0002// Functional Requirements in GD&T

GD&T is a mathematical language for designer communicate with his/her audience regarding engineering tolerance. It tell the machinist or fabricator what degree of accuracy, consistency or precision his/her is needed on each feature of part.

So, what is the factor designer will consider when apply GD&T requirements?

Ans: Functional Requirement

Functional requirement define results of a system (or sub-system). For example, functional requirement of bearing is support axial/radial loads.

In mathematics language, you can express functional requirement as function with a set of boundary conditions and variables.

How to translate function with a set of boundary conditions to GD&T specification?

Below show a simple example about translate function to feature of size specification (note: feature of size is not a geometric charateristic)

Your customer ask you to design a spring with wire diameter, d and outer diameter, D

Besides that, this customer have the requirment shown as below:

=> stiffness k=100N/mm+/-1%

=> outer diameter, D<20mm

So, what is the first step to design a spring based on requirement?

Ans: Identify function, boundary conditions and variables

In this case, function is the stiffness, k. This can express as mathematical function below

k=Gd^4/[8nD^3]

where:

G = modulus of rigidity

n = number of active coils, which number of coils subjected to flexture (Note: this number always less than total coils)

In this case, boundary condition is

D<20mm

and variables are

d and D

Second step, limit number of possible solution (design) which can meet functional requirment.

Choose material and tolerancing,

=>tolerance 19mm <D< 20mm

=>use material stainless steel 304, G = 70.3kN/mm^2

=>5 active coils

Finally, we can tolerancing our last dimension, wire diameter d.

Rearrange function to express d in term of G, n, D and k.

d= 4root({8knD^3}/G)

substitute the values with choose in material selection, we can get a range of value d with varies of value D and varies of value k (multivariable function)

By numerical optimization, we can expect maximum point (d_max) and minium point (d_min) in this multivariable function.

Therefore, I using Microsoft Excel run the optimization. Below shown the result I yield:

From the results, we know that, d_max is 4.630512 and d_min is 4.433535.

Therefore, we can set a tolerance zone within 4.433535<=d<=4.630512. In order to consider design for manufacturing, reasonable limit of size is 4.5 +/- 0.05.

All in all, we designed a spring with design specification (SI) below:

Feature of size for outer diameter : 19.5 +/- 0.5

Feature of size for wire diameter : 4.5 +/- 0.05

Material: Stainless Steel 304