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of
FOUNDRY ENGINEERING
ISSN (1897-3310)
Volume 10
Issue Special1/2010
243-246
46/1
Published quarterly as the organ of the Foundry Commission of the Polish Academy of Sciences
Effective cross-section area of a shooting
valve in core shooting machines
a
J. Dańko a*, R. Dańko a
Faculty of Foundry Engineering, AGH University of Science and Technology , Reymonta 23 str., 30-059 Kraków, Poland
*Corresponding author. E-mail address: jd@agh.edu.pl
Received 05.03.2010; accepted in revised form 23.03.2010
Abstract
Aksjonov’s model of calculation of the air stream flow rate in shooting machines was made free of the previous simplifying assumptions
and completed with more exact method of the calculation of chosen factors influencing proper compacting of core sands. The elaborated
model served for a numerical simulation of a course and intensity of pressure variations in the examined area of a shooting machine. In the
paper the more precise calculation method for determination of air valve cross-section area in foundry core-shooters have been presented.
In given formula the designed capacity of machine chamber have been considered as well as pressure value of working air, parallely with
intensity of air pressure increment and average shooting hole diameter.
Keywords: core production, core blowing, core shooting, core sand
1. Introduction
The proper selection of working parameters of the core-box
filling and sands compaction and also concerning sands
hardening by means of gaseous or thermal factors is a very
important for the optimisation of the core production process
done by shooting. Those problems were the subject of the
previous investigations of J. Dańko [2, 3, 7, 8], realised by the
application of the traditional core binders (oil or linseed oil
varnish, water-glass, resins for the hot-box process). One of the
effects of these studies was the approximation of numerous
measurement data [5, 8], which enabled taking into account, in
empirical formulas used for the calculation of the average value
of sands compaction - kind of core sands, initial apparent
density of loosely built sands ρus, working pressure pr and
diameter of an outlet of a shooting machine head d1.
As the result of experimental investigations quantitative
relations between pressure pr, supplied to the shooting machine
from the compressed air grid, and pressure pbgran which is
established in a blowing chamber – were found. Its value
depends on the following factors:
- Air shooting valve cross-section area and velocity of its
operation,
- Area of an outlet from a shooting machine head,
- Volume of a blowing chamber, constituting a container of
core or moulding sands.
The results of the average apparent density, porosity and
permeability in cores made by shooting of the determined core
sand, indicate that regardless of the kind of the core sand there is
a continuation of the character obtained from the apparent
density. This justifies their joint presentation in a form of a
synthetic diagram in Figure 1, comprising a very wide range of
the apparent sand density and related to it permeability and
porosity.
2.
Calculation and the selection of
air shooting valve cross-section area in
shooting machines
Experimental investigations of Fiškin and Lesničenko [9,
11] indicated that main parameters influencing the velocity of
sand evacuation from the blowing chamber, and due to that the
energy of the sand outflow and degree of its compaction in the
technological space (core-box, moulding box), are: intensity of
pressure growing Ip (MPa/s) and its limiting value pbgran (MPa)
in the blowing chamber. These values are, in turn, related to the
nominal cross-section area, operational velocity of air shooting
valve and the outlet area of the shooting head.
ARCHIVES OF FOUNDRY ENGINEERING Volume 10, Special Issue 1/2010, 243-246
243
1200
60
Sand SW
Sand B
Sand Ol and HU 404
50
800
40
y = -38,153x + 99,556
R2 = 0,9993
600
30
400
20
200
Porosity, %
Permability, cm4/Gmin
1000
The intensity of pressure growing is the smallest at the
beginning of the process and when it reaches the limiting value
pbgran, which is schematically illustrated in Figure 3. The
beginning of a quasi stationary outflow of a sand-air stream
from the blowing chamber, of parameters essential for the sand
compactness, occurs when pressure pb in this chamber obtains
its critical value versus working pressure (pb = 0.528 pr). This
state is simultaneously present in a borderline of the IInd and IIIrd
outflow period in the known Aksonow’s model [1].
10
y = 192968e-4,1747x
R2 = 0,9654
1,3
1,35
1,4
1,45
1,5
1,55
1,6
1,65
1,7
1,70
0
1,75
Apparent density, g/cm3
Fig. 1. Influence of an apparent density of sands on their
permeability and porosity, for the tested kinds of core sands [5]
Investigations, own and others [2, 7, 8, 9, 10] indicate, that
the intensity of pressure growing (analysed in the range: Ip = 2.3
÷ 22.5 MPa/s) has no influence on the minimum pressure in the
blowing chamber, at which starts the sand evacuation in an air
stream into the technological space, and that the time of start of
this evacuation is inversely proportional to Ip value.
An application of a fast operating valve of a large cross-section
in machines, in which shooting heads have openings of a small
equivalent diameter1, worsens conditions of a core sand
evacuation. The upper, allowable intensity of pressure growing
should not exceed in this case a value: Ip ≥ 5.0 MPa/s.
It is recommended to use in shooting machines air valves
opened in a very short time where the valve’s cross-section area
is similar to areas of outlets in the shooting head [7]. In this case
the diameter of the blowing chamber outlet changes in a wide
range however, fulfilling the condition: d1ekw. = (0.2÷0.5) Dke.
Regulation of an amount of air introduced into sand, in
order for performing its zone fluidity, is being done by means of
a perforated partition of the properly selected aerodynamic drag.
The decreased outflow resistances of a partially fluidised
sand outflow from the shooting head cause the higher
concentration of the volumetric solid phase in the air stream [8].
The effective increase of core compactness occurs at an
intensity: Ip ≥ = 10 MPa/s and the outlets of the shooting
machine head fulfilling the given above condition. However,
this concerns mainly shooting heads of the single outlet used
e.g. in moulding automats and not multi-hole opening heads.
Data from the previous investigations are shown in Figure 2.
They indicate that the optimal quotient value, on account of the
core sand compactness, d0s/Dk = 0.35 and on this basis it can be
assumed that diameters d1ekw and d0s are of similar values.
3. Problem formulation and solution
Analysis of references [3, 7, 9, 10] indicates the need of
development a theoretical dependence for calculating the crosssection area of the air valve of Hansberg type in relation to the
designed shooting machine size, working air pressure and
average area of the shooting head outlet.
244
Apparent density, ρm g/cm3
0
1,25
1,65
1,60
Dk = 94 mm
1,55
1,50
Dk = 128 mm
1,45
Dk = 154 mm
1,40
0
0,1
0,2
0,3
0,4
Diameter ratio d0S/Dk
0,5
0,6
0,7
Fig. 2. Influence of the ratio d0s/Dk on an apparent density of
core sands being shot into the core-box [10]
The basis for calculation the shooting valve cross-section
are constitutes the equation:
1
κ −1
κ
dp b κ ⋅ p a ⋅ v a
pa
=
⋅ p b κ ⋅ (µ 0 ⋅ f 0 ⋅ ψ 0 ⋅
dt
Vb
va
µ 1 ⋅ f 1 ⋅ ψ1
−
1
pa κ
⋅ pb
κ +1
κ
)
(1)
⋅ va
presenting the intensity of the air pressure growing in the
blowing chamber [3, 8], which can be rearranged into the
following form:
I p ⋅ Vb ⋅ p b
f0 =
κ
κ+2
⋅ p a 2κ
κ −1
κ
⋅ µ p ⋅ ψp ⋅ va
⋅+
µ 1 ⋅ f 1 ⋅ ψ1 ⋅ p b
κ +1
κ
κ +1
µ p ⋅ ψp ⋅ pa κ
)
(2)
where: Vb – volume of the blowing chamber; m3,
Vp – volume of a near-valve space (Vp = 0.2 Vb); m3,
ψ0, ψ1 – outflow values for the air valve (stage a→b) and from
the blowing chamber to the core-box (stage b→ c), respectively.
µ0, µ1 – flow rate of the air valve and the outlet of the shooting
machine head, respectively,
f0, f1 – area of the shooting valve cross-section and the outlet of
the shooting machine head, respectively,
vp – air specific volume in the near-valve space (behind the
perforation partition) ; m3/kg.
The area f1 is being calculated with taking into account
conclusions from tests presented in [10]. Thus, it can be
assumed that in the shooting machines d1 = 0.35 Dk .. The
corresponding area at the chamber outlet is equal to f1 = 0.0962
Dk2.
Taking into consideration, in equation (2), changes of outflow
values ψ, deciding on a character of successive air outflow
periods at stage a→b (supercritical, critical, subcritical), and
also a notation of f1 value, allowed to present in Table 1
ARCHIVES OF FOUNDRY ENGINEERING Volume 10, Special Issue 1/2010, 243-246
equations in a form useful for the numerical calculations of area
f0s, in dependence of the characteristic outflow periods –
presented in Figure 3.
Fig. 3. Generalised scheme of pressure pb in the blowing
chamber of the shooting machine for calculating the shooting
valve cross-section area
Table 1. Equations for numerical calculations of areas f0s, in
dependence of characteristic outflow periods
Optimal area of the
Calculated outflow values
outflow
shooting valve crossperiods
pb
ψ0, ψ1
µ0, µ1
section
ψ0 = 2,15 µ0 = 0,8 f0s= 0,051·Dk3·Ip·pa-1,21 +
pb =
I→II
1,894·pd ψ1 = 2,15 µ1 = 0,8
3128·Dk2·pa-0,855
kryt
ψ0 = 2,15 µ0 = 0,8 f0s= 2,08·Dk3·Ip·pa-1,5 +
pb =
II→III
0,528·pa ψ1 = 2,15 µ1 = 0,8
+0,056·Dk2
gran
pb = pb
ψ0 = var µ0 = 0,8 f0s= 2,26·Dk3·Ip·pa-15 +
=pb =
III
ψ1 = 2,15 µ1 = 0,8
0,08·Dk2
0,75·pd
The results of the computer simulation of the influence of
the method of opening the shooting valve of the same crosssection area on the limiting pressure in the blowing chamber of
the shooting machine (pbgran ) and on the intensity of pressure
growing (Ip) are presented in Figure 4. Two methods of valve
opening – possible to be realized in practice - were taken into
account in the analysis. In the first one, the directly proportional
increase of the valve cross-section to time, proceeding according
to:
τ
(3)
f =f ⋅
0s
0N
T1
was assumed. The second method takes into account a change of
the valve cross-section, which occurs according to:
(4)
f 0s = f 0 N ⋅ (1 − e − τ / Tw )
where: τ – current process time; s,
f0N – nominal area of the air shooting valve cross-section; m2,
T1 – period of valve opening; s.
Tw – valve time-constant; s.
Fig. 4. Influence of the method and time of the air shooting
valve opening on the simulated pressure in the internal air tank
(pa), in the blowing chamber (pb) and in the core-box (pc): a)
Linear opening of the valve, b) Exponential opening of the
valve.
Calculations of areas and cross-section diameters of the air
shooting valves in shooting machines, corresponding to series of
types being produced, are presented in Table 2. Three various
intensities of a growing pressure in the blowing chamber – at the
initial air pressure in a surge tank being of 0.6 MPa – were
considered in calculations.
Simulatory calculations allowed to find a deviation of the
quotient d1/Dk from value 0.35, taken into account in equations
for f0s given in Table 2. Deviations of value d0s3/Dk equals from
–6.89 to +10.85%, in dependence of the blowing chamber
dimensions. This indicates that obtaining the assumed Ip value
requires application of the outlet either of the larger diameter
(negative deviations) or the smaller (positive deviations) from
the given valve diameter d0s. The formula joining the
recommended outlet diameter d1ekw with the valve diameter d0s
is as follows:
(5)
d 0s − d 1ekw
d
d 1ekw =
0s
∆d
(1 + 1 )
100
; oraz ∆d 1 = (
d 1ekw
) ⋅ 100%
where: ∆d1 – positive or negative deviation – expressed in
percentages – of the shooting outlet diameter in relation to the
average shooting outlet diameter d1ekw = 0.35 Dk.
Investigations confirmed a significant influence of the valve
opening method on Ip value and a lack of such influence on
pbgran pressure value.
ARCHIVES OF FOUNDRY ENGINEERING Volume 10, Special Issue 1/2010, 243-246
245
Table 2. Area and diameter of the air shooting valve crosssection calculated for shooting machines of a typical volume of
the blowing chamber.
Blowing hole diameter
Deviation
and cross section
d1/Dk = 0,35
Ip
Vb
I formula
III formula
Dk
Lp.
f0s1
f0s3
MPa
∆d1
x
d0s1
x
d0s3 ds3
[m3/m] s
∆d1
Dk
104
104
obl.
[m2] [m] [m2] [m]
1 0,001 10 2,985 0,019 6,230 0,028 0,326 -6,89 -6,84
0,086 20 3,315 0,021 6,535 0,029 0,337 -3,71 -3,83
0,003 10 6,509 0,028 13,23 0.041 0,330 -5,71 -4,16
2
0,124 20 7,580 0,031 14,15 0,043 0,343 -2,00 -2,77
0,006 10 10,70 0,036 21,31 0,052 0,333 -4,83 -5,20
3
0,156 20 12,70 0,040 23,16 0,054 0,346 -1,14 -1,72
0,012 10 17,90 0,048 34,76 0,066 0,335 -4,28 -4,03
4
0,197 20 21,90 0,053 38,48 0,070 0,355 1,43 -0,25
0,025 10 30,85 0,062 58,10 0,086 0,342 -2,28 -2,27
5
0,251 20 39,00 0,070 65,80 0,091 0,362 3,42 2,62
0,040 10 44,23 0,075 81,50 0,102 0,347 -0,86 -0,73
6
0,251 20 56,74 0,085 93,85 0,109 0,370 5,70 0,14
0,063 10 62.80 0,089 113,0 0,119 0,348 -0,57 3,98
7
0,342 20 83,60 0,103 132,5
0,380 8,56 8,40
0,100 10 90,20 0,107 158,2 0,142 0,355 1,43 1,56
8
0,399 20 123,2 0,125 189,0 0,155 0,288 10,85 9,48
The obtained deviation values ∆d1 (see: Table 2) were used for
the development of the empirical dependence of the deviation as
a function of the blowing chamber volume and the assumed
value of the pressure growing intensity Ip = ∆pb/∆τ. The
developed equation is of a form:
∆d1obl = 10( a + 0,51 ⋅log Vb )
− B
(6)
where: Ip = ∆pb/∆τ [MPa/s], Vb = π·Dk3/2 [dm3].
[1,86⋅ (log I p −1) − 1,39 ]
; B = 10[0,83⋅ (log ∆p / ∆τ − 1) − 0, 44]
a = 10
Comparison of deviations calculated by means of Equation (6)
allows to state that the difference does not exceed 1.5 %.
4. Conclusions
The verified calculation method enables designing of
pneumatic core-boxes of a decreased energy consumption, with
the application of the computer simulation for the assessment of
the influence of constructional parameters of machines on
values determining the technological effects of the blowing
process.
The properly calculated air shooting valve cross-section area
should ensure obtaining the assumed intensity of pressure
growing during the quasi-stationary sand outflow period, which
corresponds to obtaining the upper limit of the IIIrd air outflow
period at the stage a→b. Equations concerning this case, given
in Table 2, provide the possibility of a fast and sufficiently
accurate determination of a maximal allowable diameter of
individual or equivalent outlet of the blowing chamber of the
shooting machine. Machine dimensions, the intensity of
246
pressure growing and the way of opening a shooting valve were
taken into account in these equations. This is especially
important in designing series of types of shooting machines, for
which operations recommended in paper (10) does not
guarantee the optimal range of machine parameters, specially
those from the upper shelf of production.
Acknowledgements
This work was elaborated under
development study no 11.11.170.318
research
and
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