# Thermosetting Coupling Analysis and Parameter Optimization of the Plastic Lining Pump Structure

Authors: Lingfeng Tang; Mingwei Liu; Feihong Ma
Journal: Advances in Materials Science and Engineering
 (2019)

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## Abstract

In order to obtain the optimum structure of the lining pump under the condition of fluid thermosetting coupling, according to the given design parameters, the structural parameters of the pump were calculated, the three-dimensional geometric model was established, and the flow field analysis was carried out by CFD; the inlet angleβb1, outlet angle βb2, wrap angle φ, inlet diameter D1, and outlet diameter D2 of the impeller were selected as the five factors to design orthogonal experiment, and the results were analyzed by range analysis; then, the efficiency and cavitation allowance were obtained as combined parameters under the evaluation index. The displacement deformation and stress distribution under the condition of the coupling field were obtained by the fluid-solid coupling analysis, and the orthogonal experimental table of the impeller structure of the lining plastic pump was established, and then the orthogonal experimental results are analyzed to obtain the influence of each structural parameter under the condition of each evaluation index and the optimum combination parameters. The influence situation and the best combination parameters under the condition of evaluation index, taking the minimum displacement deformation and minimum stress of impeller as the reference index, and the optimum combination parameters under the condition of minimum displacement and stress were as follows: the inlet diameter D1 was 76 mm, the outlet diameter D2 was 252 mm, the inlet angle was 26°, the outlet angle was 24°, and the wrap angle was 115°. Finally, the 3D printing technology was used to print out the physical model to the hydraulic performance experiment verification.


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## Body

## 1. Introduction

Pumps are widely used and undertake a very important position in the fields such as agriculture and industry. In recent years, with the development of nonferrous metallurgy, the requirements for centrifugal pumps are growing higher [1]. Compared with metal pumps, the lining plastic pump has been widely used for their excellent corrosion resistance; therefore, the study on the lining plastic pump is increasingly important [2, 3]. In the process of conveying medium, the fluid in the pump interacts with the impeller [4, 5]; the lining plastic pump generates thermal stress in the process of pumping hot medium, which causes thermal deformation and the clearance between the impeller and the front pump cover changes [6, 7]. If the clearance is too small, the liquid will cause expansion and deformation of the pump shell; in addition, it will generate friction between the impeller and the front pump cover and aggravates the wear of the impeller due to heat; relatively, if the clearance is too large, there will be backflow between the pump shell and the impeller, thus reducing the volumetric efficiency. At present, when most scholars at home and abroad conducting research [8, 9], the conduction of CFD internal flow field analysis and fluid-thermal-structure interaction on the plastic lined pump has been neglected [10, 11]. In this paper, using CFD to analyze the flow field of the lining plastic pump, through orthogonal experiment and range analysis, it could be concluded that the efficiency and cavitation allowance were taken as the combined parameters under the evaluation index. Taking the minimum displacement deformation and minimum stress of impeller as the reference index, the combined weighted scoring method and Taguchi algorithm were used to optimize the parameters of the thermal-solid coupling analysis of the lining plastic pump flow, and the optimum combination parameters under the condition of minimum displacement and stress were obtained.


## 2. Structure Design

The basic parameters of the lining plastic pump are as follows: flow rateQ = 25°m³/h, head H = 80 m, rotate speed n=2900rpm, inlet diameter of impeller D1 = 75 mm, outlet diameter D2 = 255 mm, width of impeller inlet b1 = 20 mm, outlet width b2 = 7 mm, impeller inlet angle is 25°, outlet angle is 30°, and the wrap angle is 110°. The physical model of impeller and volute-type discharge passage is established and assembled according to the above parameters, which is shown in Figure 1.Figure 1
Fluid domain model.


## 3. Meshing and Flow Field Simulation

### 3.1. Meshing

Meshing is the basis of numerical discretization of flow control equations, and the quality of meshing directly influences the convergence of analysis and the accuracy of results. The grid number of the impeller region was 127,794, the volute region 727,398, and the inlet section 2408, a total of 854,692, as shown in Figure2. The mesh is unstructured, 3D type, the minimum mesh was 0.0001, and the maximum is 0.025.Figure 2
Mesh generation.


### 3.2. Boundary Conditions

The boundary conditions were mainly set as follows: the basic properties of the fluid medium, including the density, temperature, viscosity, vapor density, gas content, saturated vapor pressure, etc. as shown in Table1. In addition to the rotor setting of the impeller blade, the setting of the inlet and outlet of the fluid medium and the setting of the rotating surface were also required.Table 1
Boundary condition setting.
Name of parameter
Parameter values
Fluid medium
Water
Density
998 kg/m3
Reference temperature
300 K
Vapour density
0.0245 kg/m3
Gas content
2.3 × 10−5
Saturated vapor pressure
3610 pa
Bulk modulus
2.15 × 109The pressure here was the standard atmospheric pressure, set to the inlet condition, the flow rate,Q = 25°m3/h, was set to the export condition, the blade as a rotating part was set to a rotating speed of 2900 rpm, and the rest surface could be directly acquiesced to the static surface.


### 3.3. Control Equations

The flow of medium in plastic-lined pump satisfies the following equation:Continuity equation:(1)∂ρμi∂xi=0.Momentum equation:(2)∂ρμiμj∂xj=−∂p∗∂xj+∂μ∂xj/∂μi+∂μj/∂xi∂xj−2εijkkωjμk.Incompressible N-S equation:(3)∂Ui∂t+Uj∂Ui∂xj=fi−1ρ∂p∗∂xi+ϑ∇2Ui.k-ε equation:(4)ρdkdt=∂∂xjμ+μtσk∂k∂xj+Gk−ρε,ρdεdt=∂∂xiμ+μtσε∂k∂xi+ρεC1E−ρC2ε2k+ϑε,μt=ρCμk2ε,where ρ is the fluid density; ρ∗ is the pressure including centrifugal force and turbulent kinetic energy k; ω is the angular velocity; εijk is the tensor; μ is the effective viscosity coefficient; U is the velocity vector; P is the pressure; t is the time; ϑ is the viscosity coefficient of fluid motion; i, j, and k, respectively, are 1, 2, and 3; σk = 1.0; σε = 1.3; Cμ = 0.09; C1 = 1.44; C2 = 1.92.


### 3.4. Flow Field Simulation

There are 1,000 iteration steps for the lining plastic pump, and it can be seen from Figure3 that the curve converged when the number of iterations reached about 500 times.Figure 3
Residual curve.Figure4 shows the pressure distribution of the lining plastic pump, from the inlet of the impeller to its outlet; the pressure value was increasing, and the value near the outlet of the volute was higher than elsewhere, mainly because the flow of the fluid is accompanied by the rotation of the impeller during the conveying process, and the inhomogeneity of its flow made it possible for vortices to appear between the adjacent.Figure 4
Pressure cloud diagram.Figure5 is a speed distribution diagram of the lining plastic pump. As can be observed from Figure 5, the value of velocity was gradually increased from the entrance of the impeller to its outlet. The flow of liquid away from the blades was much less effective than the flow of the liquid at its periphery due to the action of the blades, and there would be swirl along the radial direction away from the middle of the blade, affecting the normal flow of the liquid.Figure 5
Velocity cloud.According to the overall pressure distribution diagram in Figure6, there is a low pressure area appearing in the impeller of the lining plastic pump, and negative pressure area on the back side of the blade working close to the volute tongue, where cavitation occurs easily.Figure 6
Overall pressure distribution.As can be seen from Figure7, due to the low pressure at the impeller inlet, the medium vaporization at room temperature reached the critical pressure, so cavitation occurred at the inlet of the impeller; the gas volume fraction was 0.84836, which was consistent with the actual situation.Figure 7
Gas volume fraction diagram.


## 3.1. Meshing

Meshing is the basis of numerical discretization of flow control equations, and the quality of meshing directly influences the convergence of analysis and the accuracy of results. The grid number of the impeller region was 127,794, the volute region 727,398, and the inlet section 2408, a total of 854,692, as shown in Figure2. The mesh is unstructured, 3D type, the minimum mesh was 0.0001, and the maximum is 0.025.Figure 2
Mesh generation.


## 3.2. Boundary Conditions

The boundary conditions were mainly set as follows: the basic properties of the fluid medium, including the density, temperature, viscosity, vapor density, gas content, saturated vapor pressure, etc. as shown in Table1. In addition to the rotor setting of the impeller blade, the setting of the inlet and outlet of the fluid medium and the setting of the rotating surface were also required.Table 1
Boundary condition setting.
Name of parameter
Parameter values
Fluid medium
Water
Density
998 kg/m3
Reference temperature
300 K
Vapour density
0.0245 kg/m3
Gas content
2.3 × 10−5
Saturated vapor pressure
3610 pa
Bulk modulus
2.15 × 109The pressure here was the standard atmospheric pressure, set to the inlet condition, the flow rate,Q = 25°m3/h, was set to the export condition, the blade as a rotating part was set to a rotating speed of 2900 rpm, and the rest surface could be directly acquiesced to the static surface.


## 3.3. Control Equations

The flow of medium in plastic-lined pump satisfies the following equation:Continuity equation:(1)∂ρμi∂xi=0.Momentum equation:(2)∂ρμiμj∂xj=−∂p∗∂xj+∂μ∂xj/∂μi+∂μj/∂xi∂xj−2εijkkωjμk.Incompressible N-S equation:(3)∂Ui∂t+Uj∂Ui∂xj=fi−1ρ∂p∗∂xi+ϑ∇2Ui.k-ε equation:(4)ρdkdt=∂∂xjμ+μtσk∂k∂xj+Gk−ρε,ρdεdt=∂∂xiμ+μtσε∂k∂xi+ρεC1E−ρC2ε2k+ϑε,μt=ρCμk2ε,where ρ is the fluid density; ρ∗ is the pressure including centrifugal force and turbulent kinetic energy k; ω is the angular velocity; εijk is the tensor; μ is the effective viscosity coefficient; U is the velocity vector; P is the pressure; t is the time; ϑ is the viscosity coefficient of fluid motion; i, j, and k, respectively, are 1, 2, and 3; σk = 1.0; σε = 1.3; Cμ = 0.09; C1 = 1.44; C2 = 1.92.


## 3.4. Flow Field Simulation

There are 1,000 iteration steps for the lining plastic pump, and it can be seen from Figure3 that the curve converged when the number of iterations reached about 500 times.Figure 3
Residual curve.Figure4 shows the pressure distribution of the lining plastic pump, from the inlet of the impeller to its outlet; the pressure value was increasing, and the value near the outlet of the volute was higher than elsewhere, mainly because the flow of the fluid is accompanied by the rotation of the impeller during the conveying process, and the inhomogeneity of its flow made it possible for vortices to appear between the adjacent.Figure 4
Pressure cloud diagram.Figure5 is a speed distribution diagram of the lining plastic pump. As can be observed from Figure 5, the value of velocity was gradually increased from the entrance of the impeller to its outlet. The flow of liquid away from the blades was much less effective than the flow of the liquid at its periphery due to the action of the blades, and there would be swirl along the radial direction away from the middle of the blade, affecting the normal flow of the liquid.Figure 5
Velocity cloud.According to the overall pressure distribution diagram in Figure6, there is a low pressure area appearing in the impeller of the lining plastic pump, and negative pressure area on the back side of the blade working close to the volute tongue, where cavitation occurs easily.Figure 6
Overall pressure distribution.As can be seen from Figure7, due to the low pressure at the impeller inlet, the medium vaporization at room temperature reached the critical pressure, so cavitation occurred at the inlet of the impeller; the gas volume fraction was 0.84836, which was consistent with the actual situation.Figure 7
Gas volume fraction diagram.


## 4. Orthogonal Experiment and Range Analysis

### 4.1. Orthogonal Experiment

In the orthogonal experiment of the lining plastic pump, the interaction among the experimental factors was not yet considered. Taking the efficiency and cavitation erosion of the lining plastic pump into consideration, five structural dimensions of impeller inlet diameter, impeller outlet diameter, impeller inlet angle, outlet angle, and wrap angle were selected as experimental factors, and four levels were set for each factor, as shown in Table2.Table 2
Orthogonal experimental factors of lining pump impeller level.
Inlet diameterD1 (mm)
Outlet diameterD2 (mm)
Inlet angleβb1 (°)
Outlet angleβb2 (°)
Wrap angleφ (°)
1
72
252
18
20
100
2
74
254
22
24
105
3
76
256
26
28
110
4
78
258
30
32
115For the orthogonal experiment with four levels of five factors, the orthogonal table that could selected is L16 (45). Orthogonal experiment of lining pump is shown in Table 3.Table 3
Orthogonal experimental results of impeller structure.
Experiment number
Import diameterD1 (mm)
Exit diameterD2 (mm)
Import angleβb1 (°)
Exit angleβb2 (°)
Wrap angleφ (°)
Efficiencyη (%)
Gas volume fraction
1
72
252
18
20
100
57.13
0.848360
2
72
254
22
24
105
52.53
0.874810
3
72
256
26
28
110
53.45
0.867331
4
72
258
30
32
115
57.45
0.874301
5
74
252
22
28
115
57.80
0.880091
6
74
254
18
32
110
53.86
0.823669
7
74
256
30
20
105
57.99
0.819132
8
74
258
26
24
100
57.76
0.873608
9
76
252
26
32
105
59.39
0.828129
10
76
254
18
28
100
54.47
0.867710
11
76
256
30
24
115
55.46
0.871944
12
76
258
22
20
110
57.29
0.944049
13
78
252
30
24
110
56.88
0.882889
14
78
254
26
20
115
55.26
0.906458
15
78
256
22
32
100
53.60
0.838161
16
78
258
18
28
105
59.01
0.845031


### 4.2. Range Analyses

By means of mathematical statistics, the effects of each factor level on the efficiency and cavitation of the lining plastic pump and the combination parameters under the conditions of each evaluation index were analyzed. The following is a convenient description of the range analysis results.A, B, C, D, and E are, respectively, used to represent the inlet diameter of impeller D1, outlet diameter D2, inlet angle βb1, outlet angle βb2, and inclusion wrap angle φ.


#### 4.2.1. Analysis of the Influence Trend of Various Factors on Efficiency

Table4 shows that the influence degree of various factors on efficiency is from high to low, respectively, impeller outlet diameter D2, wrap angle φ, impeller inlet diameter D1, impeller inlet angle βb1, and impeller exit angle βb2. In order to observe the change trend more intuitively, the influence of various factors on efficiency was drawn, as shown in Figure 8. According to the evaluation indexes, the optimal level combination was A2B4C4D1E2, that is, when the inlet diameter D1 was 74 mm, outlet diameter D2 was 258 mm, inlet angle was 20°, outlet angle was 30°, and wrap angle was 105°, and a the minimum loss could be obtained, which indicated the maximum efficiency of the lining plastic pump under this parameter. The optimized structure parameters of the lining plastic pump were not included in the existing tests. The CFD software was used to conduct the experimental verification again, and the maximum efficiency of the data is 56.80%, which was found to be close to the maximum value in the orthogonal experiment by comparison with the 16 experimental data.Table 4
Influence data of various factors on efficiency.
D
1
D
2
β
b1
β
b2
φ
K1
220.56
231.2
224.47
227.67
222.96
K2
227.41
216.12
221.22
222.63
228.92
K3
226.61
220.5
225.86
224.73
221.48
K4
224.75
231.51
227.78
224.24
225.97
K
1
¯
55.14
57.8
56.1175
56.9175
55.74
K
2
¯
56.85
54.03
55.305
55.6575
57.23
K
3
¯
56.65
55.125
56.465
56.1825
55.37
K
4
¯
56.1875
57.8775
56.945
56.06
56.4925
Range
1.71
3.8475
1.64
1.26
1.86
Sequencing
3
1
4
5
2Figure 8
Influence trend of each parameter on efficiency.


#### 4.2.2. Analysis of Influence Trend of Various Factors on Cavitation Erosion

It could be clearly seen from Table5 that the influence of various factors on cavitation was, respectively, inlet angle βb1, wrap angle φ, outlet diameter of impeller D2, outlet angle βb2, and inlet diameter D1. In order to observe the change trend more intuitively, the influence of various factors on the gas volume fraction was plotted, as shown in Figure 9. According to the evaluation indexes, the optimal level combination for A2B2C1D3E1, that is, the inlet diameter D1 was 74 mm, outlet diameter D2 was 254 mm, the inlet angle was 18°, the outlet angle was 28°, and the wrap angle was 100°, while the gas volume fraction of the lining plastic pump was minimum, showed that the cavitation of the lining pump had a better improvement. The optimized structure parameters of the lining plastic pump were not included in the existing tests. The CFD software was used to remodel and verify the test results, and the minimum gas volume fraction obtained of this group was 0.84346.Table 5
Influence data of various factors on cavitation.
D
1
D
2
β
b1
β
b2
φ
K1
3.464802
3.439469
3.28477
3.517999
3.327839
K2
3.3965
3.372647
3.53711
3.503251
3.367102
K3
3.411832
3.396568
3.475526
3.360163
3.517938
K4
3.472539
3.536989
3.448266
3.36426
3.532794
K
1
¯
0.86620
0.859867
0.821190
0.87950
0.831960
K
2
¯
0.849125
0.843162
0.884278
0.875813
0.841776
K
3
¯
0.82958
0.849142
0.86888
0.840041
0.879485
K
4
¯
0.868135
0.884247
0.8620665
0.841065
0.88320
Range
0.01901
0.041085
0.063088
0.039459
0.05124
Sequencing
5
3
1
4
2Figure 9
Influence trend of each parameter on gas volume fraction.


### 4.3. Influence of Enveloping Angle on Pump Performance

The angle between the connection of the inlet edge and the center of the blade, and the connection of the outlet side and the center of the circle is called the blade packet angle. The wrap angle directly affected the length of the flow passage between the two blades. The longer the flow passage between the two blades is, the larger the wrap angle would be, and the smaller the unit load on the blade per unit length would be. Meanwhile, the smaller the diffusion degree of the flow passage is, the stronger the control ability of the flow passage on the liquid would be, and the energy could be effectively transferred.However, when the blade wrap angle was too large, the increase of the distance from the impeller inlet to the outlet of the liquid resulted in the increase of the friction loss between the blade and the liquid, which is not only conducive to the energy exchange but also caused loss of most of the head. In addition, due to the difference of casting technology level, too much wrapping angle would also be limited by the technology level, so the size of wrapping angle should be selected appropriately. It is well known that when the specific speed of the pump is between 60 and 120, wrap angle will usually beφ = 75°–150°, then the specific speed will change from low to high, and finally the blade wrap angle value changes from large to small. However, in the actual drawing process, the wrap angle should be adjusted according to the specific situation. As an important geometric parameter of the blade, on the premise of the projection diagram of the axial plane of the blade and the number of blades, the wrap angle essentially reflects the diffusion degree of the blade passage. As the blade wrap angle increases, the flow head curve drops more and more steeply while the flow powers curve flatten out. According to experience, the wrap angle generally takes 90° to 130°.Figure10 indicates blade wrap angles of 95°, 100°, 105°, 110°, and 115° of 5 kinds of centrifugal pump in the outlet flow show lift efficiency curves under 0.8 Qd, 0.9 Qd, 0.96 Qd, 1.0 Qd, 1.1 Qd, and 1.2 Qd conditions.Figure 10
Centrifugal pump head: efficiency curve.From Figure10, the following observations are made:(1)
The influence of blade wrap angle on the lift of centrifugal pump with high ratio speed was greater than that of efficiency; the smaller the wrap angle is, the larger the lift of the centrifugal pump would be, and the more the trend of decreasing tends to fit straight line.(2)
At low flow rate, the smaller the wrap angle is, the lower the efficiency of the centrifugal pump would be; in large flow, the larger the wrap angle, the lower the efficiency of the centrifugal pump, and the faster the decline, the most obvious when the wrap angle, which was 115.(3)
In 0.96Qd centrifugal pump, to achieve the highest efficiency point, when the blade angle was 110°, the efficiency was superior to the other angle of the impeller. This is because, with the increase in the wrap angle, the blade became longer, the blade's restraint on the fluid in the flow passage increased, and the efficiency increased. However, when the wrap angle was too large, the friction on the fluid increased, and the maximum efficiency dropped. There was an optimal blade wrap angle to make the centrifugal pump to have the best efficiency.


### 4.4. Multifield Coupling Analysis of Liner Pump Structure

By analyzing the flow thermal and solid coupling of the impeller structure of the lining plastic pump, the displacement distribution cloud map and stress distribution cloud map can be obtained, as shown in Figures11 and 12, respectively. It can be seen from Figure 11 that the deformation distribution showed a gradual increasing trend along the central axis of the impeller structure, and the maximum deformation was close to the edge of the impeller, the maximum deformation along the radial direction of the impeller was 1.7717 mm, and the minimum deformation was located at its central axis. This was mainly due to the fixed constraint at the central shaft and free expansion and deformation end at the edge of the impeller when the thermo-solid coupling analysis of the liner pump impeller structure was carried out.Figure 11
Total displacement deformation cloud map.Figure 12
Cloud diagram of stress distribution.Through observation and analysis of Figure12, it can be seen that the maximum stress was mainly concentrated at the central axle hole, and the increase in radial dimension along the impeller shows a decreasing trend. The closer it was to the edge, the smaller the stress was, and the maximum equivalent stress was 10.31°Mpa. Stress comes mainly from two sources, on the one hand, when the fluid pressure load was applied to the working face of the impeller, the working face of the impeller will bear large load pressure and generate stress deformation, and on the other hand, when temperature load was applied to the working face of the impeller, it will produce thermal deformation and thermal stress.


### 4.5. Orthogonal Table Design

Taking the total displacement deformation and stress distribution of the lining plastic pump into comprehensive consideration, five parameters including inlet diameter of the impeller, outlet diameter of the impeller, inlet angle, outlet angle, and cladding angle of the impeller were selected as experimental factors, and four levels were set for each factor. The orthogonal experimental factors of the liner plastic pump are shown in Table6.Table 6
Orthogonal experimental factors of lining pump impeller level table.
Import diameterD1 (mm)
Exit diameterD2 (mm)
Inlet angleβb1 (°)
Outlet angleβb2 (°)
Wrap angleφ (°)
1
72
252
18
20
100
2
74
254
22
24
105
3
76
256
26
28
110
4
78
258
30
32
115


### 4.6. Orthogonal Experimental Results and Range Analysis

By conducting orthogonal experiments on the lining plastic pump structure under fluid-thermal-structure interaction conditions, the orthogonal experimental table of the lining plastic pump structure under fluid-thermal-structure interaction conditions can be obtained as shown in Table7. According to the orthogonal experimental results of the lining plastic pump structure in Table 8, the maximum difference analysis value of the average value of total displacement and stress of each factor at each level was calculated. The calculation results are shown in Table 8.Table 7
Orthogonal experimental table of flow thermal and solid coupling of pump.
Experiment number
D
1 (mm)
D
2 (mm)
β
b1 (°)
β
b2 (°)
φ (°)
Total displacement (m)
Stress (Pa)
1
72
252
18
20
100
0.0017717
1.0310e7
2
72
254
22
24
105
0.0018074
1.0465e7
3
72
256
26
28
110
0.0018029
1.0592e7
4
72
258
30
32
115
0.0018044
1.1021e7
5
74
252
22
28
115
0.0016985
1.0678e7
6
74
254
18
32
110
0.0017669
1.1259e7
7
74
256
30
20
105
0.0018015
1.0710e7
8
74
258
26
24
100
0.0018828
1.0302e7
9
76
252
26
32
105
0.0016658
9.4937e6
10
76
254
18
28
100
0.0017558
1.1164e7
11
76
256
30
24
115
0.0017937
1.0386e7
12
76
258
22
20
110
0.0018422
1.0687e7
13
78
252
30
24
110
0.0017371
1.1217e7
14
78
254
26
20
115
0.0017607
1.0982e7
15
78
256
22
32
100
0.0018231
1.1333e7
16
78
258
18
28
105
0.0018562
1.1055e7Table 8
Influence data of various factors on total displacement.
D
1
D
2
β
b1
β
b2
φ
K1
7.1864 × 10−2
6.8731 × 10−2
7.1506 × 10−2
7.1761 × 10−2
7.2334 × 10−2
K2
7.1497 × 10−2
7.0908 × 10−2
7.1712 × 10−2
7.221 × 10−2
7.1309 × 10−2
K3
7.0575 × 10−2
7.2212 × 10−2
7.1122 × 10−2
7.1134 × 10−2
7.1491 × 10−2
K4
7.1771 × 10−2
7.3856 × 10−2
7.2088 × 10−2
7.0602 × 10−2
7.0573 × 10−2
K
1
¯
1.7966 × 10−2
1.7183 × 10−2
1.7877 × 10−2
1.7940 × 10−2
1.8084 × 10−2
K
2
¯
1.7874 × 10−2
1.7727 × 10−2
1.7928 × 10−2
1.8053 × 10−2
1.7827 × 10−2
K
3
¯
1.7644 × 10−2
1.8053 × 10−2
1.7781 × 10−2
1.7784 × 10−2
1.7873 × 10−2
K
4
¯
1.7943 × 10−2
1.8464 × 10−2
1.8022 × 10−2
1.7651 × 10−2
1.7643 × 10−2
Range
0.0326 × 10−2
0.1281 × 10−2
0.0241 × 10−2
0.0402 × 10−2
0.0441 × 10−2
Sequencing
4
1
5
3
2It can be clearly seen from Table8 that the influence of various factors on the total displacement was from large to small, respectively, the outlet diameter D2, wrap angle φ, outlet angle βb2, the inlet diameter D1, and the inlet angle βb1. Figure 13 shows the influence trend of various factors on the total displacement. According to the evaluation index, the optimal level combination was A3B1C3D4E4, that is, the inlet diameter D1 was 76 mm, outlet diameter D2 was 252 mm, the inlet angle was 26°, the outlet angle was 32°, the wrap angle was 115°, while the total displacement of the lining plastic pump was minimum, which means that the lining plastic pump under this parameter had the minimum deformation.Figure 13
The influence trend of each parameter on the total displacement.According to the orthogonal experiment results of lining plastic pump structure in Table7, the maximum difference analysis value of the average stress distribution under each level of each factor was calculated. It can be clearly seen from Table 9 that the influence of various factors on the stress was, respectively, diameter D1, the inlet angle βb1, the outlet diameter D2, wrap angle φ, and outlet angle βb2. Figure 14 shows the influence trend of various factors on stress. According to the evaluation index, the optimal level combination was A3B1C3D2E2, that is, the inlet diameter D1 was 76 mm, outlet diameter D2 was 252 mm, the inlet angle was 26°, the outlet angle was 24°, and the wrap angle was 105°, while the stress of the lining plastic pump was minimum, which showed that the lining plastic pump under this parameter has minimal stresses.Table 9
Influence data of various factors on stress.
D
1
D
2
β
b1
β
b2
φ
K1
4.2388e7
4.1699e7
4.3788e7
4.2689e7
4.3109e7
K2
4.2949e7
4.3870e7
4.3163e7
4.2370e7
4.1724e7
K3
4.1731e7
4.3021e7
4.1370e7
4.3489e7
4.3755e7
K4
4.4587e7
4.3065e7
4.3308e7
4.3107e7
4.3067e7
K
1
¯
1.0597e7
1.0425e7
1.0947e7
1.0672e7
1.0777e7
K
2
¯
1.0737e7
1.0968e7
1.0791e7
1.0593e7
1.0431e7
K
3
¯
1.0433e7
1.0755e7
1.0342e7
1.0872e7
1.0939e7
K
4
¯
1.1147e7
1.0766e7
1.0827e7
1.0777e7
1.0767e7
Range
0.0714e7
0.0543e7
0.0605e7
0.0279e7
0.0508e7
Sequencing
1
3
2
5
4Figure 14
Influence trend of various parameters on stress.


### 4.7. Taguchi Algorithms Used to Optimize the Structural Parameters of the Lining Plastic Pump

In this chapter, the comprehensive weighted scoring method was used to analyze the orthogonal experimental results in the previous chapter. The comprehensive weighting method was a mathematical statistical method which converted the multi-index experiment into a single index one. It was a method which used the total score of each experiment to represent the experimental results. In this paper, the relevant knowledge of mathematical statistics is used to analyze and process the test results, and the score value of the comprehensive weighted score is calculated [12, 13].Y
j
∗ was used to represent the sum of weighted scores of each performance index, and the larger Yj∗ was, the better the comprehensive performance of this group of tests will be. The formula for calculating the comprehensive weighted scores is as follows:(5)Yj∗=∑i=12Yi,j×ωi.


### 4.8. Comprehensive Weighted Scoring Results of Plastic-Lined Pump Impeller Structure

The results of the 16 orthogonal experiments obtained in the previous chapter were calculated by comprehensive weighted scoring. The results are shown in Table10; group 9 had the largest value and Yj∗ score was 98.8, The combined parameters were A3B1C3D4E2, that is, the inlet diameter D1 was 76 mm, the outlet diameter D2 was 252 mm, the inlet angle was 26°, the outlet angle was 32°, and the wrap angle was 105°.Table 10
Comprehensive weighted score value table of orthogonal experimental results of the plastic-lined pump structure.
Sequence number
Displacement
Grade
Stress
Grade
Comprehensively weighted gradingY∗
1
0.0010517
86
9.4958e6
92
88.4
2
0.0010629
80
9.2606e6
98
87.2
3
0.0010706
78
9.5837e6
88
82
4
0.0010470
92
1.0391e7
84
88.8
5
0.0010151
100
1.0745e7
76
90.4
6
0.0010486
88
1.0914e7
72
81.6
7
0.0010565
84
1.0403e7
82
83.2
8
0.0011110
70
9.3839e6
96
80.4
9
0.0010288
98
9.1055e6
100
98.8
10
0.0010454
94
1.1593e7
70
84.4
11
0.0010586
82
9.5659e6
90
85.2
12
0.0010863
74
9.4928e6
94
82
13
0.0010448
96
1.0801e7
74
87.2
14
0.0010479
90
1.0677e7
80
86
15
0.0010845
76
1.0732e7
78
76.8
16
0.0010888
72
9.8617e6
86
77.6


### 4.9. Formulating Controllable Factors and Their Level Tables

Taking the total displacement, deformation, and stress distribution of the plastic-lined pump into comprehensive consideration, five structural dimensions of impeller inlet diameter, impeller outlet diameter, impeller inlet angle, impeller outlet angle, and wrap angle were selected as experimental factors, and four levels were set for each factor. Table11 shows the controllable factors and their levels, the inlet angle βb1, outlet angle βb2, wrap angle φ, inlet diameter D1, and outlet diameter D2 of the pump.Table 11
Controllable factors and their levels.
Inlet diameterD1 (mm)
Outlet diameterD2 (mm)
Inlet angleβb1 (°)
Outlet angleβb2 (°)
Wrap angleφ (°)
1
72
252
18
20
100
2
74
254
22
24
105
3
76
256
26
28
110
4
78
258
30
32
115


### 4.10. Taguchi Test Design

The internal table of the orthogonal experiment was L16 (45). As shown in Table 12, since the index of the subsequent Taguchi experiment was SN ratio rather than the quality characteristic, the interaction between factors was not considered [14–16].Table 12
Inner table of orthogonal experiment.
Inlet diameterD1 (mm)
Outlet diameterD2 (mm)
Inlet angleβb1 (°)
Outlet angleβb2 (°)
Wrap angleφ (°)
1
72
252
18
°
20
°
100
°
2
72
254
22
°
24
°
105
°
3
72
256
26
°
28
°
110
°
4
72
258
30
°
32
°
115
°
5
74
252
22
°
28
°
115
°
6
74
254
18
°
32
°
110
°
7
74
256
30
°
20
°
105
°
8
74
258
26
°
24
°
100
°
9
76
252
26
°
32
°
105
°
10
76
254
18
°
28
°
100
°
11
76
256
30
°
24
°
115
°
12
76
258
22
°
20
°
110
°
13
78
252
30
°
24
°
110
°
14
78
254
26
°
20
°
115
°
15
78
256
22
°
32
°
100
°
16
78
258
18
°
28
°
105
°


#### 4.10.1. Calculating the SN Ratio

In view of the fact that in practical applications, the displacement and stress are expected to be as small as possible. In taguchi algorithm, it is called the smaller-the-better characteristicYx and its SN ratio is calculated as follows [17]:Displacement SN:(6)ηi=−10log1n∑i=1nYi2.Stress SN:(7)ηj=−10log1n∑j=1nYj2.Comprehensive SN:(8)η=0.6ηi+0.4ηj.The results of SNR calculation are shown in Table13.Table 13
Results of SNR calculation.
Sequence
A
B
C
D
E
SNRηi
SNRηj
Comprehensive SNRη
1
72
252
18
°
20
°
100
°
59.56216
−139.5566
−20.0829
2
72
254
22
°
24
°
105
°
59.47015
−139.3328
−20.0505
3
72
256
26
°
28
°
110
°
59.40746
−139.6307
−20.2078
4
72
258
30
°
32
°
115
°
59.60107
−140.3332
−20.3726
5
74
252
22
°
28
°
115
°
59.8698
−140.6241
−20.3278
6
74
254
18
°
32
°
110
°
59.5878
−140.7597
−20.5512
7
74
256
30
°
20
°
105
°
59.5226
−140.3432
−20.4237
8
74
258
26
°
24
°
100
°
59.08572
−139.4477
−20.3276
9
76
252
26
°
32
°
105
°
59.75338
−139.1861
−19.8206
10
76
254
18
°
28
°
100
°
59.61435
−141.2839
−20.7450
11
76
256
30
°
24
°
115
°
59.50536
−139.6145
−20.1426
12
76
258
22
°
20
°
110
°
59.28100
−139.5479
−20.2506
13
78
252
30
°
24
°
110
°
59.619337
−140.6693
−20.4961
14
78
254
26
°
20
°
115
°
59.593603
−140.5690
−20.4714
15
78
256
22
°
32
°
100
°
59.295409
−140.6136
−20.6693
16
78
258
18
°
28
°
105
°
59.261038
−139.8790
−20.3950According to the intuitive analysis in the above table, the signal-to-noise ratio of the test group 9 was the largest. SNmax = −19.8206; the corresponding process combination parameter was A3B1C3D4E2.


#### 4.10.2. Statistics of Internal Tables

(1)
Find the sum of SN ratios (T):(9)T=∑i=116Ti.Substitute the result to calculateT=∑i=116Ti=−325.3347.(2)
Find the sum of SN ratios wasTi, the average value of ti, and the range Ri of each column under the horizontal conditions of each factor: i = 1, 2, 3, 4. The calculation results are shown in Table 14.(3)
Find the sum of the total fluctuation squares of SN ratio andST:From the above calculation results, it can be seen that(10)T=−325.3347,y¯=Tn=−20.3342,ST=∑i=116yi−y¯2,ST=0.749729444.(4)
The sum of the squared fluctuations of SN ratio of each factor:(11)Si=14T12+T22+T32+T42−116T2.Substitute in the numerical value to getS1=0.2750; S2=0.1536; S3=0.11545352; S4=0.058691812; S5=0.146984112; and S1+S2+S3+S4+S5=0.749729444.Table 14
T
i, ti, and Ri of SN ratio at various factors.
A
B
C
D
E
T
1
−80.7138
−80.7274
−81.7741
−81.2286
−81.8248
T
2
−81.6303
−81.8181
−81.2982
−81.0168
−80.6898
T
3
−80.9588
−81.4434
−80.8274
−81.6756
−81.5051
T
4
−82.0318
−81.3458
−81.4350
−81.4137
−81.3144
t
1
−20.17845
−20.18185
−20.44353
−20.30715
−20.4562
t
2
−20.40758
−20.45453
−20.32455
−20.2542
−20.17225
t
3
−20.23970
−20.36085
−20.20685
−20.4189
−20.37643
t
4
−20.50795
−20.33645
−20.35875
−20.35343
−20.32860
R
0.3295
0.272675
0.236675
0.16470
0.28975


#### 4.10.3. Analysis of Variance

Since there was no blank column in this experiment, that is, no error term, the minimum S4 was taken as the squared sum of error fluctuations, It can be obtained thatfA=fB=fC=fD=fE=4−1=3. The analysis of variance is shown in Table 15.Table 15
Variance analysis table.
S
f
V
F
A
0.2750
3
0.091667
4.685492 (∗)
B
0.1536
3
0.0512043
2.617060
C
0.11545352
3
0.038485
1.967115
D
0.058691812
3
0.0195639
1
E
0.146984112
3
0.048995
2.504338
(e)
(0.058691812)
(3)
(0.0195639)
T
0.749729444
12From the perspective of SNR comparison, factor A has a significant impact on the quality fluctuation characteristics. It could be considered that factorA was a stabilizing factor and factors B, C, D, and E were adjustable factors. For the stabilizing factor, its level is taken as A3, and the total displacement SNR of factors B, C, D and E is listed in Table 16.Table 16
SN ratio response table of factorsB, C, D, and E.
B
C
D
E
1
238.8047
238.0253
237.9594
237.5576
2
238.2668
237.9173
237.6815
238.0081
3
237.7308
237.8402
238.1526
237.8956
4
237.2288
238.2484
238.2377
238.5698Since the influence of factorsB, C, D, and E on the quality fluctuation characteristics was not very significant, it can be considered to ignore the stress and simply adjust the parameters of B, C, D, and E to minimize the stress. As can be seen from the above table, the optimal process parameter was B1C4D4E4, considering only the stress. Finally, the optimized combination parameter was A3B1C3D2E2, which was basically consistent with the optimal combination parameter A3B1C3D4E2 obtained by the intuitive method above.


### 4.11. Optimizing Model Validation

The accuracy of the optimization model was verified by thermo-solid coupling analysis of the optimized impeller structure parameter model. The thermo-solid coupling simulation results of the optimized model are shown in Figures15 and 16. By comparing with the thermo-solid coupling simulation results before optimization, it can be seen that the total displacement and stress distribution after optimization were smaller than those before optimization. Figures 17 and 18 are, respectively, the total displacement and deformation diagram and stress distribution diagram before optimization.Figure 15
Total displacement and deformation after optimization.Figure 16
Stress distribution diagram after optimization.Figure 17
Total displacement and deformation before optimization.Figure 18
Stress distribution before optimization.In Taguchi algorithm, based on the above orthogonal experiment, the internal table of orthogonal experiment was designed and established to calculate the SNR of total displacement and stress distribution under various horizontal conditions, and its variance was calculated; by analyzing the calculated variance, the stability factor and adjustable factor could be obtained, then the adjustable factor could be optimized twice, and the final optimal process combination parameter can be obtained asA3B1C3D2E2, When the inlet diameter D1 was 76 mm, the outlet diameter D2 was 252 mm, the inlet angle was 26°, the outlet angle was 24°, and the wrap angle was 115°, the total displacement, deformation, and stress of the pump were the minimum. Simulation results showed that the optimal combination was reasonable.


## 4.1. Orthogonal Experiment

In the orthogonal experiment of the lining plastic pump, the interaction among the experimental factors was not yet considered. Taking the efficiency and cavitation erosion of the lining plastic pump into consideration, five structural dimensions of impeller inlet diameter, impeller outlet diameter, impeller inlet angle, outlet angle, and wrap angle were selected as experimental factors, and four levels were set for each factor, as shown in Table2.Table 2
Orthogonal experimental factors of lining pump impeller level.
Inlet diameterD1 (mm)
Outlet diameterD2 (mm)
Inlet angleβb1 (°)
Outlet angleβb2 (°)
Wrap angleφ (°)
1
72
252
18
20
100
2
74
254
22
24
105
3
76
256
26
28
110
4
78
258
30
32
115For the orthogonal experiment with four levels of five factors, the orthogonal table that could selected is L16 (45). Orthogonal experiment of lining pump is shown in Table 3.Table 3
Orthogonal experimental results of impeller structure.
Experiment number
Import diameterD1 (mm)
Exit diameterD2 (mm)
Import angleβb1 (°)
Exit angleβb2 (°)
Wrap angleφ (°)
Efficiencyη (%)
Gas volume fraction
1
72
252
18
20
100
57.13
0.848360
2
72
254
22
24
105
52.53
0.874810
3
72
256
26
28
110
53.45
0.867331
4
72
258
30
32
115
57.45
0.874301
5
74
252
22
28
115
57.80
0.880091
6
74
254
18
32
110
53.86
0.823669
7
74
256
30
20
105
57.99
0.819132
8
74
258
26
24
100
57.76
0.873608
9
76
252
26
32
105
59.39
0.828129
10
76
254
18
28
100
54.47
0.867710
11
76
256
30
24
115
55.46
0.871944
12
76
258
22
20
110
57.29
0.944049
13
78
252
30
24
110
56.88
0.882889
14
78
254
26
20
115
55.26
0.906458
15
78
256
22
32
100
53.60
0.838161
16
78
258
18
28
105
59.01
0.845031


## 4.2. Range Analyses

By means of mathematical statistics, the effects of each factor level on the efficiency and cavitation of the lining plastic pump and the combination parameters under the conditions of each evaluation index were analyzed. The following is a convenient description of the range analysis results.A, B, C, D, and E are, respectively, used to represent the inlet diameter of impeller D1, outlet diameter D2, inlet angle βb1, outlet angle βb2, and inclusion wrap angle φ.


### 4.2.1. Analysis of the Influence Trend of Various Factors on Efficiency

Table4 shows that the influence degree of various factors on efficiency is from high to low, respectively, impeller outlet diameter D2, wrap angle φ, impeller inlet diameter D1, impeller inlet angle βb1, and impeller exit angle βb2. In order to observe the change trend more intuitively, the influence of various factors on efficiency was drawn, as shown in Figure 8. According to the evaluation indexes, the optimal level combination was A2B4C4D1E2, that is, when the inlet diameter D1 was 74 mm, outlet diameter D2 was 258 mm, inlet angle was 20°, outlet angle was 30°, and wrap angle was 105°, and a the minimum loss could be obtained, which indicated the maximum efficiency of the lining plastic pump under this parameter. The optimized structure parameters of the lining plastic pump were not included in the existing tests. The CFD software was used to conduct the experimental verification again, and the maximum efficiency of the data is 56.80%, which was found to be close to the maximum value in the orthogonal experiment by comparison with the 16 experimental data.Table 4
Influence data of various factors on efficiency.
D
1
D
2
β
b1
β
b2
φ
K1
220.56
231.2
224.47
227.67
222.96
K2
227.41
216.12
221.22
222.63
228.92
K3
226.61
220.5
225.86
224.73
221.48
K4
224.75
231.51
227.78
224.24
225.97
K
1
¯
55.14
57.8
56.1175
56.9175
55.74
K
2
¯
56.85
54.03
55.305
55.6575
57.23
K
3
¯
56.65
55.125
56.465
56.1825
55.37
K
4
¯
56.1875
57.8775
56.945
56.06
56.4925
Range
1.71
3.8475
1.64
1.26
1.86
Sequencing
3
1
4
5
2Figure 8
Influence trend of each parameter on efficiency.


### 4.2.2. Analysis of Influence Trend of Various Factors on Cavitation Erosion

It could be clearly seen from Table5 that the influence of various factors on cavitation was, respectively, inlet angle βb1, wrap angle φ, outlet diameter of impeller D2, outlet angle βb2, and inlet diameter D1. In order to observe the change trend more intuitively, the influence of various factors on the gas volume fraction was plotted, as shown in Figure 9. According to the evaluation indexes, the optimal level combination for A2B2C1D3E1, that is, the inlet diameter D1 was 74 mm, outlet diameter D2 was 254 mm, the inlet angle was 18°, the outlet angle was 28°, and the wrap angle was 100°, while the gas volume fraction of the lining plastic pump was minimum, showed that the cavitation of the lining pump had a better improvement. The optimized structure parameters of the lining plastic pump were not included in the existing tests. The CFD software was used to remodel and verify the test results, and the minimum gas volume fraction obtained of this group was 0.84346.Table 5
Influence data of various factors on cavitation.
D
1
D
2
β
b1
β
b2
φ
K1
3.464802
3.439469
3.28477
3.517999
3.327839
K2
3.3965
3.372647
3.53711
3.503251
3.367102
K3
3.411832
3.396568
3.475526
3.360163
3.517938
K4
3.472539
3.536989
3.448266
3.36426
3.532794
K
1
¯
0.86620
0.859867
0.821190
0.87950
0.831960
K
2
¯
0.849125
0.843162
0.884278
0.875813
0.841776
K
3
¯
0.82958
0.849142
0.86888
0.840041
0.879485
K
4
¯
0.868135
0.884247
0.8620665
0.841065
0.88320
Range
0.01901
0.041085
0.063088
0.039459
0.05124
Sequencing
5
3
1
4
2Figure 9
Influence trend of each parameter on gas volume fraction.


## 4.2.1. Analysis of the Influence Trend of Various Factors on Efficiency

Table4 shows that the influence degree of various factors on efficiency is from high to low, respectively, impeller outlet diameter D2, wrap angle φ, impeller inlet diameter D1, impeller inlet angle βb1, and impeller exit angle βb2. In order to observe the change trend more intuitively, the influence of various factors on efficiency was drawn, as shown in Figure 8. According to the evaluation indexes, the optimal level combination was A2B4C4D1E2, that is, when the inlet diameter D1 was 74 mm, outlet diameter D2 was 258 mm, inlet angle was 20°, outlet angle was 30°, and wrap angle was 105°, and a the minimum loss could be obtained, which indicated the maximum efficiency of the lining plastic pump under this parameter. The optimized structure parameters of the lining plastic pump were not included in the existing tests. The CFD software was used to conduct the experimental verification again, and the maximum efficiency of the data is 56.80%, which was found to be close to the maximum value in the orthogonal experiment by comparison with the 16 experimental data.Table 4
Influence data of various factors on efficiency.
D
1
D
2
β
b1
β
b2
φ
K1
220.56
231.2
224.47
227.67
222.96
K2
227.41
216.12
221.22
222.63
228.92
K3
226.61
220.5
225.86
224.73
221.48
K4
224.75
231.51
227.78
224.24
225.97
K
1
¯
55.14
57.8
56.1175
56.9175
55.74
K
2
¯
56.85
54.03
55.305
55.6575
57.23
K
3
¯
56.65
55.125
56.465
56.1825
55.37
K
4
¯
56.1875
57.8775
56.945
56.06
56.4925
Range
1.71
3.8475
1.64
1.26
1.86
Sequencing
3
1
4
5
2Figure 8
Influence trend of each parameter on efficiency.


## 4.2.2. Analysis of Influence Trend of Various Factors on Cavitation Erosion

It could be clearly seen from Table5 that the influence of various factors on cavitation was, respectively, inlet angle βb1, wrap angle φ, outlet diameter of impeller D2, outlet angle βb2, and inlet diameter D1. In order to observe the change trend more intuitively, the influence of various factors on the gas volume fraction was plotted, as shown in Figure 9. According to the evaluation indexes, the optimal level combination for A2B2C1D3E1, that is, the inlet diameter D1 was 74 mm, outlet diameter D2 was 254 mm, the inlet angle was 18°, the outlet angle was 28°, and the wrap angle was 100°, while the gas volume fraction of the lining plastic pump was minimum, showed that the cavitation of the lining pump had a better improvement. The optimized structure parameters of the lining plastic pump were not included in the existing tests. The CFD software was used to remodel and verify the test results, and the minimum gas volume fraction obtained of this group was 0.84346.Table 5
Influence data of various factors on cavitation.
D
1
D
2
β
b1
β
b2
φ
K1
3.464802
3.439469
3.28477
3.517999
3.327839
K2
3.3965
3.372647
3.53711
3.503251
3.367102
K3
3.411832
3.396568
3.475526
3.360163
3.517938
K4
3.472539
3.536989
3.448266
3.36426
3.532794
K
1
¯
0.86620
0.859867
0.821190
0.87950
0.831960
K
2
¯
0.849125
0.843162
0.884278
0.875813
0.841776
K
3
¯
0.82958
0.849142
0.86888
0.840041
0.879485
K
4
¯
0.868135
0.884247
0.8620665
0.841065
0.88320
Range
0.01901
0.041085
0.063088
0.039459
0.05124
Sequencing
5
3
1
4
2Figure 9
Influence trend of each parameter on gas volume fraction.


## 4.3. Influence of Enveloping Angle on Pump Performance

The angle between the connection of the inlet edge and the center of the blade, and the connection of the outlet side and the center of the circle is called the blade packet angle. The wrap angle directly affected the length of the flow passage between the two blades. The longer the flow passage between the two blades is, the larger the wrap angle would be, and the smaller the unit load on the blade per unit length would be. Meanwhile, the smaller the diffusion degree of the flow passage is, the stronger the control ability of the flow passage on the liquid would be, and the energy could be effectively transferred.However, when the blade wrap angle was too large, the increase of the distance from the impeller inlet to the outlet of the liquid resulted in the increase of the friction loss between the blade and the liquid, which is not only conducive to the energy exchange but also caused loss of most of the head. In addition, due to the difference of casting technology level, too much wrapping angle would also be limited by the technology level, so the size of wrapping angle should be selected appropriately. It is well known that when the specific speed of the pump is between 60 and 120, wrap angle will usually beφ = 75°–150°, then the specific speed will change from low to high, and finally the blade wrap angle value changes from large to small. However, in the actual drawing process, the wrap angle should be adjusted according to the specific situation. As an important geometric parameter of the blade, on the premise of the projection diagram of the axial plane of the blade and the number of blades, the wrap angle essentially reflects the diffusion degree of the blade passage. As the blade wrap angle increases, the flow head curve drops more and more steeply while the flow powers curve flatten out. According to experience, the wrap angle generally takes 90° to 130°.Figure10 indicates blade wrap angles of 95°, 100°, 105°, 110°, and 115° of 5 kinds of centrifugal pump in the outlet flow show lift efficiency curves under 0.8 Qd, 0.9 Qd, 0.96 Qd, 1.0 Qd, 1.1 Qd, and 1.2 Qd conditions.Figure 10
Centrifugal pump head: efficiency curve.From Figure10, the following observations are made:(1)
The influence of blade wrap angle on the lift of centrifugal pump with high ratio speed was greater than that of efficiency; the smaller the wrap angle is, the larger the lift of the centrifugal pump would be, and the more the trend of decreasing tends to fit straight line.(2)
At low flow rate, the smaller the wrap angle is, the lower the efficiency of the centrifugal pump would be; in large flow, the larger the wrap angle, the lower the efficiency of the centrifugal pump, and the faster the decline, the most obvious when the wrap angle, which was 115.(3)
In 0.96Qd centrifugal pump, to achieve the highest efficiency point, when the blade angle was 110°, the efficiency was superior to the other angle of the impeller. This is because, with the increase in the wrap angle, the blade became longer, the blade's restraint on the fluid in the flow passage increased, and the efficiency increased. However, when the wrap angle was too large, the friction on the fluid increased, and the maximum efficiency dropped. There was an optimal blade wrap angle to make the centrifugal pump to have the best efficiency.


## 4.4. Multifield Coupling Analysis of Liner Pump Structure

By analyzing the flow thermal and solid coupling of the impeller structure of the lining plastic pump, the displacement distribution cloud map and stress distribution cloud map can be obtained, as shown in Figures11 and 12, respectively. It can be seen from Figure 11 that the deformation distribution showed a gradual increasing trend along the central axis of the impeller structure, and the maximum deformation was close to the edge of the impeller, the maximum deformation along the radial direction of the impeller was 1.7717 mm, and the minimum deformation was located at its central axis. This was mainly due to the fixed constraint at the central shaft and free expansion and deformation end at the edge of the impeller when the thermo-solid coupling analysis of the liner pump impeller structure was carried out.Figure 11
Total displacement deformation cloud map.Figure 12
Cloud diagram of stress distribution.Through observation and analysis of Figure12, it can be seen that the maximum stress was mainly concentrated at the central axle hole, and the increase in radial dimension along the impeller shows a decreasing trend. The closer it was to the edge, the smaller the stress was, and the maximum equivalent stress was 10.31°Mpa. Stress comes mainly from two sources, on the one hand, when the fluid pressure load was applied to the working face of the impeller, the working face of the impeller will bear large load pressure and generate stress deformation, and on the other hand, when temperature load was applied to the working face of the impeller, it will produce thermal deformation and thermal stress.


## 4.5. Orthogonal Table Design

Taking the total displacement deformation and stress distribution of the lining plastic pump into comprehensive consideration, five parameters including inlet diameter of the impeller, outlet diameter of the impeller, inlet angle, outlet angle, and cladding angle of the impeller were selected as experimental factors, and four levels were set for each factor. The orthogonal experimental factors of the liner plastic pump are shown in Table6.Table 6
Orthogonal experimental factors of lining pump impeller level table.
Import diameterD1 (mm)
Exit diameterD2 (mm)
Inlet angleβb1 (°)
Outlet angleβb2 (°)
Wrap angleφ (°)
1
72
252
18
20
100
2
74
254
22
24
105
3
76
256
26
28
110
4
78
258
30
32
115


## 4.6. Orthogonal Experimental Results and Range Analysis

By conducting orthogonal experiments on the lining plastic pump structure under fluid-thermal-structure interaction conditions, the orthogonal experimental table of the lining plastic pump structure under fluid-thermal-structure interaction conditions can be obtained as shown in Table7. According to the orthogonal experimental results of the lining plastic pump structure in Table 8, the maximum difference analysis value of the average value of total displacement and stress of each factor at each level was calculated. The calculation results are shown in Table 8.Table 7
Orthogonal experimental table of flow thermal and solid coupling of pump.
Experiment number
D
1 (mm)
D
2 (mm)
β
b1 (°)
β
b2 (°)
φ (°)
Total displacement (m)
Stress (Pa)
1
72
252
18
20
100
0.0017717
1.0310e7
2
72
254
22
24
105
0.0018074
1.0465e7
3
72
256
26
28
110
0.0018029
1.0592e7
4
72
258
30
32
115
0.0018044
1.1021e7
5
74
252
22
28
115
0.0016985
1.0678e7
6
74
254
18
32
110
0.0017669
1.1259e7
7
74
256
30
20
105
0.0018015
1.0710e7
8
74
258
26
24
100
0.0018828
1.0302e7
9
76
252
26
32
105
0.0016658
9.4937e6
10
76
254
18
28
100
0.0017558
1.1164e7
11
76
256
30
24
115
0.0017937
1.0386e7
12
76
258
22
20
110
0.0018422
1.0687e7
13
78
252
30
24
110
0.0017371
1.1217e7
14
78
254
26
20
115
0.0017607
1.0982e7
15
78
256
22
32
100
0.0018231
1.1333e7
16
78
258
18
28
105
0.0018562
1.1055e7Table 8
Influence data of various factors on total displacement.
D
1
D
2
β
b1
β
b2
φ
K1
7.1864 × 10−2
6.8731 × 10−2
7.1506 × 10−2
7.1761 × 10−2
7.2334 × 10−2
K2
7.1497 × 10−2
7.0908 × 10−2
7.1712 × 10−2
7.221 × 10−2
7.1309 × 10−2
K3
7.0575 × 10−2
7.2212 × 10−2
7.1122 × 10−2
7.1134 × 10−2
7.1491 × 10−2
K4
7.1771 × 10−2
7.3856 × 10−2
7.2088 × 10−2
7.0602 × 10−2
7.0573 × 10−2
K
1
¯
1.7966 × 10−2
1.7183 × 10−2
1.7877 × 10−2
1.7940 × 10−2
1.8084 × 10−2
K
2
¯
1.7874 × 10−2
1.7727 × 10−2
1.7928 × 10−2
1.8053 × 10−2
1.7827 × 10−2
K
3
¯
1.7644 × 10−2
1.8053 × 10−2
1.7781 × 10−2
1.7784 × 10−2
1.7873 × 10−2
K
4
¯
1.7943 × 10−2
1.8464 × 10−2
1.8022 × 10−2
1.7651 × 10−2
1.7643 × 10−2
Range
0.0326 × 10−2
0.1281 × 10−2
0.0241 × 10−2
0.0402 × 10−2
0.0441 × 10−2
Sequencing
4
1
5
3
2It can be clearly seen from Table8 that the influence of various factors on the total displacement was from large to small, respectively, the outlet diameter D2, wrap angle φ, outlet angle βb2, the inlet diameter D1, and the inlet angle βb1. Figure 13 shows the influence trend of various factors on the total displacement. According to the evaluation index, the optimal level combination was A3B1C3D4E4, that is, the inlet diameter D1 was 76 mm, outlet diameter D2 was 252 mm, the inlet angle was 26°, the outlet angle was 32°, the wrap angle was 115°, while the total displacement of the lining plastic pump was minimum, which means that the lining plastic pump under this parameter had the minimum deformation.Figure 13
The influence trend of each parameter on the total displacement.According to the orthogonal experiment results of lining plastic pump structure in Table7, the maximum difference analysis value of the average stress distribution under each level of each factor was calculated. It can be clearly seen from Table 9 that the influence of various factors on the stress was, respectively, diameter D1, the inlet angle βb1, the outlet diameter D2, wrap angle φ, and outlet angle βb2. Figure 14 shows the influence trend of various factors on stress. According to the evaluation index, the optimal level combination was A3B1C3D2E2, that is, the inlet diameter D1 was 76 mm, outlet diameter D2 was 252 mm, the inlet angle was 26°, the outlet angle was 24°, and the wrap angle was 105°, while the stress of the lining plastic pump was minimum, which showed that the lining plastic pump under this parameter has minimal stresses.Table 9
Influence data of various factors on stress.
D
1
D
2
β
b1
β
b2
φ
K1
4.2388e7
4.1699e7
4.3788e7
4.2689e7
4.3109e7
K2
4.2949e7
4.3870e7
4.3163e7
4.2370e7
4.1724e7
K3
4.1731e7
4.3021e7
4.1370e7
4.3489e7
4.3755e7
K4
4.4587e7
4.3065e7
4.3308e7
4.3107e7
4.3067e7
K
1
¯
1.0597e7
1.0425e7
1.0947e7
1.0672e7
1.0777e7
K
2
¯
1.0737e7
1.0968e7
1.0791e7
1.0593e7
1.0431e7
K
3
¯
1.0433e7
1.0755e7
1.0342e7
1.0872e7
1.0939e7
K
4
¯
1.1147e7
1.0766e7
1.0827e7
1.0777e7
1.0767e7
Range
0.0714e7
0.0543e7
0.0605e7
0.0279e7
0.0508e7
Sequencing
1
3
2
5
4Figure 14
Influence trend of various parameters on stress.


## 4.7. Taguchi Algorithms Used to Optimize the Structural Parameters of the Lining Plastic Pump

In this chapter, the comprehensive weighted scoring method was used to analyze the orthogonal experimental results in the previous chapter. The comprehensive weighting method was a mathematical statistical method which converted the multi-index experiment into a single index one. It was a method which used the total score of each experiment to represent the experimental results. In this paper, the relevant knowledge of mathematical statistics is used to analyze and process the test results, and the score value of the comprehensive weighted score is calculated [12, 13].Y
j
∗ was used to represent the sum of weighted scores of each performance index, and the larger Yj∗ was, the better the comprehensive performance of this group of tests will be. The formula for calculating the comprehensive weighted scores is as follows:(5)Yj∗=∑i=12Yi,j×ωi.


## 4.8. Comprehensive Weighted Scoring Results of Plastic-Lined Pump Impeller Structure

The results of the 16 orthogonal experiments obtained in the previous chapter were calculated by comprehensive weighted scoring. The results are shown in Table10; group 9 had the largest value and Yj∗ score was 98.8, The combined parameters were A3B1C3D4E2, that is, the inlet diameter D1 was 76 mm, the outlet diameter D2 was 252 mm, the inlet angle was 26°, the outlet angle was 32°, and the wrap angle was 105°.Table 10
Comprehensive weighted score value table of orthogonal experimental results of the plastic-lined pump structure.
Sequence number
Displacement
Grade
Stress
Grade
Comprehensively weighted gradingY∗
1
0.0010517
86
9.4958e6
92
88.4
2
0.0010629
80
9.2606e6
98
87.2
3
0.0010706
78
9.5837e6
88
82
4
0.0010470
92
1.0391e7
84
88.8
5
0.0010151
100
1.0745e7
76
90.4
6
0.0010486
88
1.0914e7
72
81.6
7
0.0010565
84
1.0403e7
82
83.2
8
0.0011110
70
9.3839e6
96
80.4
9
0.0010288
98
9.1055e6
100
98.8
10
0.0010454
94
1.1593e7
70
84.4
11
0.0010586
82
9.5659e6
90
85.2
12
0.0010863
74
9.4928e6
94
82
13
0.0010448
96
1.0801e7
74
87.2
14
0.0010479
90
1.0677e7
80
86
15
0.0010845
76
1.0732e7
78
76.8
16
0.0010888
72
9.8617e6
86
77.6


## 4.9. Formulating Controllable Factors and Their Level Tables

Taking the total displacement, deformation, and stress distribution of the plastic-lined pump into comprehensive consideration, five structural dimensions of impeller inlet diameter, impeller outlet diameter, impeller inlet angle, impeller outlet angle, and wrap angle were selected as experimental factors, and four levels were set for each factor. Table11 shows the controllable factors and their levels, the inlet angle βb1, outlet angle βb2, wrap angle φ, inlet diameter D1, and outlet diameter D2 of the pump.Table 11
Controllable factors and their levels.
Inlet diameterD1 (mm)
Outlet diameterD2 (mm)
Inlet angleβb1 (°)
Outlet angleβb2 (°)
Wrap angleφ (°)
1
72
252
18
20
100
2
74
254
22
24
105
3
76
256
26
28
110
4
78
258
30
32
115


## 4.10. Taguchi Test Design

The internal table of the orthogonal experiment was L16 (45). As shown in Table 12, since the index of the subsequent Taguchi experiment was SN ratio rather than the quality characteristic, the interaction between factors was not considered [14–16].Table 12
Inner table of orthogonal experiment.
Inlet diameterD1 (mm)
Outlet diameterD2 (mm)
Inlet angleβb1 (°)
Outlet angleβb2 (°)
Wrap angleφ (°)
1
72
252
18
°
20
°
100
°
2
72
254
22
°
24
°
105
°
3
72
256
26
°
28
°
110
°
4
72
258
30
°
32
°
115
°
5
74
252
22
°
28
°
115
°
6
74
254
18
°
32
°
110
°
7
74
256
30
°
20
°
105
°
8
74
258
26
°
24
°
100
°
9
76
252
26
°
32
°
105
°
10
76
254
18
°
28
°
100
°
11
76
256
30
°
24
°
115
°
12
76
258
22
°
20
°
110
°
13
78
252
30
°
24
°
110
°
14
78
254
26
°
20
°
115
°
15
78
256
22
°
32
°
100
°
16
78
258
18
°
28
°
105
°


### 4.10.1. Calculating the SN Ratio

In view of the fact that in practical applications, the displacement and stress are expected to be as small as possible. In taguchi algorithm, it is called the smaller-the-better characteristicYx and its SN ratio is calculated as follows [17]:Displacement SN:(6)ηi=−10log1n∑i=1nYi2.Stress SN:(7)ηj=−10log1n∑j=1nYj2.Comprehensive SN:(8)η=0.6ηi+0.4ηj.The results of SNR calculation are shown in Table13.Table 13
Results of SNR calculation.
Sequence
A
B
C
D
E
SNRηi
SNRηj
Comprehensive SNRη
1
72
252
18
°
20
°
100
°
59.56216
−139.5566
−20.0829
2
72
254
22
°
24
°
105
°
59.47015
−139.3328
−20.0505
3
72
256
26
°
28
°
110
°
59.40746
−139.6307
−20.2078
4
72
258
30
°
32
°
115
°
59.60107
−140.3332
−20.3726
5
74
252
22
°
28
°
115
°
59.8698
−140.6241
−20.3278
6
74
254
18
°
32
°
110
°
59.5878
−140.7597
−20.5512
7
74
256
30
°
20
°
105
°
59.5226
−140.3432
−20.4237
8
74
258
26
°
24
°
100
°
59.08572
−139.4477
−20.3276
9
76
252
26
°
32
°
105
°
59.75338
−139.1861
−19.8206
10
76
254
18
°
28
°
100
°
59.61435
−141.2839
−20.7450
11
76
256
30
°
24
°
115
°
59.50536
−139.6145
−20.1426
12
76
258
22
°
20
°
110
°
59.28100
−139.5479
−20.2506
13
78
252
30
°
24
°
110
°
59.619337
−140.6693
−20.4961
14
78
254
26
°
20
°
115
°
59.593603
−140.5690
−20.4714
15
78
256
22
°
32
°
100
°
59.295409
−140.6136
−20.6693
16
78
258
18
°
28
°
105
°
59.261038
−139.8790
−20.3950According to the intuitive analysis in the above table, the signal-to-noise ratio of the test group 9 was the largest. SNmax = −19.8206; the corresponding process combination parameter was A3B1C3D4E2.


### 4.10.2. Statistics of Internal Tables

(1)
Find the sum of SN ratios (T):(9)T=∑i=116Ti.Substitute the result to calculateT=∑i=116Ti=−325.3347.(2)
Find the sum of SN ratios wasTi, the average value of ti, and the range Ri of each column under the horizontal conditions of each factor: i = 1, 2, 3, 4. The calculation results are shown in Table 14.(3)
Find the sum of the total fluctuation squares of SN ratio andST:From the above calculation results, it can be seen that(10)T=−325.3347,y¯=Tn=−20.3342,ST=∑i=116yi−y¯2,ST=0.749729444.(4)
The sum of the squared fluctuations of SN ratio of each factor:(11)Si=14T12+T22+T32+T42−116T2.Substitute in the numerical value to getS1=0.2750; S2=0.1536; S3=0.11545352; S4=0.058691812; S5=0.146984112; and S1+S2+S3+S4+S5=0.749729444.Table 14
T
i, ti, and Ri of SN ratio at various factors.
A
B
C
D
E
T
1
−80.7138
−80.7274
−81.7741
−81.2286
−81.8248
T
2
−81.6303
−81.8181
−81.2982
−81.0168
−80.6898
T
3
−80.9588
−81.4434
−80.8274
−81.6756
−81.5051
T
4
−82.0318
−81.3458
−81.4350
−81.4137
−81.3144
t
1
−20.17845
−20.18185
−20.44353
−20.30715
−20.4562
t
2
−20.40758
−20.45453
−20.32455
−20.2542
−20.17225
t
3
−20.23970
−20.36085
−20.20685
−20.4189
−20.37643
t
4
−20.50795
−20.33645
−20.35875
−20.35343
−20.32860
R
0.3295
0.272675
0.236675
0.16470
0.28975


### 4.10.3. Analysis of Variance

Since there was no blank column in this experiment, that is, no error term, the minimum S4 was taken as the squared sum of error fluctuations, It can be obtained thatfA=fB=fC=fD=fE=4−1=3. The analysis of variance is shown in Table 15.Table 15
Variance analysis table.
S
f
V
F
A
0.2750
3
0.091667
4.685492 (∗)
B
0.1536
3
0.0512043
2.617060
C
0.11545352
3
0.038485
1.967115
D
0.058691812
3
0.0195639
1
E
0.146984112
3
0.048995
2.504338
(e)
(0.058691812)
(3)
(0.0195639)
T
0.749729444
12From the perspective of SNR comparison, factor A has a significant impact on the quality fluctuation characteristics. It could be considered that factorA was a stabilizing factor and factors B, C, D, and E were adjustable factors. For the stabilizing factor, its level is taken as A3, and the total displacement SNR of factors B, C, D and E is listed in Table 16.Table 16
SN ratio response table of factorsB, C, D, and E.
B
C
D
E
1
238.8047
238.0253
237.9594
237.5576
2
238.2668
237.9173
237.6815
238.0081
3
237.7308
237.8402
238.1526
237.8956
4
237.2288
238.2484
238.2377
238.5698Since the influence of factorsB, C, D, and E on the quality fluctuation characteristics was not very significant, it can be considered to ignore the stress and simply adjust the parameters of B, C, D, and E to minimize the stress. As can be seen from the above table, the optimal process parameter was B1C4D4E4, considering only the stress. Finally, the optimized combination parameter was A3B1C3D2E2, which was basically consistent with the optimal combination parameter A3B1C3D4E2 obtained by the intuitive method above.


## 4.10.1. Calculating the SN Ratio

In view of the fact that in practical applications, the displacement and stress are expected to be as small as possible. In taguchi algorithm, it is called the smaller-the-better characteristicYx and its SN ratio is calculated as follows [17]:Displacement SN:(6)ηi=−10log1n∑i=1nYi2.Stress SN:(7)ηj=−10log1n∑j=1nYj2.Comprehensive SN:(8)η=0.6ηi+0.4ηj.The results of SNR calculation are shown in Table13.Table 13
Results of SNR calculation.
Sequence
A
B
C
D
E
SNRηi
SNRηj
Comprehensive SNRη
1
72
252
18
°
20
°
100
°
59.56216
−139.5566
−20.0829
2
72
254
22
°
24
°
105
°
59.47015
−139.3328
−20.0505
3
72
256
26
°
28
°
110
°
59.40746
−139.6307
−20.2078
4
72
258
30
°
32
°
115
°
59.60107
−140.3332
−20.3726
5
74
252
22
°
28
°
115
°
59.8698
−140.6241
−20.3278
6
74
254
18
°
32
°
110
°
59.5878
−140.7597
−20.5512
7
74
256
30
°
20
°
105
°
59.5226
−140.3432
−20.4237
8
74
258
26
°
24
°
100
°
59.08572
−139.4477
−20.3276
9
76
252
26
°
32
°
105
°
59.75338
−139.1861
−19.8206
10
76
254
18
°
28
°
100
°
59.61435
−141.2839
−20.7450
11
76
256
30
°
24
°
115
°
59.50536
−139.6145
−20.1426
12
76
258
22
°
20
°
110
°
59.28100
−139.5479
−20.2506
13
78
252
30
°
24
°
110
°
59.619337
−140.6693
−20.4961
14
78
254
26
°
20
°
115
°
59.593603
−140.5690
−20.4714
15
78
256
22
°
32
°
100
°
59.295409
−140.6136
−20.6693
16
78
258
18
°
28
°
105
°
59.261038
−139.8790
−20.3950According to the intuitive analysis in the above table, the signal-to-noise ratio of the test group 9 was the largest. SNmax = −19.8206; the corresponding process combination parameter was A3B1C3D4E2.


## 4.10.2. Statistics of Internal Tables

(1)
Find the sum of SN ratios (T):(9)T=∑i=116Ti.Substitute the result to calculateT=∑i=116Ti=−325.3347.(2)
Find the sum of SN ratios wasTi, the average value of ti, and the range Ri of each column under the horizontal conditions of each factor: i = 1, 2, 3, 4. The calculation results are shown in Table 14.(3)
Find the sum of the total fluctuation squares of SN ratio andST:From the above calculation results, it can be seen that(10)T=−325.3347,y¯=Tn=−20.3342,ST=∑i=116yi−y¯2,ST=0.749729444.(4)
The sum of the squared fluctuations of SN ratio of each factor:(11)Si=14T12+T22+T32+T42−116T2.Substitute in the numerical value to getS1=0.2750; S2=0.1536; S3=0.11545352; S4=0.058691812; S5=0.146984112; and S1+S2+S3+S4+S5=0.749729444.Table 14
T
i, ti, and Ri of SN ratio at various factors.
A
B
C
D
E
T
1
−80.7138
−80.7274
−81.7741
−81.2286
−81.8248
T
2
−81.6303
−81.8181
−81.2982
−81.0168
−80.6898
T
3
−80.9588
−81.4434
−80.8274
−81.6756
−81.5051
T
4
−82.0318
−81.3458
−81.4350
−81.4137
−81.3144
t
1
−20.17845
−20.18185
−20.44353
−20.30715
−20.4562
t
2
−20.40758
−20.45453
−20.32455
−20.2542
−20.17225
t
3
−20.23970
−20.36085
−20.20685
−20.4189
−20.37643
t
4
−20.50795
−20.33645
−20.35875
−20.35343
−20.32860
R
0.3295
0.272675
0.236675
0.16470
0.28975


## 4.10.3. Analysis of Variance

Since there was no blank column in this experiment, that is, no error term, the minimum S4 was taken as the squared sum of error fluctuations, It can be obtained thatfA=fB=fC=fD=fE=4−1=3. The analysis of variance is shown in Table 15.Table 15
Variance analysis table.
S
f
V
F
A
0.2750
3
0.091667
4.685492 (∗)
B
0.1536
3
0.0512043
2.617060
C
0.11545352
3
0.038485
1.967115
D
0.058691812
3
0.0195639
1
E
0.146984112
3
0.048995
2.504338
(e)
(0.058691812)
(3)
(0.0195639)
T
0.749729444
12From the perspective of SNR comparison, factor A has a significant impact on the quality fluctuation characteristics. It could be considered that factorA was a stabilizing factor and factors B, C, D, and E were adjustable factors. For the stabilizing factor, its level is taken as A3, and the total displacement SNR of factors B, C, D and E is listed in Table 16.Table 16
SN ratio response table of factorsB, C, D, and E.
B
C
D
E
1
238.8047
238.0253
237.9594
237.5576
2
238.2668
237.9173
237.6815
238.0081
3
237.7308
237.8402
238.1526
237.8956
4
237.2288
238.2484
238.2377
238.5698Since the influence of factorsB, C, D, and E on the quality fluctuation characteristics was not very significant, it can be considered to ignore the stress and simply adjust the parameters of B, C, D, and E to minimize the stress. As can be seen from the above table, the optimal process parameter was B1C4D4E4, considering only the stress. Finally, the optimized combination parameter was A3B1C3D2E2, which was basically consistent with the optimal combination parameter A3B1C3D4E2 obtained by the intuitive method above.


## 4.11. Optimizing Model Validation

The accuracy of the optimization model was verified by thermo-solid coupling analysis of the optimized impeller structure parameter model. The thermo-solid coupling simulation results of the optimized model are shown in Figures15 and 16. By comparing with the thermo-solid coupling simulation results before optimization, it can be seen that the total displacement and stress distribution after optimization were smaller than those before optimization. Figures 17 and 18 are, respectively, the total displacement and deformation diagram and stress distribution diagram before optimization.Figure 15
Total displacement and deformation after optimization.Figure 16
Stress distribution diagram after optimization.Figure 17
Total displacement and deformation before optimization.Figure 18
Stress distribution before optimization.In Taguchi algorithm, based on the above orthogonal experiment, the internal table of orthogonal experiment was designed and established to calculate the SNR of total displacement and stress distribution under various horizontal conditions, and its variance was calculated; by analyzing the calculated variance, the stability factor and adjustable factor could be obtained, then the adjustable factor could be optimized twice, and the final optimal process combination parameter can be obtained asA3B1C3D2E2, When the inlet diameter D1 was 76 mm, the outlet diameter D2 was 252 mm, the inlet angle was 26°, the outlet angle was 24°, and the wrap angle was 115°, the total displacement, deformation, and stress of the pump were the minimum. Simulation results showed that the optimal combination was reasonable.


## 5. Performance Test of Lining Plastic Pump

### 5.1. Model Conversion

The principle of similitude conversion of plastic lining pump was to select a model which was equal to or similar to the designed pump speed to carry out similar conversion of its flow components [18]. Model pumps can be selected by referring to the design manual [3]: IS50-32-200: QM = 12.5 m3/h, nSM = 33, nM = 2900 rpm, D1M = 48 mm, D2M = 198 mm, b2M = 4 mm, b3M = 12 mm, and ZM = 6. The structure parameters of the lining plastic pump optimized under fluid-thermal-structure interaction conditions were as follows: QM = 25 m3/h, HM = 80m, nSM = 32.98, nM = 2900 rpm, D1 = 76 mm, D2M = 252 mm, b2M = 6.8 mm, b3M = 42 mm, and ZM = 6.


#### 5.1.1. Printing the Physical Impeller

The physical model was manufactured according to the similar converted liner pump structure parameters. Similar parameter combination was as follows: after the conversion, impeller inlet diameterD1 was 60 mm, impeller outlet D2 was 200 mm, inlet angle was 26°, outlet angle was 32°, and wrap angle was 105°. According to this set of parameters, three-dimensional modeling of the impeller structure of the lining plastic pump was conducted, as shown in Figure 19. The physical model is shown in Figure 20.Figure 19
Three-dimensional diagram of lining pump.Figure 20
Picture of lining plastic pump.


### 5.2. Performance Experiment

The similar model obtained by the similar conversion method was used for 3D printing, and the similar converted physical model was printed and then used in the external characteristic performance experiment [19, 20]. The experimental data collection platform of the lining plastic pump was equipped with the pump test system (electrical test method) V8.97 software specially used to collect the performance data onto the lining plastic pump. Data points of lift H and flow Q of each working point collected by the lining plastic pump under different flow conditions are included in Table 17.Table 17
Experimental table of performance of lining plastic pump.
Product model
Fluid density (kg/m3): water
Export caliber (mm): 80
Product number: 001
Fluid viscosity (cst): water
Surface distance (m): 0.0
Manufacturer: Anhui Polytechnic University School of Mechanical and Automotive Engineering
Water temperature (°C): 11
Measurement set number
Switch to rated speed = 1450 (r/min)
Serial number
Import pressure (kPa)
Export pressure (kPa)
Traffic (m3/h)
Rotation speed (r/min)
Input power (W)
Traffic (m3/h)
Head (m)
Shaft power (W)
1
7.79
21.62
33.85
1448.30
1363.97
67.78
6.08
8292.97
2
8.23
24.64
30.06
1447.93
1398.90
60.21
7.05
8560.39
3
8.52
26.87
27.05
1447.65
1431.84
54.19
7.78
8806.19
4
8.80
28.90
23.99
1461.60
1439.54
47.60
8.28
8711.76
5
9.05
30.92
20.93
1477.68
1490.61
41.08
8.74
8895.00
6
9.26
32.74
18.08
1447.91
1477.37
36.21
9.73
9158.49
7
9.45
34.71
14.98
1447.11
1472.91
30.02
10.43
9127.00
8
9.60
35.42
12.06
1447.97
1473.81
24.15
10.61
9131.15
9
9.74
36.87
8.93
1447.68
1433.57
17.89
11.13
8829.37
10
9.83
38.51
6.09
1447.68
1388.37
12.20
11.75
8488.16
11
9.86
39.08
4.01
1448.56
1297.83
8.03
11.95
7794.08
12
9.88
39.21
2.37
1448.92
1264.31
4.74
11.98
7539.48It can be seen from Table17 that, as the flow Q decreases, the head was gradually increased, and when the flow of the lining plastic pump was located in the Q = 2.37 m3/h, its head was about 12m, which was greatly different from the value of HM = 50 m of the model pump used for similar conversion. The reasons for this deviation mainly included the following aspects:(1)
Excessive clearance: as the axial size of the inner cavity of the volute was relatively large, large clearance will be generated at the front end of the impeller when the impeller was installed inside the pump housing (Figure21); the impeller front gap is too large, which causes the liquid backflow between the pump shell and the impeller, seriously affecting the hydraulic performance of the entire the lining plastic pump.(2)
Cracks on the pump shell: the pipe at the outlet of the pump shell was a metal pipe. This metal pipe had certain stiffness, which led to the installation of it with the pump shell outlet face, as shown in Figure22. Small cracks appear on the surface of the water outlet pipe of the pump shell when the water outlet pipe and the pipe fitting surface of the pump shell are installed, as shown in Figure 23. When the pump shell was filled with water, slight seepage water was found, the water in the whole pump chamber was dried, and glass glue was applied to the tiny crack of the pump shell. Although it does not impede the experiment, it will affect the pressure at the outlet of the pump, causing a decrease in the outlet pressure and a decrease in head of pump.(3)
Water accumulation at the outlet flange: due to the loose fitting between the outlet pipe and the pump casing, there was a wraping angle, and rubber gasket was added at the two joint surfaces, but the wraping angle of the joint has not been fully compensated. Afterwards, a certain thickness of glass glue was applied between the two bonding surfaces to make up the wrap angle gap. However, the high-speed rotation of the water from the pump shell through the impeller at the outlet had a certain pressure, so that it still has water accumulation in the outlet flange, and the water leakage occurs for a long time, as shown in Figure24. Leakage at the outlet flange seriously affects the outlet pressure of the pump, resulting in a significant reduction in the lift.Figure 21
Schematic diagram of the impeller clearance of the lining plastic pump.Figure 22
Warping position of water outlet pipe and pump shell joint.
(a)
(b)Figure 23
Location of pump shell crack.Figure 24
Water location of exit flange.
(a)
(b)Taking the minimum displacement and deformation of the impeller as the reference index, using the comprehensive weighted scoring method and the Taguchi algorithm to optimize the parameters of the thermal-solid coupling analysis of the lining plastic pump flow, the optimal combination parameters under the condition of the minimum displacement and stress were obtained asA3B1C3D2E2, that is, when the inlet diameter D1 was 76 mm, the outlet diameter D2 was 252 mm, the inlet angle was 26°, the outlet angle was 24°, and the wrap angle was 115°, and the total displacement, deformation, and stress of the pump were minimal.


## 5.1. Model Conversion

The principle of similitude conversion of plastic lining pump was to select a model which was equal to or similar to the designed pump speed to carry out similar conversion of its flow components [18]. Model pumps can be selected by referring to the design manual [3]: IS50-32-200: QM = 12.5 m3/h, nSM = 33, nM = 2900 rpm, D1M = 48 mm, D2M = 198 mm, b2M = 4 mm, b3M = 12 mm, and ZM = 6. The structure parameters of the lining plastic pump optimized under fluid-thermal-structure interaction conditions were as follows: QM = 25 m3/h, HM = 80m, nSM = 32.98, nM = 2900 rpm, D1 = 76 mm, D2M = 252 mm, b2M = 6.8 mm, b3M = 42 mm, and ZM = 6.


### 5.1.1. Printing the Physical Impeller

The physical model was manufactured according to the similar converted liner pump structure parameters. Similar parameter combination was as follows: after the conversion, impeller inlet diameterD1 was 60 mm, impeller outlet D2 was 200 mm, inlet angle was 26°, outlet angle was 32°, and wrap angle was 105°. According to this set of parameters, three-dimensional modeling of the impeller structure of the lining plastic pump was conducted, as shown in Figure 19. The physical model is shown in Figure 20.Figure 19
Three-dimensional diagram of lining pump.Figure 20
Picture of lining plastic pump.


## 5.1.1. Printing the Physical Impeller

The physical model was manufactured according to the similar converted liner pump structure parameters. Similar parameter combination was as follows: after the conversion, impeller inlet diameterD1 was 60 mm, impeller outlet D2 was 200 mm, inlet angle was 26°, outlet angle was 32°, and wrap angle was 105°. According to this set of parameters, three-dimensional modeling of the impeller structure of the lining plastic pump was conducted, as shown in Figure 19. The physical model is shown in Figure 20.Figure 19
Three-dimensional diagram of lining pump.Figure 20
Picture of lining plastic pump.


## 5.2. Performance Experiment

The similar model obtained by the similar conversion method was used for 3D printing, and the similar converted physical model was printed and then used in the external characteristic performance experiment [19, 20]. The experimental data collection platform of the lining plastic pump was equipped with the pump test system (electrical test method) V8.97 software specially used to collect the performance data onto the lining plastic pump. Data points of lift H and flow Q of each working point collected by the lining plastic pump under different flow conditions are included in Table 17.Table 17
Experimental table of performance of lining plastic pump.
Product model
Fluid density (kg/m3): water
Export caliber (mm): 80
Product number: 001
Fluid viscosity (cst): water
Surface distance (m): 0.0
Manufacturer: Anhui Polytechnic University School of Mechanical and Automotive Engineering
Water temperature (°C): 11
Measurement set number
Switch to rated speed = 1450 (r/min)
Serial number
Import pressure (kPa)
Export pressure (kPa)
Traffic (m3/h)
Rotation speed (r/min)
Input power (W)
Traffic (m3/h)
Head (m)
Shaft power (W)
1
7.79
21.62
33.85
1448.30
1363.97
67.78
6.08
8292.97
2
8.23
24.64
30.06
1447.93
1398.90
60.21
7.05
8560.39
3
8.52
26.87
27.05
1447.65
1431.84
54.19
7.78
8806.19
4
8.80
28.90
23.99
1461.60
1439.54
47.60
8.28
8711.76
5
9.05
30.92
20.93
1477.68
1490.61
41.08
8.74
8895.00
6
9.26
32.74
18.08
1447.91
1477.37
36.21
9.73
9158.49
7
9.45
34.71
14.98
1447.11
1472.91
30.02
10.43
9127.00
8
9.60
35.42
12.06
1447.97
1473.81
24.15
10.61
9131.15
9
9.74
36.87
8.93
1447.68
1433.57
17.89
11.13
8829.37
10
9.83
38.51
6.09
1447.68
1388.37
12.20
11.75
8488.16
11
9.86
39.08
4.01
1448.56
1297.83
8.03
11.95
7794.08
12
9.88
39.21
2.37
1448.92
1264.31
4.74
11.98
7539.48It can be seen from Table17 that, as the flow Q decreases, the head was gradually increased, and when the flow of the lining plastic pump was located in the Q = 2.37 m3/h, its head was about 12m, which was greatly different from the value of HM = 50 m of the model pump used for similar conversion. The reasons for this deviation mainly included the following aspects:(1)
Excessive clearance: as the axial size of the inner cavity of the volute was relatively large, large clearance will be generated at the front end of the impeller when the impeller was installed inside the pump housing (Figure21); the impeller front gap is too large, which causes the liquid backflow between the pump shell and the impeller, seriously affecting the hydraulic performance of the entire the lining plastic pump.(2)
Cracks on the pump shell: the pipe at the outlet of the pump shell was a metal pipe. This metal pipe had certain stiffness, which led to the installation of it with the pump shell outlet face, as shown in Figure22. Small cracks appear on the surface of the water outlet pipe of the pump shell when the water outlet pipe and the pipe fitting surface of the pump shell are installed, as shown in Figure 23. When the pump shell was filled with water, slight seepage water was found, the water in the whole pump chamber was dried, and glass glue was applied to the tiny crack of the pump shell. Although it does not impede the experiment, it will affect the pressure at the outlet of the pump, causing a decrease in the outlet pressure and a decrease in head of pump.(3)
Water accumulation at the outlet flange: due to the loose fitting between the outlet pipe and the pump casing, there was a wraping angle, and rubber gasket was added at the two joint surfaces, but the wraping angle of the joint has not been fully compensated. Afterwards, a certain thickness of glass glue was applied between the two bonding surfaces to make up the wrap angle gap. However, the high-speed rotation of the water from the pump shell through the impeller at the outlet had a certain pressure, so that it still has water accumulation in the outlet flange, and the water leakage occurs for a long time, as shown in Figure24. Leakage at the outlet flange seriously affects the outlet pressure of the pump, resulting in a significant reduction in the lift.Figure 21
Schematic diagram of the impeller clearance of the lining plastic pump.Figure 22
Warping position of water outlet pipe and pump shell joint.
(a)
(b)Figure 23
Location of pump shell crack.Figure 24
Water location of exit flange.
(a)
(b)Taking the minimum displacement and deformation of the impeller as the reference index, using the comprehensive weighted scoring method and the Taguchi algorithm to optimize the parameters of the thermal-solid coupling analysis of the lining plastic pump flow, the optimal combination parameters under the condition of the minimum displacement and stress were obtained asA3B1C3D2E2, that is, when the inlet diameter D1 was 76 mm, the outlet diameter D2 was 252 mm, the inlet angle was 26°, the outlet angle was 24°, and the wrap angle was 115°, and the total displacement, deformation, and stress of the pump were minimal.


## 6. Conclusion

(1)
In this paper, the orthogonal experimental table of L16 (45) was designed and the orthogonal experiment was carried out; it can be concluded that the influence of each factor on the efficiency of the lining plastic centrifugal pump was from large to small: impeller outlet diameter D2, wrap angle φ, inlet diameter D1, inlet angle βb1, and outlet angle βb2, and the influence of various factors on cavitation of the centrifugal pump is in the following order: inlet angle βb1, wrap angle φ, impeller outlet diameter D2, outlet angle βb2, and inlet diameter D1;
(2)
Under the condition of fluid-solid coupling, when the total displacement was taken as the optimization index, the optimal horizontal combination was the inlet diameterD1 is 76 mm, the outlet diameter D2 was 252 mm, the inlet angle was 26°, the outlet angle was 32°, and the wrap angle was 115°; the total displacement can be obtained to be the minimum, indicating that the plastic pump under this parameter had the minimum deformation; when the stress was taken as the optimization index, the optimal combination is that the inlet diameter D1 was 76 mm, the outlet diameter D2 was 252 mm, the inlet angle was 26°, the outlet angle was 24°, and the wrap angle was 105°; the minimum stress can be obtained, which indicated that the plastic pump under this parameter had the minimum stress.
(3)
Taking the minimum displacement and deformation of the impeller as the optimization index, using Taguchi algorithm to optimize the parameters of the flow thermo-solid coupling analysis of the lining plastic pump flow, the optimal combination parameters under the condition of the minimum displacement and stress were obtained: when the inlet diameterD1 was 76 mm, the outlet diameter D2 was 252 mm, the inlet angle was 26°, the outlet angle was 24°, and the wrap angle was 115°, the total displacement deformation and stress of plastic pump lining were minimum.



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*Source: 3790167-2019-03-11.xml*