The Coordinate Measuring Machine (CMM), as a high-precision geometric measurement device in modern manufacturing, relies on the establishment of a three-dimensional coordinate system and precise measurement to achieve accurate quantification of object geometry, dimensions, and positional tolerances. The measurement process can be broken down into three core steps:

1、 Establishment and positioning of three-dimensional coordinate system

CMM constructs a Cartesian coordinate system through three mutually perpendicular linear motion axes, X, Y, and Z, and the motion trajectory of the measuring head (such as a ruby probe) is represented by the center point of the measuring sphere. During measurement, the workpiece is fixed on the workbench, and the measuring head is in contact with the surface of the workpiece. The system captures the precise position of the center point of the measuring ball in the coordinate system in real time. For example, when measuring the bore diameter of an engine cylinder block, the measuring head needs to go deep into the hole to collect coordinates from multiple points. The software calculates the bore diameter and cylindricity through fitting algorithms, which relies on high-precision positioning of the coordinate system.

2、 Precise collection of spatial coordinate points

When the measuring head contacts the surface of the workpiece, the grating ruler or encoder instantly records the grating data of three axes, forming spatial point coordinates (X, Y, Z). Contact probes trigger signals through physical contact, while non-contact probes (such as laser probes) use optical principles to collect data. Taking the inspection of box type parts as an example, the measuring head needs to collect finite points that define its regular shape, and unify the data measured by different measuring needles into the same coordinate system through coordinate transformation to ensure the continuity of the measurement results.

3、 Mathematical Modeling and Geometric Parameter Analysis

The collected coordinate data is processed by professional software and fitted with basic geometric elements such as points, lines, planes, cylinders, etc. using algorithms such as least squares, to calculate dimensions, shapes, and positional tolerances. For example, when measuring a cone, the software automatically recognizes the difference in diameter between each section; When measuring free-form surfaces, massive point data is reconstructed into a three-dimensional digital model, achieving full coverage measurement from simple geometry to complex surfaces. In addition, the software can handle 13 geometric tolerances such as straightness, flatness, and coaxiality, and output inspection reports that comply with ISO standards.