A TECHNICAL ARTICLE 2005 VOLUME 24, #4

The Ubiquitous1 Draw Ratio

Probably the first thing a

novice hears in thermo-

forming after he/she learns to

spell thermoforming, is the

phrase, Draw Ratio. So, this

lesson focuses on the concept of

draw ratio.

Is There More Than One

Definition?

Unfortunately, yes. There are

at least three definitions. Lets

define the common ones.

Areal Draw Ratio, often given

the symbol RA, is the ratio of the

area of the part being formed

to the area of the sheet needed

to make the part. Although I

promised not to use equations

in our TF 101 lessons, some

simple ones here wont hurt all

that much:

RA = AreaPart/AreaSheet

A simple example, please?

Consider a cylinder one unit in

diameter by one unit high. The

area of the cylinder is (.+./4)

= 5..4. The area of the sheet

used to form the cylinder is

./4. Therefore the areal draw

ratio, RA, is 5. As an interesting

aside, the reciprocal of the

areal draw ratio is the average

reduced thickness of the formed

part, being 1/5 = 0.20. In other

words, the original sheet thickness

has been reduced by 80%,

on the average.

Linear Draw Ratio, often

given the symbol RL, is the ratio

of the length of a line scribed

on the part surface to the original

length of the line. Again, in

equation form:

RL = LinePart/LineSheet

For the same example, the length

of the line on the cylinder is

(1+1+1) = 3. The original length

of the line is 1. Therefore, the

linear draw ratio, RL, is 3. The

linear draw ratio is akin to

the way in which the plastic

is stretched in a tensile test

machine,

Height-to-Diameter Ratio,

often written as H:D, is the

height of the cylinder (1), to the

diameter of the cylinder (1). Or

H:D = 1. H:D is used primarily

for axisymmetric2 parts such as

cones or cylinders, such as drink

cups.

In summary, for the cylinder

described above, RA=5, RL = 3,

and H:D = 1. So you see, there

is no agreement between these

definitions.

Are Draw Ratios of

Use? Importance?

So, which one do we use?

Depends. First, we need to

determine whether draw ratio is

a useful concept.

Lets focus on areal draw

ratio to determine its utility.

As we have already learned,

the reciprocal of RA is the average

reduced thickness. But

where is this reduced thickness?

Somewhere down the side of

the formed part. In fact, there

is probably a line around the

periphery of the part where

the part thickness is exactly the

average reduced thickness. So,

what does this tell us about

the uniformity of the part wall

thickness? Or the degree of difficulty

in forming the part? Or

whether webs are formed somewhere

in the part? Or what the

plug needs to look like? Or
?

Really, nothing.

Having said that, areal draw

ratio is perhaps the easiest

concept to understand. Linear

draw ratio, as noted, is often

compared with extension limits

determined from tensile

testing equipment. And H:D is

often used in Europe to describe

formability of plastics for cup

applications.

At best, draw ratios represent

bragging rights rather than information

about the degree of

difficulty in forming the parts.

Many formers will tell you that

parts that have very small draw

ratios are much more difficult

to form reliably than parts with

large draw ratios. And parts

with many compartments are

far more difficult to form than

parts with single compartments,

even when the draw ratios of the

two types are identical.

[See? Those equations didnt

hurt at all, now, did they?] ¦

Keywords: Areal draw ratio,

linear draw ratio, H:D

THERMOFORMING

101

1 Ubiquitous: Being present everywhere

at once.

2 Axisymmetric: Having symmetry around

an axis.

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