balanced runner layout in the mold。 The shear-induced runner imbalance usually presents in the geometrically balanced run- ner system。 However, despite the geometric balance, there is nearly always some variation between cavities nearer to the center of the mold vs。 cavities further away from the center。 Although runner-induced melt variations can affect even single-cavity molds, their effects are most commonly recog- nized when there are more than eight cavities in a mold [42, 43]。 Therefore, the pressure/temperature sensor was installed on the same side of the runner system so that the relationship between the cavity pressure and runner pressure could be investigated。

The pressure/temperature sensor was mounted in the cav- ity, and the pressure sensors were mounted in the runner, as shown in Fig。 3a。 The outside diameter of the optical lens was 16 mm, the effective spherical lens diameter was 14 mm, and the maximum thickness of the center was 1。492 mm。 For convenient measurement, the optical lens was designed as a plano-convex lens, and the spheric radius was 50 mm, as shown in Fig。 3b。 The pressure/temperature sensor was installed on the planar side of the lens mold cavity, and the form accuracy measurement using a profilometer at a direc- tion perpendicular to the inlet melt flow was performed on the convex side of the same sensor-cavity。

Fig。 3 Dimensions of the plano- convex lens

(a) Part layout in mold。 (b) Dimensions of the lens。

Table 2 Form accuracies and S/N ratio for L18(21 ×37)

Table 3 Analysis of variance for S/N ratio

−10。7143。2 Experimental equipment and material

In this study,  a 220S 250–60 precision injection    molding

4。1 Taguchi experiment

This study investigates the form accuracy of spherical lenses through the Taguchi experiment; this is a smaller-the-better (STB) quality characteristic because of the lower desired values。 The signal-to-noise (S/N) ratio for STB is defined as [43, 44]

machine produced by Arburg (Germany) was used for injec- tion molding experiments。 6157 and 6190 cavity    pressure

S=N ¼ −10log10ðdBÞ ð3Þ

sensors produced by Kistler (Switzerland) were used for mea- n

¼

suring cavity pressures。 The surface form accuracy of    the

lenses was measured using the Form Talysurf PGI 840 made by Taylor Hobson (Britain)。 The experimental material was of optical grade PMMA-80N (polymethyl methacrylate), manufactured by the Asahi Kasei (Japan)。 Five specimens were sampled at the same cavity of the four-cavity mold, and the average value was taken as the experimental data。

where yi is the experimental value, and n is the number of experiments。

The Taguchi parameter design uses an L18(21 ×37) orthog- onal array。 The eight control factors are melt temperature, injection pressure, filling-to-packing switchover position, cooling time, packing time, packing pressure,     mold

Fig。 4 Response graph of S/N ratio for the lens form accuracy。 a Sensor install position。 b Runner and cavity pressure profiles