This is the manual of Studio 1.0.2, an earlier version. The manual of the latest version

The twin's models and their limits

The twin is the MC-1 as a program: the Twinwright controller (kernel) runs in it, and physical models stand for the parts of the machine around the controller. Every number the twin gives about the physical world is an estimate from a physical model. Its parameters come from the machine's design, the parts' data sheets and published values; each MC-1 is to be measured at commissioning and its twin set to the measurements (planned). Each section below ends with what its parameters rest on.

_Draft (round 14): the text is being written; the sections may still grow._

The controller

The controller in the twin is the Twinwright controller (kernel), built from the same source as the machine's firmware. What is modelled is the board around it: its timers and step pulses, its inputs with their debounce, its link to the computer (the USB serial port and its handshake), the time the controller's foreground takes.

Based on: the kernel's own code; the foreground's time is an estimate until it is measured on the board.

Motion and drives

Each axis is driven by a closed-loop stepper drive and a ball screw. The twin models them at four levels of detail; the default is a three-mass model:

the drive's position loop: the motor's magnetic spring around the commanded position, its torque falling with speed, pull-out when the load is too high, the drive's alarm when the following error grows too large;
friction in the guides, the nut and the bearings, and gravity on Z;
the transmission's compliance between the motor, the screw and the table, the nut's backlash, the frame under the X axis;
the drive's power: the E-stop chain, the contactor, the time the drives take to come up.

Based on: the design (masses, inertias, stiffness by hand calculation and finite-element analysis), the drives' and motors' data sheets; friction and the drive's internal parameters are assumptions until measured.

Geometry and accuracy model

When it is on, the twin moves the tool tip by the machine's geometric errors: each axis's lead error and its periodic part, two straightness errors and three angular errors acting through their Abbe arms, the squareness between the axes, the nut's backlash, and the screws' and the spindle's growth with heat. The limit switches see the slides, the tool setter and the probe see the tool tip, as on the machine. The model is off by default: the nominal twin is ideal.

Based on: tables of a typical assembled machine drawn from the parts' grades. They are not the machine's specification; they are replaced by the machine's ISO 230-2 measurement at commissioning (planned).

Heat

The spindle and the ball screws warm with use and cool at rest; the twin keeps their temperatures between sessions and moves the tool tip and the screws' lead by them.

Based on: first-order thermal models with assumed parameters until the machine's warm-up is measured.

Spindle and drive (VFD)

The spindle's drive is modelled as the machine's: the controller talks to it over RS-485 in the drive's own protocol, byte by byte at the configured speed, and the drive answers as its manual describes, including its parameters that decide whether it listens. Behind it: the motor's torque from its slip, its current and the drive's overcurrent, overload and undervoltage trips, the DC bus that keeps the drive alive through a short power dip, the water pump.

Based on: the drive's and the motor's data; the bus capacitance, the current's magnetising part and the friction are assumptions until measured.

The cut

The blank is a height field with finer regions where you ask for them. Every move of the tool removes what the tool's shape sweeps, so the part's shape comes from the program itself.

The cutting force comes from the material's cutting coefficients, which change with the chip's thickness and the cutting speed, worked out tooth by tooth on the tool's real shape (flat, ball, bull nose, V). From the force the twin estimates the spindle's load and power, the tool's deflection and the risk of breaking the tool: the bending stress at the flute root against the carbide's strength.

Based on: published cutting data for the materials (each material's source is in the machine profile), a sharp tool, typical tool geometry.

Chatter

For each cut the twin computes the depth at which it would start to chatter at the spindle speed in use, from the tool's and the machine's vibration modes and the cut's geometry, and picks a spindle speed where the cut is stable. It also estimates where the walls end up from the cut's forced vibration.

The tool point has three modes in each direction: the machine's structure, the tool holder in the collet and spindle, and the tool's own bending. The bending mode's frequency comes from the tool's shape - its flutes, neck and shank and how far it sticks out: about 14 kHz for a 6 mm end mill 20 mm out, over 100 kHz for a 0.2 mm one. Tools under about 1 mm chatter, if at all, at their own bending, at a depth that hardly depends on the spindle speed; the twin works that depth out in time for every cut.

Based on: the frame's modes from finite-element analysis, an assumed holder mode, and the tool's bending estimated from its geometry with beam theory; the damping of all three is assumed (3 %). None of them is measured yet: they are to be measured by a tap test on the built machine, and until then the stable depths are estimates. The damping of the cut itself is not modelled: for small tools the margin is on the safe side.

Runout

A cutter whose axis is off the spindle's cuts with its outermost tooth: bores come out larger and bosses smaller (finding 187). The twin cuts with that envelope; CAM allows for it in fits. A tool can carry its own runout - a precision collet's class, or as measured - in its spec (tir3: its TIR in micrometres); otherwise the machine's is used.

Based on: an assumed runout until it is measured on the machine.

Tool wear

In 1.0 every tool is a new one: the shape it cuts and its forces are those of a sharp tool, however long it has cut. Counting the life a program uses for each tool is planned for a later version. Tools that cut aluminium are mostly changed first because aluminium sticks to the edge and the part shows burrs or a poorer finish, not because the flank has worn.

The touch probe

The probe is a tool whose ball switches the probe input when it touches the part. The twin works out the touch exactly from the blank's shape and from the cut surfaces, slopes included. Two models: an ideal probe that switches as the ball touches, and a typical probe with pretravel that depends on the direction, three lobes, scatter and the stylus breaking when it is pushed too far.

Based on: typical values for a touch-trigger probe; calibrate the probe on a ring gauge before you measure with it.

The Z clearance

For the setup on the table the twin works out the highest point to clear and, for the tool in the spindle and each tool in the tool table, the tool tip's height at the top of Z. A tool that cannot clear the setup is reported when the setup or the tool changes (finding 188).

Based on: the machine's design and the tools' lengths as given.

Collisions and workholding

The twin checks the tool, its holder and the spindle against the part, the fixture and the machine, and warns before a near collision. The workholding (clamps, vise, V-block, tape, a fixed part) holds the part with a force; a cut that pushes harder can make it slip.

Based on: the machine's and the fixtures' geometry from the design; the holding forces are estimates.

What is not modelled

the surface's texture and roughness beyond the walls' position;
built-up edge, chips and their evacuation;
thin walls bending under the cut;
the part's own heat;
what happens after a tool breaks.

The acceptance tests that need a built machine (the drives' and the sound's measurements, the cutting forces, the surface, the heat, the frame's modes, shadow mode with a real machine) are in the twin's design notes (docs/06, section 7).