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Modélisation et simulation par éléments finis : examen

Exam 2014 « Finite element modeling and simulation »

Analysis of a quadcopter drone propeller

Name : no Sciper :

Background and aim of the study:The objective of this study is to analyse the stresses and displacements in a propeller of a quadcopter drone The drone is composed of 4 arms and one main body which concentrates the majority of the mass of the aircraft (1kg). Each arm is equipped with one electric motor on which the propelllers are directly mounted through a threaded shaft and a nut & washer. Due to their large diameter and high rotation speed the propellers are subjected to strong mechanical loads and must be optimized int terms of mass and aerodynamic performance. The aim of this study is to verify the current design of propellers for different work conditions in statics and dynamics.Principle

The propeller is in ABS plastic with a diameter of 8’’ and is subjected to the following loads:a) preload of the locking nut = 2kNb) rotation speed 0 to 15'000 RPMc) lift P corresponding to accelerations of 4g max. d) vibrations and transient loading

Analysis :A finite element analysis of this part is requested with the following detailed goals:1. Evaluate the von Mises stress, les principal strains and the vertical displacement

(Y) at blade tip (pt A) for two distinct static load cases: (1a) Maximum rotation speed only, without lift (1b) Maximum rotation speed with maximum lift In both cases, the bolt preload must be taken into account.

2. Evaluate the modal response of the propeller (6 first eigenmodes) 3. Evaluate the design criteria for the base ABS material 4. Optimize the choice of material, if necessary, according to results in 1 and 2le

choix du matériau Load case no 1a & 1b: complementary informations We will consider that: (I) the preload acts on the surface S1 and the washer prevents all radial displacement on S1; (II) the lift P (along Y) is distributed uniformerlly on the extrados surface S2; (III) the friction between the bottom face S3 and the moto ris high enough to prevent any radial, circumferential and vertical displacement. The convergence study will only be carried out on load case 1a.

J. Cugnoni, LMAF/EPFL, 2014 p. 1 / 10


Evaluation criteria in static loading, case 1a and 1b : (i) maximal Von Mises stress < yield stress on the most part of the model. (ii) A small region (up to 1x1x1mm3) in which the stress is above yield is acceptable but the principal strains (in abs value) must not exceed the ultimate strain of the material ; (iii) For case 1b only: the maximum displacement in pt A along Y must not not surpass D/10 where D is the external diameter of the propeller.

Load case 2: complementary informationPerform a finite element modal analysis to extract the 6 first eigen modes and frequencies. Displacement hypothesis on S1: radial displacement =0 ; on S3: radial, circumferential and vertical displacement =0. Dynamic evaluation criteria: the eigen frequency of the first symmetric bending mode must exceed 50Hz.Materials

Material Modulus [GPa]

. Poisson Yield stress [MPa]

Strain at failure % Mass density. [kg/m3]

ABS (injection)(nominal case)

2.8 0.35 70 5% 1200

Nylon 66 reinforced 1.7 0.35 140 40% 1200

Reinforced Epoxy 28 0.35 200 5% 1200

Cuation : Only perform a convergence analysis on the load case 1a with a maximum of 3

meshes (if it does not converge comment on the error margin). Use as much as possible the symmetries of the problem.

Work,hand out and evaluation To perform this study please follow attentively the present report templante Once finished send you documents by email to [email protected] . The following files must be sent: Word file (doc/docx) et Abaqus models ( .cae + .jnl). The present document must also be signed with your name and SCIPER and then returned to the teacher by the end of the exam. Duration : max 4h.Evaluation of the work: Modeling Hypotheses 35%; Convergence study 20% Extraction of the results : 20% ; Analysis and conclusions 20%. Load case no1a ~40%, 1b 25% and load case no3 ~20%,.Downloads : the CAD file and + the present report canvas can be found:

http://lmafsrv1.epfl.ch/jcugnoni/tmp/Iris/APC8


mailto:[email protected]


Finite Element Analysis Report

Analysis of a quadcopter drone propellerExam 2014 « Finite Element modelling and simulation »

name, email, no Sciper

1.Goal of the study1.1 Objectives and contextThe context and objectives have been described in the specification of the study thus they are not repeated here.

1..2 Type of analysis et methodology

Which type of analysis will be carried out and in which order?

On which load case and on which quantity will you check the convergence of the model?

2. Geometric hypotheses2.1 Presentation of the geometry

This project consists only in one part in IGS format. The geometry in presented in the project description.

2.2 System of units

In which system of units are you working?

Length : unitXXX

Force : unitXXX

Mass : unitXXX

Stress / moduli : unitXXX

2.3 Characteristic dimensions

The propeller has a characteristic dimension of 8” diameter.

2.4 Symmetries of the problem

Does the problem have any symmetry? If yes which ones? And do you use them in the modelling



Load Case 1a:

Load Case 1b:

Load Case 2:

2.5 Modelling space

Due to the complexity of the part, the problem cannot be simplified to 2D and thus we have to keep a full 3D description for the model.

3. Hypothesis of material behaviours3.1 Description of the materials

The propeller is produced by plastic injection molding of ABS thermoplastic polymer.

3.1.1 Material behaviour model

The materials used in this study are all considered homogeneous, isotropic and linear elastic.

3.2 Constitutive properties

The properties of the materials used here-in are completely given in the project description

3.3 Assignment of material properties

The material« ABS » is affected to all the model.

4. Load case no 1a & 1b : 4.1 Loading hypothesis 4.1.1 Boundary conditions

Load case 1a :

How do you concretely model the load case no 1?

Loads:

Which load do you apply? How do you model it? Which value? Which direction?

Displacement boundary conditions :

Which boundary conditions do you apply? ( type ? constrained degrees of freedom? Coordinate system? On which region) ?

Insert one picture to illustrate the boundary conditions .

Load case 1b :

With respect to load case 1b, what do you modify?



Loads:

Which load do you apply? How do you model it? Which value? Which direction?

Displacement boundary conditions :

Which boundary conditions do you apply? ( type ? constrained degrees of freedom? Coordinate system? On which region) ?

Insert one picture to illustrate the boundary conditions .

4.1.2 Symmetry conditions

Do you use symmetries and if yes which ones? If yes, specify the boundary conditions used to represent the symmetry conditions.

4.1.3 Rigid body motions

Are there any free rigid body motions? if yes, what do you do to treat them.

4.2. Load case no 1a&b : Discretization hypothesesONLY PERFORM A CONVERGENCE ANALYSIS ON THE LOAD CASE 1A. USE AT MOST 3 MESHES (INITIAL, RAFFINEMENT 1 + 2). ONLY PRESENT THE « INITIAL »

AND « FINAL » MESHES.

4.2.1 Initial meshChoice of the finite element typeWhich meshing technique do you choose and which type of element is used. (class,order, integration) Justify your choice briefly?

5.2 Meshing technique and mesh sizeWhich meshing technique do you use What is the characteristic finite element size (globally and locally) How many nodes?

Insert one picture of the initial mesh

4.2.2 Final refined meshChoice of the finite element type



Which meshing technique do you choose and which type of element is used. (class,order, integration)

Meshing technique and mesh sizeWhich meshing technique do you use What is the characteristic finite element size (globally and locally) How many nodes?

Insert one picture of the initial mesh

4.3. Load case no 1a&b : Problem type and solution technique4.3.1 Type de problème résolu et options de résolution

The analysis of load cases 1a&b requires the computation of the linear statics solution described by the system of equations K u = f . The system will be assembled based on the Finite Element method and solved numerically to obtain the displacement field u, the reaction / external loading vector f , the strain field and stress field .

4.3.2 Computed fieldsStatics

The computed results in a static analysis are: the displacement field U, the tensor fields of stress and strain as well as their invariants

4.4. Mesh convergence study4.4.1 Criteria

Which result do you compare in the convergence study (quantity, component and localisation) and why?

4.4.2 Convergence results

Representative values

In the following table, we present the comparison values corresponding to the initial and refined (1 maybe 2) meshes.:

Quantity to compare Initial mesh Refined mesh 1 Refined mesh 2

(if necessary)

Nb of nodes

quantity no1

quantity no2

quantity no3



4.4.3 Error estimate and discussion on the convergence of the model

Compute the relative errors. Is it acceptable?

Which mesh will you use then?

Comment on the uncertainties of your results

Note : even though it may ne necessary, don’t use more than 3 different meshes.The the model does not converge, comment and estimate a safety margin on the calculated results and gon on.

4.5. Load case no 1a : Results4.5.1 Equivalent von Mises stress field

Insert a colormap of the global stress distribution

Where is the maxima ? what is the max value. ?

4.5.2 Displacement Field, vertical component Y

Insert a picture (colormap) of the displacement field magnitude

What is the displacement in Y at pt A?

4.5.3 Strain field (max principal et min principal)

Insert a picture (colormap) of the strain field , max or min principal component

4.6. Load case no 1b : Results4.6.1 Equivalent von Mises stress field

Insert a colormap of the global stress distribution

Where is the maxima ? what is the max value. ?

4.6.2 Displacement Field, vertical component Y

Insert a picture (colormap) of the displacement field magnitude

What is the displacement in Y at pt A?



4.6.3 Strain field (max principal et min principal)

Insert a picture (colormap) of the strain field , max or min principal component

5. Load case no 2 : modal analysis5.1 Load case no 2 : Loading hypotheses5.1.1 Boundary conditions

How do you model the load case no 2 ?

Which type of boundary condition, constrained degree of freedom, in which coordinate system and on which region?

5.1.2 Symmetry conditions

Do you use symmetries? if yes how do you model them?

5.1.3 Rigid body motion

Are there any free regid body motion? If yes how do you treat that case ?

5.2. Load case no 2 : Problem type & solution5.2.1 Type of problem solved and solver options

This load case requires the solution of the eigen problem (K - 2 M) u = 0 to evaluate the eigenmodes u and eigenfrequencies of the system. The eigenvalues problem is assemblaed using the Finite Element Method and solved using the iterative Lanczos algorithm.

5.2.2 Computed resultsAnalyse modale

The output results in modal analysis are: the displacement mode shapes (normalized to 1) and the corresponding eigen frequencies: f=/ 2 .

5.3. Load case no 2 : Results5.3.1 Eigen modes and frequencies

Insert pictures (colormap) of the first three “elastic” vibration modes What are the corresponding eigen frequencies ?



Mode 1 :

Mode 2 :

Mode 3 :

6. Evaluation of results and analysis.

6.1 Load case no 1 a & b : Analysis et discussionQ : evaluate the criteria i to iii for the static load cases 1a&b with the default ABS material. Mention the obtained values and comment.

Criterion (i) : Von Mises stress

Criterion (ii) : Max / min principal strain (in absolute value)

Criterion (iii) : maximal displacement along Y (in absolute value, case 1b only)

Synthesis of load case 1a et 1b : Q : Considering both load case together , can you say that the current design pass all the criteria? Which criterion is the most critical? Comment on the error margin of your results.

6.2 Load case no 2 : Analysis and discussionQ : identify the first symmetric, bending dominated eigen mode. What is the corresponding frequency? Insert a picture.

Q : Evaluate the dynamic criterion :is it satisfied? Comment on the error margin.

6.3 Material choiceQ : based on your results, which material do you recommend at least (*)?

(*) i.e the material that satisfy all criteria but with the smalled margin (for cost reasons).

Use the linearity property of the system to answer



7. Synthesis & conclusionQ : Answer to the main question of the study: does the current design pass all criteria. If not which one are problematic?

Q : is the design and material choice of the propeller appropriate? If not what can be done to improve the situation

Q : Propose potential improvements of the geometry of the part

Name : XXXX

No sciper : XXXX

Date : XXXX

Email : XXXX


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