The geometrical simulation model of predicting surface texture of workpiece during the peripheral cylindrical grinding
Alexander A. Dyakonov1, a, Leonid V. Shipulin1, b
1454080,
Lenin ave., 76, Chelyabinsk, Russian Federation
[email protected], [email protected]
Keywords: imitation modeling, peripheral cylindrical grinding, topography and roughness of workpiece surface.
Abstract. Geometrical simulation model of interaction of grinding wheel and workpiece, which
possible to make provision for changing radial feed in the processes of peripheral cylindrical grinding is developed. The model allows to predict a roughness at processing steps, to form processing
limits by a roughness of the processed surface and to use this restriction in cycles develop. The algorithm of functioning of model is constructed and realized by means of C#. Correlation of results
of modeling and data from machining standards on the cutting modes is made.
Introduction
The main way of processing of cylindrical external surfaces providing implementation of requirements
for high accuracy and a low roughness is cylindrical grinding with radial feed. In a modern technique of
cylindrical grinding is producing most often in the form of a cycle at which all way of the tool to workpiece divide into three stages: rough, semi-rough and finish grinding. Design of a cycle is carried out taking into account a number of processing limits on durability and wear of the tool, on temperature in a cutting zone, on the accuracy of processing, power of the machine and, of course, a roughness.
At creation of limit on a roughness it is necessary to consider that fact that the processed surface is
formed not instantly, and is sequent in the process of removal of an allowance. Such problem definition of
predicting of a roughness in a cycle demands the accounting of radial feed changing from a turn to a turn.
Thus, the task of predicting of a roughness in the entire period of processing taking into account the changing radial feed is set. The solution of such task is possible only on the basis of simulated modeling. In this
line of research there are a number of works [1–6].
Task definition and process scheme
At peripheral cylindrical grinding the tool rotates with a speed of cutting and progressively
moves with a speed of feed, workpiece rotates with another speed. It is convenient to make modeling of process of interaction of the tool and workpiece not on all surface of workpiece, and being
limited only to a cutting zone (fig. 1a). Considering a grinding cycle, the whole changing of surface
texture in the contact zone will happen to a step to one rotation of a workpiece (fig. 1b). Considering that length of an arch of contact is much less than a radius of circle (for example, length of an
arch of contact is equal to 1 mm with a diameter of wheel of 600 mm), set of contact zones can be
transformed to set of flat surfaces (fig. 1c).
The scheme provided on fig. 1a and transformed to the scheme in fig. 1c allows to consider cutting depth on each turn of workpiece. It allows to modeling any variations of an grinding cycle.
Modeling of interaction of grinding wheel and workpiece
Interaction of the tool and workpiece represents multiple a micro cutting by abrasive grains as a
result of which the polished surface is formed. By analogy with real process it is offered to develop
the model based on the scheme of discrete contact. We will note that the similar model was already
created by authors for peripheral cylindrical grinding [7].
a)
b)
c)
Fig. 1. Process scheme of formation of a peripheral cylindrical grinding
Considering the process scheme in fig. 1c it is possible to note that the task has analogies to
modeling of peripheral surface grinding. The analysis of these two processes regarding comparability when modeling allowed to reveal both of identical and different components. It is solved to use
identical components which already proved in developing geometrical model of peripheral surface
grinding.
Probabilistic modeling of the abrasive tool first of all belongs to such identical components. So,
the sizes of abrasive grains submit to the normal distribution, and coordinate of their position in
volume of a wheel – to the uniform distribution. Each grain is presented by a paraboloid of revolution which moves on a circular trajectory. The relief of workpiece is presented by a matrix, which
each element – height of grid knot on a workpiece surface. At the time of contact of single abrasive
grain and workpiece calculation of topography of single scratch as result of consecutive positions of
a parabola is made. The received heights are brought in a matrix which then is subtracted from a
matrix in which the texture of workpiece surface is stored. Further activating the following grain
and so until through a zone of cutting don't pass all grains of a grinding wheel for all its turns.
In models there are also different components. So, length of an arch of contact of the wheel and
workpiece, and therefore, length of single scratches, at peripheral cylindrical grinding is significantly less, than at the surface grinding. As well the wheel carries out the additional movement towards
the processed surface (movement of feed) therefore the provision of each scratch has to be modified
on height. In addition there is a question of how it is most convenient to set input data.
On the basis of the aforesaid for modeling of interaction of the wheel and workpiece the algorithm given on fig. 2. The offered algorithm combines already available decisions for peripheral
surface grinding and the decisions concerning correction of length of an arch of contact and height
of position of scratches.
The algorithm includes the following main units: 2 – the block of reading input data from the table in the excel file, 3 – the block of stochastic generation of the abrasive tool, 4 and 5 – blocks of
start of counters, 6 – the block of calculation of topography of scratch after interaction of single
grain, 7 – the block of forming of topography of contact zone on workpiece, 10 – the block of calculation of parameters of a roughness, 11 – the block of drawing of a relief of surface texture after
processing and 14 – the block of a conclusion of results of calculation in the excel file. The developed algorithm was realized by means of the C# programming language.
Thus the model of geometrical interaction of the tool and workpiece at external cylindrical grinding is developed. Input data for modeling are set in excel file in the form of set of lines, each of
which describes the cutting modes on each turn of workpiece (fig. 3). Results are brought in the
same file (fig. 3).
Fig. 2. Algorithm of geometrical simulation model of peripheral cylindrical grinding
Fig. 3. Input and output data in excel file
Verification of geometrical model
Comparison of results of simulation modeling to the data presented in machining standards on
the cutting modes is made. Relation of a roughness on granularity of the abrasive tool is presented
in these standards based on synthesis of manufacturing practice. For the corresponding granularity
calculations in the developed simulated model are made. For each situation in imitating model the
texture of the processed surface (fig. 4) and values of a roughness are received. On values of a
roughness and data from standards graph of relation of a roughness on granularity of the tool (fig. 5)
are constructed. Comparison of schedules allows to speak about indirect confirmation of adequacy
to the developed model.
a)
b)
c)
d)
e)
f)
g)
h)
Fig. 4. Workpiece surface texture after simulation situations of grinding by wheels different granularity:
(a) F36, (b) F40, (c) F54, (d) F60, (e) F70, (f) F80, (g) F100, (h) F120
Fig. 5. The graph of relation of a roughness from wheel granularity
Conclusions
Simulation model of interaction of a grinding wheel and workpiece allowing to consider change
of radial feed in the course of peripheral cylindrical grinding is developed. In developing model the
results received earlier [7] were used. Comparison of results of imitating modeling and data from
machining standards is made. The directions of further improvement of the developed model are the
accounting of wear of abrasive grains [8, 9] and integration of the developed geometrical model in
thermophysical model [10].
References
[1]
X. Zhou, F. Xi, Modeling and predicting surface roughness of the grinding process, International Journal of Machine Tools & Manufacture 42 (2002) 969-977.
[2] Sanjay Agarwal, P. Venkateswara Rao, A probabilistic approach to predict surface roughness
in ceramic grinding, International Journal of Machine Tools and Manufacture 45 (6) 609-616
[3] R.L. Hecker, S.Y. Liang, Predictive modeling of surface roughness in grinding, International
Journal of Machine Tools and Manufacture, 43 (2003) 755-761.
[4] E.J. Salisbury, K.V. Domala, K.S. Moon, M.H. Miller, J.W. Sutherland, A three-dimensional
model for the surface texture in surface grinding, Part 2: Grinding wheel surface texture model, Journal of Manufacturing Science and Engineering, Transactions of the ASME 123(4) 582590.
[5] T. A. Nguyen, D. L. Butler, Simulation of precision grinding process, part 1: Generation of
the grinding wheel surface, International Journal of Machine Tools & Manufacture 45 (11)
1321-1328.
[6] T. A. Nguyen, D. L. Butler, Simulation of surface grinding process, part 2: Interaction of the
abrasive grain with the workpiece, International Journal of Machine Tools & Manufacture 45
(11) 1329-1336.
[7] D`yakonov, A.A. Selecting the Cutting Conditions for Plane Grinding by the Wheel Periphery
/ A.A. D`yakonov, L.V. Shipulin // Russian Engineering Research. – 2014. – Volume 34. –
№12. – P. 814–816.
[8] Ardashev, D.V. Physicochemical wear of abrasive grains during grinding processes / D.V.
Ardashev // Journal of Friction and Wear, Allerton Press, Inc. – 2014. – № 4. – pp. 284–289.
[9] Ardashev, D.V. Predicting the Working Life of Abrasive Grains// D.V. Ardashev // Russian
Engineering Research, Allerton Press, Inc., 2015, Vol. 35, No. 4, pp. 302–304.
[10] Dyakonov, A.A. Simulated Stochastic Thermo-physical Model of Grinding Process/ A.A.
D`yakonov // Lecture Notes in Engineering and Computer Science. – 2014. – V.2. – P. 914–
917.