A NEW APPROACH OF SURFACE ENVELOPING, BASED ON THE DISCREETLY SURFACES REPRESENTATION, IN ORDER TO ALGORITHMIZE AND INFORMATIZE THE GENERATING TOOLS PROFILING
The machining improvement in the sense of machining precision increasing presume, more and more, the synthesis of models for generation errors prediction and adjustment by software using: analytical models , , modeling based on genetically algorithms , as so as, methods based on polynomial neural network (PNN) , using on machine measurement systems (OMM) , in order to adjust errors, the whole system being integrated in CAD/CAM/CAI systems.
It was developed  methods for errors adjustment by developing generating software for alternative tools movement, assuring an errors reduction up to 90% by decreasing the cutting force value.
It was developed algorithms  in order to optimize the tool position, for multi‑ax machine‑tools, integrated in CAD/CAM systems  for errors adjustment, using multi‑degree of freedom (multi‑DOF) sensors , also for curves and surfaces design by interactive 3D modeling, which are approximated by interpolation methods  in order to rebuild the surface form.
Fig. 1. Geometrical modeling based process simulator
It was developed geometrical simulators  linked with physical simulators based on cutting process modeling (see fig. 1). The process physical simulator consists in cutting force models for various existing situations. Each model based on empirical knowledge use as input data the geometrical simulator output data. In this way are obtained the cutting process parameters models starting from geometrical considerations. Often, the process simulator has an optimization module, which transmits information to machine‑tools kinematics chain in order to increase the productivity and to decrease the generating errors. In figure 2, is give an result obtained with this simulator type, comparative with experimental results.
Fig. 2. Comparative between the process simulator result and experimental results
Based on the conjugated surfaces theory was developed methods for generation of surfaces expressed in discreetly form (digital gear tooth surfaces – DGTS) in 2D, as so as, in 3D, establishing solutions for enveloping surfaces determination – peripheral primary tools surfaces .
Fig. 3. Strategy for errors adjustment Fig. 4. Results comparison
Are established strategies for errors analyses and adjustment (see figure 3), applied at 2D and 3D modeling for involute teeth flank generation, , method which allow the generating tools profile drawing and in the same time the discreetly coordinates of tools generating movement (see figures 3 and 4).
Usually, the machining errors are defined on normal at machined surface as difference between this surface and the theoretically surface, discreetly expressed.
The error is detected only by surface measuring after machining.
Based on this concept is proposed an error estimation for cutting (DGTS). The machining errors are analyzed starting from the machined surface. The method makes a comparison between the two models: DGTS CAD model and a virtual model of measured surface of machined wheel teeth.
Error adjustment , , , , , 
It is known that the machined surface precision after a single correction is not total. Always remain a residual error.
So, is needed to establish an iterative scheme for machining error reduction, which will drive to increased time consumption. In current applications, the cutting process is repeated several times. If the result of first machining is processed and the data are inserted in numerical command is possible to make a more accurate machining.
The adjustment error is defined  as:
They are also used the machine‑tools spatial errors adjustment  which solve the problem starting from the idea that the static errors affect the dimensional precision up tot 70% from the machine‑tool whole error.
Exist an obviously attention regarding the prediction and adjustment by software of generation errors.
The integrated CAD/CAM/CAI systems allow to develop surfaces generating process with smaller errors.
For machines with more axes, are defined algorithms for spatial errors modeling, establishing analytical models for errors and systems for adjustment of these.
Are used genetically algorithms modeling based and methods based on polynomial neural network, using on machine measurement. Are interactive modeled 2D/3D surfaces curves which are approximated by interpolation methods in order of surface form rebuilding. At enveloping surface generation the tools shape correction regarding the generation result may be made using the geometrical modeling methods (Gohman, Willis, minimum distance, substitutive circles family, in‑plane generation trajectories, solid modeling) , , .
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