Question 7 of 7: Effect of Doubling Injection-Molded Wall Thickness on Cycle Time, Cost, and Warpage

Question 7: Effect of Doubling Injection-Molded Wall Thickness on Cycle Time, Cost, and Warpage (20 marks: 4 each)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. Wall thickness increases from $h_1=0.5\text{ mm}$ to $h_2=1\text{ mm}$ (a thickness ratio of exactly 2), with every other part dimension and every processing condition (melt temperature, mold temperature, material) held fixed.

Find. How injection time, cooling time, material cost, production rate, and warpage each change, quantified where the underlying relationship allows it.

Approach. With every other dimension fixed, doubling wall thickness doubles the part's VOLUME (and hence its mass), which drives (i) and (iii) roughly linearly; cooling time is governed by transient heat conduction through the wall thickness, which scales with the SQUARE of thickness (Groover's cooling-time relation $t_{cool}=\dfrac{h^2}{\pi^2\alpha}\ln\!\left[\dfrac{4}{\pi}\dfrac{T_{melt}-T_{mold}}{T_{freeze}-T_{mold}}\right]$), driving (ii); (iv) and (v) then follow from how (i)-(iii) combine.

1. (i) Injection (fill) time. Doubling the wall thickness (other dimensions fixed) doubles the cavity volume that must be filled. At a fixed volumetric injection (fill) rate, the fill time is directly proportional to the volume to be injected, so injection time approximately DOUBLES: $t_{inj,2}/t_{inj,1}\approx h_2/h_1=2$.
2. (ii) Cooling time. Cooling time is set by how long heat takes to conduct out through the part's wall thickness to the (cold) mold surface, and by Groover's cooling-time relation it scales with $h^2$, not $h$. Doubling the thickness therefore roughly QUADRUPLES the cooling time: $$\dfrac{t_{cool,2}}{t_{cool,1}}=\left(\dfrac{h_2}{h_1}\right)^{2}=2^2=\boxed{4}$$ This $h^2$ dependence is why cooling time, not injection time, is normally the dominant and most thickness-sensitive part of the molding cycle.
3. (iii) Material cost. Part mass (and therefore material cost, at a fixed material unit price) scales directly with volume, exactly as in step 1: doubling thickness (other dimensions fixed) roughly DOUBLES the material used per part, so material cost per part approximately doubles: $\text{cost}_2/\text{cost}_1\approx 2$.
4. (iv) Production rate. Production rate is inversely proportional to total cycle time, $T_{cycle}=t_{inj}+t_{cool}+t_{reset}$, where $t_{reset}$ (mold open/close and part ejection) is essentially independent of wall thickness. Because $t_{cool}$ (quadrupling) grows far faster than $t_{inj}$ (only doubling) as thickness increases, cooling time's SHARE of the cycle grows even larger, and the cycle-time increase approaches the $4\times$ cooling-time factor as $t_{cool}$ comes to dominate. Illustrating with representative, non-exam-given cycle-time shares (flagged in the check callout below) — $t_{inj,1}=2\text{ s}$, $t_{cool,1}=6\text{ s}$, $t_{reset}=2\text{ s}$ (constant) — gives $T_{cycle,1}=10\text{ s}$ and $T_{cycle,2}=4+24+2=30\text{ s}$: $$\dfrac{\text{rate}_2}{\text{rate}_1}=\dfrac{T_{cycle,1}}{T_{cycle,2}}=\dfrac{10}{30}=\boxed{\tfrac{1}{3}}$$ so production rate falls to roughly a third of its original value in this illustration — a substantial DECREASE, driven mainly by the quadrupled cooling time.
5. (v) Warpage. Warpage (and related sink marks) is driven by DIFFERENTIAL shrinkage and residual stress across the part's cross-section as it cools and solidifies unevenly — the outer skin freezes first against the mold wall while the core stays hot and molten longer. A thicker wall widens the temperature gradient between skin and core (the core takes proportionally much longer to reach the mold-wall temperature, per the same $h^2$ relation as (ii)), which increases the difference in shrinkage between the fast-cooling skin and the slow-cooling core. Warpage therefore tends to INCREASE with wall thickness — which is exactly why uniform, thin wall sections are a standard design-for-manufacture guideline for injection-molded parts.