The Application of the Right-hand Cartesian coordinate System in Milling Machines

The coordinate system of the CNC milling machine adopts the right-hand Cartesian coordinate system, and its application is mainly reflected in the following aspects:

I. Definition of Coordinate System and Direction Determination

Coordinate axis direction ‌ :

X-axis ‌ : horizontal direction, parallel to the workpiece clamping surface. The direction in which the tool is away from the workpiece is the positive direction.

Y-axis ‌ : perpendicular to the X-axis and z-axis, determined by the right-hand rule, that is, the thumb of the right hand points in the positive direction of the X-axis, the index finger points in the positive direction of the Y-axis, and the middle finger points in the positive direction of the z-axis.

Z-axis ‌ : parallel to the spindle axis, the direction in which the tool is away from the workpiece is the positive direction.

Rotate the coordinate axis ‌ :

Axis A ‌ : Rotate around the X-axis, and the positive direction is determined according to the right-hand screw rule.

Axis B ‌ : Rotate around the Y-axis. The positive direction is determined according to the right-hand screw rule.

C-axis ‌ : rotate around the z-axis. The positive direction is determined according to the right-hand screw rule.

Ⅱ. Coordinate System Setting Steps

Determine the machine coordinate system ‌ :

The origin of the machine tool coordinate system is usually located at a certain fixed point of the machine tool (such as the end face of the spindle, the outer circle of the chuck, etc.).

The coordinate axis direction is parallel to the main guide rails of the machine tool.

Set the workpiece coordinate system ‌ :

Select the origin of the workpiece ‌ : Usually, a certain fixed point of the workpiece (such as a corner point, center point, etc.) is chosen as the origin of the workpiece coordinate system.

Measure the origin coordinates ‌ : Use a tool setter or trial cutting method to measure the coordinate values of the workpiece origin in the machine coordinate system.

Input offset value ‌ : input the measured offset value into the corresponding G54-G59 register.

Ⅲ. Examples of Coordinate System Applications

Programming example ‌ :

Suppose the lower left corner of the workpiece is the origin of the coordinate system. The X-axis moving to the right is the positive direction, the Y-axis moving forward is the positive direction, and the Z-axis moving upward is the positive direction. If a hole located at the center of the workpiece needs to be machined with coordinates (50, 50, 10), it indicates that the hole is at a position of 50mm on the X-axis, 50mm on the Y-axis, and 10mm on the Z-axis.

Practical example ‌ :

In actual operation, it is necessary to ensure the unification of the workpiece coordinate system and the machine tool coordinate system to avoid processing errors.

During the processing, if it is necessary to adjust the coordinate system, the origin and the direction of each axis should be reset.

Iv. Precautions

The uniformity of coordinate systems ‌ : Ensure the uniformity of the workpiece coordinate system and the machine tool coordinate system to avoid processing errors.

The accuracy of the coordinate values ‌ : according to the processing requirements, determine the accuracy of the coordinate values to avoid processing failure due to insufficient accuracy.

Coordinate system adjustment ‌ : During the processing, if it is necessary to adjust the coordinate system, the origin and the direction of each axis should be reset.