Buckling Analysis on a Cyclonic Separator Stand
Aim:
To perform a buckling analysis on a cyclonic separator stand for the following three cases:
- Without adding a stiffener
- By Adding a stiffener to find out the change in buckling factor of safety and
- Use Design Study to find out the optimum position for the stiffener with respect to buckling factor of safety.
Introduction:
(1) Buckling of columns:
Source: https://en.wikipedia.org/wiki/Buckling
A column fails either by crushing, in case of short columns or buckling, in case of long columns.
Columns are designated long and short with the help of slenderness ratio. Slenderness ratio = `l/k` ; where `l` is the effective length of the column and `k` is the least radius of gyration of its cross section.
If the load on a column is applied through the centre of gravity (centroid) of its cross section, it is called an axial load.
A short column under the action of an axial load will fail by direct compression before it buckles, but a long column loaded in the same manner will fail by springing suddenly outward laterally (buckling) in a bending mode. If a long column fails by outward lateral displacement, then the phenomenon is called buckling. The load which causes buckling failure, is called buckling load.
The Euler formula gives the maximum axial load that a long, slender, ideal column can carry without buckling.
`F = (pi^2 EI)/(KL^2)`
where,
F = Critical load,
E = Elastic Modulus,
I = Moment of Inertia,
K = Column effective length factor,
L = Unsupported length of the column.
(2) Buckling Analysis:
Buckling analysis calculates buckling load magnitudes that cause buckling and associated buckling modes.
The buckling mode presents the shape the structure assumes when it buckles in a particular mode. This is in close analogy to modal analysis, which calculates the natural frequency and provides qualitative information on the modes of vibration (modal shapes), but not on the actual magnitude of displacements.
Theoretically, it is possible to calculate as many buckling modes as the number of degrees of freedom in the FEA model. Most often, though, only the first positive buckling mode needs be found. This is because higher buckling modes have no chance of taking place, since buckling most often causes catastrophic failure or renders the structure unusable.
This analysis can be Linear or Non-Linear:
- Linear buckling is the most common type of analysis and is easy to execute in which load is applied in one step.
- Non-linear buckling analysis requires that a load be applied gradually in multiple steps rather than in one step as in a linear analysis. Each load increment changes the structure’s shape, and this, in turn, changes the structure’s stiffness.
In contrast to linear-buckling analysis, which only calculates the potential buckling shape with no quantitative values of importance, nonlinear analysis calculates actual displacements and stresses.
(3) Cyclonic Separator:
The cyclone separator is a device for separating solid particles from contaminated gas streams, and has long been used in industrial applications such as power generations, gas turbines, chemical processes and so on.
Source: https://www.che.iitb.ac.in/online/labfacility/cyclone-separator
A high speed rotating (air) flow is established within a cylindrical or conical container called a cyclone.
Air flows in a spiral pattern, beginning at the top (wide end) of the cyclone and ending at the bottom (narrow) end before exiting the cyclone in a straight stream through the center of the cyclone and out the top. Larger (denser) particles in the rotating stream have too much inertia to follow the tight curve of the stream and strike the outside wall, falling then to the bottom of the cyclone where they can be removed.
In a conical system, as the rotating flow moves towards the narrow end of the cyclone the rotational radius of the stream is reduced, separating smaller and smaller particles.
The induced centrifugal force is tangentially imparted on the wall of the cyclone cylinder. This force, with the density difference between the fluid and solid, increases the relative settling velocity.
(4) Analysis of a cyclonic separator stand:
The force induced on a cyclonic separator causes the stand to fail due to buckling. This stand which is fixed onto the ground, has to balance the forces without failing.
Hence the analysis of cyclonic separator stand is important in terms of industrial applications.
The legs of the stand are long columns which fail due to buckling when critical load is applied. Therefore this comes under Buckling analysis.
The Buckling factor of safety is the ratio of Critical Load to the Applied Load.
Adding a stiffener to the legs of the stand improves its ability to withstand loads and placing the stiffener at an optimum position increases buckling factor of safety to a greater value.
Case Setup and Procedure:
In this analysis, I am going to perform three cases - one without the stiffener and one with the stiffener. After that, using design study tool of SolidWorks, I am going to find the optimum position for the stiffener that results in the highest buckling factor of safety.
The original model is as follows:
This model was refined by removing cyclonic separator and model of the stand was saved as a separate file.
Material applied to the separator and stiffener is Alloy Steel and the legs of the stand are fixed under Fixtures section.
On the top plate, a load of 150 kN is applied.
For all the cases, a fine mesh is used for meshing and the study is carried out.
In the screenshots below, the Green elements indicate fixed faces and the Purple arrows indicate the load applied.
(1) Without adding a stiffener:
Results and explanation:
For this study, the Buckling Factor Of Safety was found to be 9.3498 which means the stand will fail if a load of 9.35 times that of 150 kN is applied.
Hence the structure is safe under this loading condition.
(2) By adding a stiffener:
Here, a stiffener was modeled by extruding to 75mm and positioned at 1 m offset.
Results and explanation:
When a stiffener of 75mm is added at 1 m offset, the buckling factor of safety was found to be 27.506
Thus we can infer that, when a stiffener is used, the stand gets more strength to withstand the load applied and it can fail only when a load of 27 times higher than 150 kN is applied.
Also, the Buckling Factor Of Safety was increased 3 times compared to the previous result.
(3) Design Study:
For Design Study, the model with stiffener is taken and variables are defined.
Offset distance parameter is defined under Variables tab, with minimum value of 0.25m and a maximum value of 1.75m. The step value is set at 0.25m
Under Constraints tab, buckling factor of safety is set greater than 25 for the study.
Since the goal is to maximize the value of buckling factor of safety, the same is set under Goals tab.
The total number of scenarios are 7
Results and explanation:
When a Design Study was carried out with the parameters defined in the procedure, we can see that, if the stiffener is at 1m offset, then the Buckling Factor Of Safety is greater than 25 as indicated by the green column.
Hence, the optimized position for the stiffener is 1m offset.
Conclusion:
Three cases of buckling analysis on a cyclonic separator stand were performed and the change in Buckling factor of safety was observed. A design study was also performed and optimized position for the stiffener was found to be at 1m offset where it has the maximum Buckling factor of safety.
References:
https://en.wikipedia.org/wiki/Buckling
https://www.sciencedirect.com/topics/engineering/cyclone-separator
https://www.che.iitb.ac.in/online/labfacility/cyclone-separator