Solid Mechanics Issues - Lab Report Example

?The design was produced using SolidWorks The larger cylinder was created as an extruded boss with the initially provided dimensions. After this the smaller cylinder was created using an extruded boss with the provided dimensions. The connecting section was created using an extruded boss as well with the dimensions provided. A fillet was added to the sections indicated using the fillet feature with a uniform radius of 3 mm. A drawing was then generated for the final geometry which is shown below along with the dimensions. After this the model was exported as a *.STEP file for analysis in ALGOR FEA. After the model was imported to ALGOR FEA the log was checked to ensure that there were no import errors or missing geometry. Then a fixed boundary condition was applied to the internal surface of the larger cylinder after which a normal force of 500 N was applied to the internal surface of the smaller cylinder. The application of a fixed boundary condition to one area of the model meant that the model was constrained from moving within that axis of rotation or translation. The model could either rotate on the longitudinal axis of the constrained cylinder or it could translate in either three directions (x, y and z). Implementing a fixed boundary condition indicates that the model is unable to move in any direction at all. Generally a fixed boundary condition can be considered analogous to a welded piece that is unable to move but can bend or flex under applied force. Though this may not simulate the actual conditions one on one (where the crank actually rotates though it does not translate at all), but it does provide a satisfactory numerical investigation model. Furthermore the application of a normal force to the other cylinder’s internal surface indicates the application of normal average force when the crank will be in use. This application of force assumes that the pin attached to the smaller cylinder of the crank will be able to transmit the applied force at the pedal completely and uniformly all across the surface of the cylinder and that this force will be normal to the provided surface. However practically this is not going to be possible as the pin will bear some kind of clearance to ensure free rotation and the clearance in turn will mean that the pin will contact the cylinder non-uniformly. Moreover the pin’s contact will produce a normal force at areas with complete contact while they will produce slightly skewed forces where the cylinder only partially contacts the subject surface. This method of applying a force to the model is non ideal yet the approximation is tolerable enough because what will take place inside the cylinder is similar. Any differences in force will not be very significant so using normal force’s application is a viable technique. The model was given a material of Steel 4130 which was present in the software’s library. After this the model was meshed using default settings. After meshing the model was simulated for calculating the developed stress and for the FOS (factor of safety) calculations. The results for the first run are shown below. The mesh was redefined for element size (which was lowered) although the mesh was still based on a 4 point Jacobian approach. The newly meshed model was then simulated in order to see the effects of a changed mesh size on the numerical investigation. The results from the re-meshed run are shown below. The results above clearly indicate that the stress distribution levels and the FOS distribution did not change at all indicating that the previous mesh control was providing a mesh independent solution. Therefore for the purpose of this analysis and optimisation the previous mesh controls were re-implemented as a mesh independent solution had been achieved. The results above clearly show that the lowest FOS is very high which indicates a rather overdesigned scenario. The current situation dictates that the FOS ought to be around 3:1 for a viable design. In order to achieve a more suitable FOS the design was optimised for a number of parameters. The stress plot is shown below to indicate the regions of minimum and maximum stress. The lowest amount of stress lies in the larger cylinder which indicates that the cylinder’s dimensions can be optimised further. The first parameter under consideration was the external diameter of the larger cylinder. The internal diameter of the removed portion was not optimised as it may be constrained due to pin sizing or other considerations. The total range of optimisation was chosen between 16 mm and 50 mm with a step size of 1 mm. The objective of the design study was to keep the stress levels as such while reducing the amount of material being used to create the part. The optimised value for the external diameter was found to be 16 mm with a newer lowered stress level. The results of this are shown in the plot below. The next parameter under consideration based on the results above is the thickness of the central connecting portion. The dimension between the centres of the internal cylinders (180 mm) was not optimised given sizing concerns so instead the thickness (10 mm) was optimised. The total range was chosen between 1 mm and 10 mm with a step size of 1 mm. The design study run showed that only two possible scenarios existed with thickness of either 6 mm or 10 mm as the other design scenarios failed due to radius of fillet. However the radius of fillet could not be optimised given the fact that the radius of fillet is a driven dimension and not a driving dimension. Hence the current level of optimisation was left in place. The next dimension that could be optimised is the external diameter of the other cylinder. The previous results indicated that the current stress levels for the other cylinder were higher on the internal cylinder’s surfaces. The total range that was available for optimisation was taken from 11 mm to 30 mm with a step size of 1 mm. The optimisation run showed that the optimal diameter was 25 mm leading to the lowest stress levels in the given run. Given that the entire crank arrangement is optimised structurally the next step is to optimise the crank for connecting it to other components such as chain sprocket. The larger cylinder was chosen for connection investigation. A number of different methods were investigated to connect the crank which included: pin based connection; key based connection; splined connection. These connections were investigated by applying a fixed boundary condition at the pin, key and spline interface keeping the same assumptions in place as highlighted initially. The first modification was introducing a hole for a pin in the cylinder optimised first of all. A hole was introduced with a diameter of 2.5 mm as shown in the figure below. The default meshing controls were applied as the solution is already mesh independent and the results are shown below. The plot above clearly indicates that the stress levels are still low in the given section so using a pin as a jointing mechanism is a feasible option. The next option was to use a key way type arrangement as indicated in the figure below. The keyway introduced into the cylinder measured 2.5 mm in breadth and ranged from the centre of the cylinder to its edge. The default meshing controls were applied and the results are shown in the plot below. The results above clearly indicate that the keyway does not introduce any new problems in terms of increased stress levels. A high FOS is also generated using the key way approach so it can be safely concluded that this design modification is valid for practical implementation. The last method was based on the use of a splined profile on the internal surface of the concerned cylinder. The model was modified to include the splined geometry while the splined geometry was based on circular profiles that resembled milled surfaces. This ensured that the model was practicable when analysed on a manufacturing plane. A new circle was introduced with a diameter of 12.5 mm through which the spline was extruded. The modified model and the spline’s details are shown in the diagrams below. The model was analysed using the default mesh settings and the results are shown below. The plot above clearly indicates that the stress levels are still low in the subject region and hence the splined model can be used with complete confidence as a means of jointing. Read More