# FDM Rapid Prototyping Technology of Complex-Shaped Mould Based on Big Data Management of Cloud Manufacturing

Authors: Yan Cao; Liang Huang; Yu Bai; Qingming Fan
Journal: Complexity
 (2018)

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## Abstract

In order to solve the problem of high cost and long cycle in the process of traditional subtractive material manufacturing of a complex-shaped mould, the technology of FDM rapid prototyping is used in combination with the global service idea of cloud manufacturing, where the information of various kinds of heterogeneous-forming process data produced in the process of FDM rapid prototyping is analysed. Meanwhile, the transfer and transformation relation of each forming process data information in the rapid manufacturing process with the digital model as the core is clarified, so that the FDM rapid manufacturing process is integrated into one, thus forming a digital and intelligent manufacturing system for a complex-shaped mould based on the cloud manufacturing big data management. This paper takes the investment casting mould of a spur gear as an example. Through research on the forming mechanism of jet wire, the factors affecting forming quality and efficiency is analysed from three stages: the pretreatment of the 3D model, the rapid prototyping, and the postprocessing of the forming parts. The relationship between the forming parameters and the craft quality is thus established, and the optimization schemes at each stage of this process are put forward through the study on the forming mechanism of jet wire. Through a rapid prototyping test, it is shown that the spur face gear master mould based on this technology can be quickly manufactured with a critical surface accuracy within a range of 0.036 mm–0.181 mm and a surface roughness within the range of 0.007–0.01μm by only 1/3 the processing cycle of traditional subtractive material manufacturing. It lays a solid foundation for rapid intelligent manufacturing of products with a complex-shaped structure.


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## Body

## 1. Introduction

As a modern process equipment, the mould has been widely used in industrial production with its high precision, high complexity, and high consistency products. However, the way of manufacturing using a mould has been a technology bottleneck that has not yet found a breakthrough. This is especially true for the complex-shaped mould. The subtractive material manufacturing does not only have a long processing cycle and high processing costs, but the consistency of the products is hard to guarantee due to the constraints of the processing machinery itself. With the development and application of the additive material manufacturing technology in recent years, the rapid prototyping mould method appeared (RT technology) [1–3]. This technology integrates the rapid prototyping technology with the traditional nonmachining cavity replication technology. Compared with the traditional subtractive material manufacturing method, the rapid manufacturing of a complex-shaped mould can be accomplished with only one third of the traditional processing cycle and processing cost. It can realize the rapid production of a small batch of the complex-shaped products by docking the technology with the investment casting.Since the FDM rapid prototyping technology is the only high quality rapid prototyping method at present with industrial grade thermoplastic material as the forming material [4], it is suitable for the production of an investment casting mould. However, in the rapid prototyping process, with the development of forming technology research, a large number of heterogeneous-forming process data information related to the quality and efficiency of the forming process will be produced. Furthermore, these sources of information are also related to each other. Therefore, how to extract, sum up, and utilize the forming process big data produced in the above forming process has become a research hotspot of advanced manufacturing technology under the background of the information age [5–7]. In order to adapt to the complex and changeable market demand, a new networked manufacturing model based on the integration of information technology and manufacturing industry has emerged—cloud manufacturing [8, 9]. Cloud manufacturing provides a new network manufacturing model for users with various types of on-demand manufacturing services. The architecture of cloud manufacturing integration is a set of models describing the integration of cloud manufacturing functions, including functional definitions, interface rules, and architecture. These models describe how the cloud manufacturing platform forms a loosely coupled distributed environment, including the functional structure, characteristics, and operation mode. So, in the rapid prototyping process, these so-called “forming processes big data” will take the digital model as the core to transfer and transform in the manufacturing process and ultimately directly affect the processing quality and efficiency. Typical work, such as that of Professor D. Li, proposes a cloud manufacturing network model for workshop manufacturing [10]. Combined with the intelligent evaluation and control algorithm of big data feedback, the accuracy of the workshop cloud manufacturing network model was improved. Meanwhile, a cloud manufacturing process model for hydrostatic systems based on manufacturing big data was proposed by Z. F. Liu, and the intelligent manufacturing process was realized by combining the cloud service platform [11].Based on the above analysis, combined with the cloud manufacturing service concept [12], by taking big data as the main processing basis, the paper studies the internal relationship between data and the mechanism of data acting on product demand, and constructs a network of data function coordination relations. The big data produced in the miscellaneous manufacturing process is organized effectively, so that the intelligent and efficient rapid manufacturing of complex products can be realized by the manufacturing system based on the cloud manufacturing big data management. Therefore, this paper takes the investment casting mould of a spur gear as an example (that is, the master mould of a spur face gear), starting with the material-forming mechanism of the FDM rapid prototyping technology, and studies the various stages of the rapid prototyping of a spur face gear master mould. By analysing the influence of the process information data in each stage on the forming accuracy and efficiency, as well as the research on the change of the wire during the forming process, from the angle of reducing the surface roughness and improving the forming precision, the expression relationship between the information data of rapid prototyping and the forming quality is established. Based on this expression, the reasonable selection method of forming process parameters is determined. Finally, the theoretical model of the process system is constructed by using the moulding process big data obtained by the process, and connected with the cloud manufacturing technology. Thus, the intelligent manufacturing system of the FDM rapid prototyping complex-shaped mould based on the big data management of cloud manufacturing is realized (the flow chart is shown in Figure 1).Figure 1
The intelligent manufacturing system of the FDM rapid prototyping complex-shaped mould based on the big data management of cloud manufacturing.


## 2. Analysis of the Spur Face Gear Master Mould Structure

Considering that the master mould of a spur face gear is mainly used as a wax injection mould in the investment casting process and that this mould has the problem of poor thermal conductivity when FDM rapid prototyping technology is used to manufacture a mould with thermoplastic material, in order to remove the master mould conveniently without affecting the precision of the wax mould, the master mould of the spur face gear is designed by UG software as a three-layer structure consisting of a top die, a bottom die, and a core with a movable centre-locating shaft according to the injection mould design method with movable parts [13, 14] (as shown in Figure 2, the top die and the bottom die are moving dies, and the core is a static die).Figure 2
Sketch of the spur face gear master mould.
(a)
(b)
(a)


## 3. Process Big Data Analysis of Rapid Prototyping Spur Face Gear Master Mould Based on FDM

According to the investment casting process requirements on the use of a wax injection mould material with high temperature performance, hardness, and strength, as well as having characteristics of low viscosity, low shrinkage necessary, and good bonding ability for thermoplastic materials used in FDM rapid prototyping technology [15, 16], the forming material selected is ABS. The performance parameters of ABS materials are shown in Table 1, and the corresponding rapid prototyping equipment is the BOX 3D rapid prototyping machine provided by Beijing Lingyang Aipu Technology Co. Ltd.Table 1
The performance parameters of ABS materials.
Materials
Tensile strength
Ultimate tensile ratio
ABS
≥43 Mpa
4%
Melting temperature
Distortion temperature
Linear shrinkage
200°C–250°C
93°C–118°C
0.4%
Bending strength
Impact strength
Coefficient of linear expansion
790 kg/cm2
20 kJ/m2
7 × 10−5/°C


### 3.1. Analysis of Process Parameters of Spur Face Gear Master Mould in the Preprocessing Stage of Rapid Prototyping

Firstly, before adopting the FDM rapid prototyping technology to produce the master mould of the spur face gear, some factors need to be considered; for example, ABS is a thermoplastic material that causes the dimensions of the forming parts to shrink during the forming process and the shrinkage of each forming part is carried out in different directions [17]. Thus, there are some relationships between the size shrinkage of each forming part SL, the corresponding 3D model size LCAD, and the actual size of the moulded part L that are shown in Figure 3.
(1)SL=LCAD−LLCAD,where LCAD is the three-dimensional model of the spur face gear master mould and L is the actual part of spur face gear master mould.Figure 3
Sketch of rapid prototyping shrinkage for the spur face gear master mould.Therefore, according to (1), the shrinkage percentage of each mould part can be calculated through a rapid prototyping test (as shown in Table 2). Furthermore, according to the shrinkage percentage of each mould part shown in Table 2, the original 3D model of the spur face gear master mould is enlarged by using UG software.Table 2
The shrinkage percentage of each spur face gear master mould.
Core
Cylindrical base
Reflexive mould of spur face gear
Pouring cavity of keyway
Centre-locating hole of core
Centre-locating shaft
1.12%
0.22%
0.35%
0.51%
0.64%
Bottom die
Square base
Cylindrical boss
1.46%
0.19%
Top die
Square base
Cylindrical groove
Pouring cavity of keyway
Centre-locating hole of core
1.41%
0.10%
0.41%
0.57%Secondly, the three-dimensional model of the enlarged spur face gear master mould is used for the extraction of the shell. Because of proper shell disposal, the manufacturing cost can be reduced and the forming speed can be improved on the basis of not affecting the original performance of the master mould (including the high temperature performance, strength, and hardness). Furthermore, the distortion and cracking of the mould surface can also be prevented. In order to determine the influence of different shell thicknesses on the quality and performance of the mould parts, simulation experiments of shell extraction and wax injection are carried out for 6 different shell thicknesses in Figure3 by adopting the control variety method. According to the experimental results shown in Table 3, a reasonable shell thickness of 0.8 mm is selected for the master mould taking into account both forming efficiency and manufacturing cost.Table 3
Setting of the shell thickness.
Sequence number
1
2
3
4
5
6
Shell thickness (mm)
1.0
0.9
0.8
0.7
0.6
0.5
Experimental result
Normal
Normal
Normal
Warp and distortion
Warp and distortion seriously
DeformationThe model data of the master mould must be converted into the data format that can be recognized by the RP equipment after finishing the optimization of the 3D model of the spur face gear master mould, because the forming process parameters are set up on the basis of the imported model data. The mainstream data format that can be identified by the current rapid prototyping machine is STL [18, 19]. The essence of the STL data format is to use hundreds of tiny triangular patches to replace a curved surface, thus reconstructing the original 3D model. The error of the STL model is controlled by the chord deviation H (as shown in Figure 4). If you get the high precision STL model by increasing the number of triangles, it will not only exceed the maximum forming accuracy that FDM can achieve, but it will also increase the data storage during the STL model data slicing process. Therefore, it is important to find a balance point between forming precision and forming efficiency.Figure 4
Effect of different chord deviations on the accuracy of the STL model.
(a)
The fitting precision of model is low when the chord deviation is larger
(b)
The fitting precision of the model is high when the chord deviation is smallerAt present, the most optimized parameter setting method for converting the STL model by using UG software is shown in Table4, and by this method, the STL model of the spur face gear master mould can be obtained (as shown in Figure 5).Table 4
The most optimized parameter setting method for converting the STL model.
UG(1) File → export → STL → the setting type is binary(2) The triangle tolerance is 0.0025(3) The adjacent tolerance is 0.12(4) Open automatic normal generation(5) Close normal indication(6) Open triangle indicationFigure 5
The STL model of the spur face gear master mould.


### 3.2. Analysis of Forming Process Parameters of Spur Face Gear Master Mould in the Processing Stage of Rapid Prototyping

Although many factors have more or less influence on forming efficiency and forming quality (including dimensional accuracy and surface roughness) in the FDM rapid prototyping process, it is mainly controlled by seven important technological parameters, which are the thickness of the layer and the forming direction, the extrusion speed and filling speed, the nozzle temperature and the ambient temperature, and the compensation of the ideal contour line [20–22].


#### 3.2.1. Selection of Layer Thickness and Forming Direction

The layer thickness is the slice thickness of the three-dimensional model, and it is also the manufacturing height of each layer of the FDM rapid prototyping machine for laminated object manufacturing. The forming direction refers to the spatial arrangement of forming parts in the forming process. Since the manufacturing method of the FDM rapid prototyping technology is superimposed layer by layer, the contour of each slice is inconsistent and has a certain thickness during formation [23]. As a result, the surface of the moulded parts often exhibits a “Step Effect” (as shown in Figure 6), which would further affect the quality of the moulded parts. At present, the technical indexes of the “Step Effect” in the FDM rapid prototyping process are mainly ε and δ, where ε reflects the shape error of the moulded part, and δ reflects the roughness of the moulded part. According to the geometric relationship shown in Figure 6, the relation between the layer thickness h and forming direction α, ε, and δ can be concluded, respectively.
(2)ε=Rcosα−1−sinα+hR2,(3)δ=R1−1−2hsinαR−hR2.Figure 6
The local schematic of the “Step Effect” for forming parts.To investigate the influence of different slice heights and forming directions on the surface of the moulded partsε and δ, taking the hemisphere model of R = 100 mm as an example, the corresponding relation curve is plotted by Matlab in accordance with (2) and (3) (as shown in Figure 7).Figure 7
The relation curves ofα−ε and α−δ on the surface of the forming parts are presented when R=100mm.
(a)
Theα−ε curves of different layer thicknesses
(b)
Theα−δ curves of different layer thicknessesAccording to Figure7, the larger the h value is, the greater the ε value and δ value on the surface of moulded parts is, and the more severe the “Step Effect” is when the α is constant, in view of α being a fixed value in the forming process. Thus, h should be taken as small as possible in the selection. At the same time, the selection of h is also limited by the nozzle diameter and forming efficiency of the rapid prototyping machine. Since the nozzle diameter of the BOX 3D rapid prototyping machine is 0.4 mm, the upper limit should be less than 0.4 mm to first determine the thickness of the layer; in order to reduce the influence of the “Step Effect” on the surface of the model, the layer thickness of 0.2 mm is selected next. In addition, according to Figure 6, an increase in the ε value and δ value of the forming parts’ surface can also be obtained with the increase of the α value when the value of h is fixed. During the time when the value of α is zero, the “Step Effect” is at its minimum, while the “Step Effect” is at its largest when the value of α is ninety. As for the complex-shaped master mould of the spur face gear, there are many different shapes of the surface in the mould, so it is impossible to keep the forming direction of each mould surface at 0° with a high forming quality. For the sake of ensuring the quality of each critical surface involved in the wax injection process, it is necessary to minimize the forming direction α of this surface part. According to Figure 2, the surfaces of 4, 6, 8, 10, and 17 are critical surfaces, and the forming direction of the corresponding forming parts is shown in Figure 8.Figure 8
Selection of the forming direction for the spur face gear master mould.
(a)
The forming direction of the bottom die
(b)
The forming direction of the top die
(c)
The forming direction of the centre-locating shaft
(d)
The forming direction of the core


#### 3.2.2. Selection of Extrusion Speed and Filling Speed

Extrusion speed refers to the speed at which the forming material is extruded from the nozzle. Filling speed refers to the movement speed of the extruded wire to fill the filling trajectory. The amount of wire extruded from the nozzle in unit time will be much smaller than the amount of consumable material when the filling speed is much greater than the extrusion speed, which shall lead to the phenomenon of broken wires and parts difficult to form. The amount of wire extruded from the nozzle in unit time will be much larger than the amount of consumable material when the filling speed is much less than the extrusion speed, which will cause the excess molten wire to pile up on the sprinkler head that leads to each layer material distributed unevenly during forming, thus affecting the production quality [24]. To avoid the above problems, the amount of wire extruded from the nozzle during unit time shall be equal to the amount of consumable material used when filling, that is
(4)vj×S1=vt×S2,where vj is the extrusion speed, vt is the filling speed, S1 is the section area of the sprinkler head, and S2 is the cross-sectional area of the wire in the process of filling. Since the shape of the nozzle cross section is approximately circular, thus
(5)S1=π×d22,where d refers to the diameter of the sprinkler head.In the process of extrusion, the cross section of the wire is similar to that of the rectangular section due to the squeezing between layers and layers (as shown in Figure9), and the sectional area S2 is as follows:
(6)S2=h×p,where p is the equivalent width of the filling wire section, which is slightly smaller than the actual width, and h refers to layer thickness.Figure 9
Cross section of the wire at filling.Since the rapid prototyping machine controls the layer thickness by varying the screw speed, there is a corresponding relationship between them. In order to facilitate the study, it is assumed that the correspondence between them is a linear relation, and the linear regression equationh=a′+b′s of h with respect to s is solved by using maximum likelihood estimation. Then, the linear regression equation is solved in conjunction with (4), (5), and (6). So an expression between the speed of extrusion vj and the filling speed vt is concluded as follows:
(7)vj=4hb′vtπd2×s−4ha′vtπd2.In this paper, we took a cuboid of 10 mm × 5 mm × 5 mm as an example. The linear regression equation between the layer thicknessh and the screw speed s of the BOX 3D rapid prototyping machine is h=−0.22+0.004s based on the different screw speeds that are shown in Table 5. When the filling speed vt is selected, the document points out that the high filling speed will lead to less fluctuation stress during the forming process; the low filling speed will lead to a greater fluctuation of stress during the forming process, which will further cause fatigue effect and deformation of parts. Therefore, we determined that the filling speed vt is 60 mm/s in this paper and the corresponding extrusion speed is 61.1 mm/s.Table 5
The layer thickness measurement results of different screw speeds.
Screw speeds
100
110
120
130
140
150
160
170
180
190
200
Layer thicknessh (mm)
0.18
0.22
0.26
0.30
0.34
0.38
0.42
0.46
0.50
0.54
0.58


#### 3.2.3. Selection of Nozzle Temperature and Ambient Temperature

Nozzle temperature refers to the temperature when the nozzle is heated, which determines the bonding property, accumulation performance, and flow capacity of the extruded wire; ambient temperature refers to the forming box temperature during the operation of the rapid prototyping machine, which determines the internal stress of the forming parts. The extruded wire will change from a molten state to a liquid with a small cohesion coefficient and high fluidity; when the nozzle temperature is too high, the next layer of wire material is piled up on the previous contour even if the shape has not been cooled and moulded, leading to the collapse and destruction of the previous layer and making it difficult to form the parts. When the nozzle temperature is too low, the extruded wire is in a semimolten state with a large cohesion coefficient and poor fluidity, which causes it not only to jam easily during extrusion, but also to crack between the lamellae. Furthermore, the overall strength of the formed parts is low because the temperature of the extruded wire is low and the bonding force between the layers and the filler material is very small. For ambient temperature, a high ambient temperature will help reduce the internal stress of the forming, but the surface of the forming parts is prone to wrinkling. The cooling speed of the extruded wire will be accelerated during the forming process if the ambient temperature is too low, and then the phenomenon of bonding and buckling of all the layers will occur as reported in [25]. Consequently, it is important to discuss the influence of different nozzle temperatures and ambient temperatures particularly on the quality of the moulded parts. Based on the large number of forming experiments performed on the 10 mm × 5 mm × 5 mm cuboid sample, the reasonable ambient temperature range at different nozzle temperatures is obtained (as shown in Figure 10). Meanwhile, the nozzle temperature and ambient temperature of the spur face gear master mould are 230°C and 60°C, respectively (Table 6).Figure 10
The reasonable ambient temperature range of different nozzle temperatures.Table 6
Layered slice processing results of each model for spur face gear master mould.
Spur face gear master mould
Layer number of forming (layers)
Forming time
Consumption of ABS materials (g)
Centre-locating shaft
385
9 h 10 min
60
Core
305
11 h 6 min
238
Bottom die
150
6 h 40 min
92
Top die
219
8 h 23 min
136


#### 3.2.4. Compensation Design of the Ideal Contour

The forming wire is extruded with a certain width when forming parts are produced by using the FDM rapid prototyping technology, and there is a distance between the actual contour line and the theoretical contour line when the nozzle is filled (as shown in Figure11). The width of extruded forming wire is a variable due to the influence of extrusion speed, filling speed, layer thickness, and nozzle diameter, so it is necessary to establish a cross-sectional model of the extruded wire [26] (as shown in Figure 12), so as to make clear the quantitative relationship between the extrusion width W and the technological parameters, in order to lay a theoretical foundation for the next step of postprocessing.
(1)
The section of the extrusion wire can be simplified as area III in Figure12 (i.e., the rectangular BCEF) when the extrusion speed is small and the corresponding extrusion wire width W is as follows:
(8)W=B=πd24hvjvt.
(2)
The section of the extrusion wire can be composed of areas I, II, and III in Figure12 when the extrusion speed is large, and the corresponding extrusion wire width W is as follows:
(9)W=B+2ΔB=B+2×h22B=B2+h2B,where B=λ2−h2/2λ, λ=πd2/2hvj/vt, vj is the extrusion speed, d is the nozzle diameter, B is the width of the rectangular BCEF in area III, h is the layer thickness, and vt is the filling speed.Figure 11
The error caused by the width of the extrusion wire.Figure 12
The sectional model of the extruded wire.According to Section3.2.2, the extrusion speed vj is 61.1 mm/s, which belongs to a situation when the speed of extrusion is greater. Thus, the width of the nozzle extrusion wire under the above process parameters is calculated as 0.68 mm in (9); that is, the actual dimension of the formed master mould is more than 0.68 mm of the theoretical size.


#### 3.2.5. Rapid Prototyping of Spur Face Gear Master Mould

Based on the above discussion and analysis of seven important technological parameters that affect forming quality and forming efficiency in FDM rapid prototyping, each process parameter of the rapid prototyping spur face gear master mould is based on the settings by the BOX 3D rapid prototyping machine operation software, and each slice of the master model is processed by slicing in accordance with the subsequent set of forming process parameters, while the slicing results of each model and the corresponding G code for controlling the RP machine are obtained (as shown in Figure13). Finally, the centre-locating shaft, core, bottom die, and top die are rapidly moulded by using this G code and the forming parts of the master mould for the spur face gear is obtained (as shown in Figure 14).Figure 13
The results of the stratified slice processing for the spur face gear model.
(a)
G code for the rapid prototyping of the core
(b)
G code for the rapid prototyping of the top die
(c)
G code for the rapid prototyping of the bottom die
(d)
G code for the rapid prototyping of the centre-locating shaftFigure 14
The parts forming the spur face gear master mould.


### 3.3. Analysis of Process Parameters of Spur Face Gear Master Mould in the Reprocessing Stage of Rapid Prototyping

In view of the characteristics of the FDM rapid prototyping technology, it is necessary to carry out the supporting, sanding, and polishing process for the formed parts in sequence. However, the model selected in this paper does not generate any external support structures during the forming process. Therefore, only sanding and polishing are performed here. First of all, the purpose of the sanding process is to compensate for the errors caused by the extrusion nozzle wire width and to eliminate the “Step Effect” of each formed parts so as to meet the assembling accuracy requirements [27, 28]. Secondly, in order to further improve the surface roughness and smoothness of the polished parts, mechanical polishing is used to polish the surface of the forming parts. Finally, the final postprocessing results are shown in Table 7 according to the postprocessing process shown in Figure 15.Table 7
The final postprocessing results of the spur face gear master mould.
Measurement object (critical surface)
Theoretical value
Actual measurement value
Error
Roughness
4
Diameter of the cylindrical die cavity
137.700 mm
137.610 mm
0.090 mm
Ra=0.007μm
Height of the cylindrical die cavity
30.000 mm
30.111 mm
0.111 mm
6
Surface of the reflexive mould of the spur face gear
—
—
0.083 mm
Ra=0.01μm
Inner diameter of the reflexive mould of the spur face gear
117.402 mm
117.460 mm
0.058 mm
External diameter of the reflexive mould of the spur face gear
137.40 mm
137.482 mm
0.082 mm
Height of the reflexive mould of the spur face gear
8.886 mm
8.956 mm
0.070 mm
8 cores
Inner diameter of the keyway pouring cavity
65.888 mm
65.852 mm
0.036 mm
Outer diameter of the keyway pouring cavity
81.600 mm
81.526 mm
0.074 mm
Height of the keyway pouring cavity
3.061 mm
3.152 mm
0.091 mm
8 top dies
Inner diameter of the keyway pouring cavity
65.988 mm
65.900 mm
0.088 mm
External diameter of the keyway pouring cavity
81.600 mm
81.520 mm
0.080 mm
Height of the keyway pouring cavity
3.061 mm
3.138 mm
0.077 mm
10
External diameter of the centre-locating shaft
65.688 mm
65.750 mm
0.062 mm
Ra=0.0075μm
17
Diameter of the cylindrical groove
158.000 mm
158.181 mm
0.181 mm
Ra=0.01μm
Height of the cylindrical groove
2.000 mm
2.069 mm
0.069 mm
1
Length of the square base
197.700 mm
198.022 mm
0.322 mm
Ra=0.007μm
Height of the square base
28.000 mm
28.245 mm
0.245 mm
5
Outer diameter of the cylindrical boss
157.700 mm
158.067 mm
0.121 mm
Height of the cylindrical boss
30.000 mm
30.192 mm
0.192 mm
7
Diameter of the cylindrical base
169.700 mm
170.043 mm
0.343 mm
Ra=0.01μm
Height of the cylindrical base
14.000 mm
14.247 mm
0.247 mm
9
Diameter of the centre-locating hole
65.888 mm
65. 781 mm
0.107 mm
Height of the centre-locating hole
36.860 mm
36.973 mm
0.113 mm
11
Length of the square base
197.700 mm
197.950 mm
0.250 mm
Height of the square base
35.060 mm
35.233 mm
0.173 mm
13
Height of the centre-locating hole
30.000 mm
30.312 mm
0.312 mmFigure 15
The postprocessing flow chart for the spur face gear master mould.As it is shown in Table5, the dimension accuracy of the master mould critical surface ranges from 0.036 mm to 0.181 mm, the dimension accuracy of the noncritical surface ranges from 0.107 mm to 0.343 mm, and the surface roughness of the master mould is within the range of 0.007–0.01 μm. Thus, the forming parts of the spur face gear master mould have a higher quality precision and surface smoothness.


## 3.1. Analysis of Process Parameters of Spur Face Gear Master Mould in the Preprocessing Stage of Rapid Prototyping

Firstly, before adopting the FDM rapid prototyping technology to produce the master mould of the spur face gear, some factors need to be considered; for example, ABS is a thermoplastic material that causes the dimensions of the forming parts to shrink during the forming process and the shrinkage of each forming part is carried out in different directions [17]. Thus, there are some relationships between the size shrinkage of each forming part SL, the corresponding 3D model size LCAD, and the actual size of the moulded part L that are shown in Figure 3.
(1)SL=LCAD−LLCAD,where LCAD is the three-dimensional model of the spur face gear master mould and L is the actual part of spur face gear master mould.Figure 3
Sketch of rapid prototyping shrinkage for the spur face gear master mould.Therefore, according to (1), the shrinkage percentage of each mould part can be calculated through a rapid prototyping test (as shown in Table 2). Furthermore, according to the shrinkage percentage of each mould part shown in Table 2, the original 3D model of the spur face gear master mould is enlarged by using UG software.Table 2
The shrinkage percentage of each spur face gear master mould.
Core
Cylindrical base
Reflexive mould of spur face gear
Pouring cavity of keyway
Centre-locating hole of core
Centre-locating shaft
1.12%
0.22%
0.35%
0.51%
0.64%
Bottom die
Square base
Cylindrical boss
1.46%
0.19%
Top die
Square base
Cylindrical groove
Pouring cavity of keyway
Centre-locating hole of core
1.41%
0.10%
0.41%
0.57%Secondly, the three-dimensional model of the enlarged spur face gear master mould is used for the extraction of the shell. Because of proper shell disposal, the manufacturing cost can be reduced and the forming speed can be improved on the basis of not affecting the original performance of the master mould (including the high temperature performance, strength, and hardness). Furthermore, the distortion and cracking of the mould surface can also be prevented. In order to determine the influence of different shell thicknesses on the quality and performance of the mould parts, simulation experiments of shell extraction and wax injection are carried out for 6 different shell thicknesses in Figure3 by adopting the control variety method. According to the experimental results shown in Table 3, a reasonable shell thickness of 0.8 mm is selected for the master mould taking into account both forming efficiency and manufacturing cost.Table 3
Setting of the shell thickness.
Sequence number
1
2
3
4
5
6
Shell thickness (mm)
1.0
0.9
0.8
0.7
0.6
0.5
Experimental result
Normal
Normal
Normal
Warp and distortion
Warp and distortion seriously
DeformationThe model data of the master mould must be converted into the data format that can be recognized by the RP equipment after finishing the optimization of the 3D model of the spur face gear master mould, because the forming process parameters are set up on the basis of the imported model data. The mainstream data format that can be identified by the current rapid prototyping machine is STL [18, 19]. The essence of the STL data format is to use hundreds of tiny triangular patches to replace a curved surface, thus reconstructing the original 3D model. The error of the STL model is controlled by the chord deviation H (as shown in Figure 4). If you get the high precision STL model by increasing the number of triangles, it will not only exceed the maximum forming accuracy that FDM can achieve, but it will also increase the data storage during the STL model data slicing process. Therefore, it is important to find a balance point between forming precision and forming efficiency.Figure 4
Effect of different chord deviations on the accuracy of the STL model.
(a)
The fitting precision of model is low when the chord deviation is larger
(b)
The fitting precision of the model is high when the chord deviation is smallerAt present, the most optimized parameter setting method for converting the STL model by using UG software is shown in Table4, and by this method, the STL model of the spur face gear master mould can be obtained (as shown in Figure 5).Table 4
The most optimized parameter setting method for converting the STL model.
UG(1) File → export → STL → the setting type is binary(2) The triangle tolerance is 0.0025(3) The adjacent tolerance is 0.12(4) Open automatic normal generation(5) Close normal indication(6) Open triangle indicationFigure 5
The STL model of the spur face gear master mould.


## 3.2. Analysis of Forming Process Parameters of Spur Face Gear Master Mould in the Processing Stage of Rapid Prototyping

Although many factors have more or less influence on forming efficiency and forming quality (including dimensional accuracy and surface roughness) in the FDM rapid prototyping process, it is mainly controlled by seven important technological parameters, which are the thickness of the layer and the forming direction, the extrusion speed and filling speed, the nozzle temperature and the ambient temperature, and the compensation of the ideal contour line [20–22].


### 3.2.1. Selection of Layer Thickness and Forming Direction

The layer thickness is the slice thickness of the three-dimensional model, and it is also the manufacturing height of each layer of the FDM rapid prototyping machine for laminated object manufacturing. The forming direction refers to the spatial arrangement of forming parts in the forming process. Since the manufacturing method of the FDM rapid prototyping technology is superimposed layer by layer, the contour of each slice is inconsistent and has a certain thickness during formation [23]. As a result, the surface of the moulded parts often exhibits a “Step Effect” (as shown in Figure 6), which would further affect the quality of the moulded parts. At present, the technical indexes of the “Step Effect” in the FDM rapid prototyping process are mainly ε and δ, where ε reflects the shape error of the moulded part, and δ reflects the roughness of the moulded part. According to the geometric relationship shown in Figure 6, the relation between the layer thickness h and forming direction α, ε, and δ can be concluded, respectively.
(2)ε=Rcosα−1−sinα+hR2,(3)δ=R1−1−2hsinαR−hR2.Figure 6
The local schematic of the “Step Effect” for forming parts.To investigate the influence of different slice heights and forming directions on the surface of the moulded partsε and δ, taking the hemisphere model of R = 100 mm as an example, the corresponding relation curve is plotted by Matlab in accordance with (2) and (3) (as shown in Figure 7).Figure 7
The relation curves ofα−ε and α−δ on the surface of the forming parts are presented when R=100mm.
(a)
Theα−ε curves of different layer thicknesses
(b)
Theα−δ curves of different layer thicknessesAccording to Figure7, the larger the h value is, the greater the ε value and δ value on the surface of moulded parts is, and the more severe the “Step Effect” is when the α is constant, in view of α being a fixed value in the forming process. Thus, h should be taken as small as possible in the selection. At the same time, the selection of h is also limited by the nozzle diameter and forming efficiency of the rapid prototyping machine. Since the nozzle diameter of the BOX 3D rapid prototyping machine is 0.4 mm, the upper limit should be less than 0.4 mm to first determine the thickness of the layer; in order to reduce the influence of the “Step Effect” on the surface of the model, the layer thickness of 0.2 mm is selected next. In addition, according to Figure 6, an increase in the ε value and δ value of the forming parts’ surface can also be obtained with the increase of the α value when the value of h is fixed. During the time when the value of α is zero, the “Step Effect” is at its minimum, while the “Step Effect” is at its largest when the value of α is ninety. As for the complex-shaped master mould of the spur face gear, there are many different shapes of the surface in the mould, so it is impossible to keep the forming direction of each mould surface at 0° with a high forming quality. For the sake of ensuring the quality of each critical surface involved in the wax injection process, it is necessary to minimize the forming direction α of this surface part. According to Figure 2, the surfaces of 4, 6, 8, 10, and 17 are critical surfaces, and the forming direction of the corresponding forming parts is shown in Figure 8.Figure 8
Selection of the forming direction for the spur face gear master mould.
(a)
The forming direction of the bottom die
(b)
The forming direction of the top die
(c)
The forming direction of the centre-locating shaft
(d)
The forming direction of the core


### 3.2.2. Selection of Extrusion Speed and Filling Speed

Extrusion speed refers to the speed at which the forming material is extruded from the nozzle. Filling speed refers to the movement speed of the extruded wire to fill the filling trajectory. The amount of wire extruded from the nozzle in unit time will be much smaller than the amount of consumable material when the filling speed is much greater than the extrusion speed, which shall lead to the phenomenon of broken wires and parts difficult to form. The amount of wire extruded from the nozzle in unit time will be much larger than the amount of consumable material when the filling speed is much less than the extrusion speed, which will cause the excess molten wire to pile up on the sprinkler head that leads to each layer material distributed unevenly during forming, thus affecting the production quality [24]. To avoid the above problems, the amount of wire extruded from the nozzle during unit time shall be equal to the amount of consumable material used when filling, that is
(4)vj×S1=vt×S2,where vj is the extrusion speed, vt is the filling speed, S1 is the section area of the sprinkler head, and S2 is the cross-sectional area of the wire in the process of filling. Since the shape of the nozzle cross section is approximately circular, thus
(5)S1=π×d22,where d refers to the diameter of the sprinkler head.In the process of extrusion, the cross section of the wire is similar to that of the rectangular section due to the squeezing between layers and layers (as shown in Figure9), and the sectional area S2 is as follows:
(6)S2=h×p,where p is the equivalent width of the filling wire section, which is slightly smaller than the actual width, and h refers to layer thickness.Figure 9
Cross section of the wire at filling.Since the rapid prototyping machine controls the layer thickness by varying the screw speed, there is a corresponding relationship between them. In order to facilitate the study, it is assumed that the correspondence between them is a linear relation, and the linear regression equationh=a′+b′s of h with respect to s is solved by using maximum likelihood estimation. Then, the linear regression equation is solved in conjunction with (4), (5), and (6). So an expression between the speed of extrusion vj and the filling speed vt is concluded as follows:
(7)vj=4hb′vtπd2×s−4ha′vtπd2.In this paper, we took a cuboid of 10 mm × 5 mm × 5 mm as an example. The linear regression equation between the layer thicknessh and the screw speed s of the BOX 3D rapid prototyping machine is h=−0.22+0.004s based on the different screw speeds that are shown in Table 5. When the filling speed vt is selected, the document points out that the high filling speed will lead to less fluctuation stress during the forming process; the low filling speed will lead to a greater fluctuation of stress during the forming process, which will further cause fatigue effect and deformation of parts. Therefore, we determined that the filling speed vt is 60 mm/s in this paper and the corresponding extrusion speed is 61.1 mm/s.Table 5
The layer thickness measurement results of different screw speeds.
Screw speeds
100
110
120
130
140
150
160
170
180
190
200
Layer thicknessh (mm)
0.18
0.22
0.26
0.30
0.34
0.38
0.42
0.46
0.50
0.54
0.58


### 3.2.3. Selection of Nozzle Temperature and Ambient Temperature

Nozzle temperature refers to the temperature when the nozzle is heated, which determines the bonding property, accumulation performance, and flow capacity of the extruded wire; ambient temperature refers to the forming box temperature during the operation of the rapid prototyping machine, which determines the internal stress of the forming parts. The extruded wire will change from a molten state to a liquid with a small cohesion coefficient and high fluidity; when the nozzle temperature is too high, the next layer of wire material is piled up on the previous contour even if the shape has not been cooled and moulded, leading to the collapse and destruction of the previous layer and making it difficult to form the parts. When the nozzle temperature is too low, the extruded wire is in a semimolten state with a large cohesion coefficient and poor fluidity, which causes it not only to jam easily during extrusion, but also to crack between the lamellae. Furthermore, the overall strength of the formed parts is low because the temperature of the extruded wire is low and the bonding force between the layers and the filler material is very small. For ambient temperature, a high ambient temperature will help reduce the internal stress of the forming, but the surface of the forming parts is prone to wrinkling. The cooling speed of the extruded wire will be accelerated during the forming process if the ambient temperature is too low, and then the phenomenon of bonding and buckling of all the layers will occur as reported in [25]. Consequently, it is important to discuss the influence of different nozzle temperatures and ambient temperatures particularly on the quality of the moulded parts. Based on the large number of forming experiments performed on the 10 mm × 5 mm × 5 mm cuboid sample, the reasonable ambient temperature range at different nozzle temperatures is obtained (as shown in Figure 10). Meanwhile, the nozzle temperature and ambient temperature of the spur face gear master mould are 230°C and 60°C, respectively (Table 6).Figure 10
The reasonable ambient temperature range of different nozzle temperatures.Table 6
Layered slice processing results of each model for spur face gear master mould.
Spur face gear master mould
Layer number of forming (layers)
Forming time
Consumption of ABS materials (g)
Centre-locating shaft
385
9 h 10 min
60
Core
305
11 h 6 min
238
Bottom die
150
6 h 40 min
92
Top die
219
8 h 23 min
136


### 3.2.4. Compensation Design of the Ideal Contour

The forming wire is extruded with a certain width when forming parts are produced by using the FDM rapid prototyping technology, and there is a distance between the actual contour line and the theoretical contour line when the nozzle is filled (as shown in Figure11). The width of extruded forming wire is a variable due to the influence of extrusion speed, filling speed, layer thickness, and nozzle diameter, so it is necessary to establish a cross-sectional model of the extruded wire [26] (as shown in Figure 12), so as to make clear the quantitative relationship between the extrusion width W and the technological parameters, in order to lay a theoretical foundation for the next step of postprocessing.
(1)
The section of the extrusion wire can be simplified as area III in Figure12 (i.e., the rectangular BCEF) when the extrusion speed is small and the corresponding extrusion wire width W is as follows:
(8)W=B=πd24hvjvt.
(2)
The section of the extrusion wire can be composed of areas I, II, and III in Figure12 when the extrusion speed is large, and the corresponding extrusion wire width W is as follows:
(9)W=B+2ΔB=B+2×h22B=B2+h2B,where B=λ2−h2/2λ, λ=πd2/2hvj/vt, vj is the extrusion speed, d is the nozzle diameter, B is the width of the rectangular BCEF in area III, h is the layer thickness, and vt is the filling speed.Figure 11
The error caused by the width of the extrusion wire.Figure 12
The sectional model of the extruded wire.According to Section3.2.2, the extrusion speed vj is 61.1 mm/s, which belongs to a situation when the speed of extrusion is greater. Thus, the width of the nozzle extrusion wire under the above process parameters is calculated as 0.68 mm in (9); that is, the actual dimension of the formed master mould is more than 0.68 mm of the theoretical size.


### 3.2.5. Rapid Prototyping of Spur Face Gear Master Mould

Based on the above discussion and analysis of seven important technological parameters that affect forming quality and forming efficiency in FDM rapid prototyping, each process parameter of the rapid prototyping spur face gear master mould is based on the settings by the BOX 3D rapid prototyping machine operation software, and each slice of the master model is processed by slicing in accordance with the subsequent set of forming process parameters, while the slicing results of each model and the corresponding G code for controlling the RP machine are obtained (as shown in Figure13). Finally, the centre-locating shaft, core, bottom die, and top die are rapidly moulded by using this G code and the forming parts of the master mould for the spur face gear is obtained (as shown in Figure 14).Figure 13
The results of the stratified slice processing for the spur face gear model.
(a)
G code for the rapid prototyping of the core
(b)
G code for the rapid prototyping of the top die
(c)
G code for the rapid prototyping of the bottom die
(d)
G code for the rapid prototyping of the centre-locating shaftFigure 14
The parts forming the spur face gear master mould.


## 3.2.1. Selection of Layer Thickness and Forming Direction

The layer thickness is the slice thickness of the three-dimensional model, and it is also the manufacturing height of each layer of the FDM rapid prototyping machine for laminated object manufacturing. The forming direction refers to the spatial arrangement of forming parts in the forming process. Since the manufacturing method of the FDM rapid prototyping technology is superimposed layer by layer, the contour of each slice is inconsistent and has a certain thickness during formation [23]. As a result, the surface of the moulded parts often exhibits a “Step Effect” (as shown in Figure 6), which would further affect the quality of the moulded parts. At present, the technical indexes of the “Step Effect” in the FDM rapid prototyping process are mainly ε and δ, where ε reflects the shape error of the moulded part, and δ reflects the roughness of the moulded part. According to the geometric relationship shown in Figure 6, the relation between the layer thickness h and forming direction α, ε, and δ can be concluded, respectively.
(2)ε=Rcosα−1−sinα+hR2,(3)δ=R1−1−2hsinαR−hR2.Figure 6
The local schematic of the “Step Effect” for forming parts.To investigate the influence of different slice heights and forming directions on the surface of the moulded partsε and δ, taking the hemisphere model of R = 100 mm as an example, the corresponding relation curve is plotted by Matlab in accordance with (2) and (3) (as shown in Figure 7).Figure 7
The relation curves ofα−ε and α−δ on the surface of the forming parts are presented when R=100mm.
(a)
Theα−ε curves of different layer thicknesses
(b)
Theα−δ curves of different layer thicknessesAccording to Figure7, the larger the h value is, the greater the ε value and δ value on the surface of moulded parts is, and the more severe the “Step Effect” is when the α is constant, in view of α being a fixed value in the forming process. Thus, h should be taken as small as possible in the selection. At the same time, the selection of h is also limited by the nozzle diameter and forming efficiency of the rapid prototyping machine. Since the nozzle diameter of the BOX 3D rapid prototyping machine is 0.4 mm, the upper limit should be less than 0.4 mm to first determine the thickness of the layer; in order to reduce the influence of the “Step Effect” on the surface of the model, the layer thickness of 0.2 mm is selected next. In addition, according to Figure 6, an increase in the ε value and δ value of the forming parts’ surface can also be obtained with the increase of the α value when the value of h is fixed. During the time when the value of α is zero, the “Step Effect” is at its minimum, while the “Step Effect” is at its largest when the value of α is ninety. As for the complex-shaped master mould of the spur face gear, there are many different shapes of the surface in the mould, so it is impossible to keep the forming direction of each mould surface at 0° with a high forming quality. For the sake of ensuring the quality of each critical surface involved in the wax injection process, it is necessary to minimize the forming direction α of this surface part. According to Figure 2, the surfaces of 4, 6, 8, 10, and 17 are critical surfaces, and the forming direction of the corresponding forming parts is shown in Figure 8.Figure 8
Selection of the forming direction for the spur face gear master mould.
(a)
The forming direction of the bottom die
(b)
The forming direction of the top die
(c)
The forming direction of the centre-locating shaft
(d)
The forming direction of the core


## 3.2.2. Selection of Extrusion Speed and Filling Speed

Extrusion speed refers to the speed at which the forming material is extruded from the nozzle. Filling speed refers to the movement speed of the extruded wire to fill the filling trajectory. The amount of wire extruded from the nozzle in unit time will be much smaller than the amount of consumable material when the filling speed is much greater than the extrusion speed, which shall lead to the phenomenon of broken wires and parts difficult to form. The amount of wire extruded from the nozzle in unit time will be much larger than the amount of consumable material when the filling speed is much less than the extrusion speed, which will cause the excess molten wire to pile up on the sprinkler head that leads to each layer material distributed unevenly during forming, thus affecting the production quality [24]. To avoid the above problems, the amount of wire extruded from the nozzle during unit time shall be equal to the amount of consumable material used when filling, that is
(4)vj×S1=vt×S2,where vj is the extrusion speed, vt is the filling speed, S1 is the section area of the sprinkler head, and S2 is the cross-sectional area of the wire in the process of filling. Since the shape of the nozzle cross section is approximately circular, thus
(5)S1=π×d22,where d refers to the diameter of the sprinkler head.In the process of extrusion, the cross section of the wire is similar to that of the rectangular section due to the squeezing between layers and layers (as shown in Figure9), and the sectional area S2 is as follows:
(6)S2=h×p,where p is the equivalent width of the filling wire section, which is slightly smaller than the actual width, and h refers to layer thickness.Figure 9
Cross section of the wire at filling.Since the rapid prototyping machine controls the layer thickness by varying the screw speed, there is a corresponding relationship between them. In order to facilitate the study, it is assumed that the correspondence between them is a linear relation, and the linear regression equationh=a′+b′s of h with respect to s is solved by using maximum likelihood estimation. Then, the linear regression equation is solved in conjunction with (4), (5), and (6). So an expression between the speed of extrusion vj and the filling speed vt is concluded as follows:
(7)vj=4hb′vtπd2×s−4ha′vtπd2.In this paper, we took a cuboid of 10 mm × 5 mm × 5 mm as an example. The linear regression equation between the layer thicknessh and the screw speed s of the BOX 3D rapid prototyping machine is h=−0.22+0.004s based on the different screw speeds that are shown in Table 5. When the filling speed vt is selected, the document points out that the high filling speed will lead to less fluctuation stress during the forming process; the low filling speed will lead to a greater fluctuation of stress during the forming process, which will further cause fatigue effect and deformation of parts. Therefore, we determined that the filling speed vt is 60 mm/s in this paper and the corresponding extrusion speed is 61.1 mm/s.Table 5
The layer thickness measurement results of different screw speeds.
Screw speeds
100
110
120
130
140
150
160
170
180
190
200
Layer thicknessh (mm)
0.18
0.22
0.26
0.30
0.34
0.38
0.42
0.46
0.50
0.54
0.58


## 3.2.3. Selection of Nozzle Temperature and Ambient Temperature

Nozzle temperature refers to the temperature when the nozzle is heated, which determines the bonding property, accumulation performance, and flow capacity of the extruded wire; ambient temperature refers to the forming box temperature during the operation of the rapid prototyping machine, which determines the internal stress of the forming parts. The extruded wire will change from a molten state to a liquid with a small cohesion coefficient and high fluidity; when the nozzle temperature is too high, the next layer of wire material is piled up on the previous contour even if the shape has not been cooled and moulded, leading to the collapse and destruction of the previous layer and making it difficult to form the parts. When the nozzle temperature is too low, the extruded wire is in a semimolten state with a large cohesion coefficient and poor fluidity, which causes it not only to jam easily during extrusion, but also to crack between the lamellae. Furthermore, the overall strength of the formed parts is low because the temperature of the extruded wire is low and the bonding force between the layers and the filler material is very small. For ambient temperature, a high ambient temperature will help reduce the internal stress of the forming, but the surface of the forming parts is prone to wrinkling. The cooling speed of the extruded wire will be accelerated during the forming process if the ambient temperature is too low, and then the phenomenon of bonding and buckling of all the layers will occur as reported in [25]. Consequently, it is important to discuss the influence of different nozzle temperatures and ambient temperatures particularly on the quality of the moulded parts. Based on the large number of forming experiments performed on the 10 mm × 5 mm × 5 mm cuboid sample, the reasonable ambient temperature range at different nozzle temperatures is obtained (as shown in Figure 10). Meanwhile, the nozzle temperature and ambient temperature of the spur face gear master mould are 230°C and 60°C, respectively (Table 6).Figure 10
The reasonable ambient temperature range of different nozzle temperatures.Table 6
Layered slice processing results of each model for spur face gear master mould.
Spur face gear master mould
Layer number of forming (layers)
Forming time
Consumption of ABS materials (g)
Centre-locating shaft
385
9 h 10 min
60
Core
305
11 h 6 min
238
Bottom die
150
6 h 40 min
92
Top die
219
8 h 23 min
136


## 3.2.4. Compensation Design of the Ideal Contour

The forming wire is extruded with a certain width when forming parts are produced by using the FDM rapid prototyping technology, and there is a distance between the actual contour line and the theoretical contour line when the nozzle is filled (as shown in Figure11). The width of extruded forming wire is a variable due to the influence of extrusion speed, filling speed, layer thickness, and nozzle diameter, so it is necessary to establish a cross-sectional model of the extruded wire [26] (as shown in Figure 12), so as to make clear the quantitative relationship between the extrusion width W and the technological parameters, in order to lay a theoretical foundation for the next step of postprocessing.
(1)
The section of the extrusion wire can be simplified as area III in Figure12 (i.e., the rectangular BCEF) when the extrusion speed is small and the corresponding extrusion wire width W is as follows:
(8)W=B=πd24hvjvt.
(2)
The section of the extrusion wire can be composed of areas I, II, and III in Figure12 when the extrusion speed is large, and the corresponding extrusion wire width W is as follows:
(9)W=B+2ΔB=B+2×h22B=B2+h2B,where B=λ2−h2/2λ, λ=πd2/2hvj/vt, vj is the extrusion speed, d is the nozzle diameter, B is the width of the rectangular BCEF in area III, h is the layer thickness, and vt is the filling speed.Figure 11
The error caused by the width of the extrusion wire.Figure 12
The sectional model of the extruded wire.According to Section3.2.2, the extrusion speed vj is 61.1 mm/s, which belongs to a situation when the speed of extrusion is greater. Thus, the width of the nozzle extrusion wire under the above process parameters is calculated as 0.68 mm in (9); that is, the actual dimension of the formed master mould is more than 0.68 mm of the theoretical size.


## 3.2.5. Rapid Prototyping of Spur Face Gear Master Mould

Based on the above discussion and analysis of seven important technological parameters that affect forming quality and forming efficiency in FDM rapid prototyping, each process parameter of the rapid prototyping spur face gear master mould is based on the settings by the BOX 3D rapid prototyping machine operation software, and each slice of the master model is processed by slicing in accordance with the subsequent set of forming process parameters, while the slicing results of each model and the corresponding G code for controlling the RP machine are obtained (as shown in Figure13). Finally, the centre-locating shaft, core, bottom die, and top die are rapidly moulded by using this G code and the forming parts of the master mould for the spur face gear is obtained (as shown in Figure 14).Figure 13
The results of the stratified slice processing for the spur face gear model.
(a)
G code for the rapid prototyping of the core
(b)
G code for the rapid prototyping of the top die
(c)
G code for the rapid prototyping of the bottom die
(d)
G code for the rapid prototyping of the centre-locating shaftFigure 14
The parts forming the spur face gear master mould.


## 3.3. Analysis of Process Parameters of Spur Face Gear Master Mould in the Reprocessing Stage of Rapid Prototyping

In view of the characteristics of the FDM rapid prototyping technology, it is necessary to carry out the supporting, sanding, and polishing process for the formed parts in sequence. However, the model selected in this paper does not generate any external support structures during the forming process. Therefore, only sanding and polishing are performed here. First of all, the purpose of the sanding process is to compensate for the errors caused by the extrusion nozzle wire width and to eliminate the “Step Effect” of each formed parts so as to meet the assembling accuracy requirements [27, 28]. Secondly, in order to further improve the surface roughness and smoothness of the polished parts, mechanical polishing is used to polish the surface of the forming parts. Finally, the final postprocessing results are shown in Table 7 according to the postprocessing process shown in Figure 15.Table 7
The final postprocessing results of the spur face gear master mould.
Measurement object (critical surface)
Theoretical value
Actual measurement value
Error
Roughness
4
Diameter of the cylindrical die cavity
137.700 mm
137.610 mm
0.090 mm
Ra=0.007μm
Height of the cylindrical die cavity
30.000 mm
30.111 mm
0.111 mm
6
Surface of the reflexive mould of the spur face gear
—
—
0.083 mm
Ra=0.01μm
Inner diameter of the reflexive mould of the spur face gear
117.402 mm
117.460 mm
0.058 mm
External diameter of the reflexive mould of the spur face gear
137.40 mm
137.482 mm
0.082 mm
Height of the reflexive mould of the spur face gear
8.886 mm
8.956 mm
0.070 mm
8 cores
Inner diameter of the keyway pouring cavity
65.888 mm
65.852 mm
0.036 mm
Outer diameter of the keyway pouring cavity
81.600 mm
81.526 mm
0.074 mm
Height of the keyway pouring cavity
3.061 mm
3.152 mm
0.091 mm
8 top dies
Inner diameter of the keyway pouring cavity
65.988 mm
65.900 mm
0.088 mm
External diameter of the keyway pouring cavity
81.600 mm
81.520 mm
0.080 mm
Height of the keyway pouring cavity
3.061 mm
3.138 mm
0.077 mm
10
External diameter of the centre-locating shaft
65.688 mm
65.750 mm
0.062 mm
Ra=0.0075μm
17
Diameter of the cylindrical groove
158.000 mm
158.181 mm
0.181 mm
Ra=0.01μm
Height of the cylindrical groove
2.000 mm
2.069 mm
0.069 mm
1
Length of the square base
197.700 mm
198.022 mm
0.322 mm
Ra=0.007μm
Height of the square base
28.000 mm
28.245 mm
0.245 mm
5
Outer diameter of the cylindrical boss
157.700 mm
158.067 mm
0.121 mm
Height of the cylindrical boss
30.000 mm
30.192 mm
0.192 mm
7
Diameter of the cylindrical base
169.700 mm
170.043 mm
0.343 mm
Ra=0.01μm
Height of the cylindrical base
14.000 mm
14.247 mm
0.247 mm
9
Diameter of the centre-locating hole
65.888 mm
65. 781 mm
0.107 mm
Height of the centre-locating hole
36.860 mm
36.973 mm
0.113 mm
11
Length of the square base
197.700 mm
197.950 mm
0.250 mm
Height of the square base
35.060 mm
35.233 mm
0.173 mm
13
Height of the centre-locating hole
30.000 mm
30.312 mm
0.312 mmFigure 15
The postprocessing flow chart for the spur face gear master mould.As it is shown in Table5, the dimension accuracy of the master mould critical surface ranges from 0.036 mm to 0.181 mm, the dimension accuracy of the noncritical surface ranges from 0.107 mm to 0.343 mm, and the surface roughness of the master mould is within the range of 0.007–0.01 μm. Thus, the forming parts of the spur face gear master mould have a higher quality precision and surface smoothness.


## 4. Construction of FDM Rapid Prototyping Process Model for Spur Face Gear Master Mould

In order to establish the mathematical model of the FDM rapid prototyping complex-shaped mould according to the data relationship between the forming parameters and moulding quality in each process stage, this paper adopts the method of stepwise regression analysis. Using theF significance test, the influence of the above process parameters on the forming quality is determined firstly, and then the corresponding mathematical model is solved by combining the linear regression equation. It is found that the quantitative relationship between the forming parameters of rapid prototyping and the forming quality is as follows:
(10)y=ASLb0hb1αb2vtb3Tb4tb5,where y denotes the forming accuracy and A,b0~b5 denotes the regression equation coefficient of the FDM rapid prototyping complex-shaped mould (related to the structure and process of forming parts, etc.)Therefore, using the above big data process parameter model, this paper verifies and compares the spur face gear master mould manufactured by this technology with the traditional milling mould. The results are as shown in Table8.Table 8
Comparison of two processing methods for manufacturing spur face gear master mould.
Processing mode
Processing cycle (days)
Processing cost (dollars)
Forming quality
Machining accuracy (mm)
Machining roughness (μm)
Subtractive material manufacturing
7–10
300
0.02–0.05 mm
<0.01 μm
Additive material manufacturing
1-2
100
0.036 mm–0.181 mm
0.007–0.01 μm


## 5. Conclusion

Based on the FDM rapid prototyping technology of the spur face gear master mould, firstly, the mechanism of the preprocessing of the three-dimensional model of the mould in magnification and shell extraction is studied from the point of view of the material forming characteristics, and combined with the STL model conversion algorithm, the theoretical analysis of the preprocessing is realized. Secondly, from the angle of the forming and spraying mechanism of the forming materials and the quantitative relationship between each forming process parameter and forming quality, the forming efficiency is studied, and the postprocessing technology of the FDM rapid prototyping mould based on this relation is put forward. Finally, according to the measurement results of the workpiece, the reasonableness of big data extraction and mathematical expression in the FDM rapid prototyping process is verified. Thus, it lays a solid theoretical foundation and data guarantee for the construction of the rapid prototyping process system based on cloud manufacturing data management, so that it can better carry on the technology docking.



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*Source: 9432897-2018-11-01.xml*