以均勻實驗設計法及克利金代理模型法探討塑膠射出成型傘齒輪翹曲變形之最佳化設計

The Optimization of Plastics Injection Process for Eliminating Distortion of Inclined Gear by Uniform Experimental Design of Kriging Method

本研究探討塑膠射出成型傘齒輪翹曲變形量之最佳化設計，而以傘齒輪三種型態：直齒傘齒輪、蝸線傘齒輪、零度傘齒輪分析射出成型後翹曲變形量。應用之研究方法為均勻實驗設計法、模流分析法、克利金代理模型法及遺傳演算法。以料溫、模溫、射出壓力、保壓壓力、保壓時間、冷卻水溫等控制因子為均勻設計分析製程參數，採用U18*（186）的均勻設計表，進而使用Moldflow軟體分析探討傘齒輪翹曲值，依據模流分析數據應用克利金建立模型，以反應曲面去探討每一控制因子對翹曲值的關係，再經由遺傳演算法搜索最佳化參數組合。模擬分析驗證的數據如下：由分析得到直齒傘齒輪翹曲值為0.2589mm，其最佳製程參數組合為料溫180℃、模溫91℃、射壓120MPa、保壓壓力87MPa、保壓時間3s、冷卻水溫25℃的環境下，翹曲值由0.2589mm縮小至最佳0.2563mm，翹曲值改善1.01%。蝸線傘齒輪所得到翹曲值為0.2990mm，其最佳製程參數為料溫180℃、模溫95℃、射壓122MPa、保壓壓力87MPa、保壓時間3s、冷卻水溫24℃的環境下，其翹曲值可由0.2990mm縮小至最佳0.2948mm，翹曲值改善1.40%。零度傘齒輪所得到之最佳參數組合為料溫180℃、模溫120℃、射壓136MPa、保壓壓力100MPa、保壓時間3s、冷卻水溫20℃的環境下，翹曲值由0.2909mm縮小至最佳0.252mm，翹曲值改善15.44%。傘齒輪在製造前，先用數值軟體Moldflow進行分析，再應用克利金反應曲面及遺傳演算法，即可得傘齒輪射出成型最佳化製程參數，經實驗驗證，證明該研究方法，確實是很有效率。 In this study, we demonstrate an optimization of the plastic injection process for eliminating structure distortion of shot away bevel gears and its related products by using Kriging optimization method. Three types of bevel gears such as straight tooth bevel gears, worm bevel gears, and zero degree bevel gears were tested, and process parameters such as injection temperature, mold temperature, injection pressure, packing pressure, mold holding time, and mold cooling temperature were used to generate the numericalsimulation results of bevel gears by Moldflow software. In addition, same process parameters used above were used to generate the U18*(186)tables based on uniform experimental method to generate the Kriging agent surfaces, and by applying interpolation and genetic algorithm to achieve the optimized set of process parameters in mold injection in order to minimize the distortion of bevel gears. The results showed that the optimized process parameters for the straight tooth bevel gear could be achieved with warpage of 0.2563 mm by applying with injection temperature at 180℃, molding temperature at 91℃, injection pressure at 120 MPa, packing pressure at 87 MPa, holding time for 3 sec, and cooling temperature at 25℃. Warpage of 0.2948 mm of the zero degree bevel gear could be achieved by applying parameters of temperature 180℃, mold temperature 95℃, pressure 122 MPa, packing pressure 87 MPa, holding time 3s, cooling time 24℃. Warpage of 0.2520 mm of the worm bevel gear could be achieved by applying parameters of injection temperature at 180℃, mold temperature at 120℃, pressure at 136 MPa, packing pressure at 100 MPa, holding time for 3 sec, cooling time at 20℃. The improvement of the distortion is 1.01% for straight tooth bevel gear, 1.40% for zero degree bevel, and 15.44% for worm bevel gear.In conclusion, we demonstrate that it is an effective approach to achieve the optimized process parameters of bevel gears in plastic injection manufacture by applying Kriging Surrogate modeling and genetic algorithm with numerical simulation software Moldflow before production.

In this study, we demonstrate an optimization of the plastic injection process for eliminating structure distortion of shot away bevel gears and its related products by using Kriging optimization method. Three types of bevel gears such as straight tooth bevel gears, worm bevel gears, and zero degree bevel gears were tested, and process parameters such as injection temperature, mold temperature, injection pressure, packing pressure, mold holding time, and mold cooling temperature were used to generate the numericalsimulation results of bevel gears by Moldflow software. In addition, same process parameters used above were used to generate the U18*(186)tables based on uniform experimental method to generate the Kriging agent surfaces, and by applying interpolation and genetic algorithm to achieve the optimized set of process parameters in mold injection in order to minimize the distortion of bevel gears. The results showed that the optimized process parameters for the straight tooth bevel gear could be achieved with warpage of 0.2563 mm by applying with injection temperature at 180℃, molding temperature at 91℃, injection pressure at 120 MPa, packing pressure at 87 MPa, holding time for 3 sec, and cooling temperature at 25℃. Warpage of 0.2948 mm of the zero degree bevel gear could be achieved by applying parameters of temperature 180℃, mold temperature 95℃, pressure 122 MPa, packing pressure 87 MPa, holding time 3s, cooling time 24℃. Warpage of 0.2520 mm of the worm bevel gear could be achieved by applying parameters of injection temperature at 180℃, mold temperature at 120℃, pressure at 136 MPa, packing pressure at 100 MPa, holding time for 3 sec, cooling time at 20℃. The improvement of the distortion is 1.01% for straight tooth bevel gear, 1.40% for zero degree bevel, and 15.44% for worm bevel gear.In conclusion, we demonstrate that it is an effective approach to achieve the optimized process parameters of bevel gears in plastic injection manufacture by applying Kriging Surrogate modeling and genetic algorithm with numerical simulation software Moldflow before production.