Article citation information:
Cieślar,
K., Płonka, S. Modeling of rough rotary milling of crankshaft
pins. Scientific
Journal of Silesian University of Technology. Series Transport.
2023, 121, 45-61. ISSN: 0209-3324. DOI:
https://doi.org/10.20858/sjsutst.2023.121.4.
Kacper
CIEŚLAR[1], Stanisław PŁONKA[2]
MODELING OF ROUGH ROTARY MILLING OF CRANKSHAFT PINS
Summary. The
development of the modern automotive industry requires a quick adaptation of
new production methods. This is possible thanks to software capable of
simulating manufacturing processes. The paper discusses the modeling of the
machining operation of a crankshaft’s crankpins for a diesel engine with
the use of the planetary milling method. i.e., modeling of milling operation
when a disc milling cutter, having its cutting inserts directed inwards, is
performing rotary motion, and at the same time, the axis of this milling cutter
circulates around the axis of a machined crankpin. For this purpose, a
geometrical model of the machining of the crankshaft’s crankpin has been
developed. Based on the design documentation of the crankshaft of the 4C90 type
diesel engine and the documentation of the Steyr internal disc milling cutter,
their CAD models have been developed, and the both models were linked together
with suitable kinematic dependencies. In the next step, the crankpin having a
length of 25 mm was divided by planes (in quantity lp=21) into 1.25 mm
sections. On the main cutting edge of two cutting inserts of the disc milling
cutter, points were marked at intersection locations with these planes. Using
the Inventor 2016 system, twelve spline curves have been generated for each
plane because each plane intersects 12 cutting inserts mounted in cassettes
positioned around the circumference of the body of the disc milling cutter.
Next, the spline curves were brought to a common coordinate system, rotating
them at an angle resulting from the positioning of the cassettes with cutting
inserts in the body of the disc milling cutter. Prepared in such a way, spline
curves were written in dwg format, which allowed for trimming of the spline
curves at the circle with a radius of rcp = 27.90 mm, corresponding to the
radius of the crankpin after milling, considering grinding allowance
(ø55h6 + 0.80 mm grinding allowance). As a result, it enabled to leave
sections of the arcs tangential to the diameter ø55.80 mm and, in such a
way, generate the outline of the shape of the crankpin using the REGION command
for 21 cross-sections. The outline of the cylindricity of the crankpin was
obtained using the strategy of outlines of the roundness, which were generated
earlier; this strategy consisted in the collection of 360 points on the
circumference of 21 mutually parallel sections cut by planes perpendicular to
the axis of the crankpin. To determine the effects of the circular feed rate of
the circulating move of the axis of rotation of the internal disc milling
cutter on the accuracy of the machining, simulations of the shape of the
crankpin were performed for three values of the feedrate: vf = 1200 mm/min; vf
= 2100 mm/min and vf = 3000 mm/min. The spline curves with a determined (depending
on the duration of the simulation) number of points: 3500, 2100 and 1409 were
obtained for each simulation. The calculated cylindricity deviation for the
feedrate vf = 1200 mm/min amounted to CYLrck = 0.2272 mm, for the feedrate vf =
2100 mm/min – CYLrck = 0.2406 mm, while for the feedrate vf = 3000 mm/min
– CYLrck = 0.2929 mm.
Keywords: modeling
of machining, crank shaft, internal rotary milling
1. INTRODUCTION
The development of the modern
automotive industry requires constant improvements. This is caused by the
desire to increase the power of internal combustion engines while reducing the
pollution they emit. It should be remembered that the effect of the design
phase will have an impact on the operational process, including an increased
probability of unexpected engine failures resulting from damage to its various
components [18, 19]. Modeling with the use of computer programs makes it
possible to accelerate the implementation of new technical solutions, e.g. by
analyzing the production of crankshafts, it can be concluded that the
technological processes of their machining are very complex, and by performing
machining simulation, the process can be improved even before its actual
implementation. The crankshaft belongs to one of the most responsible
structural components of the combustion engine, participating in the conversion
of reciprocating movement of the piston into rotational movement, and at the
same time, it repeatedly transfers quite high, periodically acting loads [17].
Due to the imposed requirements and shape of the crankshafts, their
manufacturing processes must meet high qualitative requirements. The choice of
manufacturing process depends mainly on production volumes and the overall
dimensions of the crankshaft, and, to a lesser extent, on the kind of blank. In
the last century, in the course of unit and small series production, the main
journals and the crankpins were machined by turning operations, wherein the
crankpins were generally machined with the use of special machining fixtures.
On the other hand, in cases of mass volume production, machining of the
crankpins was carried out using the three-shaft method on a special
automatic lathe, consisting of simultaneous turning of all crankpins [17]. Such
a method was used to machine the journals of a crankshaft with four cranks,
produced as a casting from spheroidal cast iron, and mounted in the 899
ccm passenger cars of the Seicento brand. Nowadays, in the production of the
crankshafts, due to production efficiency, in the case of rough and shaping
machining of both the main journals and the crankpins, external rotary milling
or internal rotary milling systems are used, or relatively, planetary milling
with special disc milling cutters having cutting inserts mounted mechanically
[2, 7-9, 11]. Except for the above-mentioned methods of rotary and
planetary milling, turn broaching with the use of flat broaches, or more often,
turn-turn broaching operations, are used in the mass production of the
crankshafts. The second solution, due to its kinematic features, is called a
turning & broaching operation (rotary broaching) [2, 5, 6]. The shaping
operation of the main journals of the 1.3 SDE diesel engine’s crankshaft,
performed in the Bielsko-Biala plant, is an example of the turning &
broaching operation with the use of rotary broaches. To machining of the main
journals in course of mass production and small-volume production, turning
machining on CNC center lathes was generally
used, whereas machining of the crankpins was performed using internal rotary
milling or planetary milling operations. Nowadays, machining of both the main
journals and the crankpins is performed most frequently in the course of
internal planetary milling, while basing on already machined main journals, one
machines alternatively the crankpin, and next the main journal, changing
position of the angular prop. In case of unit or
prototype production, the crankshafts can be manufactured from rolled bars in
milling-turning operations on WFL turning-milling centers with 5 axes controlled
[10].
The main objective of rough
machining is to provide a large depth of cutting and, therefore, high
productivity. Less attention is paid to geometrical accuracy and surface
quality as obtained in subsequent operations of shaping and finishing, i.e., in
operations of shaping and grinding, and next, in the case of mass production,
the most often, oscillating superfinishing with abrasive foils.
Presentation of geometrical modeling stages of planetary milling operation of crankshaft crankpins and determination of the effects of the circular feedrate of the circulating movement of the axis of rotation of the internal disc milling cutter (rotational speed of the eccentric housing
2. METHOD OF PLANETARY MILLING OF THE
CRANKSHAFTS
A die forging from 42CrMo4 steel was used as a semifinished product in
the production of the crankshaft with 4 cranks for the 4C90 type diesel engine.
In the study, one analyzed the rough machining using the method of planetary
milling of selected crankpins of this engine using an internal disc milling
cutter on a special numerically controlled Steyr FKP-20/1 milling machine [9].
The machining scheme of the crankpin performed by planetary milling is shown in
Figure 1, while individual machining stages of the crankpin are shown in Figure
2.
Unlike external and internal rotary milling, the crankshaft is at a
standstill during planetary milling. The planetary movement is performed by internal disc milling cutter,
this movement is composed of rotational movement of the cutter with speed
Fig. 1. Scheme of planetary milling of
crankshaft’s crankpin using internal disc milling cutter: 1 –
crankshaft of 4C90 type diesel engine with 4 cranks; 2 – internal disc
milling cutter;
3 – crankpin, 4 – main journal (bearing journal), 5 –
eccentric housing, 6 – axis of symmetry of machined crankpin, 7 –
axis of rotation of internal disc milling cutter
Fig.
2. Machining stages of
crankshaft’s crankpin during planetary milling:
1 – crankpin of the crankshaft, 2 – internal disc milling cutter, 3
– eccentric housing
In the initial position, the axis of
symmetry of the crankpin which undergoes the machining, and the axis of
rotation of the internal milling cutter, rotating with speed
3. METHOD OF GEOMETRICAL MODELING
In general, geometrical modeling
based on 3D modeling modules of CAD systems implements Boolean operations on
the models that are the subject of the analysis [15, 16]. The models generated
in such a way can serve as examples to assess the geometrical accuracy of the
machining, modeling traces of the machining, or as a basis for further
analyses.
In the case described here, in
the first succession, a geometrical model of the crankshaft of 4C90 diesel
engine was developed based on its design documentation, and a geometrical model
of the internal disc milling cutter was developed based on the design
documentation of this cutter published by Steyr. In the next step, using the 3D
parametric modeling module of CAD system, the following system has been
modeled: internal disc milling cutter, machined crankshaft crankpin. By
defining the appropriate geometrical constraints, the mobility of the internal
disc milling cutter was determined, i.e.,
-
rotational movement with constant speed
-
movement of the axis of rotation along a circular path
with radius
The tracking function was used during the simulation
of the movement of the model to generate paths of movement for the points lying
on the main cutting edge of the cutting inserts of the internal disc milling
cutter. In order to reproduce machining conditions, the simulation time was
restricted because of the determined circular feed rate of the axis of rotation
of the internal disc milling cutter, which required its circulation at
360°. The path of motion of the analyzed point in the form of a spline curve
is the effect of the tracking during the simulation. In the case discussed
here, this curve was exported in native format, and its further analysis was
performed in the 2D modeling module of the CAD system. The function of creating
an envelope was used to generate a model of the cross-section of the crankpin
being machined in the analyzed plane of motion of the point on the cutting edge
of the cutting insert of the internal disc milling cutter.
Necessary
designations adopted in the model of machining of the crankshaft's crankpin
during planetary milling are shown in Figure 3. As aresult of circulating
movement of the axis of rotation M of
the internal disc milling cutter rotating about the axis of the crankpin P, the disc cutter, represented by a
substitutive cylindrical surface having radius
Fig. 3. Machining model of the
crankpin during planetary milling with
use of an internal disc milling cutter
The internal disc milling cutter consists of six repeating sets on each
of its side. Each set, in turn, contains three cassettes equipped with single
cutting inserts, i.e. there are 18 cassettes in total on one side of the disc
milling cutter (36 on the both sides).
The cassettes with mounted cutting inserts are positioned in the body
tangentially to the circle with diameter 31.10±0.05 mm. In
each set, the first two cassettes are equipped with E-type cutting inserts to
machining cylindrical surface of the crankpin, while the third cassette –
is equipped with S-type cutting insert to machining transition radius area and
web of crank, connecting crankpin with the main journal. For instance, the Figure 4 shows view
of two sets of cassettes with cutting inserts from both sides of the body of
the internal disc milling cutter. In addition, on the edges of E-type inserts,
which are milling cylindrical surface of the crankpin, numbers of planes p, for which the calculations were
carried out in the model, were marked.
Fig. 4. Two sets of
cassettes from the both sides of the body of the internal disc milling cutter:
1;3;5, and 2;4;6, where 1,2,3 and 4 - E-type cutting inserts (27.A58 and
27.A59) shaping the cylindrical surface of the crankpin; 5 and 6 - S-type
cutting inserts (27.A62 and 27.A66) shaping the transition radius and web of
the crank
The machining cycle of a single crankpin consists of three operations:
-
pushing with straight-line motion of the eccentric
housing with internal disc milling cutter close to the standstill crankpin (or
main journal) of the crankshaft, and indentation of the cutter into the crankpin
into the required depth, (starting position),
-
real machining cycle consisting of a single complete
rotation of the eccentric housing with speed
-
stoppage and retracting of the eccentric housing with
a rotating internal disc milling cutter away from the crankpin, and positioning
for machining of the next crankpin.
Modeling of the machining process
was limited to the second operation, where the cylindrical surface of the
milled crankshaft’s crankpin, transition radius area, and web of the
crank are shaped (the calculations were carried out for the shaping of the
cylindrical surface of the crankpin only).
At the beginning of this operation (for the
time
where:
Modeling of the machining process, i.e., removal of successive layers of
material, is connected with the calculation of the mutual location of cutting
inserts in the set of cassettes and with the calculation of the axis of
rotation of the spinning internal disc milling cutter at any moment of time
Then, the angular position
where:
Moreover, a coordinate system has
been assumed in which axis Y passes
through the axis of the main journals and axis of the machined
crankshaft’s crankpin at the moment
The position of cutting inserts of individual sets of the internal disc
milling cutter on plane XY of the
assumed coordinate system is connected with the position of the point M of the axis of rotation of the disc
cutter. The coordinates of the point
while the clockwise displacement of the axis of rotation of the rotating
internal disc cutter, with respect to the starting position, is described by
the dependencies:
where:
Coordinates of the contact point C = [XC, YC]T
are calculated from the following dependencies:
where:
The axis (center) of the cylindrical surface of the machined crankpin
Calculations of the coordinates of points on the surface of the
crankpin, generated as a result of the movement of the tool, were carried out
in selected cross-sections of the internal disc milling cutter. It has been
assumed, that on width B of the disc cutter, p parallel
cross-sections uniformly spaced will be analysed (Fig. 5). Planes of these
sections intersect edges of cutting inserts of the cassettes located on both
the sides of the housing of internal disc milling cutter in lp points (Fig. 5). Hence, work
of the edges of cutting inserts within a set of the points
Fig. 5. Analysed cross-section planes
of the internal disc milling cutter,
1;2 – E-type cutting insert, shaping cylindrical surface of the crankpin,
5 – S-type cutting insert, shaping transition radius and web of crank
In the
Figure 3 location of the j-th point
what
enables modeling of the geometric shape of the crankpin after rough milling or
shaping milling.
Finally, the model of the surface of the machined
crankpin results from the mutual locations of analysed set of points at the edges
of cutting inserts relative to the machined crankpin of the crankshaft. For
instance, Figure 6 shows the determined trajectory of motion for a selected
point on the edge of the cutting insert during the shaping of the cylindrical
surface of the crankpin.
Fig.
6. Trajectory of motion of a
selected point of the edge of the cutting insert
during shaping of the surface of machined crankpin
4. RESULTS OF THE STUDY AND THEIR
ANALYSIS
In the study, one analysed
simulation of the machining of the first crankpin from the flywheel side of the
4C90 diesel engine’s crankshaft with four cranks mounted in a delivery
vans. The geometry of machined crankpins is determined by diameter 2
From industrial practice, it is seen that the optimal
cutting speed in the case of planetary milling of crankshaft crankpins with
four cranks, made of 42CrMo4 steel, equals 110 m/min. Based on this, the
rotational speed of the internal disc milling cutter has been calculated, which
was considered a constant value
During the study, the influence of circular
feedrate
Example results of modeling of the outline of the roundness of the
crankpin in cross-section cut by plane Z9=10.0
mm, for three values of circular feed rate, are presented in the Fig. 7, where
the average circle (LSC) was additionally marked with a thin line [1, 12].
Whereas, calculated from the model values of the radii of the crankpin for the
average circle (reference one), determined using the least squares method
b) a)
c)
Fig.
7. Outline of the roundness and
average circle (reference one) in cross-section cut by plane Z9=10.0 mm of the crankpin
after rough machining for different values of circular feed rate – 1200
mm/min; b – 2100 mm/min; c – 3000 mm/min; magnification of the
deviation in relation to the reference circle amounts to 200×
Tab. 1
Values of the reference circle radii
|
|
|
|
|
|
|
1200 |
27.6988 |
27.6995 |
27.6982 |
0.0013 |
|
2100 |
27.6999 |
27.7048 |
27.6995 |
0.0053 |
|
3000 |
27.7003 |
27.7076 |
37.6995 |
0.0081 |
A particularly useful parameter,
called cylindricity deviation and denoted in practice as
To determine and evaluate the
outlines of the cylindricity of the surface of the crankpin machined with
planetary milling, a strategy of outlines of roundness was implemented,
consisting of collecting points on the circumference of the series of mutually
parallel cross-sections cut by planes perpendicular to the axis of the
workpiece [12-14].
In the Fig. 8 are presented
outlines of the cylindricity of surface of the crankpin, obtained on the basis
of the geometrical model for three values of circular feed rate
In the next step, the outline of the cylindricity of the surface of the
crankpins, obtained on the basis of the geometrical model, was longitudinally
intersected by planes passing through the axis of the cylinder for the angles
0°; 90°; 180° and 270°. The intersections were made for the
outline of the cylindricity of the surface of the crankpins obtained for a
constant value of rotational speed of the internal disc milling cutter
a)
b)
c)
Fig. 8. Outline of generatrix
of the crankpin for angular position 0° from the geometrical model (generatrix of the cylinder, radius
of reference cylinder, radius of circumscribed cylinder, radius of inscribed
cylinder):
a) for value of circular feed rate
b) for value of circular feed rate
c) for value of circular feed rate
the deviations relative to the reference cylinder amounts to 100×
4. SUMMARY
Based on calculations carried out in selected planes of cross-sections
of crankpins of the crankshaft with 4 cranks, after simulation of planetary
milling with the use of an internal disc milling cutter, i.e., with cutting
inserts directed inwards, it was found that:
-
increase in the value of the circular feed rate of the
axis of rotation of the internal disc milling cutter practically does not cause
an increase in the value of the radius of the biggest inscribed circle
-
values of deviations of the roundness
-
values of cylindricity deviation for the crankpin
after planetary milling with a circular feed rate
The simulation
presented in this paper of the machining operation of the crankshaft's
crankpins belongs to one of many examples of machining of a workpiece having
complex shapes carried out on nc machine tools. The geometrical model presented
in this paper can serve to develop an appropriate parametric machining program
destined for other types of nc machine tools, as well as to make a preliminary
selection of optimal machining parameters due to the value of machining
allowances for grinding operations.
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Received 18.07.2023; accepted in
revised form 22.09.2023
Scientific Journal of Silesian University of Technology. Series
Transport is licensed under a Creative Commons Attribution 4.0
International License
[1] Faculty of Mechanical Engineering, University of Bielsko-Biala, Willowa
2 Street, 43-309 Bielsko-Biala, Poland. Email: kcieslar@ath.bielsko.pl. ORCID: https://orcid.org/0000-0001-9552-025X
[2] Faculty of Mechanical Engineering, University of Bielsko-Biala,
Willowa 2 Street, 43-309 Bielsko-Biala, Poland. Email: splonka@ath.bielsko.pl.
ORCID: https://orcid.org/0000-0001-7586-7854