Question

Consider the pneumatic cylinder as shown in Figure 1 which is an illustration from the Starcyl space-saver
range, as can be found in their Star2.pdf catalogue, www.starcyl.com. Some pneumatic cylinders can have a
push/pull rod (item I in Figure 1) protruding from either head (item A in Figure 1), but this cylinder clearly
has only one, making it a “single rod end” type of cylinder. This cylinder is however “double acting”, which
means it can be pressurised on either side of the piston (item B in Figure 1). Under normal operating
conditions, if pressure is applied on one side of the piston, the other side of the piston would be vented to
atmosphere.
Figure 1. Cut-away illustration of a pneumatic cylinder (www.starcyl.com)
If the cylinder is pressurised on the left hand side of the piston (as viewed in Figure 1), the rod will tend to
push against whatever load it is connected to. If the cylinder is pressurised on the right hand side of the
piston, the rod will tend to pull the load. Provided the piston is not in contact with either the left or the right
hand heads, the configuration can be treated as an “open cylindrical pressure vessel” meaning there is no load
being carried by the cylinder in the longitudinal direction. However, if the piston reaches either end of its
travel and the pressure load is causing the piston to rest hard against either the left hand head or the right hand
head with no load being carried by the push/pull rod, then the longitudinal forces must be carried by the
pressure vessel design. Note that in this design, when these longitudinal loads are present, they will actually
be carried by the four tie rods (item J in Figure 1) rather than in the cylinder material (item C in Figure 1).
To answer this question, you need to analyse a pneumatic cylinder, like the one described above, but as
described on page 17 of the catalogue: starcyl-04isometric.pdf. These are relatively large bore cylinders of a
metric style. The details of the relevant geometry for your analysis depends on the last digit of your student
number as listed in Table 1. For example if your student number is 0061095776, then the last digit of your
student number is 6, and the numerical values you must use will be: internal diameter of 250 mm; diameter of rod of 90 mm; diameter of tie rod: 20 mm. The specified maximum working pressure of all of the cylinders in
this range is 10 bar or 1 MPa.
Table 1. Geometric details for the pneumatic cylinders, according to student number.
Feature: cylinder push/pull rod tie rods (4 in total)
Material: anodised aluminium chromium coated steel steel
Last digit of SN Internal diameter (mm) diameter (mm) diameter (mm)
0, 1 or 2 160 40 [previous: 65]
* 16
3, 4 or 5 200 40 [previous: 75] 16
6, 7, or 8 250 50 [previous: 90] 20
8 or 9 320 63 [previous: 110] 25
* Values listed as “previous” have been updated following identification of an error in original release of this assignment; and
values are now consistent with the drawing on page 17 of the catalogue. Application of the “previous” value will not be penalised
during assessment of your solutions.
(a) For your designated cylinder configuration, calculate the maximum pushing force and the maximum
pulling force by the push/pull rod. [10 marks]
(b) Calculate the maximum direct (normal) stress in each of the four tie rods when the piston reaches its full
pushing stroke and no load is being carried by the push/pull rod. [10 marks]
(c) For the situation described in part (b), calculate the direct strains in the tie rods in the longitudinal and
transverse direction if the steel material has elastic properties of ? = 200 GPa, and ? = 77.2 GPa.
[10 marks]
(d) Calculate the minimum thickness of the cylinder wall required in order to keep the hoop stress below
15 MPa based on thin-walled pressure vessel theory. [10 marks]
(e) Based on the specified hoop stress of 15 MPa, determine the strains in the longitudinal and hoop directions
if the aluminium material has elastic properties of ? = 70 GPa, and ? = 26 GPa.
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Answer 1

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