旋轉(zhuǎn)式管端成型機結(jié)構(gòu)設(shè)計
旋轉(zhuǎn)式管端成型機結(jié)構(gòu)設(shè)計,旋轉(zhuǎn)式管端成型機結(jié)構(gòu)設(shè)計,旋轉(zhuǎn),式管端,成型,結(jié)構(gòu)設(shè)計
附錄1
蠟?zāi)＞_成型在澆注中的實驗性研究
摘要：澆注是經(jīng)常用于從犧牲模型中生產(chǎn)全功能的標準部件，這些模型（標準）可以用特殊的快速原形技術(shù)如立體圖或者三維尺寸印刷技術(shù)來制造。當要求復(fù)合的多樣功能的模型時，制造蠟?zāi)１徊捎糜谶^度時期的工具。這個研究工作的目的是為了決定判斷出準確細致和精確的蠟?zāi)Ｉa(chǎn)用于若干模型工具中。線性收縮常常在決定其精度上起著作用，蠟?zāi)踩雲(yún)?shù)常用于低壓噴入造型.蠟?zāi)３３Ｓ糜谏a(chǎn)聚氨脂和矽樹脂橡膠工具。從這兩種相似的工具中他將展示出模型的精確度.可知,蠟?zāi)９ぞ呱a(chǎn)的產(chǎn)品模型有較高的收縮比這些有聚氨脂工具生產(chǎn)的產(chǎn)品。自然模型尺寸收縮分別是矽樹脂為3.44±0.40%而聚氨脂為1.70±0.60%。另外受壓制的尺寸收縮分別為在矽樹脂工具的應(yīng)用中是2.20±0.20%，在聚氨脂工具中的應(yīng)用為1.40±0.20%。
關(guān)鍵字：澆注 蠟?zāi)?尺寸精度
1、 介紹
澆注模型能制造用快速模型技術(shù)能提供大多數(shù)成型輪廓，一些復(fù)雜的輪廓成型在選擇材料上有一些限制。然而當要求需要多功能的模型部件時，這中過程成為太昂貴和使用蠟?zāi)Ｗ鳛檫^度工具派上用場。
多步驟的模型過程是易于被錯誤地計算介紹通過每一個時期，Mor-wod .et al。[1] 分析在澆注上的自始至終的錯誤累積過程，可以清晰的指示出最大的變化是被介紹通過在蠟?zāi)５拇蟪叽绲淖兓小?
澆注是被認為是一種多精度的鑄造過程在一系列的成型設(shè)計尺寸中，但是，有食品儲藏室改進了在鑄造中的尺寸精度。通常采用的公差的是±0.5%[3]，但是更嚴格的公差可以被實現(xiàn)在特定的環(huán)境中，為了增加提高澆注成型的形狀和尺寸精度，澆注過程需要更好更明白和更顯著的提升改進。
模型典型的制造方式是將流動的蠟液澆入進一個印模里，使蠟液在印模里凝固，在更深的冷卻之后，將形成的蠟?zāi)挠∧Ｖ腥〕觥?蠟?zāi)＞鹊挠绊懸蛩赜校合災(zāi)２牧?，澆注參?shù)（包括壓力，溫度，支持時間，冷卻率）以及模型的幾何形狀。模型幾何形狀的影響使特別困難的在預(yù)測引起尺寸的改變的原因使蠟?zāi)Ｄ?。幾何形狀的影響的一些現(xiàn)象，以及強加在收縮模型上的當?shù)氐睦鋮s率喝當時的限制條件，這樣導(dǎo)致一些復(fù)雜的不同收縮現(xiàn)象在模型上，可能影響蠟?zāi)沧⒌淖罱K尺寸的是澆注過程中的澆注參數(shù)。最近研究發(fā)現(xiàn)最大的澆鑄影響因素是澆注過程的時期包括澆注時間、填充時間、和支持時間。
這項工作的目標是決定蠟?zāi)＞壬a(chǎn)在寶石澆注擠壓的應(yīng)用，聚氨脂和矽樹脂橡膠過程工具是頻繁使用在快速模型中。經(jīng)過選擇的尺寸線性收縮過去常用于決定精度，這項研究的目的不是全部的研究在蠟?zāi)沧⒌恼麄€領(lǐng)域。相反地，這僅僅打算用藍圖提供鑄造品這些過程的參數(shù)值在澆注中在最大尺寸上的模型精度。一件寶石的澆注擠壓常用來生產(chǎn)蠟?zāi)?，機器的高壓力澆注是十分困難的通常應(yīng)用于工藝上。
2、 試驗性結(jié)論
2.1 樣品機構(gòu)的測試和測量
圖1，展示了生產(chǎn)的測試樣品等結(jié)構(gòu)。在選擇這個結(jié)構(gòu)模型時，下列因素時被考慮的：
該模型應(yīng)該反映出鑄件的平均壁厚在昆士蘭制造協(xié)會（QMI）
模型應(yīng)該考慮管理和測量，約束收縮和無約束收縮應(yīng)該要呈現(xiàn)自身的特色。
尺寸考慮的因素指示在圖2中，這些尺寸的計算是從相關(guān)點的坐標得來得，如圖3中所示。坐標與測量使用的是坐標測量儀（CMM）僅僅尺寸4是約束尺寸其他尺寸作為無約束尺寸來考慮對待。然而，在模型中出現(xiàn)收縮缺乏導(dǎo)致與收縮發(fā)生沖突，因而把這些尺寸作為特殊約束尺寸。
2.2蠟?zāi)５膭?chuàng)建
在圖1`中展示的立體圖模型是用于生產(chǎn)聚氨脂和矽樹脂橡膠工具（RTV）聚氨脂橡膠工具是用EbltaSG310和鋁粉來作為填充物制造的，其比率在1中是1：3.5
參數(shù)的配置能改變寶石的澆注壓力。參數(shù)包括澆注溫度，澆注壓力，模型預(yù)熱和在模型中的占用時間。相對于工業(yè)澆注壓力，澆注壓力在這些事件中涉及的是溶蠟通過孔進入印模中的壓力。在這個系統(tǒng)中當充滿印模后壓力應(yīng)該被取消。這些試驗是采用獨特的澆注液和蠟使用QMI。表格1展示的是試驗進程和考慮合格的標準值，模型預(yù)熱使試驗在整個過程中保證40度，在印模中，主模的中心被填完時（對稱點）。參照試驗圖表，設(shè)置了24個測量點，每個蠟塊包括26個尺寸，聚集在每一個工件中。
蠟?zāi)５南嚓P(guān)尺寸的易變是由生產(chǎn)他們的印模的實際尺寸來決定的。印模的實際尺寸是決定使用檢查在圖3中有所展現(xiàn)。在印模和蠟?zāi)Ｖg呈現(xiàn)的不同是比率的相對改變，并不是尺寸改變而表示的收縮。
表格1 澆注蠟?zāi)＿^程參數(shù)值
臘式樣
數(shù)字
澆注壓力 (kPa)
澆注溫度（℃）
占用時間（分）
1
207
65
6
2
138
65
6
3
69
65
6
4
34.5
65
6
5
207
65
8
6
138
65
8
7
69
65
8
8
34.5
65
8
9
207
65
10
10
138
65
10
11
69
65
18
12
34.5
65
10
13
207
70
6
14
138
70
6
15
69
70
6
16
34.5
70
6
17
207
70
8
18
138
70
8
19
69
70
8
20
34.5
70
8
21
207
70
10
22
138
70
10
23
69
70
10
24
35.7
70
10
3結(jié)果和論證
測量數(shù)目是太大而不能在無規(guī)律的組成中被描述，為了統(tǒng)一和分析有意義的結(jié)果，數(shù)據(jù)經(jīng)過觀測分析判斷基本上分為以下幾組：
1， 存在由兩個方向的收縮，X方向（沿著字母H的手臂方向）和Y方向（見圖3所示）第三個方向，字母H的厚度方向，是沒有被測量的。
2， 存在兩種類型的幾何圖樣特點，這兩種類型為約束和非約束收縮。
3， 收縮的程度可以依據(jù)幾何形狀的不同定義了X和Y坐標來協(xié)助表示如圖3所示。
4， 收縮的程度可以依據(jù)于模型的尺寸大小。有5個基本尺寸，100mm（尺寸標注為20，21和25，26）70mm（尺寸標注為4）20mm（圖中標注為22.23.和24）15mm（圖中標注為1－13除了4）
5， 尺寸14和19不是在收縮模型中直接測量的，他們是模型變形的測量依據(jù)是澆注參數(shù)。舉個例子說明，澆注占用時期將決定模型自由收縮的時間。過長的澆注占用時期意味著蠟液的完全凝固，通過印模約束了收縮時間。這個變形的意義為從點17到20和25到28的垂直位置中字母H
6， 方向的角度偏差。如圖3所示。
第一組（G—Ⅰ）由標注4組成，僅僅是收縮中的一個方向的約束。這收縮是在X方向被認為是過大的。經(jīng)歷這個形狀的保持收縮，由于在蠟?zāi)：陀∧１砻鎯烧唛g的摩擦受到不約束和特殊約束，根據(jù)這樣我們劃分為以下三這組，
1， G—Ⅱ組包括標注20，21，25和26，是過大的在Y方向上的收縮。
2， G—Ⅲ組包括標注22，23和24，是過小的在Y方向的收縮（20mm）。
3， G—Ⅳ組包括標注1到13除了4，是小的在 X方向上的收縮。
最后在描述其變形時分為了5組，事實上，除去第一組，剩下的被考慮的每一個點都是對稱的。在每一組里面收縮的平均值是采用比較兩種工具生產(chǎn)蠟?zāi)５牟煌Y(jié)果。表格2展示了這些不同的結(jié)果，首先，聚氨脂和矽樹脂工具的生產(chǎn)收縮的不同的變化展示在I到Ⅳ組，他們角度的改變不同變化在Ⅴ組，變化值用±％來表示評定的標準誤差。
矽樹脂工具生產(chǎn)的模型有過大的扭曲變形導(dǎo)致了較大的收縮比用聚氨酯工具生產(chǎn)的模型。第一組和第二組表示的是在全約束或特殊約束下表現(xiàn)出來的收縮是較小的比第三組和第四組在無約束條件的展示出來的收縮。對于這兩種工具，在全約束和特殊約束下展示出來的收縮平均值在標準誤差下是符合公差允許的。約束和非約束的尺寸收縮是非常不同的且是特別顯著的在應(yīng)用矽樹脂工具時。同時表現(xiàn)出來的現(xiàn)象是采用矽樹脂工具產(chǎn)生的變化是采用聚氨酯工具的變化的兩倍還大。
在第四組和第五組表現(xiàn)出來的大的平均偏差相對于標準誤差是進行了平均的結(jié)果。這種忽視事情的進程在他們之間相同改變易變的各種各樣的數(shù)值，他們的收縮情況可能依據(jù)于他們之間的相對位置關(guān)系和大小。采用逐步回歸的復(fù)原分析方法可以解釋出出現(xiàn)在這之間的進程參數(shù)和收縮情況在這每一個組成的團體中。
P1=-0.0195Ti-0.27P+0.0041TiP+0.032HP-0.00048TiHP
標準誤差＝±0.11％
S1=-0.0352Ti+0.000132HP
標準誤差＝±0.12％
P2=-0.34Ti+0.04H*H+2.7H-6P+0.0042Ti*Ti-0.031Tih
標準誤差＝±0.15％
S2=-0.0043P+0.000021P*P+0.000109XY*Y-0.0093Ti㏒(XY)
標準誤差＝±0.17％
P3=-1.5
標準誤差＝±0.46％
S3=-3.46
標準誤差＝±0.26％
P4=-2.1XY+0.00033XY*Y-0.025XY-0.125H-5.5H*H
標準誤差＝±0.62％
S4=-0.0243Ti+0.00033XY*Y-6.22H-0.01365H*H
標準誤差＝±0.41％
P5=0.00834Ti-0.0087XY+0.0000667XY*Y-0.00129H*H
標準誤差＝±0.95％
S5=0.0043XY+0.57㏒(H)-0.081㏒(XY)-0.000683P-0.0493H
標準誤差＝±0.121°
在這里的數(shù)值中P和S分別指示的是在使用聚氨酯和矽樹脂工具工作試驗是展示出來的收縮百分比。下標數(shù)字表示的是不同的組別團體的代號，舉例來說P1指第一組即G-I組中與聚氨酯有關(guān)的數(shù)值，Ti是指在澆注時注入的溫度（℃）,H是指在其過程中占用的時間（分），P是指在澆注注入時的壓強（kPa），XY 是來自方向的與方向 X 或 Y 的距離（m）并且時與標準誤差的比較的平均估計值，表示為預(yù)測的收縮標準的誤差值或是角度的扭曲的誤差值。
這些統(tǒng)計分析的細節(jié)是不被提供的，把這些有用的相等的條件限制在QMI的鑄造練習和使用于特別的幾何測試部分，在這里他們的重要性通過這兩種工具來展現(xiàn)是非常明顯的。同時有計劃的約束誤差的估算表示了改進了的收縮超出了簡單的平均值。
在G-I組里面，對于這兩種工具約束包括了最有影響的蠟液溫度Ti注入壓力P和占用時間H，收縮的精度值兩者類似的差了差不多兩倍，（±0.20相對于±0.11）增加提高蠟液的溫度將增加收縮率，同時占用時間和注入壓力將相對減少。
表格2 每一組的平均測量值
組別
矽樹脂工具
聚氨脂工具
方向
包含大小
G-Ⅰ
-2.20±0.18％
-1.30±0.21％
X
70mm(FC)
G-Ⅱ
-2.10±0.27％
-1.46±0.24％
Y
100mm(PC)
G-Ⅲ
-3.43±0.26％
-1.50±0.46％
Y
20mm(U)
G-Ⅳ
-3.44±0.57％
-1.93±0.74％
X
15mm(U)
G-Ⅴ
0.68±0.15°
0.31±0.15°
注：FC－全約束，PC－部分約束，U－無約束
在特殊的約束條件下的事例，G－Ⅱ組那聚氨酯工具表現(xiàn)了相似的附屬關(guān)系和G－I組的全約束條件下差不多，同時矽樹脂工具生產(chǎn)的結(jié)果表示了增加約束依賴于位置的特點與占用時間沒有直接的關(guān)系。尺寸特點的坐標與冷卻率有關(guān)系，可給出蠟?zāi)５哪厅c，在這里沒有直接測量，坐標點可能是隱式的將給出重新計算點。
G－Ⅲ組和G－Ⅳ組表示出來的尺寸是在無約束條件下產(chǎn)生的。這里聚氨酯和矽樹脂工具表現(xiàn)的不同變得更加明顯。聚氨酯工具展示出來的約束依據(jù)于占用時間和坐標位置。矽樹脂表現(xiàn)出來的收縮主要式注入的蠟液溫度Ti。這些不同可以歸納于兩者的熱的傳導(dǎo)率的不同而引起的。在這兩種情況下的收縮精度的評價中，沒有增加回歸分析上的重要性，事實上在G－Ⅲ組的事例中，沒有相關(guān)的數(shù)值可以能評價這兩者的不同，這說明還有另外一些重要的因素、條件沒有被考慮在內(nèi)，或者在這次試驗生產(chǎn)一些其他的條件沒有盡到足夠的精確測量。
占用時間H和（XY）的坐標位置關(guān)系有著顯著的影響在扭曲變形上，此外在聚氨酯作為生產(chǎn)工具時，蠟液的溫度Ti也能顯著的影響改變其扭曲變形。
回歸復(fù)原分析法給出了有價值的結(jié)論，僅僅在約束和特殊約束的尺寸條件下，對于其他更多的尺寸情況，通過強烈的相互關(guān)系作用能決定這兩者的約束或變形以及過程參數(shù)。沒有完全準備好的特定數(shù)量關(guān)系作為收縮的傳導(dǎo)類似于誤差的傳導(dǎo)，這些能從標準誤差中看出來。標準誤差沒有顯著提高當標準誤差通過簡單的平均比較后，然而這些數(shù)值給出了怎樣控制收縮和約束變形過程參數(shù)的前景。
結(jié)論:
約束和特殊約束尺寸，在平均上來說，在用矽樹脂工具中收縮了-2.20±0.20％，在用聚氨酯工具中收縮了-1.40±0.20％。
無約束尺寸在平均上來說，收縮了-3.44±0.40％和-1.70±0.60％分別對于矽樹脂和聚氨酯工具。
蠟?zāi)５呐で冃问褂梦鶚渲瑫r兩倍多比使用聚氨酯工具。
蠟?zāi)５臏蚀_度被定義是通過對標準誤差的評價從兩種類似的工具中。在他們的試驗中使用聚氨酯帶來的效益是高于使用矽樹脂工具的。蠟?zāi)５氖湛s使用矽樹脂是要考慮更多的因素比使用聚氨酯，可能是因為他們的冷卻率不同的緣故。大體說來大的收縮率導(dǎo)致難于控制其尺寸。
收縮尺寸的選擇能被簡化，當然有更好的顯示，那就是通過在進程中對相互關(guān)系的參數(shù)控制，同時采用已開發(fā)的回歸復(fù)原方程分析法來解決。類似地，蠟?zāi)５呐で冃我矊⒈伙@示和控制。
無約束尺寸展示出兩倍的易變性比約束尺寸。
感謝
作者非常感謝鑄造合作中心（CAST）提供的經(jīng)濟支持，同時，特別感謝由QMI的鑄造基礎(chǔ)部的全體員工的大力支持。
附錄2
Experimental studies on the accuracy of wax patterns used in investment casting
Abstract: Investment casting is often used to produce fully functional prototype components from sacrificial patterns. These patterns may be made using specialized rapid prototyping techniques such as stereo lithography or three-dimensional printing. When multiple functional prototypes are required, interim tools for making wax patterns are employed. The objective of this research work was to determine the precision and accuracy of wax patterns produced using several prototype tools. Linear contraction was used to determine the accuracy as a function of the wax injection parameters used in low-pressure injection moulding. Wax patterns were produced using polyurethane and silicone rubber tools. It has been shown that the accuracy of patterns from both tools is similar. However, silicone tools produce patterns with much higher contraction than those produced by polyurethane tools. Unconstrained patterns dimensions contracted as much as 3.44±0.40 per cent and 1.70±0.60per cent for silicone and polyurethane tools respectively. The constrained dimensions contracted by 2.20±0.20 per cent in the case of silicone tools and 1.40±0.20 per cent in the case of polyurethane tools.
Keywords: investment casting, wax pattern, dimensional accuracy
1 INTRODUCTION
Patterns for investment casting can be made using rapid prototyping techniques that can provide shapes of almost any complexity but in a limited choice of materials. However, when multiple functional prototype components are required, this process becomes too expensive and interim tools for wax pattern production are usually utilized.
The multi-step prototyping process is prone to error accumulation introduced by each of the stages. Mor-wood etal [1] analyses the error propagation through-out the investment casting process and clearly indicated that the biggest variability is introduced by high dimensional variability of wax patterns.
Investment casting is considered to be one of the more accurate casting processes in terms of shape and dimensions [2]. Nonetheless there is still room for improvement in the dimensional accuracy of castings. General tolerances quoted are ±0.5 per cent [3], but tighter tolerances may be achieved in certain circumstances. To increase the shape and dimensional accuracy of investment cast prototypes, the investment casting process needs to be better understood and improved significantly [4]. Patterns are typically made by injecting liquid wax into a die. The wax soldiers in the die and then further cools after it is removed from the die. The accuracy of the wax pattern is in influenced by the wax material, injection parameters (pressure, temperature, holding time, cooling rates) and the pattern geometry. The influence of the pattern geometry is especially difficult to capture in predicting dimensional changes caused by wax solicitation, the geometry influences such phenomena as local cooling rate and local constraints imposed on the shrinking pattern .This leads to a complex non-uniform shrinking of the pattern [3]. It is possible to affect the final dimensions of the wax with the injection process parameters. Previous studies have found the most important factor to be the processing times (injection, packing and holding times) [5].
The aim of this work was to determine the accuracy of wax patterns produced using a jeweler’s injection press and polyurethane and silicone rubber interim tools that are frequently used I rapid prototyping. Linear contraction of selected dimensions was used to determine the accuracy. The purpose of this study was not thoroughly to research the entire topic of wax injection. Rather, it was intended to provide the foundry with a blueprint as to what process parameter values give the most dimensionally accurate patterns for investment casting. A jeweler’s injection press was used to produce was patterns, quite different from the high-pressure injection machines that are more commonly used in industry.
2 EXPERIMENTAL METHODOLOGY
2.1 Test specimen design and measurements
Figure 1 shows the design of the test specimens produced. The following factors have been considered in choosing this design:
The pattern should reflect the average wall thickness of castings made at Queensland Manufacturing Institute (QMI).
Pattern handling and measurement should be easy.
Features with constrained and unconstrained shrinkage should be present.
The dimensions considered were designated as shown in Fig.2. These dimensions were calculated from the coordinates of reference points, shown in Fig.3, measured using a coordinate measuring machine (CMM).
Dimension 4 is the only constrained dimension, while the others are treated as unconstrained. However, lack of tapers in the pattern leads to friction during shrinkage, and hence classifies these dimensions as partially constrained.
2.2 Creation of wax patterns
A stereo lithography pattern of the polyurethane and the silicone rubber (RTV) tool. The polyurethane tool was made from Ebalta SG130 with aluminum powder as the filler, in a ratio of 1:1:3.5.
A range of parameters can be altered on the jeweler’s injection press. These are injection temperature, injection pressure, mould preheat and holding time in the mould. In contrast to industrial injection presses, injection pressure in this case refers to the pressure forcing molten wax through the orifice and into the mould. Pressure is removed from the system after filling of the mould. These experiments are specific to the injection machine and the wax used at the QMI. Table 1 shows the sequence of experiments and the values of the process parameters considered. Mould preheat was kept constant at 40° through the centre of the specimen (point of symmetry). Following this experimental plan, 24 sets of measurements, each containing 26 wax pattern dimensions, were collected from each tool.
The dimensional variability of the wax patterns was determined with reference to the actual dimensions of the moulds used to produce them. The dimensions of the moulds were determined using the inspection plan from Fig.3. the difference between the mould and the wax pattern was presented as percentage relative change. Negative dimensional change indicated shrinkage.
3 RESULTS AND DISCUSSION
The number of measurements was too large to present data in raw form. To facilitate analysis and consolidate results into meaningful outcomes, the date were divided into several groups based on the following observations:
1. Two directions of shrinking exist, the X direction (along the connecting arm of the letter H) and the Y direction (see Fig.3). The third direction, the thickness of the letter H was not measured.
2. Two types of geometrical feature exist, those with constrained and those with unconstrained shrinkage,
3. The degree of shrinkage may depend on the position of the geometrical feature as defined by X and Y coordinates and expressed in millimeters (see Fig.3).
4. The degree of shrinkage may depend on the size of the feature. There are basically five sizes: 100mm (features 20,21,25 and 26),70mm (features 4),20mm (features 22,23 an 24) and 15mm (features 1 to 13 excluding feature 4).
5. Dimensions 14 to 19 are not direct measurements of pattern shrinkage. They are a measure of the pattern distortion which may depend strongly on the injection parameters. For example, the holding time will determine the fraction of the time during which the wax pattern is freely shrinking. A very long holding time means that the wax pattern fully solidifies while at all times being constrained by the mould. The distortion was defined as angular deviation of the arms of the letter H from the vertical position at measurement points 17 to 20 and 25 to 28, as shown in Fig.3.
The first group(G-I) consists of feature 4, which is the only dimension that is fully constrained while shrinking. It shrinks in the X direction and is considered to be large. The remaining features that undergo shrinkage are unconstrained or partially constrained owing to friction between the wax and mould surfaces. These can be further divided into three groups:
1. Group G-II consists of features 20, 21, 25 and 26, which shrink in the Y direction and are large.
2. Group G-III consists of features 22, 23 and 24, which shrink in the Y direction and are small (20 mm).
3. Group G-IV consists of features 1 to 13, excluding feature 4, which shrink in the X direction and are small (15 mm).
Finally, there is the fifth group (G-V) which describes the distortion. In all cases, apart from group G-I, the position of each feature with regard to the point of symmetry is also considered.
The average contraction within each group was determined to allow comparison of the two tools used to produce wax patterns. Table 2 shows the results, the first entry for the silicon and polyurethane tools indicating the dimensional change (G-I to G-IV) or angular deviation (G-V) with ± representing the estimated standard error.
The silicone tool produced more heavily distorted patterns and caused greater contraction than the poly-urethane tool. Groups G-I and G-II represent features that are constrained or partially constrained and show less contraction than groups G-III and G-IV which freely contract. For both tools, the average contraction of constrained and partially constrained features is equal within the tolerance defined by the standard
errors. The difference between constrained and unconstrained dimensions is especially pronounced in the case of the silicone tool. It is also apparent that distortion when employing the silicone tool is twice as great as that in the case of the polyurethane tool.
Large deviations from average values indicated by the standard error within groups G-IV and G-V are the result of averaging. This disregards the fact that process variables between patterns varied considerably and that contraction may depend on feature relative position and size. Regression analysis revealed the following dependences between process parameters and the con-traction within each of the groups:
P1=-0.0195Ti-0.27P+0.0041TiP+0.032HP-0.00048TiHP
standard error＝±0.11％
S1=-0.0352Ti+0.000132HP
standard error＝±0.12％
P2=-0.34Ti+0.04H*H+2.7H-6P+0.0042Ti*Ti-0.031Tih
standard error＝±0.15％
S2=-0.0043P+0.000021P*P+0.000109XY*Y-0.0093Ti㏒(XY)
standard error＝±0.17％
P3=-1.5
standard error＝±0.46％
S3=-3.46
standard error＝±0.26％
P4=-2.1XY+0.00033XY*Y-0.025XY-0.125H-5.5H*H
standard error＝±0.62％
S4=-0.0243Ti+0.00033XY*Y-6.22H-0.01365H*H
standard error＝±0.41％
P5=0.00834Ti-0.0087XY+0.0000667XY*Y-0.00129H*H
standard error＝±0.95％
S5=0.0043XY+0.57㏒(H)-0.081㏒(XY)-0.000683P-0.0493H
standard error＝±0.121°
where P and S denote the linear percentage contraction for the polyurethane and silicone tool respectively and the subscript numbers indicate the relevant group, i.e. P1 relates to polyurethane group G-I, Ti is the wax temperature at the time of injection (8C), H is the
holding time (min), P is the injection pressure (kPa), XY is the distance in direction X or Y from the origin (m) and standard error is the estimate of the average standard error for the predicted contraction or angular
distortion.
The details of the statistical analysis are not provided, as the usefulness of these equations is limited to QMI’s foundry practices and the particular geometry of the test part. Their importance here lies in showing which process parameters are the most influential within each
group and for each tool. At the same time the estimated standard error of the calculated contraction indicates the improvement in shrinkage estimation over simple averaging.
Within group G-I, for both tools, contraction is influenced by wax temperature Ti , injection pressure P and holding time H. The accuracy of approximation of the contraction is almost doubled ( ± 0.20 as against ± 0.11). The increase in wax temperature will increase the shrink-age, while holding time and pressure will decrease it.
In the case of the partially constrained features, group G-II, the polyurethane tool exhibits similar dependences as in group G-I (fully constrained), while the silicone tool produces results indicating that contraction additionally depends on the position of features with no connection to the holding time. The coordinates of the dimensions of
the feature can be linked to cooling rate at a given point of the solidifying wax pattern. This has not been measured directly, and the coordinates of the feature may implicitly account for this, given that the conditions are repeatable.
Groups G-III and G-IV represent dimensions that shrink without constraint. There, the differences between the silicone and polyurethane tools become more apparent. The polyurethane tool shows that contraction depends on holding time and the feature coordinates. The silicone tool shows that the contraction is additionally influenced by the temperature of the wax, Ti . These differences can be attributed to the differences in heat conductivity. In both cases the accuracy of estimation of contraction did not improve significantly with the implementation of regression analysis. In fact, in the case of group G-III, no relationships could be established for the two cases. This indicates that some other, possibly more influential, elements have not been considered, or either the measurements are not accurate or repeatability of the experimental procedure was not good enough.
The holding time H and the position of the feature (XY) has
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