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Design optimization of CAD model
Available online at www.sciencedirect.com
ScienceDirect
www.materialstoday.com/proceedings
Materials Today: Proceedings 4 (2017) 7357–7364
ICAAMM-2016
Design optimization of CAD model Ramakrishnan Balaji Iyera*, VijayKumar Jattia, Yeshpal Yadavb, Anurag Vermab, Jaimin Desaib, C.P. Dewanb a
Symbiosis Institute of Technology, Symbiosis International University, Pune 412115, India Optical Payload Mechanical Group, Space Application Center, Indian Space Research Organization, Ahmedabad 380015, India
b
Abstract This paper demonstrates the optimization process of a CAD model using the results of CAE Simulation result and computation in MathCad as an integrated approach. MathCad is generally used for calculations that take input from either dimensions of the CAD model or user defined parameters in CAD environment of Creo. The technique described here links the Creo Simulation result as the input in the PTC MathCad, while the output of this program is again directed to Creo Parametric and using this output result the CAD model is optimized. This process is a seamless integration of CAD model, CAE result and a MathCad computation using CAE results. To demonstrate this technique a mirror (used in space telescope) is selected and the aim is to find out the optimum location of mounting points that give minimum surface figure distortion under gravity loading. To check the trueness of this result, it was reviewed against the theoretically calculated values and it was observed that the optimized result was similar to the theoretical one. © 2017 Elsevier Ltd. All rights reserved. Selection and Peer-review under responsibility of the Committee Members of International Conference on Advancements in Aeromechanical Materials for Manufacturing (ICAAMM-2016). Keywords: design optimization analysis; PROE to MATHCAD; Zernike polynomials; Simulation; wave front error.
*Corresponding author. Tel.: +919429628713 E-mail address: [email protected] 2214-7853© 2017 Elsevier Ltd. All rights reserved. Selection and Peer-review under responsibility ofthe Committee Members of International Conference on Advancements in Aeromechanical Materials for Manufacturing (ICAAMM-2016).
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Ramakrishnan Iyer Balaji / Materials Today: Proceedings 4 (2017) 7357–7364
Introduction
Optimization allows refining the design so that the final model consists of the best possible design without violating a set limit [1]. For example, if it is required to decide the mounting points of a mirror which is used in space related application then the main objective will be to select dimension of pitch circle diameter/radius where the mirror will be fully constrained and also the wave front error of the mirror surface is to be as minimum as possible [2,3]. Moreover to calculate the wave front error of the mirror under a specified loading condition is itself a lengthy process that is first it is required to plot the points on the surface of the mirror and then the displacement of this points under the specified loading condition is to be calculated using the Creo Simulation and then simulated result is taken to other software namely MATLAB where the Zernike polynomials are used to calculate the wave front error of the mirror. However, Creo automates the process of optimizing the given parameters by using an algorithm and varying the parameters in selected combinations to achieve the goal which are predefined in Creo itself [4]. In Optimization Design Analysis, user is required to define a goal and a limit for the design. In the example given above the goal is to find the mounting points where the mirror has its minimum wave front error and the design limit is that it should be in between the inner diameter/radius and the outer diameter/radius of the mirror. The Optimization Design Analysis should be fully automated process. There should not be any intervention by the user otherwise it fails. So the optimization process which is to be carried out in the given illustration should strictly follow the flowchart mentioned in figure1.
Fig 1: Flow Chart of Design Optimization
Ramakrishnan Iyer Balaji / Materials Today: Proceedings 4 (2017) 7357–7364
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In practice any structural optimization process CAD software, CAE software and analytical software for Math programming. The optimizer is obtained mainly by manual transferring of data from one software to other serially and iteratively [5]. For each iteration the CAE result has to be transferred from CAE software to analytical software so there is no scope of optimization. But the technique proposed here make the process of transferring the CAE result automatic and also the result achieved from Math software is directed automatically to the CAD software. Due to this atomization the design optimization using CAE result and Math program is possible in same CAD environment for any case study or CAD model. In the above flow chart shown to explain with the running example then it is found that first four steps can be carried out in one software but to calculate the wave front error the different software is required that is the software in which all the Zernike polynomials can be programmed and the error can be calculated. Previously the design optimization was carried out with the design parameter which were predefined in Creo itself .But what if the design optimization has a different goal parameter other than the predefined like in this case study as the predefined parameter in Creo does not involve wave front error. Here is one such example where the design optimization failed. The calculation of the wave front error was carried out using the 3 Matlab software where it was easy to compute the Zernike terms [6]. But for the optimization, the entire loop should be fully automated which was not possible if the wave front error was calculated in Matlab as the user has to provide the input i.e. the displacement of the points to the Matlab program which cannot be made automated as both the GUI are different. So right here a way has been proposed in which this loop can be made automatic and is explained with the above example and the design optimization will be carried our successfully. 2
Technique of Design Optimization
The solution to the above problem is by using a different software that has a provision for accepting theCreo Simulation result automatically and the end output is again redirected to Creo itself where the Optimization Analysis can be taken to the final step. The entire process runs in such way that on change of the design of the parameter the model is analysed once again in the Creo Simulation and the analysed result is directed to the software where further calculation is being carried out and then the output of this is redirected to Creo which uses the output result and finally optimizes the design. So the design optimization loop is interconnected in the same CAD environment. Explaining the above process with reference to the case study taken earlier, first the CAD model of the mirror is defined in Creo Parametric then for the first run of the analysis in Creo Simulation the mount points are taken anywhere in between the inner diameter/radius and outer diameter/radius. Some points have to be plotted on the mirror surface whose displacement is to be measured while the analysis is taking place. This displacement value is assigned as an input parameter to the MATHCAD program which gives the wave front error as the output value and it is redirected to the Creo Parametric where the Design Optimization Analysis is carried out. To make the entire loop automatic the Zernike polynomials is programmed in MathCad. 2.1
Procedure carried out to perform Design Optimization
1. Design of the model in Creo: A CAD model is to be developed in Creo. In this case study a simple mirror has been modelled as shown in figure 2 with a dimension suitable for the application where it is to be used with main parameter as outer diameter/radius, inner diameter/radius, radius of curvature and the thickness. To optimize the design there should be a goal, which in this case is to find the mounting points where there is minimum wave front error. To find the wave front error is it required to plot the points on the mirror surface. The model is created using revolve command and the points are made by using pattern command. Also after patterning the points the coordinate of the points are extracted using the 2D drawing of this model and preparing a spreadsheet. To optimize the design there should be a goal, which in this case is to find the mounting points where there is minimum wave front error. To find the wave front error is it required to plot the points on the mirror surface. The model is created using
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Ramakrishnan Iyer Balaji / Materials Today: Proceedings 4 (2017) 7357–7364
revolve command and the points are made by using pattern command. Also after patterning the points the coordinate of the points are extracted using the 2D drawing of this model and preparing a spreadsheet.
Mounting points Fig 2: CAD model of the mirror
2. Defining a Design Parameter which to be optimized: After the completion of the CAD model design the next and the main step is to define the design parameter which is to be optimized. In Creo, it is done by using the Relation and Parameter tool. Here a new parameter is added with suitable name. This is the parameter which is to be studied and optimized. To make this parameter user control that is on given some value to this parameter it should accept the value and change accordingly in model the relation is being established. The establishment of this relation is given by following command. Dimension id = Parameter name The above command is to be mentioned in the relation window. Parameter name is the name given when a new parameter was added and the dimension id is in shown the info option available in the CAD model tree. To make it clearer the example is carried further where the design parameter mentioned earlier would be the mounting points which are created by simply making 3 holes 1200 apart from each other at some random diameter/radius from the mirror center which is illustrated in figure 2. This diameter/radius is being varied over the entire region between the inner diameter/radius and outer diameter/radius of the mirror. 3. Analysis of the CAD Model in Creo Simulation: - Now the model has to be analysed because for further calculation these simulated results are also needed for the completion of design optimization.For Analysis in Creo Simulation two things are most important one is the surface on which the model is to be fixed and other is the value of the load[7, 8]. With these two the analysis study is possible. For the example described earlier the surface from which it is fixed are the mounting holes created and the load is 9810mm/sec2 at the centroid of the mirror and a static analysis is to be carried out which also measure the displacement of the points plotted on the surface. Afterwards the analysis carried is added in the model tree as a feature so that all the analysed results can be converted as an input parameter. 4. MATHCAD ANALYSIS: -Here comes the crucial part of the design optimization, the programming part. The programming has to be structured as per the requirement that is what is to be calculated using the simulated result. The programming in the MATHCAD is simple it’s just like writing the formula in a paper only the graphic
Ramakrishnan Iyer Balaji / Materials Today: Proceedings 4 (2017) 7357–7364
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interface should be understood. After the completion of the programming part the parameter which is assigned as input and the analysis result is fed should be added with a tag line of ‘proe2mc’ and the end output result of this program which is assigned as the output parameter which is to be fed to the CAD model itself should be added with the tag line of ‘mc2proe’.While programming the value of both the input and the output parameter can be assigned with any value, once the program is in use the value will be same as the analysis result and accordingly the end output result will change. After the programming part is over in Creo parametric the option namely MathCad analysis is to be used to call the MATHCAD program and run the analysis and get the output result of the program. Note this output result is very much needed to perform the optimization of the design so like a feature of the simulation analysis was created the feature of the MathCad analysis is created so that the parameter shows up in the optimization analysis 5. Design Optimization Analysis: -This is the final step of the design optimization. Till now whatever required for running the optimization analysis has been created. As discussed in the introduction the main two things are required one is the goal and other is the limit. To achieve the goal a parameter has been created which is featured by using MathCad analysis and the limit has been set using the relation and the parametric tool in the Creo itself. If the input parameter is given and the design parameter is set the only thing is left is the design goal for which the options are available like maximizing, minimizing etc. for this case study which was taken the optimization goal was to find the mounting points were the wave front error is minimum. User has options available like number iteration to be carried out, the convergence or accuracy needed in the optimization process which one can decided. 3
Validation and Results
As this tool was newly developed hence it is important to validate the tool with the model whose result is known. To validate this tool a CAD model of simply supported beam was developed and a static analysis was carried to find out that at which point of application the deflection of the beam will be maximum. The final result given by the software after many iteration was compared against the theoretical result so that the tool can be validated.
Fig 3: CAD model of simply supported beam
As shown in the above figure 3, a beam of length 100mm was taken and which was supported at both the end and the force of 200N was applied at some distance 22mm from one end of the beam. Here to find the deflection of the beam the displacement of the points at the bottom edge was measured due to the application of the force. Afterward the distance of point where load is applied and varied over the length of the beam in order to find out the point where deflection is maximum. The validation result obtained after the optimization using the tool is shown in the below figure 4. After the completion of the design optimization study the result are shown in terms of the graph. There are mainly two graph pop up after completion of the study. one graph is the design goal parameter value v/s number of iteration and the other one is design parameter v/s number of iteration as the X-axis are same in both the graphs the user can interpolate by compiled the both the graph in one which has design goal parameter v/s the parameter which is to be optimized.
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Ramakrishnan Iyer Balaji / Materials Today: Proceedings 4 (2017) 7357–7364
(a) Before Optimization
(b) After Optimization
(a)
(b)
Fig 4: Validated Results (a) Before Optimization (b) After optimization
The above figure can be interpreted that the distance of the point forces was found out to be approximately half of the length of the beam that is 50.10mm away from the axis where the deflection of the beam was maximum [9]. For comparison the result was calculated theoretically using the deflection beam formula which is written below.
(1) Where δ is deflection P is the load, b is the distance of load from one end of the beam, l is the length, E and I are the young's modulus and Moment of Inertia respectively. To find the maximum deflection of the beam the equation (1) is differentiated with respect to b and equated to zero. Finally the value comes to be half of the length of beam. So it can be said that the tool developed is fully validated and the result are almost similar. The result of the case study which was taken throughout this paper is shown below in figure 5. The PCD of the mount point where the wave front is minimum is around 105.5mm as it can be seen in the below graph.
Ramakrishnan Iyer Balaji / Materials Today: Proceedings 4 (2017) 7357–7364
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To check the trueness of the relation for mounting a circular disc in the 3 points is found[10]. The relation is as follow ⁄
⁄
0.707 ∗
2
Considering the mirror whose optimization was carried out as a circular disc so the PCD of the mounts will be 0.7 times the diameter/radius of the mirror. So theoretically the result comes out to be 105 mm which is closest to the result obtained from the optimization result that is 106 mm. So the design optimization carried out is true.
(a)
(b) Fig 5: End Output Result of the design optimization analysis (a) Graph of Wavefront error v/s number of iteration (b) Graph of Pitch circle radius of mounting points
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Ramakrishnan Iyer Balaji / Materials Today: Proceedings 4 (2017) 7357–7364
CONCLUSION
An optimization technique using seamless integration between CAD, CAE and MathCad is demonstrated here. The programming in MathCad can be replaced with any other analytical code for the purpose of computing optimization function. Compared to earlier approaches where simulation results are exported to text file or spread sheet in order to make it an input file to analytical softwares like Matlab or MathCad, the integrated approach given in this paper allows seamless flow of data between CAD, CAE and MathCad environment without any user intervention or interaction. The optimizer of CAD takes control of entire scenario and decides change in parameter values to reach the goal of optimization function computed by MathCad and fed back to CAD optimizer for its comparison with its earlier value. These output values are easily accessible in CAD environment itself in the form of parameters. The concept is demonstrated in case of mirror design and output is successfully validated with theoretical computation. Acknowledgements I am grateful to Shri Sandeep Singh, Shri Sahil Patel and Shri Naimesh Patel of the Optical Mechanical Group Space Application Center for their help and support throughout this experiment. A mention of all colleagues at Optical Payload Mechanical Group including trainee and contract person who helped, guided me and also for provided support on the software and hardware fronts over the entire process. Lastly, I would like to lay my gratitude towards Prof. Nitin Solke and Prof. Yash Parikh Symbiosis Institute of Technology for allowing me to carry out the project work at Space Application Center, Indian Space Research Organization. Reference [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
Optimization in Creo, ragarwal Mounting of Optical Components, Jim Burge Design and Optimization of Lightweight Space Telescope Structures, Andrzej M. Stewart and David W. Miller James C. Wyant, basic Wave front Abberration Theory for Optical Metrology. Design and Optimization of Lightweight Space Telescope Structures, Andrzej M. Stewart and David W. Miller. James C. Wyant, basic Wave front Abberration Theory for Optical Metrology. Learningexchange.ptc.com Roger, Creo Simulation, SDC publication. Mechanics of Solid, Egor Popov. Paul Yoder, Design and Mounting Small, Nonmetallic Mirrors, Gratings, and Pellicles, Opto-Mechanical System Design, Third Edition.
ScienceDirect
www.materialstoday.com/proceedings
Materials Today: Proceedings 4 (2017) 7357–7364
ICAAMM-2016
Design optimization of CAD model Ramakrishnan Balaji Iyera*, VijayKumar Jattia, Yeshpal Yadavb, Anurag Vermab, Jaimin Desaib, C.P. Dewanb a
Symbiosis Institute of Technology, Symbiosis International University, Pune 412115, India Optical Payload Mechanical Group, Space Application Center, Indian Space Research Organization, Ahmedabad 380015, India
b
Abstract This paper demonstrates the optimization process of a CAD model using the results of CAE Simulation result and computation in MathCad as an integrated approach. MathCad is generally used for calculations that take input from either dimensions of the CAD model or user defined parameters in CAD environment of Creo. The technique described here links the Creo Simulation result as the input in the PTC MathCad, while the output of this program is again directed to Creo Parametric and using this output result the CAD model is optimized. This process is a seamless integration of CAD model, CAE result and a MathCad computation using CAE results. To demonstrate this technique a mirror (used in space telescope) is selected and the aim is to find out the optimum location of mounting points that give minimum surface figure distortion under gravity loading. To check the trueness of this result, it was reviewed against the theoretically calculated values and it was observed that the optimized result was similar to the theoretical one. © 2017 Elsevier Ltd. All rights reserved. Selection and Peer-review under responsibility of the Committee Members of International Conference on Advancements in Aeromechanical Materials for Manufacturing (ICAAMM-2016). Keywords: design optimization analysis; PROE to MATHCAD; Zernike polynomials; Simulation; wave front error.
*Corresponding author. Tel.: +919429628713 E-mail address: [email protected] 2214-7853© 2017 Elsevier Ltd. All rights reserved. Selection and Peer-review under responsibility ofthe Committee Members of International Conference on Advancements in Aeromechanical Materials for Manufacturing (ICAAMM-2016).
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Ramakrishnan Iyer Balaji / Materials Today: Proceedings 4 (2017) 7357–7364
Introduction
Optimization allows refining the design so that the final model consists of the best possible design without violating a set limit [1]. For example, if it is required to decide the mounting points of a mirror which is used in space related application then the main objective will be to select dimension of pitch circle diameter/radius where the mirror will be fully constrained and also the wave front error of the mirror surface is to be as minimum as possible [2,3]. Moreover to calculate the wave front error of the mirror under a specified loading condition is itself a lengthy process that is first it is required to plot the points on the surface of the mirror and then the displacement of this points under the specified loading condition is to be calculated using the Creo Simulation and then simulated result is taken to other software namely MATLAB where the Zernike polynomials are used to calculate the wave front error of the mirror. However, Creo automates the process of optimizing the given parameters by using an algorithm and varying the parameters in selected combinations to achieve the goal which are predefined in Creo itself [4]. In Optimization Design Analysis, user is required to define a goal and a limit for the design. In the example given above the goal is to find the mounting points where the mirror has its minimum wave front error and the design limit is that it should be in between the inner diameter/radius and the outer diameter/radius of the mirror. The Optimization Design Analysis should be fully automated process. There should not be any intervention by the user otherwise it fails. So the optimization process which is to be carried out in the given illustration should strictly follow the flowchart mentioned in figure1.
Fig 1: Flow Chart of Design Optimization
Ramakrishnan Iyer Balaji / Materials Today: Proceedings 4 (2017) 7357–7364
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In practice any structural optimization process CAD software, CAE software and analytical software for Math programming. The optimizer is obtained mainly by manual transferring of data from one software to other serially and iteratively [5]. For each iteration the CAE result has to be transferred from CAE software to analytical software so there is no scope of optimization. But the technique proposed here make the process of transferring the CAE result automatic and also the result achieved from Math software is directed automatically to the CAD software. Due to this atomization the design optimization using CAE result and Math program is possible in same CAD environment for any case study or CAD model. In the above flow chart shown to explain with the running example then it is found that first four steps can be carried out in one software but to calculate the wave front error the different software is required that is the software in which all the Zernike polynomials can be programmed and the error can be calculated. Previously the design optimization was carried out with the design parameter which were predefined in Creo itself .But what if the design optimization has a different goal parameter other than the predefined like in this case study as the predefined parameter in Creo does not involve wave front error. Here is one such example where the design optimization failed. The calculation of the wave front error was carried out using the 3 Matlab software where it was easy to compute the Zernike terms [6]. But for the optimization, the entire loop should be fully automated which was not possible if the wave front error was calculated in Matlab as the user has to provide the input i.e. the displacement of the points to the Matlab program which cannot be made automated as both the GUI are different. So right here a way has been proposed in which this loop can be made automatic and is explained with the above example and the design optimization will be carried our successfully. 2
Technique of Design Optimization
The solution to the above problem is by using a different software that has a provision for accepting theCreo Simulation result automatically and the end output is again redirected to Creo itself where the Optimization Analysis can be taken to the final step. The entire process runs in such way that on change of the design of the parameter the model is analysed once again in the Creo Simulation and the analysed result is directed to the software where further calculation is being carried out and then the output of this is redirected to Creo which uses the output result and finally optimizes the design. So the design optimization loop is interconnected in the same CAD environment. Explaining the above process with reference to the case study taken earlier, first the CAD model of the mirror is defined in Creo Parametric then for the first run of the analysis in Creo Simulation the mount points are taken anywhere in between the inner diameter/radius and outer diameter/radius. Some points have to be plotted on the mirror surface whose displacement is to be measured while the analysis is taking place. This displacement value is assigned as an input parameter to the MATHCAD program which gives the wave front error as the output value and it is redirected to the Creo Parametric where the Design Optimization Analysis is carried out. To make the entire loop automatic the Zernike polynomials is programmed in MathCad. 2.1
Procedure carried out to perform Design Optimization
1. Design of the model in Creo: A CAD model is to be developed in Creo. In this case study a simple mirror has been modelled as shown in figure 2 with a dimension suitable for the application where it is to be used with main parameter as outer diameter/radius, inner diameter/radius, radius of curvature and the thickness. To optimize the design there should be a goal, which in this case is to find the mounting points where there is minimum wave front error. To find the wave front error is it required to plot the points on the mirror surface. The model is created using revolve command and the points are made by using pattern command. Also after patterning the points the coordinate of the points are extracted using the 2D drawing of this model and preparing a spreadsheet. To optimize the design there should be a goal, which in this case is to find the mounting points where there is minimum wave front error. To find the wave front error is it required to plot the points on the mirror surface. The model is created using
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Ramakrishnan Iyer Balaji / Materials Today: Proceedings 4 (2017) 7357–7364
revolve command and the points are made by using pattern command. Also after patterning the points the coordinate of the points are extracted using the 2D drawing of this model and preparing a spreadsheet.
Mounting points Fig 2: CAD model of the mirror
2. Defining a Design Parameter which to be optimized: After the completion of the CAD model design the next and the main step is to define the design parameter which is to be optimized. In Creo, it is done by using the Relation and Parameter tool. Here a new parameter is added with suitable name. This is the parameter which is to be studied and optimized. To make this parameter user control that is on given some value to this parameter it should accept the value and change accordingly in model the relation is being established. The establishment of this relation is given by following command. Dimension id = Parameter name The above command is to be mentioned in the relation window. Parameter name is the name given when a new parameter was added and the dimension id is in shown the info option available in the CAD model tree. To make it clearer the example is carried further where the design parameter mentioned earlier would be the mounting points which are created by simply making 3 holes 1200 apart from each other at some random diameter/radius from the mirror center which is illustrated in figure 2. This diameter/radius is being varied over the entire region between the inner diameter/radius and outer diameter/radius of the mirror. 3. Analysis of the CAD Model in Creo Simulation: - Now the model has to be analysed because for further calculation these simulated results are also needed for the completion of design optimization.For Analysis in Creo Simulation two things are most important one is the surface on which the model is to be fixed and other is the value of the load[7, 8]. With these two the analysis study is possible. For the example described earlier the surface from which it is fixed are the mounting holes created and the load is 9810mm/sec2 at the centroid of the mirror and a static analysis is to be carried out which also measure the displacement of the points plotted on the surface. Afterwards the analysis carried is added in the model tree as a feature so that all the analysed results can be converted as an input parameter. 4. MATHCAD ANALYSIS: -Here comes the crucial part of the design optimization, the programming part. The programming has to be structured as per the requirement that is what is to be calculated using the simulated result. The programming in the MATHCAD is simple it’s just like writing the formula in a paper only the graphic
Ramakrishnan Iyer Balaji / Materials Today: Proceedings 4 (2017) 7357–7364
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interface should be understood. After the completion of the programming part the parameter which is assigned as input and the analysis result is fed should be added with a tag line of ‘proe2mc’ and the end output result of this program which is assigned as the output parameter which is to be fed to the CAD model itself should be added with the tag line of ‘mc2proe’.While programming the value of both the input and the output parameter can be assigned with any value, once the program is in use the value will be same as the analysis result and accordingly the end output result will change. After the programming part is over in Creo parametric the option namely MathCad analysis is to be used to call the MATHCAD program and run the analysis and get the output result of the program. Note this output result is very much needed to perform the optimization of the design so like a feature of the simulation analysis was created the feature of the MathCad analysis is created so that the parameter shows up in the optimization analysis 5. Design Optimization Analysis: -This is the final step of the design optimization. Till now whatever required for running the optimization analysis has been created. As discussed in the introduction the main two things are required one is the goal and other is the limit. To achieve the goal a parameter has been created which is featured by using MathCad analysis and the limit has been set using the relation and the parametric tool in the Creo itself. If the input parameter is given and the design parameter is set the only thing is left is the design goal for which the options are available like maximizing, minimizing etc. for this case study which was taken the optimization goal was to find the mounting points were the wave front error is minimum. User has options available like number iteration to be carried out, the convergence or accuracy needed in the optimization process which one can decided. 3
Validation and Results
As this tool was newly developed hence it is important to validate the tool with the model whose result is known. To validate this tool a CAD model of simply supported beam was developed and a static analysis was carried to find out that at which point of application the deflection of the beam will be maximum. The final result given by the software after many iteration was compared against the theoretical result so that the tool can be validated.
Fig 3: CAD model of simply supported beam
As shown in the above figure 3, a beam of length 100mm was taken and which was supported at both the end and the force of 200N was applied at some distance 22mm from one end of the beam. Here to find the deflection of the beam the displacement of the points at the bottom edge was measured due to the application of the force. Afterward the distance of point where load is applied and varied over the length of the beam in order to find out the point where deflection is maximum. The validation result obtained after the optimization using the tool is shown in the below figure 4. After the completion of the design optimization study the result are shown in terms of the graph. There are mainly two graph pop up after completion of the study. one graph is the design goal parameter value v/s number of iteration and the other one is design parameter v/s number of iteration as the X-axis are same in both the graphs the user can interpolate by compiled the both the graph in one which has design goal parameter v/s the parameter which is to be optimized.
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Ramakrishnan Iyer Balaji / Materials Today: Proceedings 4 (2017) 7357–7364
(a) Before Optimization
(b) After Optimization
(a)
(b)
Fig 4: Validated Results (a) Before Optimization (b) After optimization
The above figure can be interpreted that the distance of the point forces was found out to be approximately half of the length of the beam that is 50.10mm away from the axis where the deflection of the beam was maximum [9]. For comparison the result was calculated theoretically using the deflection beam formula which is written below.
(1) Where δ is deflection P is the load, b is the distance of load from one end of the beam, l is the length, E and I are the young's modulus and Moment of Inertia respectively. To find the maximum deflection of the beam the equation (1) is differentiated with respect to b and equated to zero. Finally the value comes to be half of the length of beam. So it can be said that the tool developed is fully validated and the result are almost similar. The result of the case study which was taken throughout this paper is shown below in figure 5. The PCD of the mount point where the wave front is minimum is around 105.5mm as it can be seen in the below graph.
Ramakrishnan Iyer Balaji / Materials Today: Proceedings 4 (2017) 7357–7364
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To check the trueness of the relation for mounting a circular disc in the 3 points is found[10]. The relation is as follow ⁄
⁄
0.707 ∗
2
Considering the mirror whose optimization was carried out as a circular disc so the PCD of the mounts will be 0.7 times the diameter/radius of the mirror. So theoretically the result comes out to be 105 mm which is closest to the result obtained from the optimization result that is 106 mm. So the design optimization carried out is true.
(a)
(b) Fig 5: End Output Result of the design optimization analysis (a) Graph of Wavefront error v/s number of iteration (b) Graph of Pitch circle radius of mounting points
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Ramakrishnan Iyer Balaji / Materials Today: Proceedings 4 (2017) 7357–7364
CONCLUSION
An optimization technique using seamless integration between CAD, CAE and MathCad is demonstrated here. The programming in MathCad can be replaced with any other analytical code for the purpose of computing optimization function. Compared to earlier approaches where simulation results are exported to text file or spread sheet in order to make it an input file to analytical softwares like Matlab or MathCad, the integrated approach given in this paper allows seamless flow of data between CAD, CAE and MathCad environment without any user intervention or interaction. The optimizer of CAD takes control of entire scenario and decides change in parameter values to reach the goal of optimization function computed by MathCad and fed back to CAD optimizer for its comparison with its earlier value. These output values are easily accessible in CAD environment itself in the form of parameters. The concept is demonstrated in case of mirror design and output is successfully validated with theoretical computation. Acknowledgements I am grateful to Shri Sandeep Singh, Shri Sahil Patel and Shri Naimesh Patel of the Optical Mechanical Group Space Application Center for their help and support throughout this experiment. A mention of all colleagues at Optical Payload Mechanical Group including trainee and contract person who helped, guided me and also for provided support on the software and hardware fronts over the entire process. Lastly, I would like to lay my gratitude towards Prof. Nitin Solke and Prof. Yash Parikh Symbiosis Institute of Technology for allowing me to carry out the project work at Space Application Center, Indian Space Research Organization. Reference [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
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