Analyzing Helical Spring Behavior Using Finite Element Method

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Central Mindanao University**We aren't endorsed by this school

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MECHANICAL 101

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Mechanical Engineering

Date

Dec 10, 2024

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Uploaded by JudgeGrousePerson853

Republic of the PhilippinesCentral Mindanao UniversityUniversity Town, Musuan, 8710 BukidnonDepartment of Mechanical EngineeringFinite Element MethodActivity No. 6Analysis of Solid Element Components: Helical SpringName of StudentLouine Jacob P. ButalidSection BSME 4ScheduleM (10:00AM-12:00PM)Date PerformedOctober 14, 2024Date SubmittedOctober 20, 2024DeadlineOctober 21, 2024Total Score1Criteria: Equivalent ScoreContent (20%)Accuracy (25%)Format (15%)Quality (15%)Analysis (20%)Overall Impression (5%)

I.ObjectivesTo be able to create a simulation study of a helical springTo be able to display the distribution of spring displacement, probe displacementresults, and variation of shear stressTo be able to obtain the maximum deflection, average value of the probedisplacement results, and maximum shear stressTo be able to compare the theoretical and the computational results of springdeflection and the shear stressTo be able to analyze the results of the simulationII.Theory(Research from reliable sources on the internet (indicate the references) and include here thefollowing: 1. Helical Spring deflection formula, 2. Helical Spring shear stress formula, and 3.Finite Element Simulation of a Helical Spring. You can Refer to this book: Practical FiniteElement Simulations with SOLIDWORKS 2022.)Helical Spring Deflection FormulaThe deflection of a helical spring can be calculated using the formula δ=64P R3nGd48, where P is the applied load, R is the mean radius, n is the number of active coils, G is the modulus of rigidity, and d is the wire diameter. This formula helps determine how much the spring will compress or extend under a given load.Helical Spring Shear Stress FormulaThe maximum shear stress in a helical spring is given by τmax=16PRπ d34d2+4Rdwhere P is the applied load, R is the mean radius, and d is the wire diameter. This formula accounts for both direct shear stress and torsional shear stress.Finite Element Simulation of a Helical Spring2

Finite Element Analysis (FEA) is used to model the behavior of helical springs under loadingconditions. The process involves:Discretizing the spring into small elements.Solving for stress, deflection, and other mechanical properties numerically.FEA helps predict stress distribution and deflection more accurately, especially in complex ordynamic loading conditions, by dividing the spring into finite elements for localized analysis.These principles are fundamental for understanding how springs behave in practicalengineering applications and ensuring they are designed for safety and performance.III.Materials and InstrumentsSolidWorks SoftwareSolidWorks Flow Simulation 2012 TutorialIV.Procedure1.Open SOLIDWORKS software.2.Perform the analysis of a shaft via SOLIDWORKS Simulation by following theinstructions of the book entitled Practical Finite Element Simulations withSOLIDWORKS 2022, from page 236 to page 265. 3.Document your activity by taking a time lapse video of yourself doing the activity.Make sure that the screen activity is also clear in the recorded video.4.Attach screenshots of the results in the “data and results” section, showing samevalue with the reference book.5.Make your work commendable. Please see the rubrics for the criteria in grading youractivity.6.Upload your time lapse video in your Google drive and share your link to me in ourGC.7.Attached in the appendix the screenshots of your time lapse video.V.Data and Results1.Distribution of spring displacement,3

2.4

2.) Probe displacement results3. Variation of shear stress5

VI.Conclusion (Summarize the key findings and insights gained from the activity. Here are some of elements youmay include: Summary of Results, Interpretation of Results, Discussion of Errors or Limitations,Implications and Applications, Conclusion Statement, and Recommendations. Remember to keepyour conclusion clear, concise, and focused on the main points of the objectives. Avoidintroducing new information or delving into tangential topics that are not directly relevant to theactivity.)The SolidWorks simulation of a helical spring was conducted to evaluate its deflection, shearstress distribution, and overall mechanical behavior under an applied load. The simulationrevealed a maximum deflection of 34.834 mm, closely matching theoretical predictions. It alsoidentified the highest shear stress at 74.727 MPa near the inner radius of the spring's coils,validating the use of Wahl’s correction factor. These results align with analytical models thatforecast stress concentration in loaded helical springs.Key factors influencing the simulation’s accuracy include mesh density and the precision ofmaterial properties. A coarse mesh may lead to less accurate stress predictions, while incorrectmaterial properties, such as the modulus of elasticity, can significantly affect the results.Additionally, the simulation assumes ideal boundary conditions, which may differ from real-worldfactors like manufacturing flaws or material imperfections. These insights are critical fordesigning springs in applications like automotive suspensions, mechanical systems, andindustrial equipment, where predicting failure points and optimizing designs before productionhelp ensure reliability and reduce material costs.VII.Questions/ Problems1.What is the value maximum of the maximum spring deflection?6

The maximum deflection of the spring is 34.824 mm, occurring as a downward contraction at the uppermost part of the spring.2.How many percent does it differ with the theoretical spring deflection?The theoretical spring deflection rate is 18.13 mm and the simulation has the average spring deflection of 18.163 mm%=¿18.13−18.163∨¿18.13=0.001654≈16.54%¿3.What is the value maximum shear stress of the spring?The maximum shear stress of the spring is 74.727 MPa at the interior part of the spring.4.How many percent does it differ with the theoretical maximum shear stress?With a theoretical shear stress value of 71.42 MPa and a maximum shear stress of 74.727 MPa from the simulation, the percentage difference between the two values is%=¿71.42−74.727∨¿71.42=0.04630≈4.63%¿5.How much is the value of the average probe displacement results?The average displacement of the probe is 15.758 mm, indicating a downward movement or contraction.6.Is the helical spring safe? Explain your answer. If it is not safe, please improve the design and verify.Based on the SOLIDWORKS simulation results, the spring is deemed safe with asafety factor of 1.659.VIII.References(Follow APA format citations. APA website citations usually include the author, the publicationdate, the title of the page or article, the website name, and the URL. If there is no author, start thecitation with the title of the article. If the page is likely to change over time, add a retrieval date.)COMSOL. (2020). A Simulation App for Helical Spring Design and Analysis. Retrieved from https://www.comsol.com/blogs/a-simulation-app-for-helical-spring-design-and-analysisJames Spring. (2021). Calculating Spring Deflection | Formula for Hooke’s Law. Retrieved fromhttps://www.jamesspring.com/news/calculating-spring-deflection/MATHalino. (n.d.). Helical Springs | Strength of Materials Review at MATHalino. Retrieved from https://mathalino.com/reviewer/mechanics-and-strength-of-materials/helical-springsMDPI. (2023). Dynamic Finite Element Model Based on Timoshenko Beam Theory for Simulating High-Speed Nonlinear Helical Springs. Retrieved from https://www.mdpi.com/1424-8220/23/7/3737SAE International. (2013). An Efficient, One-Dimensional, Finite Element Helical Spring Modelfor Use in Planar Multi-Body Dynamics Simulation. Retrieved from https://www.sae.org/publications/technical-papers/content/2013-01-1118/IX.Appendix(Attach pictures of you during the activity showing your face and the screen of the computer.7

ME 82 Activity Evaluation RubricsCriteriaExcellent (5)Good (4)Satisfactory (3)Needs Improvement (2)Poor (1)Completenessof Content (20%)All required elements are present, including acomprehensive introduction, methodology, results, discussion, and conclusion.Most required elements are present, but some details may be lacking.Some required elements are missing or incomplete.Many required elements are missing or unclear.Most required elements are missing or incomplete.Accuracy of Data and Calculations (25%)All data is accurate,and calculations are generally correct, with only minor errors.Most data is accurate, and calculations are generally correct, with only minor errors.Some inaccuracies in data and calculations are present, affecting the overall reliability of the results.Numerous inaccuracies in data and calculations significantly impact the validity of the results.Data and calculations are largely incorrect or missing.Presentation and Formatting (15%)The activity is well-organized, with clear headings, labels, and a logicalflow. Formatting is The activity is organized, but there may be some inconsistencies The organization is somewhat confusing, and formatting is inconsistent, The activity lacks clear organization and formatting, making it difficult to follow.The activity is disorganized, with little to no attention to formatting, 8

consistent and professional.in headings, labels, or formatting.affecting overall clarity.hindering understandingQuality of Graphs and Figures (15%)Graphs and figures are clear, well-labelled, and directly support the analysis. They enhance the understanding of the presented data.Most graphs and figures are clear and adequately labelled, contributing to the overall understanding of the content.Some graphs and figures are unclear or poorly labelled, making itchallenging to interpret the data.Graphs and figures are confusing, hindering the ability to comprehend the information.Graphs and figures are missing or of very poor quality.Analysis and Interpretation (20%)The analysis is insightful, demonstrating a deep understanding of the experimental outcomes. Connections between theory andresults are well-established.The analysis is sound, with a good understanding of the experimental outcomes and some connections to theory.The analysis is basic with limited connections between theory and results. The analysis is superficial, and connections between theory and results are unclear. Little to no analysis is provided, and connections to theory are absent.Overall Impression (5%)The activity demonstrates exceptional effort and understanding,showcasing a high level of competency in the laboratory work.The activity is well-done, indicating a good level of effort and understanding in the laboratorywork.The activity is satisfactory, but improvements could enhance overall quality.The activity showsminimal effort or understanding, requiring significant improvements.The activity is of poor quality,reflecting a lack of effort orunderstanding in the laboratory work.9