Cost Penalty Analysis

Cost penalty measures the incurred cost of saving 1 kg of mass. Cost penalty analysis is a critical procedure that helps the automotive manufactures to make decisions on materials substitution. The decision maker usually sets up an upper bound of cost penalty, below which the materials substitution is cost-effective and vice versa.

Consider the following scenario. A truck manufacturer intends on light weighting the front panel and engine's cradle, provided the extra expenses are below $5/kg. The front panel is currently made of a forged Aluminum plate while the engine's cradle is made of inter-connected Aluminum bars.

Suppose both components are loaded in bending and the deflection must be less than δ. Please help this manufacturer to assess the feasibility of replacing Aluminum by Magnesium for these two components. The relevant materials properties are listed in the table below.

Hint: The cost penalty, α_i, for a specific pair of materials, X and Y, can be expressed by

where ‘c' is cost; ‘m' is mass and ‘M' is the material index.

Suggested steps:

(1) Derive the Material index for stiffness-limited design and fill the formulas into the table attached Please type equations using Microsoft word equation feature. Present the derivation steps in the next page.

(2) Calculate the Material index for Al and Mg, and fill the values into the table attached

(3) Calculate the resultant cost penalty values and fill them into the table attached

Attachment:- Cost Penalty Analysis.rar