diffusion wear. Coolant removes heat from the workpiece side and reduces the thermal gradient at the interface.

Hardness ratio. The tool must be harder than the workpiece at the operating temperature. This is why HSS (≈ 900 HV at 600 °C) works on mild steel but not on hardened tool steel, while CBN (≈ 4000 HV) and diamond (≈ 10 000 HV) can machine hardened steels and non-ferrous alloys respectively. The ratio $H_{\text{tool}} / H_{\text{work}}$ should exceed 3 for acceptable tool life.

These fundamentals explain the process hierarchy: roughing uses high feed and depth of cut (high material removal rate, tolerating larger forces and heat), while finishing uses low feed and shallow cuts (low forces, low heat, better surface finish). Grinding replaces the macroscopic shear plane with millions of microscopic abrasive grains, each performing a tiny shear event, which is why it achieves finer finishes but at lower material removal rates.

• Up-milling (conventional): cutter rotates against the feed. Chip thickness grows from zero; better for roughing, less tool wear.
• Down-milling (climb): cutter rotates with the feed. Chip thickness is maximum at entry; better surface finish, requires a rigid setup and backlash-free feed.
• 5-axis milling: the workpiece or cutter is oriented in five degrees of freedom (3 linear + 2 rotary), enabling complex freeform surfaces (impellers, molds, turbine blades) in a single setup.
• Tool path: generated by CAM software from a CAD model (see Process planning and DFM). Strategy (zig-zag, contour-parallel, spiral) determines cycle time, material removal rate, and surface quality.

The cutting speed is set by the tool material (HSS, carbide, CBN, diamond) and the workpiece material. A typical carbide end mill on 7075 aluminium runs at 200–400 m/min; on 4340 steel, 130–180 m/min.

• CNC turning: the tool is positioned by servo-controlled axes (X, Z, and often a C-axis for workpiece rotation). Live tooling (drilling, milling) on the turret enables Swiss-type parts in one setup.
• Swiss-type (sliding headstock) lathes: the workpiece slides in and out of the tool, enabling the machining of long, thin parts (surgical instruments, watch components) with minimal deflection.
• Thread cutting: a single-point tool or a form tool cuts external or internal threads. Pitch accuracy depends on spindle servo resolution.

• Surface grinding: a flat or cylindrical wheel grinds a flat surface. Tolerance ±0.005 mm, Ra 0.2–0.8 µm (see Metrology and quality control).
• Cylindrical grinding: a cylindrical wheel grinds the OD or ID of a cylindrical part.
• Internal grinding: a small wheel grinds the bore of a part.
• Superfinishing / lapping: a very fine abrasive (3–15 µm grit) produces Ra < 0.1 µm for optical or sealing surfaces (see Surface finishing).

Grinding is the final step for high-precision parts: bearing races, gauge blocks, optical flats. The grinding wheel is a self-sharpening tool: as grains fracture, fresh cutting edges are exposed.

• Pure waterjet: cuts any material (metal, composite, glass, food) without a heat-affected zone. Tolerance ±0.1 mm, Ra 10–25 µm. Used for aerospace composites and multi-layer sandwich panels.
• Abrasive waterjet: adds garnet or SiC to the water stream, enabling cutting of hardened steel (up to 100 mm) and titanium.
• Abrasive jet (air): a lower-pressure stream (0.5–1 MPa) for deburring and light cutting of soft materials.

1. Rough turning: remove the bulk stock (e.g. 2 mm per side) with a carbide single-point tool at $v_c = 200$ m/min, $f = 0.2$ mm/rev. This leaves 0.3 mm of stock for finishing.
2. Finish turning: reduce to within 0.05 mm of final size at $v_c = 250$ m/min, $f = 0.05$ mm/rev, with a sharp PVD-coated carbide insert. Achieves Ra 0.8 µm.
3. Cylindrical grinding: the final 0.05 mm is removed with a CBN wheel at $v_w = 35$ m/s, infeed 3 µm/pass. Achieves ±0.005 mm and Ra 0.4 µm.

Grinding is necessary because turning alone cannot reliably hold ±0.005 mm on a 300 mm length (thermal growth and tool wear accumulate). The CBN wheel avoids the thermal damage that a conventional alumina wheel would cause on HRC 30 steel.