Nine constraints, scored against your actual machine
Each one answers a different physical question, and each is reported as a percentage of its own limit. Five of them move when the depth of cut moves; four are fixed the moment you choose your machine, spindle, cutter and material.
| Constraint | What it asks | Depth moves it |
|---|---|---|
| Spindle minimum speed | Can the spindle turn slowly enough for the surface speed this material wants? The most common limit on hobby CNC, and a spindle problem rather than a machine problem. | No |
| Spindle maximum speed | Can it turn fast enough? Scored only where the material has a published surface speed, which wood, foam and wax do not. | No |
| Spindle power | Are there enough watts at the RPM you are actually running? Below base speed an induction spindle is constant-torque, so a 2.2 kW spindle is about 730 W at 8,000 RPM. | Yes |
| Drive force | Can the drive sustain the tangential cutting force before belt teeth skip, steps are lost or pinion backlash takes off? | Yes |
| Belt stretch / guideway deflection / gantry twist | How far does the structure flex at the tool under load? Named after the part that actually gives on your machine, because that is what you would go and fix. | Yes |
| Tool deflection | How far does the cutter bend at your stickout? Scales with the cube of stickout and the fourth power of diameter. | Yes |
| Machine feed rate | Can the machine physically move fast enough to keep the chip thick enough? | No |
| Published removal rate | Where a maker publishes a maximum removal rate for the machine, you are held to it. | Yes |
| Positional accuracy | On machines that hold ±0.5 mm, feeds and speeds are not the thing limiting your part, and saying so is more useful than a number. | No |
Machines are not one formula with a different stiffness number in it
Sixteen architectures, each with its own loop stiffness, drive force and failure mode. A belt machine and a cast-iron mill do not fail the same way, so they are not modelled the same way.
| Architecture | Loop stiffness | Drive force | Fails by |
|---|---|---|---|
| Belt-and-anchor, no rigid frame | — | — | Positional accuracy |
| Small leadscrew, light frame | 0.15 N/µm | 60 N | Guideway |
| 9 mm toothed belt on V-wheels | 0.35 N/µm | 90 N | Belt stretch |
| Leadscrew on V-wheels | 0.50 N/µm | 220 N | Guideway |
| 15 mm toothed belt | 0.55 N/µm | 160 N | Belt stretch |
| Ballscrew on 30 mm round shaft | 0.90 N/µm | 500 N | Moment |
| Ballscrew on 35–50 mm round shaft | 1.40 N/µm | 700 N | Moment |
| Cast iron, hand-scraped ways | stiffest | — | Spindle, not structure |
This is why the advice differs. A toothed belt is a spring in series with your cutting force, so the fix is to reduce force — lighter radial engagement at a higher feed, which removes the same material for a fraction of the load. Dropping the feed while staying full-width keeps the force and loses the chip, and makes the problem worse.
On V-wheels the screw is rigid and the wheel joint is not: a point contact through a plastic wheel on an eccentric has roughly an order of magnitude less moment stiffness than a preloaded rail block pair, and gantry roll is exactly a moment load. Check the eccentrics before you change a single number.
On round shaft the drive is excellent and the guideway trades moment stiffness for span, so cuts that push the gantry sideways cost you more than cuts that push it along.
Rigidity classes are engineering judgement built from guideway type, drive stiffness, structural loop length and frame mass. Two reasonable people could differ by one class. Trim router output power is derived from the one vendor who publishes both input and output. Speed droop under load is real, well understood, and the magnitude used here is inference rather than measurement. None of it has been checked against a cut.