## Gear Manufacturing

### Two philosophies: direct forming vs. kinematic generation

Gears can be manufactured according to two fundamental principles:

1. **Direct-form machining:** A tool with the exact profile of the tooth space (or of the tooth) removes material. Conceptually simple, but every module and number of teeth requires a specific tool.

2. **Generating machining (hobbing/shaping):** The tool simulates the meshing motion with the workpiece, "generating" the involute profile through kinematics. A single tool serves for all tooth counts of a given module. It is the dominant method in industrial production.

<img src="./figs/imagenes_tema_07/Imagen10.jpg" alt="imagen10" width="720px">

### Main manufacturing methods
This [video](https://www.youtube.com/watch?v=YrC0KZNmcH4) shows the manufacturing process of toothed wheels.

- **Molding/casting/sintering:** For **very large production runs** (thousands of units) or special materials (bronze, plastic). The profile is formed directly in the mold.
  - **Advantage:** very low unit cost for large runs, complex shapes possible (e.g. double helical).
  - **Limitation:** **medium** tolerances (DIN 9-12); requires subsequent machining if precision is needed.
  - **Use:** Toys, household appliances, starter gears in automotive applications.

- **Form milling:** A **cutter with the profile of the tooth space** removes material tooth by tooth. Each module requires a specific cutter (or a set of cutters for different ranges of $z$).
  - **Advantage:** Economical for **short runs** or prototypes; flexibility.
  - **Limitation:** The profile is not exact (approximated by sectors), less precise than generation.
  - **Use:** Repairs, spare parts, manufacturing of large gears (cranes, mills).

- **Generating milling (hobbing):** The most common tool is the **hob**, a screw-shaped tool with cutting teeth that, rotating in sync with the workpiece, "cuts" the teeth. For spur gears, the **Fellows shaper cutter** (reciprocating motion) is also used. For helical and worm gears, the hob is standard.
  - **Advantage:** **High precision** (DIN 5-7), one tool serves for all values of $z$ of the same module, high productivity.
  - **Limitation:** Requires specialized machines (gear-cutting/hobbing machines).
  - **Use:** Industrial production of medium/high-precision gears.

- **Broaching:** A **broach** (a long tool with progressive teeth) is pushed or pulled through the workpiece, cutting all the teeth in a single pass. Very fast (seconds per part).
  - **Advantage:** **Very high productivity** for large runs.
  - **Limitation:** **Very expensive** tool (thousands of euros), only for **internal** gears (internal ring gear), fixed geometry.
  - **Use:** Internal gears in automatic gearboxes, synchronizers.

- **Gear grinding:** After cutting and heat treatment (hardening), the gear distorts slightly. **Grinding** with an abrasive wheel (Maag, Reishauer type) corrects the profile without heating the material (avoiding new stresses).
  - **Advantage:** **Very tight** tolerances (DIN 3-5), correction of hardening distortion, excellent surface finish.
  - **Limitation:** Slow, expensive process; only justified for high precision.
  - **Use:** Turbine gears, aerospace transmissions, precision machine tools.

- **Lapping and honing:** **Final finishing** operations with fine abrasive pastes or honing tools. They remove micro-irregularities, improve **surface roughness** (Ra < 0.4 µm), and reduce noise and initial wear (running-in).
  - **Use:** High-speed gears, luxury transmissions, quiet applications (premium automobiles).

### Quality control

After manufacturing, the following are checked:
- **Pitch:** with a pitch tester (pitch comb gauge).
- **Involute profile:** with coordinate measuring machines (CMM) or profile projectors.
- **Roughness:** contact/optical roughness testers.
- **Hardness:** Rockwell/Vickers tests on the surface zone (important after hardening).
- **Noise:** dynamic bench tests (single-flank test).