Analysis of buckling phenomena using Solidworks

AIM : To perform a buckling analysis on a cyclonic separator stand.

OBJECTIVES :

1. To create a metallic stiffener on the legs of the stand and run the analysis to find out the change in buckling factor of safety.
2. To run a design study and find the optimum position for the stiffener.

INTRODUCTION : Cyclone separators or simply cyclones are separation devices (dry scrubbers) that use the principle of inertia to remove particulate matter from flue gases. Cyclone separators is one of many air pollution control devices known as precleaners since they generally remove larger pieces of particulate matter. This prevents finer filtration methods from having to deal with large, more abrasive particles later on. In addition, several cyclone separators can operate in parallel, and this system is known as a multicyclone. It is important to note that cyclones can vary drastically in their size. The size of the cyclone depends largely on how much flue gas must be filtered, thus larger operations tend to need larger cyclones. For example, several different models of one cyclone type can exist, and the sizes can range from a relatively small 1.2-1.5 meters tall (about 4-5 feet) to around 9 meters (30 feet)—which is about as tall as a three story building.

Working Principle - Cyclone separators work much like a centrifuge, but with a continuous feed of dirty air. In a cyclone separator, dirty flue gas is fed into a chamber. The inside of the chamber creates a spiral vortex, similar to a tornado. This spiral formation and the separation is shown in Figure . The lighter components of this gas have less inertia, so it is easier for them to be influenced by the vortex and travel up it. Contrarily, larger components of particulate matter have more inertia and are not as easily influenced by the vortex. Since these larger particles have difficulty following the high-speed spiral motion of the gas and the vortex, the particles hit the inside walls of the container and drop down into a collection hopper. These chambers are shaped like an upside-down cone to promote the collection of these particles at the bottom of the container. The cleaned flue gas escapes out the top of the chamber. Most cyclones are built to control and remove particulate matter that is larger than 10 micrometers in diameter. However, there do exist high efficiency cyclones that are designed to be effective on particles as small as 2.5 micrometers. As well, these separators are not effective on extremely large particulate matter. For particulates around 200 micrometers in size, gravity settling chambers or momentum separators are a better option. Out of all of the particulate-control devices, cyclone separators are among the least expensive. They are often used as a pre-treatment before the flue gas enters more effective pollution control devices. Therefore, cyclone separators can be seen as "rough separators" before the flue gas reaches the fine filtration stages.

Buckling - Buckling of Columns is a form of deformation as a result of axial- compression forces. This leads to bending of the column, due to the instability of the column. This mode of failure is quick, and hence dangerous. Length, strength and other factors determine how or if a column will buckle. Long columns compared to their thickness will experience elastic buckling similar to bending a spaghetti noodle. This will occur at stress level less than the ultimate stress of the column.

The Euler equation(Euler theory of Elastic buckling), `P=(n*pi^2*E*I)/(L^2)`,

The ‘L’ in this equation symbolizes length and ‘P’ symbolizes the allowable load before buckle. As the length increases, the allowable load decreases. With shorter columns compared to its thickness, one can infer from the same equation above that the allowable stress on a column before buckling increases as length decreases. The type of end connections for the column is another important factor in determining buckling stress. From pinned-pinned to fixed-fixed to fixed-pinned connection, they are each represented in the Euler equation with different values of ‘n.’ The fixed-fixed connection increases the allowable stress before buckling more than any of the other end connections. In construction, it occurs differently for different materials. This factor of material is captured in the Euler’s equation with ‘E” and ‘I,’ different material properties. In steel columns, this occurs elastically. This differs for reinforced concrete. In the image below, the steel rebar is bent outward and the concrete is broken apart. With a more brittle material, the phenomenon is more sudden.

PROCEDURE :

• Design of Cyclonic separator stand -
• The step file of cyclone separator was provided along the video. It was opened in Solidworks and the unnecessary parts excluding it's stand were suppressed.
• Case 1. : Design for simulation of stand of cyclone separator without stiffener,

• Case 2. : Design for simulation of stand of cyclone separator with stiffener,
• After that it was saved as a part file and was opened to add a stiffener around the legs of stand of cyclone separator. Two rectangles were drawn between legs and were extruded at an offset distance of `1000mm` from the plane (top plane) with a thickness of `50mm`.

• Simulation Setup -
• After sketching, simulation was setup and buckling analysis was selected. At first, the material was provided for all the part. The material selected was 'Alloy Steel (SS)'. The properties of 'Alloy Steel (SS)' are,
• The bottom faces of the legs of cyclone separator was fixed using fixture tool and an external force of `100kN` was applied on the top face of separator as shown in the following figure. The meshing were applied on the part and global mesh size was selected as `20mm`.
• Case 1. : Meshing for simulation of stand of cyclone separator without stiffener,

• Case 2. : Meshing for simulation of stand of cyclone separator with stiffener,
• Meshing Propetries
• After these processes, the model was made to run and the results were saved.

• Parametric Design Study -
• A new design study was selected to perform parametric study to find out optimum position of the stiffener.
• Case 3. : For the variables, offset distance of stiffener was selected with range with steps. The minimum value of this offset was `200mm` and maximum value was `1800mm` with steps of `200mm`. For constraints, buckling factor of safety was selected which would be greater than `25` for the above performed buckling test. For goals, this buckling factor of safety will be maximised.

RESULT :

• At first the result of buckling analysis,
• Case 1. : Simulation of stand of cyclone separator without stiffener,
• Buckling amplitude plot
• Load factor for this case = `14.027`
• Case 2. : Simulation of stand of cyclone separator with stiffener,
• Buckling amplitude plot
• Load factor for this case = `31.442`

• The above case for parametric design study was made to run and the following result was obtained.
• Case 3. :

• Apart from these, parametric studies for finding suitable thickness of stiffener and maximum force that can be applied on the top face of the cyclone separator within same constraints and goals as mentioned above were also calculated.

• Case 4. : For finding suitable thickness of stiffener, the thickness of stiffener was selected and minimum and maximum values of these thickness were `25mm` and `100mm` respectively with step size of `25mm` , while the optimum distance of stiffener was set to `1000mm`.

• The result obtained for this case,

• Case 5. : For finding maximum force that can be applied on the top face of the cyclone separator with the same constraints and goals, the minimum and maximum values of these forces were `50kN` and `250kN` respectively with step size of `50kN` , while the optimum distance of stiffener was set to `1000mm` and optimum thickness of `100mm`.
• The result obtained for this case,

CONCLUSION :

1. For Buckling Analysis, the results obtained indicates that the load factor of safety was `14.027` for the case of without stiffener, and with stiffener it was `31.442`. Hence, including a stiffener around the legs of stand of cyclone separator improved the design stability and reliability so that it can withstand a huge force if applied on the top face of the model.
2. From the parametric study to find out optimum position of the stiffener, it can be concluded from the results, that the optimum position is around `1000mm` from the top face as the buckling factor of safety is maximum for this position.
3. From the parametric study to find out optimum thickness of the stiffener, it can be concluded that as the thickness increases the buckling factor of safety also increases simultaneously. For the stiffener thickness of `100mm` the factor of safety is maximum.
4. From the parametric study to find out maximum force that can be applied on the top plate, it can be concluded that the maximum force should be less than `20kN`so that the buckling factor of safety for the structure lies above `25`.

REFERENCES :

1. cyclone separator
2. buckling