1. International Journal of Advanced Research in Engineering RESEARCH IN ENGINEERING
INTERNATIONAL JOURNAL OF ADVANCED and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online)TECHNOLOGY (IJARET)
AND Volume 4, Issue 7, November – December (2013), © IAEME
ISSN 0976 - 6480 (Print)
ISSN 0976 - 6499 (Online)
Volume 4, Issue 7, November - December 2013, pp. 192-197
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IJARET
©IAEME
THE SPATIAL MANIFESTATION OF NOMINAL CONVEYING ABILITY
OF TRAPEZOIDAL V- BELTS – CONTRIBUTION FOR OPTIMIZATION
Azem Kyçyku1, Nijazi Ibrahimi1, Heset Cakolli1
1)
Faculty of Mechanical Engineering in Prishtine Bregu i Diellit, Prishtina, Kosova
ABSTRACT
In all expressions for calculating the conveying ability of trapezoidal belts there are two
variables: the number of rotations and the kinematic diameter of the steering pulley. From this it is
concluded that the nominal conveying is a two-variable function. Through planar diagrams it is
possible to express the conveying ability as a function of the number of rotations for the constant
value of the kinematic diameter of the steering pulley and vice-versa. Spatial diagrams have
precedence over planar diagrams because conveying ability can be expressed simultaneously by
treating as variables both the number of rotations and the kinematic diameter of the steering pulley.
Therefore, we have the spatial function Pn1 = f(n1,d1). Contour diagrams are derived if this function is
cut in equidistant plateaus Pn1 = const., and are of unique contribution for optimizing the nominal
conveying ability.
Key words: trapezoidal belts, conveying ability.
1.
INTRODUCTION
All tests done on the nominal conveying ability of trapezoidal belts show that the number of
rotations and the kinematic diameter of the steering pulley are the two main parameters with direct
effect. For practical calculations belt of respective profile it is important to determine the number of
rotations and the diameter of the steering pulley for which the conveying ability will have a
maximum value. A concrete answer can be derived through contour diagrams. For the analysis in
this paper will be taken the trapezoidal belts, with coated narrow-profile (SPZ, SPA, SPB and SPC)
and the same profiles, but produced with cutting (SPZX, SPAX, SPBX and SPCX).
2.
NOMINAL CONVEYING ABILITY AS A SPATIAL FUNCTION
The nominal conveying ability can be expressed in a general mathematical function as a
function of two variables.
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2. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 7, November – December (2013), © IAEME
Pn1 (n1 , d1 ) = f (n1 , d 1 )
……………….………. (1)
It is known that such functions in space in general express a curved surface, the form of
which depends on the mathematical expression (1.0) from these diagrams is derived the physical
understanding of the influence of the number of rotations and the diameter of the steering pulley on
the nominal conveying ability. The mathematical model for calculating the nominal conveying
ability for the trapezoidal belts narrow profile, produced with coated and cutting is:


C
2
Pn1 (n1 , d1 ) = n1 ⋅ d1 ⋅ C1 − 2 − C3 ⋅ (n1 ⋅ d1 ) − C 4 ⋅ log(n1 ⋅ d1 )
d w1


(2)
where:
Pn1 (kW)-nominal conveying ability,
n1(min-1)-number of rotations of the steering pulley,
d1(mm)-steering pulley kinematic diameter,
ci ( i =1,2,3,4) – constants, which have different values for different profiles of belts, which
calculation values are carried out experimentally, depending on the materials used in the construction
of the belt and technological features of the production process.
Applying the equation (2) by using Mathcad program we obtained nominal conveying ability
tables for trapezoidal belts profiles examined in this paper, depending on two variables (number of
rotations of the steering pulley n1 and steering pulley kinematic diameter d1), but due to volume
limits of the paper tables will not appear, but only the relevant diagrams. In space diagrams on the x
axis is shown the number of rotations of the wheel guiding divided by 1000, the y axis - kinematic
diameter, while the z-axis Pn1 (kW) nominal conveying ability.
a)
The Spatial diagram
b) The Countour diagram
Figure 1. The spatial and countural diagram of the nominal conveying ability for SPZ profile.
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3. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 7, November – December (2013), © IAEME
a) The Spatial diagram
b) The Countour diagram
Figure 2. The spatial and countural diagram of the nominal conveying ability for SPZX profile
a)
The Spatial diagram
b) The Countour diagram
Figure 3. The spatial and countural diagram of the nominal conveying ability for SPA profile.
a)
The Spatial diagram
b) The Countour diagram
Figure 4. The spatial and countural diagram of the nominal conveying ability for SPAX profile.
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4. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 7, November – December (2013), © IAEME
a)
The Spatial diagram
b) The Countour diagram
Figure 5. The spatial and countural diagram of the nominal conveying ability for SPB profile.
a)
The Spatial diagram
b) The Countour diagram
Figure 6. The spatial and countural diagram of the nominal conveying ability for SPBX profile.
Profile SPC
Profile SPC
P n1
P n1
a)
The Spatial diagram
b) The Countour diagram
Figure 7. The spatial and countural diagram of the nominal conveying ability for SPC profile.
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5. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 7, November – December (2013), © IAEME
Profile SPCX
Profile SPCX
P n1
P n1
a)
The Spatial diagram
b) The Countour diagram
Figure 8. The spatial and countural diagram of the nominal conveying ability for SPCX profile.
The diagram in Fig.1 to Fig.8 a) show the physical understanding of the influence of the
number of rotations and the steering pulley kinematic diameter on the nominal conveying ability.
The diagrams show that the nominal conveying ability represents a spatial surface that from the
engineering aspect comprised of two characteristic parts:
- increasing monotonous, and
- decreasing monotonous.
From Fig.1. to Fig.8 a) is shown that as both input variables (n1 and d1) increase, the spatial
surface narrows down. This means that steering pulleys of bigger diameters should not have a large
number of rotations.
Also it is shown the decreasing part of the surface that represents the decreasing field of
conveying ability, where the number of rotations and diameters of driven pulley should not be
considered during transmission design of trapezoid belts. If the spatial surface depicted in Fig.1 to
Fig.8 a) are cut in several equidistant planes with Pn1=const., the contour diagram shown in Fig. 1 to
Fig.8 b) can be obtained.
All the presented diagrams from Fig.1 to Fig.8 b) in x axis is given the number of rotations
n1/1000, whereas the y axis shows the kinematic diameter d1(mm). The curvatures on the diagrams
represent the tracks of the cutting of surface in Pn1=const plans shown in Fig. 1 to Fig.8 b). The
curvatures represent the contour diagrams. The numbers next to each curvature represent the
respective value of the nominal conveying ability. From the mathematical aspect the curvatures of
monotonous decreasing surface from which during the design should be taken the number of
rotations and kinematic diameters resemble a hyperbole. All the presented diagrams in Fig.1 to Fig. 8
b), is shown that the nominal conveying ability determined value can be calculated through a series
of combinations of the number of rotations and the kinematic diameter of the steering pulley.
Therefore, the usage of above mentioned diagrams from designer of trapezoidal belt transmission
will facilitate the work on finding the optimal variant.
3. CONCLUSION
The spatial presentation of the nominal conveying ability is calculated for 100…8000 min-1
number of rotations and the kinematic diameter of the steering pulley of 50…600 mm, depending on
belts profile. The spatial surface depicted in Fig. to Fig. 8 a) represent the values of the nominal
conveying ability Pn1(n1, d1)(kW). The various colors in diagrams represent different levels of power
Pn1. The contour diagrams represent a unique contribution on the field of optimization of the
conveying ability of trapezoid belts. By using these diagrams the designer will be able to use a series
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6. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 7, November – December (2013), © IAEME
of possible combinations of the number of rotations and the kinematic diameters in order to calculate
the assigned nominal power.
REFERENCES:
[1]. Kyçyku,A.: “Contribution on optimization the conveying ability of trapezoid belts”, Master
Thesis, Prishtina, 2003,
[2]. Technical documentation of rubber industry “Ballkan” Suhareka,
[3]. Standards for trapezoidal belts research.
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