15.6 Coordinate Measuring Machines & Machine Tool Alignment Testing

The Coordinate Measuring Machine

A coordinate measuring machine measures the position of discrete points on a workpiece in three-dimensional space, along three mutually perpendicular axes, each with its own high-resolution linear scale. It does not measure diameters, angles or flatness directly. Instead, software fits geometric elements to the measured points and computes the required features and tolerances.

This distinction is conceptually important. A diameter is derived by fitting a circle to points probed around a bore; perpendicularity is derived from the angle between two fitted planes. Everything is computation on coordinates, which is precisely why a CMM can evaluate geometric dimensioning and tolerancing callouts — position, profile, runout, true position with material condition modifiers — that no combination of hand instruments could assess.

Configurations

The bridge type dominates because it balances rigidity, accuracy, cost and access. The moving-bridge variant is the most usual; a fixed-bridge with a moving table is more accurate but limits part weight.

Probes

The stylus tip is normally a ruby sphere, chosen for hardness, wear resistance and low affinity for aluminium. A key software step is probe qualification: the machine measures a calibrated reference sphere to determine the exact stylus tip radius and its offset, so that the recorded surface points can be corrected for the tip radius. Skipping this step is a classic source of systematic error.

Measurement Practice

The minimum number of points to define each element is fixed by geometry, but more are used in practice to assess form:

Using only the minimum gives a perfect mathematical fit with zero apparent form error, which is misleading: three points always lie exactly on a circle. Assessing roundness requires substantially more points.

Sources of Error

Thermal effects deserve emphasis. Steel expands about 11.7 micrometres per metre per degree Celsius, so a one-metre part measured at 23 degrees rather than 20 reads about 35 micrometres oversize. On tolerances of a few tens of micrometres this is not a refinement but the dominant error.

Volumetric accuracy is specified in the form $E = A + L/K$ micrometres, where $A$ is a constant, $L$ is the measured length in millimetres and $K$ a machine constant. A specification of $2.5 + L/300$ means a 600 mm measurement carries a permitted uncertainty of $2.5 + 2 = 4.5$ micrometres.

Machine Tool Alignment Testing

A machine tool can only produce components as accurate as its own geometry. Alignment tests — also called geometric tests — verify that the machine's own axes, slides and spindles are true. They are performed on installation, after major repair, and periodically thereafter.

The standard reference is the set of Schlesinger acceptance tests, which specify both the test method and the permissible error for each machine type.

Two categories of test

Both are needed. A machine can pass geometric tests and still cut inaccurately because of vibration, thermal drift under load, or slide stick-slip that a static test does not reveal.

Principal geometric tests

Key instruments

Autocollimator. Projects a collimated beam onto a reflector mounted on a carriage; any angular tilt of the reflector displaces the returned image, which is read on a graduated eyepiece. Resolution reaches fractions of an arc-second. Traversing the reflector in steps and summing the angular readings reconstructs the straightness profile of a guideway.

Spirit level (precision). A sensitive level graduated in seconds of arc, or in millimetres per metre, used for levelling beds and checking flatness by the moving-level method.

Test mandrel. A precision-ground bar fitted into the spindle taper, providing an accurate extension of the spindle axis against which parallelism and coaxiality are checked. Readings are always taken at two positions with the mandrel rotated 180 degrees, and averaged, so that any error in the mandrel itself cancels out.

Ballbar. A telescoping bar with precision balls at each end, one held in a magnetic cup on the table and the other on the spindle. The machine is commanded to traverse a circle, and departures from a true circle are plotted. The resulting polar plot diagnoses specific faults by their signature: backlash appears as step discontinuities at the axis reversal points, servo mismatch as an oval at 45 degrees, squareness error as an oval along the diagonals, and scale error as a change in overall radius. A ballbar test takes a few minutes and is the standard periodic health check for a CNC machine.

Why this matters in a maintenance workshop

For a Management Trainee responsible for a coal subsidiary's central workshop, alignment testing is the link between machine condition and product quality. A lathe with worn guideways will turn a taper no matter how skilled the operator; a milling machine whose column is out of square will not produce a perpendicular face. Recording geometric test results over time also gives a condition-monitoring trend, allowing slideway regrinding or spindle bearing replacement to be planned rather than forced by a scrapped batch.