Api Pneumatic. GENERAL CATALOG (2019) - page 2
1
THEORETICAL FORCE Ft
The theoretical force generated by a cylinder can be calculated by multiplying the actual area of the piston subjected to
pressure by the operating pressure.
For cylinders during pushing, the effective area of the piston corresponds to the bore::
Ft =
p F
2
p / 40
[
N
]
F =
bore
[
mm
]
P =
operating pressure
[
bar
]
N.B.: the formula considers passages from bars to N/m2 and from mm
2
to m
2
.
For cylinders in traction, it is necessary to subtract the area of the rod from that of the piston:
Ft =
p (F
2
- d
2
) p / 40
[ N ]
The
MOTIVE POWER F
available to the piston rod is:
F = Ft - R
Where R represents a force of reaction that comprises numerous factors:
friction, form and type of seals, operating pres-
sure, counter-pressure at discharge
.
The value of R is not easy to quantify as its component factors are not only numerous, but also variable. A cautious estimate
for usual applications could be 30%
Ft
.
As shown by the graph illustrated below, which indicates the progress of the pressure values of delivery and discharge during
the uniform movement of a cylinder, the delivery value Pm and the discharge value Ps remain constant during the stroke
of the cylinder, if we exclude the brief transitory periods: of acceleration following the switching of the distributing valve and
cushion at the end of the stroke.
The cylinder is thus prevalently subject to a motive power F proportional to Pm and the pushing surface, and to a coun-
ter-pressure force
Fs
proportional to the pressure Ps and the section upon which it acts, both of which are constant. The load
reaction Fc must be added to these two forces.
In other words, the cylinder, in dynamic equilibrium, will - like all engines in this state - find itself under the action of contrasting
forces that balance each other. It will move at a constant speed under the action of a constant force.
Ft - Fs - Fa = Fc
Where Fs is the counter-pressure force and Fa is a force that bears in mind the friction and reduction of
the operating power, to which Ft is linked, which does not reach the static network pressure, as can be seen in the graph.
During the transitory acceleration period, the force Fs is very low, as the air is being discharged. As the speed of the piston
increases, the air being discharged is compressed and the force Fs increases until the state of equilibrium is reached.
For example, we wish to find the cylinder capable of overcoming the load value Fc = 1200 [ N ].
The theoretical force Ft must be at least 30% greater. Let’s assume that Ft = 1600 [ N ].
This gives the following result:
F =
√
40Ft/
p
p
F =
√
40x1600/3,14x6
@
58
[
mm
]
The closest standardized bores turn out to be: 50 mm and 63 mm. It is advisable to choose the bore F = 63 mm, also because
it enables a reserve of power to be obtained.
The uniform movement of the cylinder can be obtained by regulating the air at the discharge.
In order to obtain high values, on the other hand, it is necessary to make an appropriate increase in the discharge space in
order to obtain accelerated movements, as the equilibrating force of counter-pressure is no longer present.
PEAK LOAD
In the case of long strokes, the load that can be applied to the piston rod is reduced due to the decrease in resistance at
peak load.
The lifespan of a cylinder depends largely on its mechanical application. Installation must be performed in such a way as to
avoid, or at least minimize, bending moments and radial loads on the piston rod (the most onerous kind of anchorage is the
hinge type).
If only axial loads need be applied, the piston rod will be subjected to the peak load during pushing.
As the acceptable peak load is proportional to the diameter of the piston rod d (through the elastic modulus and the inertia
moment) and inversely proportional to twice the stroke (length of free inflexion), in the case in which it does not allow the
application of the required force, it is necessary to increase the diameter of the piston rod, passing to a suitably larger bore.
The choice of the standardized bore that best satisfies the requirements of the application in question is not just linked to the
satisfaction of the force to be provided, but also to that of other conditions. These include the need to always have a power
reserve (by choosing a larger size) and that of not causing excessive stress to the cushionings.
1.1.2
Cylinders
Technical data
1.1.3
Cylinders
Technical data
AIR CONSUMPTION [ nl/min ]
Air consumption air is a working value; it has a significant influence on costs.
It is possible to calculate the average air consumption using the following formula:
Q = p F 2 /4x 60 c/t x (p+p0) / p0 x 10 _3 x 10 _3 [ nl/min ]
Where:
Q
= air consumption [ nl/min ]
F
= bore [ mm ]
c
= stroke [ mm ]
t
= time taken to perform the stroke [ s]
p
= atmospheric operating pressure [ bar ]
p0
= atmospheric pressure: 1 bar
For example, we want to calculate the consumption of the following cylinder:
d = 50 mm; c = 300 mm; t = 0,45 s; p = 6 bar
Q = 3,14 x 25 x 102/4 x (60 x 3 w 102/0,45) x 7 10 _3 x 10 _3 = 550 [ nl/min ]
THEORETICAL TABLE OF CYLINDER FORCES
PISTON FORCE
The piston force (F) can be determined on the basis of the following formulae relating to the area of the piston rod (A),
operating pressure (p) and friction (R):
Piston force F = a · p - R
(final pressure) F = p · 10
d2 ·
p
· 10
4
- R
p = bar
d = bore (mm)
R = friction = 10% (N)
A = area of piston rod
F = actual force of piston (N)
Pressure/force table for pneumatic cylinders
Operating
pressure bar
1
2
3
4
5
6
7
8
9
10
Bore
mm
Piston force (N)
6
2,5
5,1
7,6
10,2
12,7
15,3
17,8
20,4
22,9
25,4
8
4,5
9,0
13,6
18,1
22,6
27,1
31,7
36,2
40,7
45,2
10
7,1
14,1
21,2
28,3
35,3
42,4
49,5
56,5
63,6
70,7
12
10,2
20,4
30,5
40,7
50,9
61,0
71,3
81,4
91,6
101
16
18,1
36,2
54,3
72,4
90,5
109
127
145
163
181
20
28,3
56,5
84,8
113
141
170
198
226
254
283
25
44,2
88,4
133
177
221
265
309
353
398
442
32
72,3
145
217
290
362
434
507
579
651
724
40
113
226
339
452
565
679
792
905
1020
1130
50
177
353
530
707
884
1060
1240
1410
1590
1770
63
281
561
842
1120
1400
1680
1960
2240
2520
2810
80
452
905
1360
1810
2260
2710
3170
3620
4070
4520
100
707
1410
2120
2830
3530
4240
4950
5650
6360
7070
125
1100
2210
3310
4420
5520
6630
7730
8840
9940
11000
160
1810
3620
5430
7240
9050
10900
12700
14500
16300
18100
200
2830
5650
8480
11300
14100
17000
19800
22600
25400
28300
250
4420
8840
13300
17700
22100
26500
30900
35300
39800
44200
320
7240
14500
21700
29000
36200
43400
50700
57900
65100
72400