Basic Theory of Molding Shrinkage Ratio

Molding shrinkage ratio is one of the most important factors in the design of molds for plastic injection molding.

The molding shrinkage ratio α can be expressed by the following equation.

α=（L₀-L）/L₀, where,
α：Molding shrinkage ratio (no units) L₀：Mold dimensions (mm) L：Product dimensions（mm）

However, in actuality, since the volume shrinks when the molten plastic cools, if the concept of volume shrinkage ratio is used, it can be expressed by the following equation.

αv=（V₀-V₁）/V₀, where,
αv：Volume shrinkage ratio (no units)
V₀：Volume of the mold cavity（mm³）
V₁：Volume of the molded product（mm³）

Here, if the volumes V₀ and V₁ are considered as three dimensional objects, it is possible to express them using the following equations.

L₀=3√V0 L₁=3√V1

Therefore,

αv=（V₀-V₁）/V₀
=1-（V₁/V₀）1/3 =1-（v₁/v₀）1/3 , where,
v₁：Specific volume at room temperature （mm³/g） v₀：Specific volume under molding conditions （mm³/g）

In addition, it is known that the state equation of the molten plastic can be expressed as follows.

（P+πi）（v-ω）=R'T, where,
v：Specific volume of the molten plastic（mm³/g）
πi：Internal pressure (atm)
ω：Specific volume at absolute zero degrees（mm³/g）
R'：R/M（Corrected gas constant atm mm³/g・mol）
M：Molecular weight in units of molecular activity

If αv =1-(v₁/v₀)1/3 is substituted in the above equation, we get:

α=1-3√y
=（1-y）/3+（1-y）2/9

y=v₀（P+πi）/R'T+ω（P+πi）

From this, it is also clear theoretically that the Pressure P and the temperature T of the molten plastic have a large influence on the molding shrinkage ratio α.