INVESTIGATION OF SPATIAL CAM BY THE LEAN METHOD

1. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 12, December (2014), pp. 47-54 © IAEME
47
INVESTIGATION OF SPATIAL CAM BY THE LEAN
METHOD
Renata Jackuvienė1
, Rimas Karpavičius2
, Tatjana Sokolova3
, Povilas Šaulys4
1
Dept. of Ship Energy, Lithuanian Maritime Academy, Klaipėda, Lithuania
2,3
Dept. of Mechanical Engineering, Kaunas University of Technology, Kaunas, Lithuania
4
Faculty of Engineering, Kaunas University of Applied Engineering Sciences, Kaunas, Lithuania
ABSTRACT
The Lean manufacturing is important for many companies which want to eliminatethe waste
and improve the quality.The research paper presents analysis of the metal processing company that
makes packing automatics with the spatial cams of complex geometry, which allows specifying the
law of motion of the spatial cam. The MatLab software has been used for the work.
Key words: Lean Manufacturing, Metal Processing, Spatial Cam, Reversing Engineering, Matlab.
1. INTRODUCTION
In present global market the integration and introduction of new technologies into the market is
one of the modes, how to control successful business using the up-to-date technologies to create new
products, processes and services. The basis of the Lean philosophy is to reduce the expenses and to
increase the value received by the user as much as possible [1]. The purpose of this system is to
provide such a value to the user as he expects. The companies, which have adapted the Lean
principles in their activities, notice positive changes in many areas [2, 3]. When the Lean principles
were started to be implanted, the execution time of orders got much shorter, while the work
efficiency improved.
The Lean method allows achieving more efficient production competition in its environment in
case of any difficult environment. The Lean production stresses that the reduction of resources in
various companies is determined by application of projecting, production and management
possibilities. However, the Lean producers may employ various competent employees in all the work
levels of the organization and use a very flexible system. The automatic CNC machines result in
increased volume of the products. It may be different. In order to reduce the expenses of production
process, the methods of production process have to be removed or simplified. In order to simplify the
production of complex spatial cam, the Lean system has to be used as it allows reducing the sources
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2. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 12, December (2014), pp. 47-54 © IAEME
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through application of projecting and production possibilities, and determining the law of motion.
We will analyze in this article the production of complex spatial cam during the process of
mechanical treatment and we will determine the law of motion.
2. PRODUCTION AND MODELLING OF SPATIAL CAM
In order to make the spatial cam of complex form, it is necessary to choose a technologically
effective production method. The method is technologically effective when there is no other method
that would allow making the same production amount using smaller number of production factors, or
when the usage of precisely defined (limited) number of production factors results in maximally
permissible amount of production. The technological effectiveness of production method covers
cost-saving usage of production factors. The spatial cam is made by copy milling machine HRF 500,
which is shown in the Fig. 1.
Fig. 1: HRF 500 copy milling machine
The technological possibilities of this machine depend often on the number of controlled
coordinates. The machine is controlled according to three coordinates x, y, z.
Table 1
Type HRF 500
Disc’s diameter, mm 400
Rotation speed, rpm 100-1600
Bobbin’s diameter, mm 80
Max. diameter of the bobbin, mm 50
Bobbin’s feather, mm 225
Milling tool SK 50
Feeding, v 24 from 10-2000 mm/min
The technological possibilities of this machine increase a lot when the rotations of the spindle
and the tools are changed. For this purpose the turrets or magazines of tools are installed. The
machine has a turning drum (1). When the blank is fixed there once, it is possible to treat the detail
by shortening the treatment period and reducing the basing errors. The characteristics of HRF 500
machine are presented in the Table 1.

3. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 12, December (2014), pp. 47-54 © IAEME
49
The spatial cam is made from one-piece detail. This detail is made in 4hours. The detail is
made from cast iron, grade EN 1563:1997.The mechanically treated spatial cam is illustrated in the
Fig. 2.
Fig. 2: Mechanically treated spatial cam
The made model of spatial cam may be used to design the same model using the SolidWorks
software. SolidWorks software is a technological platform that secures flexible usage of engineering
information in all the projecting and production stages. First of all, SolidWorks has very big
possibilities to import/export data, which guarantees usage of graphical information of any type,
starting with 2D sketches and ending with data of 3D scanning machines. The spatial cam is modeled
using the SolidWorks software as illustrated in the Fig. 3.
Fig. 3: Model of spatial cam made by SolidWorks software
When the detail is modeled using the SolidWorks software, the constructional and
geometrical parameters of the detail’s surface are assessed: detail’s construction; constructional
materials (cast iron); detail’s height (200 mm); detail’s diameter (240 mm), width of tracer (60 mm),
and width of coil (183 mm).
The guide plate present in the automatic CNC machine has to be used to make complex
detail. The guide plate is a detail of copying device that moves the tool, which cuts the set profile of
surface in the blank.
The detail is made in two cases: in the first case the detail is received when the guide plate
turns by 720˚, and in the second case the detail is received when the guide plate turns by 360˚. In the
first case the intervals 45˚- 90˚ and 630˚- 720˚ are especially important because the phase in the
made detail is the table’s rotation – beginning and end. Not one but two tracers are rotating in the
cam at the same time. When this detail is made it is used in automatic ARM packing machine that is
meant to form and pack butter to the packs of 200 g, 250 g at 0°
C working temperature. The
automatic ARM machine is shown in Fig. 4.

4. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976
ISSN 0976 – 6359(Online), Volume 5, Issue 12, December (2014), pp.
Fig. 4: ARM automatic machine: 1
The ARM automatic machine is designed in such a way that all the pre
operations would proceed consistently in the circle. The main binding link between the key units is
the table (1) with eight, evenly arranged sockets on it, and (2) spatial cam.
The guide plate of spatial cam is shown in Fig
the tracer, while the tracer’s diameter is not important. The dependency of the cam’s radius on
angle is presented not every 5, but every 2 degrees in the technical documentation.
Fig. 5: The sketch of guide plate of spatial cam with the tracer’s axial line
In order to shorten the production time of the detail, it is necessary to form such la
would reduce the time down to minimum. This is the reason why the employees of the companies
encounter major problems. When the proper law of motion is formed, the mathematical model of the
law of spatial cam’s motion has to be created.
3. CREATION MATHEMATICAL LAW OF MOTION BY LEAN METHOD
The mathematical model of spatial cam is created in order to determine the law of motion.
The equations of this law are described using the Matlab software
technical calculations meant for quick
digital analysis, actions with matrixes and arrays, processing of signals and graphics. The
mathematical law of motion in the Matlab env
3rd
, 4th
and 5th
series. Moreover, the Fourier line of the n
is “zero”. The motion equations:
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976
6359(Online), Volume 5, Issue 12, December (2014), pp. 47-54 © IAEME
50
ARM automatic machine: 1 – table, 2 – spatial cam
The ARM automatic machine is designed in such a way that all the pre
operations would proceed consistently in the circle. The main binding link between the key units is
ith eight, evenly arranged sockets on it, and (2) spatial cam.
The guide plate of spatial cam is shown in Fig. 5. It has the same starting point
the tracer, while the tracer’s diameter is not important. The dependency of the cam’s radius on
angle is presented not every 5, but every 2 degrees in the technical documentation.
The sketch of guide plate of spatial cam with the tracer’s axial line
In order to shorten the production time of the detail, it is necessary to form such la
would reduce the time down to minimum. This is the reason why the employees of the companies
encounter major problems. When the proper law of motion is formed, the mathematical model of the
law of spatial cam’s motion has to be created.
CREATION MATHEMATICAL LAW OF MOTION BY LEAN METHOD
The mathematical model of spatial cam is created in order to determine the law of motion.
described using the Matlab software [4]. Matlab
technical calculations meant for quick-acting digital treatment and visualization. M
digital analysis, actions with matrixes and arrays, processing of signals and graphics. The
mathematical law of motion in the Matlab environment will be described by the Fourier lines of the
series. Moreover, the Fourier line of the nth
series will be used, where the starting point
1
2
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
© IAEME
spatial cam
The ARM automatic machine is designed in such a way that all the pre-packing and packing
operations would proceed consistently in the circle. The main binding link between the key units is
5. It has the same starting point-axial line for
the tracer, while the tracer’s diameter is not important. The dependency of the cam’s radius on the
angle is presented not every 5, but every 2 degrees in the technical documentation.
The sketch of guide plate of spatial cam with the tracer’s axial line
In order to shorten the production time of the detail, it is necessary to form such law of motion that
would reduce the time down to minimum. This is the reason why the employees of the companies
encounter major problems. When the proper law of motion is formed, the mathematical model of the
CREATION MATHEMATICAL LAW OF MOTION BY LEAN METHOD
The mathematical model of spatial cam is created in order to determine the law of motion.
. Matlab is the environment of
acting digital treatment and visualization. MatLab covers
digital analysis, actions with matrixes and arrays, processing of signals and graphics. The
ironment will be described by the Fourier lines of the
series will be used, where the starting point

5. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 12, December (2014), pp. 47-54 © IAEME
51
Fourier line of the 3rd
series:
݂ሺ‫ݔ‬ሻ = ܽ଴ + ܽଵ cosሺ‫ݔ‬ωሻ + ܾଵ sinሺ‫ݔ‬ωሻ + ܽଶ cosሺ2‫ݔ‬ωሻ + + ܾଶ sinሺ2‫ݔ‬ωሻ +
+ܽଷ cosሺ3‫ݔ‬ωሻ + ܾଷsin ሺ3‫ݔ‬ωሻ.
Fourier line of the 4th
series:
݂ሺ‫ݔ‬ሻ = ܽ଴ + ܽଵ cosሺ‫ݔ‬ωሻ + ܾଵ sinሺ‫ݔ‬ωሻ + ܽଶ cosሺ2‫ݔ‬ωሻ + ܾଶ sinሺ2‫ݔ‬ωሻ +ܽଷ cosሺ3‫ݔ‬ωሻ
+ ܾଷ sinሺ3‫ݔ‬ωሻ +ܽସ cosሺ4‫ݔ‬ωሻ + ܾସ sinሺ4‫ݔ‬ωሻ .
Fourier line of the 5th
series:
݂ሺ‫ݔ‬ሻ = ܽ଴ + ܽଵ cosሺ‫ݔ‬ωሻ + ܾଵ sinሺ‫ݔ‬ωሻ + ܽଶ cosሺ2‫ݔ‬ωሻ +
+ ܾଶ sinሺ2‫ݔ‬ωሻ +ܽଷ cosሺ3‫ݔ‬ωሻ + ܾଷ sinሺ3‫ݔ‬ωሻ +ܽସ cosሺ4‫ݔ‬ωሻ
+ ܾସ sinሺ4‫ݔ‬ωሻ +ܽହ cosሺ5‫ݔ‬ωሻ + ܾହ sinሺ5‫ݔ‬ωሻ .
Fourier line of the nth
series:
݂ሺ‫ݔ‬ሻ = ܽ cosሺ
ሺ‫ݔ‬πሻ
180
ሻ + ݀,
where:
a0, a1, a2, a3, b1, b3, b4 are the rigidity and inhibition coefficients characterized by rigid and inhibiting
features;
x –direction of movement;
ω - coordinate of torsion angle;
d –part diameter;
π–rational number.
When we describe the model by the motion equations presented above, we know that the
system’s movement is aperiodic or swings in gradually decreasing amplitude depending on the
system’s parameters. Fig. 6 shows the results of the compliance of used Fourier function of the 3rd
series with the present coordinates.
Fig. 6: Compliance of Fourier function of the 3rd
series with the present coordinates
3-osios eilės Furjė f-jos atitikimas su turimomis
koordinatėmis
0
20
40
60
80
100
120
140
160
180
200
0 20 40 60 80 100 120 140 160 180
x
y
fit1

6. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 12, December (2014), pp. 47-54 © IAEME
52
The received coordinates allowed encountering difference that exceeds the permissible
tolerance limit of 0,04 mm (the results are even worse when the cosine function is used), where the
received tolerance limit exceeds the permissible limit by 0,65 mm. Fig. 7 shows the results of the
compliance of Fourier function of the 4th
series with the present coordinates.
Fig. 7: Compliance of Fourier function of the 4th
series with the present coordinates
The received coordinates allowed encountering difference that exceeds the permissible
tolerance limit of 0, 04 mm (the results are even worse when the cosine function is used), where the
received tolerance limit exceeds the permissible limit by 0, 25 mm. Fig. 8 shows the results of the
compliance of Fourier function of the 5th
series with the present coordinates.
Fig. 8: Compliance of Fourier function of the 5th
series with the present coordinates
When the dependency of the Fourier model of the 5th
series was used, the difference of the
mathematical model and interpolated points was within the tolerance limits. This means that the
received data may be used further in the Lean area.The received diagrams of the practically received
and theoretically calculated values are compared with the equivalent of received cosine function with
the present coordinates. The compliance of the cosine function with present coordinates is illustrated
in Fig. 9. Fig. 9 shows the results of the compliance of Fourier function of the nth
series or cosine
function with the present coordinates.
4-osios eilės Furjė f-jos atitikimas su turimomis
koordinatėmis
0
20
40
60
80
100
120
140
160
180
200
0 20 40 60 80 100 120 140 160 180
x
y
fit1
5-osios eilės Furjė f-jos atitikimas su turimomis
koordinatėmis
0
20
40
60
80
100
120
140
160
180
200
0 20 40 60 80 100 120 140 160 180
x
y
fit1

7. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 12, December (2014), pp. 47-54 © IAEME
53
Fig. 9: Compliance of Fourier function of the nth
series or cosine function with the present
coordinates
One of the main movements of the device was the table’s rotation in this investigation. The
table may be turned by 90˚ degrees and such an angle would manifest the symmetry of rotation
cycle, i.e. in this phase the rotated table gets faster, and the table slows down at 90˚- 180˚. Fig. 10
shows the interdependency of the law of rotation of spatial cam and mechanically treated cam.
Fig. 10: Interdependency of the law of rotation of spatial cam (2) and mechanically treated cam (1)
The diagram shows that the law of rotation of the mechanically treated cam is more
symmetrical than that of the spatial cam. The mechanically treated cam rotates more smoothly than
the spatial cam. Following the received diagrams, the Lean method helped to determine that this is
the law of rotation motion.
In order to determine smooth motion of spatial cam in pair with the trace that overturns the
table, it is necessary to take into account the predominant motion trajectory of elements, i.e.
projective geometric correction coefficient.

8. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 5, Issue 12, December (2014), pp. 47-54 © IAEME
54
4. CONCLUSION
1. The law of rotation motion was received on the basis of the coordinates of spatial cam
described using the dependency of the Fourier model of the 5th
series. The data of the results
of the mathematical model were received without exceeding the tolerance limits of 0.04 mm.
2. The Lean methodology allows assessing properly the production process of the spatial cam in
the competitive environment and its geometrical peculiarities at 90˚- 180˚.
3. If the coordinates of tracer of the mechanically treated cam are used, it is possible to make
more precise tracer of spatial cam. If the dimensions of made cam are compared with the
theoretically set dimensions, the average deviation may decrease by 31%.
4. The motion equations of the mathematical model allow us determining that one of the
received curves is the dependency of the law of rotation motion. This dependency shows,
which cam is more symmetrical and faster.
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