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 adiameter of 8’’ and is subjected to the following loads:
a) preload of the locking nut = 2kN
b) rotation speed 0 to 15'000 RPM
c) lift P correspondingto accelerations of 4g max.
d) vibrations and transient loading
Analysis:
A finite element analysis of this part is requested with the following detailed goals:
- 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.
- Evaluate the modal response of the propeller(6 first eigenmodes)
- Evaluate the designcriteria for the base ABS material
- Optimizethe 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.
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 acceptablebut theprincipal strains (inabs 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 information
Perform a finite element modal analysis to extract the 6 first eigen modes and frequencies. Displacement hypothesisonS1:radial displacement =0 ; on S3: radial, circumferential and vertical displacement =0.
Dynamic evaluation criteria: the eigen frequency of the first symmetric bending modemust exceed 50Hz.
Materials
Material / Modulus [GPa] / . Poisson / Yield stress [MPa] / Strain at failure % / Massdensity. [kg/m3]ABS (injection)
(nominal case) / 2.8 / 0.35 / 70 / 5% / 1200
Nylon 66 reinforced / 1.7 / 0.35 / 140 / 40% / 1200
ReinforcedEpoxy / 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 . 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 Hypotheses35%; Convergence study 20%Extraction of the results : 20%; Analysis and conclusions20%.Load case no1a ~40%, 1b 25% and load caseno3 ~20%,.
Downloads: the CAD file and +the present report canvas can be found:
Finite Element Analysis Report
Analysis of a quadcopter drone propeller
Exam2014«Finite Element modelling and simulation»
name, email, no Sciper
1.Goal of the study
1.1Objectives and context
The context and objectives have been described in the specification of the study thus they are not repeated here.
1..2Type 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 hypotheses
2.1Presentation of the geometry
This project consists only in one part in IGS format. The geometry in presented in the project description.
2.2System of units
In which system of units are you working?
Length: unitXXX
Force: unitXXX
Mass: unitXXX
Stress / moduli: unitXXX
2.3Characteristic dimensions
The propeller has a characteristic dimension of 8” diameter.
2.4Symmetries 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:
2.5Modelling 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 behaviours
3.1Description of the materials
The propeller is produced by plastic injection molding of ABS thermoplastic polymer.
3.1.1Material behaviour model
The materials used in this study are all considered homogeneous, isotropic and linear elastic.
3.2Constitutive properties
The properties of the materials used here-in are completely given in the project description
3.3Assignment of material properties
The material«ABS» is affected to all the model.
4.Load case no 1a & 1b:
4.1 Loading hypothesis
4.1.1Boundary 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 .
4.1.2Symmetry conditions
Do you use symmetries and if yes which ones? If yes, specify the boundary conditions used to represent the symmetry conditions.
4.1.3Rigid 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 hypotheses
ONLY 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 mesh
Choice of the finite element type
Which meshing technique do you choose and which type of element is used. (class,order, integration) Justify your choice briefly?
5.2Meshing technique and mesh size
Which meshing technique do you useWhat is the characteristic finite element size (globally and locally) How many nodes?
Insert one picture of the initial mesh
4.2.2 Final refined mesh
Choice 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 size
Which meshing technique do you useWhat 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 technique
4.3.1Type 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 Ku = f. The system will be assembled based on the Finite Element method and solved numerically to obtain the displacement field u, thereaction / external loading vector f, the strain field and stress field .
4.3.2Computed fields
Statics
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 study
4.4.1Criteria
Which result do you compare in the convergence study (quantity, component and localisation) and why?
4.4.2Convergence 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 / Refinedmesh 1 / Refinedmesh 2(if necessary)
Nb of nodes
quantity no1
quantity no2
quantity no3
4.4.3Error 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: Results
4.5.1Equivalent 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: Results
4.6.1Equivalent 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 analysis
5.1Load case no 2: Loading hypotheses
5.1.1Boundary 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?
5.1.2Symmetry conditions
Do you use symmetries? if yes how do you model them?
5.1.3Rigid 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 & solution
5.2.1Type of problem solved and solver options
This load case requires the solution of the eigen problem (K - 2M) 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.
5.2.2Computed results
Analyse 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: Results
5.3.1Eigen 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 discussion
Q: 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.
6.2Load case no 2: Analysisand discussion
Q: 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.
6.3Material choice
Q: based on your results, which material do you recommend at least (*)?
(*) i.ethe material that satisfy all criteria but with the smalled margin (for cost reasons).
Use the linearity property of the system to answer
7.Synthesis & conclusion
Q: 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
J. Cugnoni, LMAF/EPFL, 2014p. 1 / 10