Prediction of machining errors on the geometric accuracy of a milled guide

U. Prisco, G. Giorleo, F. Coticelli

University of Naples Federico II, Italy

Two views of the simulated guide

 

 

Two views of the simulated guide

Prediction of machining errors on the geometric accuracy of a milled guide

U. Prisco, G. Giorleo, F. Coticelli

The envelope surface of a swept volume is the set of points which are part of the frontier of the swept solid. The solid which generates the swept volume (i.e. the tool) is called generator. The envelope surface can be subdivided in two types of surfaces. The surfaces of the first type are a subset of the generator surface at the beginning and the end of the trajectory, while the surfaces of the second type are generated during the motion of the generator. For many industrial application only the second type of surfaces is relevant.

• From the beginning of the industrial era surface characteristic drive the machine development.
• The layout influence on the working error has been assested long time ago.
• In recent years many studies have been made in order to understand influence of gauges and vibrations on the surface topography.
• Computer simulation permit to verify the influence of machining errors on the working.
  

Accuracy prediction of a milled guideThe concept of form shaping is the base on which our work is based. Introduced by Reshetov and Portman in their book "Accuracy of Machine Tools". The starting point is the Machine/Fixture /Tool/Workpiece system, or MFTW.

The  characteristic of a form shaping system is the fact that two consecutive links subject to relative motion does not have more than a degree of freedom. This implies that it is possible to describe the relative motion between two links by the use of a single coordinate.

It is also possible to describe the layout of a machine by the use of simple codes. 

Three tipes of codes are needed in order to describes machine:

• Machine coordinate code: describes the type of motion between two links
• Velocity code: describes the nature of the motion between two links
• Arrangment code: describes the physical structure of the machine 

The Form Shaping function, along with the constraints imposed on the motion of the tool, give us a perfect description of the ideal surface obtained by machining. In order to implementate the errors generated by vibrations and deformation, a series of virtual links are added to the Form Shaping function. These links give us the possibility to describe the machining errors by using only six variables.

• The method has been applied to the milling of a guide
• Envelope surfaces can be calculated by using of appropriate parallelism consideration
• A Mathemathica algorithm has been used for implementate the method

For the simulation the following machining parameters were chosen: feed velocity = 500 mm/min and RPM = 1200. The simulated errors were j_x = 2° and j_y = 3°.

Because of the complex form of some tools and the complexity of some trajectories it is impossible to find a closed form expression for the swept volume. This description of the cutting process through swept envelopes gives a simple clue about the simulation of this process by computer. Using a very simple simulation it is possible to find the whole number of points swept by the tool, but this method require a lot of calculation and it is not efficient, because there are other solutions which require shorter calculation.