## Knowledge Zone

Dynamic Analysis of Vectors ™

In control systems which process a single block of the cnc code, i.e. one coordinate at a time, it is not possible to finish the motion along a given vector at a speed other than zero. This is because the driver does not analyse the data concerning consecutive vectors following the vector being just executed. Not knowing what the next move will be, it has to stop to start the subsequent move after downloading the next block.

This results in a situation in which the movement on the tool path is interrupted, despite the fact that, e.g. successive vectors are tangent to each other. For the tool paths dominated by long vectors it is of little significance, because during the movement along such a vector, the machine has a sufficiently long way to achieve the preset motion speed. The time after which the machine reaches this speed, and whether this speed can be achieved with the vector of a given length or not, is dependent on its value and the specified acceleration.

The problem starts to appear while performing vectors which are so short that you cannot reach the preset speed on them. In this case, the average feed rate is much lower than the preset speed. This results in a significant reduction in treatment capacity, and what is more, the accelerated wear which is caused by frequent changes of cutting parameters due to frequent stops.

This problem is particularly apparent at HSM (High Speed Machining) operation mode, involving work with significantly increased cutting speeds. In this technology the feed rate is greater than the speed of propagation of the temperature in the workpiece, which means that almost all the energy accumulated when peeling the chip is thrown out together with it. Therefore, the tool and the material heat up less during cutting than in the course of conventional treatment.

To precede the propagation of the temperature in the material and to keep the thickness of the chip at a safe level at the same time, the rotational speed of the spindle must be higher respectively. It must be so high that it would lead to overheating and damage to the tool in hard materials at low feed rates (below HSM).

The use of HSM technology on machines with such a control system is not possible because frequent stops of the tool in the material result in its frequent overheating, which lead to very rapid wear.

To eliminate these problems, the machine should maintain the feed rate on the level set by the operator as far as possible. The maximum speed in the node between vectors should depend on the angle between them and on the shape of the tool path represented by these vectors. The solution might be the analysis of more than one vector at a time, which enables obtaining a non-zero value of the speed in the nodes of the tool path. Unfortunately, we cannot analyse only one vector forward, because it may be so short that on the length of this vector it will not be possible to reduce the speed to the value of its limitations at the end of the vector.

Therefore, it is necessary to apply an iterative analysis of consecutive vectors and such a modification (raising) of initially zero speeds in the nodes between the vectors which will satisfy the anticipated speed limits in the nodes of the tool path, and simultaneously which will reduce the time in which the tool is moving slower than the preset speed.

The method has been called the Dynamic Analysis of Vectors and its implementation has been very successful. For a complicated tool path numbering tens of thousands of vectors with an overall length of about 20m, at a preset feed rate 100mm/s and using the Dynamic Analysis of Vectors, the operating time was less than 4 minutes. When the function of the Dynamic Analysis of Vectors was off, the operating time came to about 20 minutes. This huge difference in the operating time of the machine allows to achieve significant benefits in the performance of work using complex tool paths, such as machining moulds, dies, die boards, casting models, matrices and other tools.