Interrelation of processing modes with the current parameters of the contact zone during thermofriction processing

. The establishment of the interrelation between the processing modes and the current parameters of the contact zone during the thermofriction processing of flat surfaces of workpieces by a rotating disk tool is considered. Dependencies are presented allowing assignment of cutting modes, prediction of the size of the removed material layer, and determination of the control actions value.


Introduction
Mathematical modeling of workpiece processing operations allows solving many practical problems in the selection and design of the tool, the designation of methods and processing sequence, and optimal control of technological equipment [1][2][3].
Determination of the output technological parameters of thermofriction processing (TFP) by means of mathematical models makes it possible to simplify significantly the search for optimal modes and is a relevant task.
The operation is very often treated as a dynamic system during simulation [4]. One possible scheme for the decomposition of an operation as a dynamical system is considered in work [5]. According to the functional characteristics, the operation is divided into subsystems of the machine tool, fixtures, tools, workpieces. Each of the subsystems has its own set of properties, state parameters, development history, a vector of input and output variables, a vector of perturbing influences.
The central subsystem is the contact area of the workpiece with the tool. The zone state parameters [4] include its dimensions, shape, parameters of the chip formation process, material removal rate, wear parameters and tool material destruction. The dimensions of the zone are in direct connection with the dimensions and spatial arrangement of the tool and the workpiece, as well as the state of their surfaces. Due to changes in the size, spatial location and condition of the contacting surfaces, the parameters of the state of the contact zone and, as a consequence, the parameters of the quality and efficiency of the TFP, will change with each new rotation of the disk.
Therefore, the purpose of this work is to establish the inteconnection of processing modes with the current parameters of the contact zone.
To establish the parameters of the contact zone, let us consider the scheme of the TFP process ( Fig. 1).
In a section plane, perpendicular to the surface being processed, the contact zone has the form of two mutually intersecting rectangles. In TFP after leaving the zone, the thickness of the workpiece decreases by the amount of material removal h ∆ , the height of the disk -by the amount of wear H ∆ . The surface to be processed is faced with microprotrusions farthest from the base surface of the cutting blade. The shape of the zone also changes due to the appearance of elastic deformations of the disk and the workpiece.
Let us denote the maximum possible (nominal) depth of insertion of the microprotrusions of the tool into the workpiece material with f t . The actual depth will be less than the maximum possible for the amount of material removal. After leaving the contact zone, the roughness remains on the surface of the workpiece, since the cutting blade has a cutting edge with microprotrusions. The surface roughness is distributed in a layer with thickness max R . The actual depth of cut is interrelated with the material removal and the depth of the roughness layer by the simple relationship [3]: To derive a relation characterizing the balance of displacements, let us consider Fig. 1, according to which for the ith pass we have: Accordingly, for the i-1th pass we get: h h − -the dimensions of the workpiece before the completion of the i-th and i-1-th pass [6].
After subtracting the dependence (1) from (2), we get i A ∆ -the distances between the base surfaces i A on the i-th pass:   (3) and (4), taking into account the direction of the feed, we obtain the balance equation of displacements in the technological system in increments: Dependencies (5) and (6) determine the change in the state of the technological system for any time moment in TFP [7][8].
Equations demonstrate that the state of the system under TFP depends on the current and previous stages of processing, depends on the state of the tool, elastic deformations, etc.
Analysis of the dependences (5), (6) shows that the vertical feed on the i-th pass is spent on incrementing the depth of microcutting, compensating for the removal of material from the previous passage, wear of the disk, increment of elastic and temperature deformations. The dependence differs from the known ones by the presence on the right of the increment of the depth of microcutting, which in some cases may be greater than the other summands [9][10].
A schematic diagram of the change in increments over the period of processing one surface is shown in Fig. 2.
So, for TFP on vertical milling machines with a workpiece size of 30×50×200 mm, the flexibility of the «milling head spindle-tool» system is 0,04 to 0,06 μm/N. When processing with disks with a height of 50 mm, the resultant cutting force is 800...1000 N. Consequently, the elastic depressions in the system lie in the range from 0,03 to 0,06 mm, the depth of microcutting varies from 0,05 to 0,2 mm, and the temperature deformation significantly exceeds the elastic ones (on average 2 and 2,2 times). With the course of time, material removal and disc wear increase, so the increments of deformations and depth decrease for the further part of the process, and at the stage of the steady-state process they tend to zero. Vertical feed at this stage is almost completely spent on material removal and tool wear.
Analysis of the dependence (6) shows that the establishment of the parameters of the i-th contact is possible only if there is information about the i-th contact.
The use of the dependence (6) allows us to keep to the second principle of the analysis of the TFP operations. The equation of the balance of displacements (6) in TFP with changing cutting conditions and the parameters of the state of subsystems is the basis for predicting the spatial arrangement of the tool and the workpiece, the dimensions of the contact zone, and, consequently, the quality parameters of the processed surface.
To solve it, it is necessary to have dependencies for calculating the cutting force, material removal, disc wear, elastic and thermal deformation of the elements of the technological system.

Conclusion
The equation (6) allows us to assign modes, predict the value of the remote layer of the material, determine the value of control actions, for which it is necessary to determine the functions included in the equation (6), which is the task of the following studies.