Method To Determine Cost And Dimension

A Method To Determine Cost And Dimension of Product or Design Synthesis

 Design integration is defined as a process of selecting optimum configuration, shape, size and material for the product. There are three steps in design synthesis.

1.     In the first step, there is need to fix up the objective. These objectives can be the minimum cost, minimum material, maximum life, etc.

2.     The second step is a geometrical configuration of these aims.

3.     The third and final step is mathematical analysis for optimization of the result.

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We are going to learn design synthesis by an example of cylindrical can. For example, u need to fit a cylindrical can on the shelf. Now here there are two objectives which are as follow:

a)     The amount of material going to be used in the design of the can should be as minimum as possible.

b)     The radius of the cylindrical can should not be more than max possible radius of the shelf. Assume that max radius of the rack is Rmax.

Now,                                       r = radius of can

                                                h = height of can

                                                A = area of can

                                                V = volume of can

Let’s get started,

                        First area of the can       A = 2πr² + 2πrh   ------------ (1)

                        And volume                   V = πr²h               ------------- (2)

Now combine both equations

                        A = 2πr² + 2V/r

Now take differentiate of above equation on “r.”

            d A / d r = 4πr + [ - (2V ÷ r²)]

for the minimum amount of the material above equation will be equal to zero.

So, 2V/r² = 4πr   Þ   r = ( V ÷ 2π )^1/3

The amount of equipment. Now see above objectives, by applying the value of r₁ we have completed first one.

 Now in order to apply second objective or requirement,

            0 < r < R_max

                                                                 

Here there are two possible cases,

CASE: (1)

                        IF r₁ > R_max ,

In this case radius of can which is ‘r’ wil be equal to R_max

            So,       r = R_max

CASE: (2)

                        IF  r₁ < R_max

In this case radius of can ‘r’ will be equal to r₁

            So,        r  = r₁  ( as shown in figure )