# Research on Vibration Reduction in the Transmission System of Plastic Centrifugal Pump
## 2 Structural Design of the Plastic Centrifugal Pump
Based on \(Q\) = 50 m\({}^{3}\)/h, the inlet diameter \(D_{s}\) is determined to be 80 mm, and the inlet velocity vs. is 2.76 m/s. The pump’s outlet diameter is calculated with Formula (2) and rounded off to a standard pipe diameter [15]. \[D_{d}=(1\sim 0.7)D_{s} \tag{2}\]  
where  
\(D_{d}\)—Pump outlet diameter (mm). The outlet velocity of the pump is computed using Formula (3) [15]. \[v_{d}=\frac{4Q}{\pi D_{d}^{2}} \tag{3}\]  
where  
\(v_{d}\)—Pump outlet flow rate (m/s). Setting \(D_{d}\) = 0.9\(D_{s}\), gives \(D_{d}\) = 72 mm and \(v_{d}\) = 3.41 m/s. (2) Determining the Specific Speed of the Plastic Centrifugal Pump  
The specific speed, as per similarity laws, acts as an integrated indicator for assessing flow, speed, and head. It is calculated using Formula (4) [15]. \[n_{s}=\frac{3.65n\sqrt{Q}}{H^{\frac{3}{4}}} \tag{4}\]  
where  
\(n_{s}\)—Specific speed. The calculated result is \(n_{s}\) = 89.56  
(3) Efficiency Estimation of the Plastic Centrifugal Pump  
The hydraulic efficiency of the plastic centrifugal pump is calculated using the following Formula (5) [15]. \[\eta_{h}\approx 1+0.08351 lg\sqrt[3]{\frac{Q}{n}} \tag{5}\]  
where  
\(\eta_{h}\)—The hydraulic efficiency of the plastic centrifugal pump. The calculated result is \(\eta_{h}=0.86\)  
The volumetric efficiency of the plastic centrifugal pump is calculated using the following Formula (6) [15]. \[\eta_{\sigma}\approx\frac{1}{1+0.68n_{s}^{-\frac{2}{3}}} \tag{6}\]  
where  
\(\eta_{\sigma}\)--The volumetric efficiency of the plastic centrifugal pump. The calculated result is \(\eta_{\sigma}=0.97\)  
The mechanical efficiency due to disc friction losses is calculated using the following Formula (7) [15]. \[\eta^{\prime}_{m}=1-0.07\frac{1}{\left(\frac{n_{s}}{100}\right)^{\frac{2}{6}}} \tag{7}\]  
where  
\(\eta^{\prime}_{m}\)--The mechanical efficiency due to disc friction losses. The calculated result is \(\eta^{\prime}_{m}=0.90\)  
The mechanical efficiency of the plastic centrifugal pump is calculated using the following Formula (8) [15]. \[\eta_{m}=\eta^{\prime}_{m}-\eta_{b} \tag{8}\]  
where  
\(\eta_{b}\)--is the loss due to bearings and packing, \(\eta_{b}=0.02\eta^{\prime}m^{\prime\prime}\);  
\(\eta_{m}\)--The mechanical efficiency of the plastic centrifugal pump. The calculated result is \(\eta_{m}=0.88\)  
The overall efficiency of the plastic centrifugal pump is calculated using the following Formula (9) [15]. \[\eta=\eta_{m}\eta_{\sigma}\eta_{h} \tag{9}\]  
where  
\(\eta\)--The overall efficiency of the plastic centrifugal pump. The calculated result is \(\eta=0.74\)  
(4) Pump Shaft Diameter and Impeller Hub Diameter  
The minimum diameter of the pump shaft is calculated using the following Formula (10) [15]. \[d=\sqrt[3]{\frac{M_{n}}{0.2[\tau]}} \tag{10}\]  
where  
[\(\tau\)]--The permissible shear stress of the material, (Pa);  
\(d\)--The minimum diameter of the pump shaft, (mm). The plastic centrifugal pump in this study is made of 45# steel with tempering treatment. According to the Mechanical Engineering Materials Handbook, its permissible shear stress value is 45 MPa. The calculated minimum shaft diameter is \(d=12.93\) mm. As the medium conveyed in this study is clean water, we chose \(d=20\) mm. To ensure the sufficient strength and rigidity of the impeller hub, when designing the impeller hub diameter, dh, the metal pump generally takes \(d_{h}=\) (1.4-2) \(d_{min}\) and the material of the pump in this paper is plastic, so the final hub diameter takes three times the diameter of the pump shaft, and \(d_{h}=60\) mm is selected. (5) Selection of Impeller and Other Components for Plastic Centrifugal Pump  
The blade profile determines the performance of the impeller. According to the literature [16], the shape of the blade profile selected in this paper is an equiangular logarithmic spiral. The paper adopts a uniformly varying blade thickness [17; 18; 19], with an inlet thickness of 4 mm and an outlet thickness of 8 mm, where the blade thickness ranges between 4 and 8 mm.