A Semi-Analytical Method for Designing a Runner System of a Multi-Cavity Mold for Injection Molding

. 2022 Dec 12;14(24):5442. doi: 10.3390/polym14245442

η	viscosity
m	the flow consistency index
$\dot{γ}$	shear rate
s	power law exponent
(r, $θ$ , z)	the cylindrical coordinate
$υ_{θ}$	flow velocity in the $θ$ -direction
$v_{r}$	melt velocity in the r-direction
$v_{z}$	melt velocity in the z-direction
P	pressure
τ_rz	shear stress in the r-z plane
R	runner radius
Q	volume flow rate
ΔP	pressure drop
$T_{i}$ , $T_{i}^{'}$	the ith transverse runners at the right and the left sides, respectively
$L_{i}$ , $L_{i}^{'}$	the ith longitudinal runners, respectively
$J_{i}$ , $J_{i}^{'}$	the ith cavities at the right and the left sides, respectively
$g_{i}$ , $g_{i}^{'}$	the ith gate locations at the right and the left sides, respectively
$c_{i}$ , $c_{i}^{'}$	the ith ends of the cavity J_i and $J_{i}^{'}$ , respectively
k_i	the ith junction node connecting the transverse runner and the longitudinal runner
$v_{L_{i}}$	the filling velocity at the longitudinal runner $L_{i}$
$Δ P_{L_{i}}$	pressure drop at the longitudinal runner $L_{i}$
$k_{i} g_{i}$	distance from k_i to g_i
t ₀	initial filling time
$Q_{L_{i}}$	volume flow rate in the runner L_i
$\emptyset_{T_{n}}$	diameter of the transverse runner T_n