1. Springs for vehicles: In vehicle suspension, it is desirable to minimize the cost as well as the mass of all components. Leaf spring suspensions for a vehicle are constrained to have a specific length l and stiffness S. In addition, due to the repeated loading, leaf spring should not fail due to fatigue loading. The geometry of the leaf spring is shown in Figure.
a. Identify the function, constraints, objective and free variables for the leaf spring design
b. Derive the material indices for minimizing cost and mass of material for the identified constraints
c. Explore the trade-off between cost and mass of the leaf spring using the plot of the two indices for minimizing cost and mass of the leaf spring. Restrict the material for plot to metallic and composite materials as they are commonly used for springs.
d. Formulate a penalty function that combines the cost and mass of the leaf spring using an exchange constant.
e. Use the penalty function to identify candidate materials for two different cases: exchange constant =0.1 (conventional vehicles minimum cost is important than mass) and exchange constant = 100 (Performance vehicles: minimizing mass is more important than cost)
2. A parallel plate clutch geometry is shown in Figure
a. State the two assumptions required in determining the frictional torque applied by parallel plate clutches for a given lining material
b. Explain the physical basis for validity of the two assumptions?
c. In the figure, inside diameter is equal to 50 mm and outside diameter is equal to 100 mm. Use one of the assumptions you stated in part (a) to determine the maximum frictional torque and actuation force required for one of following friction lining materials
|
Material
|
Friction Coefficient
|
Maximum temperature
|
Maximum allowable pressure
|
|
Leather
|
0.3
|
100 °C
|
200 kPa
|
|
Molded Asbestos
|
0.35
|
250 °C
|
700 kPa
|
|
Sintered metal
|
0.25
|
500 °C
|
1000 kPa
|
d. Why is the maximum temperature an important parameter in selection of the clutch or brake lining materials?
3. Evaluate the shape factor for stiffness limited design in bending of a square box section of outer edge length h= 100 mm and wall thickness t = 3 mm.
a. Is this shape more efficient than one made of the same material in the form of a tube of diameter 2r = 100 mm and the wall thickness = 3 .82mm (giving it the same mass per unit length as the square cross-section).
Treat both as thin-walled shapes. (See figure for the crosssections)
4. A sandwich structure made of steel sheets and Poly vinyl chloride (PVC) foam is commonly used for refrigerator walls.
a. What functions do the steel sheets and PVC foam perform in the sandwich structure.
b. Write down the thermal conductivity and bending stiffness for the sandwich structure
c. Is it possible to achieve the same functionality, if the sandwich structure is replaced by a composite composed of steel fibers and PVC foam matrix?
d. Write down the thermal conductivity and bending stiffness for the composite and support your argument for part (c)