蜡模精确成型在浇注中的实验性研究

摘要：浇注是经常用于从牺牲模型中生产全功能的标准部件，这些模型（标准）可以用特殊的快速原形技术如立体图或者三维尺寸印刷技术来制造。当要求复合的多样功能的模型时，制造蜡模被采用于过度时期的工具。这个研究工作的目的是为了决定判断出准确细致和精确的蜡模生产用于若干模型工具中。线性收缩常常在决定其精度上起着作用，蜡模浇入参数常用于低压喷入造型.蜡模常常用于生产聚氨脂和矽树脂橡胶工具。从这两种相似的工具中他将展示出模型的精确度.可知,蜡模工具生产的产品模型有较高的收缩比这些有聚氨脂工具生产的产品。自然模型尺寸收缩分别是矽树脂为3.44±0.40%而聚氨脂为1.70±0.60%。另外受压制的尺寸收缩分别为在矽树脂工具的应用中是2.20±0.20%，在聚氨脂工具中的应用为1.40±0.20%。

关键字：浇注蜡模尺寸精度

介绍

浇注模型能制造用快速模型技术能提供大多数成型轮廓，一些复杂的轮廓成型在选择材料上有一些限制。然而当要求需要多功能的模型部件时，这中过程成为太昂贵和使用蜡模作为过度工具派上用场。

多步骤的模型过程是易于被错误地计算介绍通过每一个时期，Mor-wod .et al。[1] 分析在浇注上的自始至终的错误累积过程，可以清晰的指示出最大的变化是被介绍通过在蜡模的大尺寸的变化中。

浇注是被认为是一种多精度的铸造过程在一系列的成型设计尺寸中，但是，有食品储藏室改进了在铸造中的尺寸精度。通常采用的公差的是±0.5%[3]，但是更严格的公差可以被实现在特定的环境中，为了增加提高浇注成型的形状和尺寸精度，浇注过程需要更好更明白和更显著的提升改进。

模型典型的制造方式是将流动的蜡液浇入进一个印模里，使蜡液在印模里凝固，在更深的冷却之后，将形成的蜡模从印模中取出。蜡模精度的影响因素有：蜡模材料，浇注参数（包括压力，温度，支持时间，冷却率）以及模型的几何形状。模型几何形状的影响使特别困难的在预测引起尺寸的改变的原因使蜡模凝固。几何形状的影响的一些现象，以及强加在收缩模型上的当地的冷却率喝当时的限制条件，这样导致一些复杂的不同收缩现象在模型上，可能影响蜡模浇注的最终尺寸的是浇注过程中的浇注参数。最近研究发现最大的浇铸影响因素是浇注过程的时期包括浇注时间、填充时间、和支持时间。

这项工作的目标是决定蜡模精度生产在宝石浇注挤压的应用，聚氨脂和矽树脂橡胶过程工具是频繁使用在快速模型中。经过选择的尺寸线性收缩过去常用于决定精度，这项研究的目的不是全部的研究在蜡模浇注的整个领域。相反地，这仅仅打算用蓝图提供铸造品这些过程的参数值在浇注中在最大尺寸上的模型精度。一件宝石的浇注挤压常用来生产蜡模，机器的高压力浇注是十分困难的通常应用于工艺上。

试验性结论

2.1 样品机构的测试和测量

图1，展示了生产的测试样品等结构。在选择这个结构模型时，下列因素时被考虑的：

该模型应该反映出铸件的平均壁厚在昆士兰制造协会（QMI）

模型应该考虑管理和测量，约束收缩和无约束收缩应该要呈现自身的特色。

尺寸考虑的因素指示在图2中，这些尺寸的计算是从相关点的坐标得来得，如图3中所示。坐标与测量使用的是坐标测量仪（CMM）仅仅尺寸4是约束尺寸其他尺寸作为无约束尺寸来考虑对待。然而，在模型中出现收缩缺乏导致与收缩发生冲突，因而把这些尺寸作为特殊约束尺寸。

2.2蜡模的创建

在图1`中展示的立体图模型是用于生产聚氨脂和矽树脂橡胶工具（RTV）聚氨脂橡胶工具是用EbltaSG310和铝粉来作为填充物制造的，其比率在1中是1：3.5

参数的配置能改变宝石的浇注压力。参数包括浇注温度，浇注压力，模型预热和在模型中的占用时间。相对于工业浇注压力，浇注压力在这些事件中涉及的是溶蜡通过孔进入印模中的压力。在这个系统中当充满印模后压力应该被取消。这些试验是采用独特的浇注液和蜡使用QMI。表格1展示的是试验进程和考虑合格的标准值，模型预热使试验在整个过程中保证40度，在印模中，主模的中心被填完时（对称点）。参照试验图表，设置了24个测量点，每个蜡块包括26个尺寸，聚集在每一个工件中。

蜡模的相关尺寸的易变是由生产他们的印模的实际尺寸来决定的。印模的实际尺寸是决定使用检查在图3中有所展现。在印模和蜡模之间呈现的不同是比率的相对改变，并不是尺寸改变而表示的收缩。

表格1 浇注蜡模过程参数值

腊式样数字	浇注压力 (kPa)	浇注温度（℃）	占用时间（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结果和论证

测量数目是太大而不能在无规律的组成中被描述，为了统一和分析有意义的结果，数据经过观测分析判断基本上分为以下几组：

存在由两个方向的收缩，X方向（沿着字母H的手臂方向）和Y方向（见图3所示）第三个方向，字母H的厚度方向，是没有被测量的。
存在两种类型的几何图样特点，这两种类型为约束和非约束收缩。
收缩的程度可以依据几何形状的不同定义了X和Y坐标来协助表示如图3所示。
收缩的程度可以依据于模型的尺寸大小。有5个基本尺寸，100mm（尺寸标注为20，21和25，26）70mm（尺寸标注为4）20mm（图中标注为22.23.和24）15mm（图中标注为1－13除了4）
尺寸14和19不是在收缩模型中直接测量的，他们是模型变形的测量依据是浇注参数。举个例子说明，浇注占用时期将决定模型自由收缩的时间。过长的浇注占用时期意味着蜡液的完全凝固，通过印模约束了收缩时间。这个变形的意义为从点17到20和25到28的垂直位置中字母H
方向的角度偏差。如图3所示。

第一组（G—Ⅰ）由标注4组成，仅仅是收缩中的一个方向的约束。这收缩是在X方向被认为是过大的。经历这个形状的保持收缩，由于在蜡模和印模表面两者间的摩擦受到不约束和特殊约束，根据这样我们划分为以下三这组，

G—Ⅱ组包括标注20，21，25和26，是过大的在Y方向上的收缩。
G—Ⅲ组包括标注22，23和24，是过小的在Y方向的收缩（20mm）。
G—Ⅳ组包括标注1到13除了4，是小的在 X方向上的收缩。

最后在描述其变形时分为了5组，事实上，除去第一组，剩下的被考虑的每一个点都是对称的。在每一组里面收缩的平均值是采用比较两种工具生产蜡模的不同结果。表格2展示了这些不同的结果，首先，聚氨脂和矽树脂工具的生产收缩的不同的变化展示在I到Ⅳ组，他们角度的改变不同变化在Ⅴ组，变化值用±％来表示评定的标准误差。

矽树脂工具生产的模型有过大的扭曲变形导致了较大的收缩比用聚氨酯工具生产的模型。第一组和第二组表示的是在全约束或特殊约束下表现出来的收缩是较小的比第三组和第四组在无约束条件的展示出来的收缩。对于这两种工具，在全约束和特殊约束下展示出来的收缩平均值在标准误差下是符合公差允许的。约束和非约束的尺寸收缩是非常不同的且是特别显著的在应用矽树脂工具时。同时表现出来的现象是采用矽树脂工具产生的变化是采用聚氨酯工具的变化的两倍还大。

在第四组和第五组表现出来的大的平均偏差相对于标准误差是进行了平均的结果。这种忽视事情的进程在他们之间相同改变易变的各种各样的数值，他们的收缩情况可能依据于他们之间的相对位置关系和大小。采用逐步回归的复原分析方法可以解释出出现在这之间的进程参数和收缩情况在这每一个组成的团体中。

P1=-0.0195Ti-0.27P+0.0041TiP+0.032HP-0.00048TiHP

标准误差＝±0.11％

S1=-0.0352Ti+0.000132HP

标准误差＝±0.12％

P2=-0.34Ti+0.04H*H+2.7H-6P+0.0042Ti*Ti-0.031Tih

标准误差＝±0.15％

S2=-0.0043P+0.000021P*P+0.000109XY*Y-0.0093Ti㏒(XY)

标准误差＝±0.17％

P3=-1.5

标准误差＝±0.46％

S3=-3.46

标准误差＝±0.26％

P4=-2.1XY+0.00033XY*Y-0.025XY-0.125H-5.5H*H

标准误差＝±0.62％

S4=-0.0243Ti+0.00033XY*Y-6.22H-0.01365H*H

标准误差＝±0.41％

P5=0.00834Ti-0.0087XY+0.0000667XY*Y-0.00129H*H

标准误差＝±0.95％

S5=0.0043XY+0.57㏒(H)-0.081㏒(XY)-0.000683P-0.0493H

标准误差＝±0.121°

在这里的数值中P和S分别指示的是在使用聚氨酯和矽树脂工具工作试验是展示出来的收缩百分比。下标数字表示的是不同的组别团体的代号，举例来说P1指第一组即G-I组中与聚氨酯有关的数值，Ti是指在浇注时注入的温度（℃）,H是指在其过程中占用的时间（分），P是指在浇注注入时的压强（kPa），XY 是来自方向的与方向 X 或 Y 的距离（m）并且时与标准误差的比较的平均估计值，表示为预测的收缩标准的误差值或是角度的扭曲的误差值。

这些统计分析的细节是不被提供的，把这些有用的相等的条件限制在QMI的铸造练习和使用于特别的几何测试部分，在这里他们的重要性通过这两种工具来展现是非常明显的。同时有计划的约束误差的估算表示了改进了的收缩超出了简单的平均值。

在G-I组里面，对于这两种工具约束包括了最有影响的蜡液温度Ti注入压力P和占用时间H，收缩的精度值两者类似的差了差不多两倍，（±0.20相对于±0.11）增加提高蜡液的温度将增加收缩率，同时占用时间和注入压力将相对减少。

表格2 每一组的平均测量值

组别	矽树脂工具	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－全约束，PC－部分约束，U－无约束

在特殊的约束条件下的事例，G－Ⅱ组那聚氨酯工具表现了相似的附属关系和G－I组的全约束条件下差不多，同时矽树脂工具生产的结果表示了增加约束依赖于位置的特点与占用时间没有直接的关系。尺寸特点的坐标与冷却率有关系，可给出蜡模的凝固点，在这里没有直接测量，坐标点可能是隐式的将给出重新计算点。

G－Ⅲ组和G－Ⅳ组表示出来的尺寸是在无约束条件下产生的。这里聚氨酯和矽树脂工具表现的不同变得更加明显。聚氨酯工具展示出来的约束依据于占用时间和坐标位置。矽树脂表现出来的收缩主要式注入的蜡液温度Ti。这些不同可以归纳于两者的热的传导率的不同而引起的。在这两种情况下的收缩精度的评价中，没有增加回归分析上的重要性，事实上在G－Ⅲ组的事例中，没有相关的数值可以能评价这两者的不同，这说明还有另外一些重要的因素、条件没有被考虑在内，或者在这次试验生产一些其他的条件没有尽到足够的精确测量。

占用时间H和（XY）的坐标位置关系有着显著的影响在扭曲变形上，此外在聚氨酯作为生产工具时，蜡液的温度Ti也能显著的影响改变其扭曲变形。

回归复原分析法给出了有价值的结论，仅仅在约束和特殊约束的尺寸条件下，对于其他更多的尺寸情况，通过强烈的相互关系作用能决定这两者的约束或变形以及过程参数。没有完全准备好的特定数量关系作为收缩的传导类似于误差的传导，这些能从标准误差中看出来。标准误差没有显著提高当标准误差通过简单的平均比较后，然而这些数值给出了怎样控制收缩和约束变形过程参数的前景。

结论:

约束和特殊约束尺寸，在平均上来说，在用矽树脂工具中收缩了-2.20±0.20％，在用聚氨酯工具中收缩了-1.40±0.20％。

无约束尺寸在平均上来说，收缩了-3.44±0.40％和-1.70±0.60％分别对于矽树脂和聚氨酯工具。

蜡模的扭曲变形使用矽树脂时两倍多比使用聚氨酯工具。

蜡模的准确度被定义是通过对标准误差的评价从两种类似的工具中。在他们的试验中使用聚氨酯带来的效益是高于使用矽树脂工具的。蜡模的收缩使用矽树脂是要考虑更多的因素比使用聚氨酯，可能是因为他们的冷却率不同的缘故。大体说来大的收缩率导致难于控制其尺寸。

收缩尺寸的选择能被简化，当然有更好的显示，那就是通过在进程中对相互关系的参数控制，同时采用已开发的回归复原方程分析法来解决。类似地，蜡模的扭曲变形也将被显示和控制。

无约束尺寸展示出两倍的易变性比约束尺寸。

感谢

作者非常感谢铸造合作中心（CAST）提供的经济支持，同时，特别感谢由QMI的铸造基础部的全体员工的大力支持。

附录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:

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.
Two types of geometrical feature exist, those with constrained and those with unconstrained shrinkage,
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).
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).
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 significant impact on the distortion. Addition-ally, in the case of the polyurethane tool, wax temperature Ti significantly altered the distortion.

The regression analysis gave worthy results only in the case of constrained and partially constrained dimensions. In all other cases, although a strong correlation was determined between the contraction or distortion and the process parameters, these were not really viable in quantitative terms as the spread of the contraction was similar to the spread of the errors. This can be seen from the standard errors, which did not improve significantly when compared with standard errors attained through simple averaging. Nonetheless, these equations gave an insight into how the process parameters affect the contraction and distortion.

4 CONCLUSIONS

The constrained and partially constrained dimensions, on average, shrink 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.

Unconstrained dimensions, on average, contract by - 3:44 ± 0:40 per cent and -1:70 ±0:60 per cent for silicone and polyurethane tools respectively.

The distortion of wax patterns made using the silicone tool is twice as great as that in the case of wax patterns made using the polyurethane tool.

The accuracy of wax patterns as determined by the estimate of standard errors is similar for both tools. The benefit of using polyurethane tools over silicone tools is in their precision. Wax patterns made using the silicone tool shrink considerably more than those made by the polyurethane tool, possibly owing to differences in solidification cooling rates. In general, greater con-traction leads to more difficult control of dimensions. The contraction of selected dimensions can be reduced, and certainly better predicted, by appropriately selecting controlling the process parameters in accordance with the regression analysis equations developed. Similarly, the distortion of the wax pattern could be predicted and controlled. Unconstrained dimensions exhibit twice the variability of constrained ones.

ACKNOWLEDGEMENTS

The authors would like to acknowledge the financial support from CAST (Cooperative Research Centre for Cast Metals Manufacturing). Also, many thanks are due to QMI’s investment foundry staff for the support provided.

REFERENCES

1 Moorwood, G., Christodoulou, P., Lahnam, B. and Byrnes, D.

Contraction of investment cast H13 tool steel. Int. J. Cast

Metals, 2000, 12, 457±467.

2 Dimensional Tolerances for Metal and Metal Alloy Castings,

1985 (British Standards Institution, London).

3 Piwonka, T. S. and Wiest, J. M. Factors a V ecting invest-ment

casting pattern die dimensions. INCAST, June 1998,

8±13.

4 Halford, B. Advanced low cost tooling manufacturing.

Prototyping Technol. Int., 1997, 309±311.

5 Horacek, M. and Lubos, S. In¯uence of injection parameters

on the dimensional stability of wax patterns. In 9th World

Conference on Investment Casting, San Francisco, Califor-nia,

1996, paper 1.

Table2 Average measured values for each group

Group	Silicone tool	Polyurethane tool	Direction	Size constraint
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°

FC－fully constrained，PC－partially constrained，U－unconstrained

Table 1 Process parameters for wax injection

Wax pattern number	Injection pressure (kPa)	Injection temperature（℃）	Holding time(time)
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

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