Yesterday, we talked about the first part of how CNC machines work. Today we will continue to talk about it.

Part shape too "free"? It's done by interpolation.

If the motion trajectory can be expressed analytically, the whole movement can be decomposed into the synthetic motion of independent motion with several coordinates, and the motor-generator can be directly controlled.

However, the shape of many parts in the manufacturing process can be said to be very "free", which is neither round nor square and even do not know what shape it is. For example, products such as cars, ships, aircraft, molds, and works of art often encounter curves and surfaces that cannot be described analytically. Such curves and surfaces are called free form curves or free surfaces.

To cut out these "free" shapes, the relative motion between the tool and the workpiece is also very complex. Specifically, in the operation, it is necessary to control the workpiece table and tool to move according to the designed position time curve and control them to reach the specified position with the specified attitude at the specified time.

The machine tool can well complete the relative motion of linear segments, arcs, or other analytical splines between the workpiece and the tool, and how can this complex "free" motion be completed? The answer is to rely on interpolation.

The so-called interpolation is the process of determining the motion path of the tool on the NC machine tool according to a certain method. According to the given speed and track, add some new intermediate points between the known points of the track, and control the workpiece table and tool to pass through these intermediate points, to complete the whole movement.

These intermediate points are connected by line segments, arcs, or splines. It is equivalent to approaching the required curve and surface with several small segments and arcs, which is the essence of interpolation.

Popular interpolation algorithms include point by point comparison method and digital increment method. NURBS spline interpolation is favored by high-end NC machine tools because of its high efficiency and good precision.

The posture of the knife is wrong and cannot be processed? Five coordinate linkages will be completed in minutes.

Machining complex curved surfaces not only can be machined in theory but also needs to consider the relative position relationship between the tool and the machined surface.

On the one hand, if the tool attitude is not appropriate, it will lead to low surface quality; On the other hand, the tool will interfere with the processed part structure. There is no way to process without adjusting the relative posture of the tool. This requires giving CNC machine tools more freedom of movement and making them more dexterous.

Since the relative motion in our three-dimensional space only contains six degrees of freedom (three translational degrees of freedom and three rotational degrees of freedom), the five-coordinate linkage is to increase the rotational degrees of freedom in two directions in addition to the translational degrees of freedom in X, Y and Z directions, plus the rotational degrees of freedom for cutting of the tool itself. 

In this way, the relative motion between the tool and the workpiece has all six degrees of freedom, so that the tool and the workpiece can present any relative position and attitude.

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