Introduction:
A vehicle jack is being select as a project to find
out what kind of materials is suitable. It should able to withstand 500kg of load
which is means it must has high yield strength or elastic limit. The price of
the material should be cheap as well.
The material which is going to be consider for the
vehicle jack:
·
Steel alloy: high yield strength, low
cost· Composites: high tensile strength, low density
· Other metal alloys: lower density
By checking from CES software the designer comes out
of a solution to distinguish using other metal alloys as it is low yield
strength or elastic limit and distinguish composites as well as the percentage
composition material price is higher. Consequently, the materials which is
going to compare is low carbon steel (AISI 1020), low alloy steel (AISI 4130
steel) and nodular graphite cast iron.
Theory
Generate
Performance Index Formula Material Weight (Mass)
Constraint:
Yield strength
Objective:
Mass
Constraint
equation, σ = F/A (1)
Objective
equation, m (cylinder) = Cross section area, A x Length, L x Density, ρ (2)
Substitute
this expression for A from equation (1) into equation (2), m = FL
ρ / σ (3)The performance index, M1 = σ /ρ
Material Cost
Constraint:
MassObjective: Minimum material cost
For
a component of mass, m kg, which costs £ C/kg, the material cost is m x C (4)
Substitute
this expression for m from equation (3) into equation (4), cost = FLρC/ σ
Hence
to minimise material cost the performance index to be maximised is
M2
= σ/ρC
A Materials Selection
Chart can be made where elastic limit is displayed in function of the volume
(figure1) and another displayed in function of the material cost per volume
(figure 2). Figure 1 is useful to get a clear view on the material density that
can be expected for certain material classes while figure 2 is useful to get a
clear view on the material costs that can be expected for certain material classes.
Figure 1 show a graph Elastic Limit versus Density. The straight
lines with slope = 1 (gradient) is constant. [The
performance index, M1 = σ /ρ; log M1 = log σ – log ρ.
Rearrange, log σ = log ρ + log M1 = (y = mx + c). So, m = 1]. It is clear that low alloy steel will be low weight with the
highest strength among all the materials selection.
Figure 2 show a graph
Elastic Limit versus Density x Price. It is clear that nodular graphite cast
iron will be expensive for this case. Carbon steel, AISI 1020 is beneficial
from the viewpoint of cost but have low strength properties. This graph also
shows that low alloy steel, AISI 4130 is more strength, low cost and very
advantageous materials.
Figure 3 show a graph
Elastic Limit/ Density which is represent performance index M1. The
best result regarding low weight (index M1) is achieved with low
alloy steel, AISI 4130 which is amongst other used in vehicle jack.
Figure 4 show a graph
Elastic Limit/ Density/ Price which is represent performance index M2.
With respect to material cost (index M2), low alloy steel, AISI 4130
give the best result and the selected carbon steel, AISI 1020 is situated
closer to the defined lower limit.
Conclusion:
When all performance
indices are taken into account, low alloy steel, AISI 4130 appear to be very
attractive material for vehicle jack. This low alloy steel has elastic limit of
483-533.8MPa. For this material M1 = 0.062-0.068 And M2 =
0.151-0.248 (table).
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