In the present competitive world, products should be designed to be reliable in every aspect, taking into consideration the reliability of the component to function under the different applied loads without any failure. After the design of the component is completed we need to know whether the designed component is able to fulfil the required conditions without any failure. So design is the very important part where manufacturer can analyse the behaviour of the component. Therefore use of Finite Element Analysis (FEA) is now widespread in engineering design. While it is increasingly the norm to use FEA, many initial design calculations are still carried out using approximate stress-strain (e.g. strength of materials) techniques.
This project addresses FEA approaches in the Engineering Design field. Mechanical elements such as shaft, structure/frames, brackets and seat belt tongue is analysed using FEA and approximate stress analysis approaches. The analysis includes variation in sizes in each machine element and also,
Collection of equations and calculation of approximate stress-strain analysis for mechanical elements.
FEA results for mechanical elements.
Comparative analysis of results from approximate stress-strain analysis and FEA.
Recommendations /guidelines selecting analysis approach for mechanical elements design.
Chapter-2
Introduction to each mechanical element considered for analysis
Frame-truss
A frame or space structure is a truss-like, lightweight rigid structure constructed from interlocking struts in a geometric pattern. Frames usually utilize a multidirectional span, and are often used to accomplish long spans with few supports. They derive their strength from the inherent rigidity of the triangular frame; flexing loads (bending moments) are transmitted as tension and compression loads along the length of each strut.
Most often their geometry is based on platonic solids. The simplest form is a horizontal slab of interlocking square pyramids built from aluminium or tubular steel struts. In many ways this looks like the horizontal jib of a tower crane repeated many times to make it wider. A stronger purer form is composed of interlocking tetrahedral pyramids in which all the struts have unit length. More technically this is referred to as an isotropic vector matrix or in a single unit width an octet truss. More complex variations change the lengths of the struts to curve the overall structure or may incorporate other geometrical shapes.
Figure-frame-truss
Seat belt tongue
Seat belt plays a vital role in automobiles especially in cars. Seat belts prevent the car driver from colliding with the steering other co-travellers hitting from front board, at the time accident. Seat belt possesses a self locking system, which works principle of whip lash action. When a force or load is applied suddenly the seat belt gets locked.
Figure -seat belts with locking system
Therefore the locks are very important in preventing the accidents. Failure of these locks causes life loss. This is of press fit type. As shown in the above figures.
Shaft
Shaft is a mechanical component for transmitting torque and rotation, usually used to connect other components of a drive train that cannot be connected directly because of distance or the need to allow for relative movement between them. Drive shafts are carriers of torque: they are subject to torsion and shear stress, equivalent to the difference between the input torque and the load. They must therefore be strong enough to bear the stress, whilst avoiding too much additional weight as that would in turn increase their inertia.
Figure-shafts
Shafts based upon nature of work called with different names as axle, drive shaft, ventilation shafts, etc
Bracket
A bracket is a mechanical component made of metal or metal alloys that overhangs a wall to support or carry weight. It may also support a statue, the spring of an arch, a beam, or a shelf. Brackets are often in the form of scrolls, and can be carved, cast, or moulded.
Figure-bracket
Brackets also act as an element in the systems used to mount modern facade cladding systems onto the outside of modern buildings as well as interior
Chapter-3
Problem definition of each mechanical component
Frame-truss
Frame figure with dimensions (inches)
Loads= vertical =25000lb.
=horizontal =20000lb
Thickness of the cross section=(1x1)in2, (2x2)in2, (3x3)in2
Material considered= steel= E=29.5 e 6 psi
=0.3
Frame is fixed and provided loads as shown in the figure, vertical and horizontal. Design and analysis is done by considering these loads and varying the thickness.
Seat belt tongue
Seat belt tongue figure with dimensions (mm)
Load= 1000N.
Thickness=2.5mm and 5mm
Material considered= Aluminium alloy, E=71.1e3 N/mm2,
=0.34
Due to whip lash moment, sudden load is applied on the seat belt tongue. Design and analysis is done considering this load and varying the thickness.
Shaft
Shaft figure with dimensions (mm)
Loads= axial=2000N.
Radius of the shaft=25mm, 35mm
Material considered= steel, E=2e5N/mm2
=0.3
Shaft is fixed at one end and is made to support load, axial. Design and analysis is done by considering this load and varying the shaft radius.
Bracket
Bracket figure with dimensions (mm)
Loads= vertical =2500N.
=horizontal =4330N
Thickness of the cross section=(35x35)mm2, (35x70)mm2
Material considered= steel, E=2.1e5MPa
=0.3
Bracket is fixed at one end and is made to support load, vertical and inclined (components are resolved and considered as horizontal and vertical loads). Design and analysis is done by considering these loads and varying the thickness.
Chapter-4
Design and analysis of each mechanical component
Frame-truss
Mechanical properties-E=29.5 e 6 psi, v=0.3
Area of cross section considered 1X1 sq.in , 2X2 sq.in and 3x3 sq.in
Element Number ----
Displacements ------ Q
Units considered-load =lb
Distance=inches
Design & Analysis Solution
Nodal coordinates
NODE
X
Y
1
0
0
2
40
0
3
40
30
4
0
30
Element connectivity table
ELEMENT
1
2
1
1
2
2
3
2
3
1
3
4
4
3
Directional cosines-,
Where, =effective length
x,y are coordinates
ELEMENT
le
l
m
1
40
1
0
2
30
0
-1
3
50
0.8
0.6
4
40
1
0
Stiffness matrix-k
Here we calculate the k for each element and assemble for entire problem based on element connectivity.
Calculating the k for area of cross section----1x1
E----29.5e6
For element-1
or
Here the top numerical, 1234-dof indicate the degrees of freedom
For element-2
Or
For Element -3
Or
For element-4
Or
Assembling k matrix
Or
As, Q1=Q2=Q4=Q7=Q8=0, can be seen from the fig.
Therefore only Q3, Q5, Q6 possess force or displacement.
Reducing the above assembled matrix
We get,
Solving the above matrix, we get
Stresses
Calculating the stress in elements 1 and 2
=20000 psi
=-21880 psi
Strains
=20000/29.5e6
=0.00676
=-21880/29.5e6
=-0.000268
Element considered for analysis in ansys
Beam2D- elastic 3
Figure-Beam3 geometry
BEAM3 is a uniaxial element with tension, compression, and bending capabilities. The element has three degrees of freedom at each node: translations in the nodal x and y directions and rotation about the nodal z-axis.
Figure -BEAM3 Geometry shows the geometry, node locations, and the coordinate system for this element. The element is defined by two nodes, the cross-sectional area, the area moment of inertia, the height, and the material properties. The initial strain in the element (ISTRN) is given by Δ/L, where Δ is the difference between the element length, L (as defined by the I and J node locations), and the zero strain length. The initial strain is also used in calculating the stress stiffness matrix, if any, for the first cumulative iteration.
BEAM3 Stress Output
Figure-BEAM3 Stress Output
For 1x1 cross section
Defined problem model in ansys with two views-oblique and front
Boundary conditions
Boundary conditions and load application on the model-oblique and front view
Deformed and Displacements figures for 1x1cs prob
Q5,Q3,Q6 values and at their respective deformed locations
Stress and strain diagrams for 1x1 cs problem
For 2x2 cs problem
Deformed shape and displacement value for 2x2 cs problem
Stress and strain diagrams for 2x2 cs problem
For 3x3 cs problem
Deformed, stress and strain figures for 3x3 cs problem
Comparative table among the values for different cross sections of frame-truss
1x1
2x2
3x3
Q3
0.027099
0.00676
0.002993
Q5
0.005658
0.001421
0.000636
Q6
-0.02224
-0.00555
-0.002463
σ1
19985
4985
2208
σ2
-21867
-5460
-2422
ϵ1
0.000677
0.000169
0.000074
ϵ2
-0.00074
-0.00019
-0.0000821
Results
Maximum Stress in all cases is below the yield stress of the steel, so the design of frame truss is safe.
As the area cross section of the frame truss increases, the stress value decreases hence factor of safety increases.
The deformation of the frame truss decreasing as the cross section of the frame truss is increasing. Hence the frame trusses possess good stiffness.
Seat belt tongue
Mechanical properties of aluminium alloy, E=71.1e3 N/mm2,=0.34
Thickness=2.5mm and 5mm.
Design & Analysis Solution
Seat belt tongue is considered to be in plane stress condition with thickness option. One end of the seat belt tongue is fixed as boundary condition (shown in ansys figure).
Fem related equations to calculate the stress and strain
Plane stress condition
-----D
Jacobian matrix,J=
B=displacement matrix,
KQ=F
σ=DBq
ϵ=Bq
Element considered for analysis in ansys
Solid-quad 4node 42 (plane 42)
Figure-PLANE42 Geometry
PLANE42 is used for 2-D modeling of solid structures. The element can be used either as a plane element (plane stress or plane strain) or as an axisymmetric element. The element is defined by four nodes having two degrees of freedom at each node: translations in the nodal x and y directions. The element has plasticity, creep, swelling, stress stiffening, large deflection, and large strain capabilities.
Seat belt tongue model in ansys
Seat belt tongue model in ansys-meshed
Seat belt tongue model in ansys-boundary conditions and load application and reaction forces (shown in pink colour)
For 2.5mm thickness
Stress, =1000/ (50x2.5)=8 N/mm2
Strain, =1.11e-4
Seat belt tongue in ansys-stress results
Seat belt tongue in ansys-strain results
For 5mm thickness
Stress,=1000/(5x50)=4 N/mm2
Strain, =4/71.7e3=5.57e-5
Seat belt tongue in ansys-stress results
Seat belt tongue in ansys-strain results
Comparison
Thickness
stress N/mm2
strain
2.5
8
1.11E-04
5
4
5.57E-05
Results
Maximum Stress in both cases is below the yield stress of the aluminium alloys, so the design of the seat belt tongue is safe.
Maximum stress is found in the vicinity of sharp corners, so sharp corners can be avoided to reduce the stress concentration in those particular areas to avoid failure.
As the thickness of the seat belt tongue increases, the stress value decreases hence factor of safety increases.
The deformation of the seat belt tongue is decreasing as the thickness is increasing. Hence the seat belt tongue possess good stiffness.
Shaft
A circular shaft given axial load of 2000N, varying its radius,25mm, 35mm. its mechanical properties, E=2e5 N/mm2,=0.3
Design & Analysis Solution
The circular shaft is considered to be a line segment to carry on the analysis on the shaft. Load is applied axially.
Fem related equations to calculate the stress and strain
[k][q]=[F]
ϵ=σ/E
Element considered for analysis in ansys
Beam -3D-2node 188
Figure-BEAM188 Geometry
BEAM188 is suitable for analyzing slender to moderately stubby/thick beam structures. This element is based on Timoshenko beam theory. Shear deformation effects are included.
BEAM188 is a linear (2-node) or a quadratic beam element in 3-D. BEAM188 has six or seven degrees of freedom at each node, with the number of degrees of freedom depending on the value of KEYOPT(1). When KEYOPT(1) = 0 (the default), six degrees of freedom occur at each node. These include translations in the x, y, and z directions and rotations about the x, y, and z directions. When KEYOPT(1) = 1, a seventh degree of freedom (warping magnitude) is also considered. This element is well-suited for linear, large rotation, and/or large strain nonlinear applications.
shaft line model in ansys
shaft model in ansys
shaft model in ansys-boundary conditions and load application
for shaft radius=25mm
stress,N/mm2
strain, =5x10-6
shaft model in ansys-stress results
shaft model in ansys-strain results
for shaft radius=35mm
stress, N/mm2
strain,=2.595 x10-6
Shaft model in ansys-stress results
shaft model in ansys-strain results
Comparison
radius of shaft
stress N/mm2
strain
25
1.018
5x10-6
35
0.519
2.595x10-6
Results
Maximum Stress in both cases is below the yield stress of steel, so the design of the shaft is safe.
Since the load is applied axially the stress distribution is same through out the line segment.
As the radius of the shaft increases, the stress value decreases hence factor of safety increases.
The deformation of the shaft is decreasing with the increase in radius of the shaft. Hence the shaft possess good stiffness
Bracket
A bracket fixed to the wall, supports the vertical and horizontal load.
Material properties are ,
E=2.1e5MPa
=0.3
Area of cross section considered for the bracket
35 x 70 sq.mm
35 x 35 sq.mm
Design & Analysis Solution
The bracket is assumed to be fixed to the wall to support the vertical and inclined loads. Inclined loads are resolved in to components and assigned as vertical and horizontal loads. The bracket is represented in the form of line segments in ansys to carry on analysis.
Fem related equations to calculate the stress and strain
[k][q]=[F]
ϵ=σ/E
Element considered for analysis in ansys
Beam2D- elastic 3
Figure-Beam3 geometry
BEAM3 is a uniaxial element with tension, compression, and bending capabilities. The element has three degrees of freedom at each node: translations in the nodal x and y directions and rotation about the nodal z-axis.
Figure -BEAM3 Geometry shows the geometry, node locations, and the coordinate system for this element. The element is defined by two nodes, the cross-sectional area, the area moment of inertia, the height, and the material properties. The initial strain in the element (ISTRN) is given by Δ/L, where Δ is the difference between the element length, L (as defined by the I and J node locations), and the zero strain length. The initial strain is also used in calculating the stress stiffness matrix, if any, for the first cumulative iteration.
BEAM3 Stress Output
Figure-BEAM3 Stress Output
Bracket- line model in ansys
Bracket model in ansys
Bracket element model in ansys
Bracket element model in ansys- boundary conditions and load application
For cs=35x70
Stress, =1.7673 N/mm2
Strain, =8.415x10-6
Bracket element model in ansys- stress results
Bracket element model in ansys- strain results
For cs=35x35
Stress, =3.535 N/mm2
Strain, =1.683x10-5
Bracket element model in ansys- stress results
Bracket element model in ansys- strain results
Comparison
area of cross section
stress N/mm2
strain
35x35
3.535
1.683x10-5
35x70
1.7673
8.415x10-6
Results
Maximum Stress in all cases is below the yield stress of the steel, so the design of the bracket is safe.
As the area cross section of the bracket increases, the stress value decreases hence factor of safety increases.
The deformation of the bracket is decreasing as the area of cross section is increasing. Hence the bracket possess good stiffness.
Chapter-5
Conclusions
In all the cases the maximum stresses are under their respective yield strengths. So, their designs are safe under their respective applied loading conditions.
The deformation of all the components are decreasing as the area of their respective cross section or thickness is increasing. Hence the components possess good stiffness.
The factor of safety is acceptably high considering the deformation to the loads in all the cases.
Recommendation
The stresses are very below to the yield strength of their respective materials. Material optimization i.e. decreasing the dimensions can be done to the same working loads i.e. applied loads.
Sharp corners induce high stresses which leads failure due to high stress concentration, which is a major factor for the fracture of the components.
Chapter-6
General procedure carried to solve the problems in ansys.
The following procedure is followed to solve the problem in ansys.
Pre-processor>element type-required element is selected
Pre-processor>real constants-areas of cross section, moment of inertia is selected.
Pre-processor>material properties-material properties are selected.
Pre-processor>modelling-the modelling of the required geometry is created.
Pre-processor>meshing-full model is made into finite elements using the meshing.
Solution>define loads-boundary conditions and load are applied.
Solution>solve-the defined problem is solved.
General post processor>plot results-to read and plot the results.
