Design and vibration characteristics of sandwich constrained damping gasket for diaphragm air pump

There are certain problems of vibration reduction and isolation relevant to the working stability of diaphragm air pumps. To make the diaphragm air pump meet the use requirements, a sandwich-constrained damping gasket is designed and prepared in this paper. The research focuses on examining the impact of varying damping layer thickness on the efficacy of damping gaskets in reducing and isolating vibrations. Meanwhile, with the increase of the damping layer thickness, the total vibration severity of the diaphragm air pump body continues to increase, indicating a weakened performance of vibration reduction, while the vibration isolation performance is gradually improved.


Introduction
As a common rotating machine, a diaphragm air pump has the advantages of being maintenance-free, having high air tightness, strong corrosion resistance, and good stability.Therefore, the diaphragm air pump is widely used in biochemical, medical and health, environmental protection, mine ventilation, military, and other fields.However, during the stable working of the diaphragm air pump, the circular motion of its eccentric wheel will produce periodic harmonic force, which will lead to a certain vibration response.
This vibration response will not only damage the physical and mental health of people around the equipment but also damage the parts of the diaphragm air pump, thereby affecting its application performance.Therefore, it is necessary to carry out a vibration reduction design for the diaphragm air pump.In addition, the diaphragm air pump will also transmit the vibration to the installation foundation during the working process, thus damaging the other parts and equipment on the installation foundation.Therefore, based on the vibration reduction design, a vibration isolation design should also be carried out for the diaphragm air pump [1].
Several researchers have investigated the vibration control and isolation techniques pertinent to rotating machinery.Zhang et al. [2] investigated the vibration concerns associated with the vehicle's steering wheel.The findings indicate a notable reduction of over 50% in the steering wheel's amplitude at the resonance frequency after the integration of the metal rubber isolators.Santosh et al. [3] have analyzed the vibration problems of the engine and studied the vibration isolation characteristics of the rubber mount.The results show that the suspension gasket with high damping and low stiffness has better vibration isolation performance.Wang et al. [4] examined the impact of the dynamic stiffness of rubber isolators on the vibration behavior of the seawater hydraulic piston pump system.Their investigation, which entailed a hammering experiment, revealed an improvement in the vibration attenuation with heightened dynamic stiffness of the rubber isolators.However, the study also indicated a concurrent deterioration in the vibration isolation effect.

Preparation of SCDGs
2.1.1.Structure design.Sandwich-constrained damping gaskets commonly consist of two constraint layers and one damping layer.As shown in Figure 1, the sandwich-constrained damping gasket prepared in this study is composed of an upper constrained layer (5 mm), a damping layer, and a lower constrained layer (2 mm).Theoretical investigation has indicated the significant influence of stiffness on the vibration reduction and isolation capabilities of the damping gasket.Consequently, the present study aims to vary the thickness of the damping layer to analyze the implications of altered stiffness levels on vibration reduction and isolation performance.The selected thickness values for the damping layer are 10 mm, 20 mm, 30 mm, and 40 mm, respectively.
During the application, the gasket is placed between the upper and lower structures.To facilitate the replacement of gaskets, they are designed to be fixed with bolts.One bolt is used to secure the structure above the gasket, and two bolts are used to secure the lower structure.All these bolts do not penetrate the damping layer of the gasket.Because, if the bolt penetrates the gaskets, the vibration between the upper and lower structures of the gasket be will directly transmitted through the bolt, and the damping layer in the gasket will not have any effect.Based on the gasket structure design used in this study, the vibration will not be transmitted through the bolt, but will completely act on the damping layer.
During the preparation process of these gaskets, all layers were first cleaned to remove the oil stain on the surface of the plates, to improve the bonding strength of all layers.Then, the epoxy resin adhesive was applied to bond the stacked three-layer plates together.Finally, to ensure that all layers were fully bonded, the G-clamps were used to clamp the three-layer plates for 48 hours.Figure 2 shows the sandwich-constrained damping gaskets prepared during this study.

Materials selection.
The constraint layer generally adopts light alloys or fiber-reinforced composite materials, which could improve the bending stiffness and buckling resistance of the whole structure, so that the force distributed on the damping layer is uniform, and the service life of the gasket could be improved.
In this study, 6061 aluminum alloy is selected as the material of the constrained layer.This material has low density, high strength, and stiffness, and is widely used in aerospace and large ships.
The damping layer is generally made of polymers.The most remarkable mechanical property of such materials is viscoelasticity [5], so they are also called viscoelastic damping materials, such as polyethylene and polyurethane foam [6].Viscoelastic material property is formed by the combination of energy storage capacity (elastic part) and energy loss capacity (viscous part) in a certain proportion.When it is subjected to alternating load, the elastic part will store part of its energy.After the external force is removed, the deformation will recover, and the energy will be released.At the same time, the energy acting on the viscous part is used to overcome the internal friction of viscoelastic materials, and this leads to the transformation of mechanical energy into thermal energy and a decrease in vibration amplitude.In this study, rubber is utilized as the damping layer owing to its high damping coefficient and its prevalent application as a thin plate in car and bus vibration and noise attenuation.

Vibration characteristic tests 2.2.1. Experimental bench.
Considering practical application requirements and system centroid balance factors, the diaphragm air pump was fixed on a base with a certain mass by bolts during the vibration characteristic testing process.Then the base with installed diaphragm air pump was installed on a rigid workbench, forming a vibration characteristic testing system.The installation diagram of this system including the diaphragm air pump, base, and rigid workbench is shown in Figure 3.During the testing process, the rigid workbench was also fixed to the ground through bolts, and the SCDGs were installed between the base and the workbench.During the research, the vibration responses of the rigid bench and diaphragm air pump body before and after the installation of sandwich constrained damping gasket were tested and compared respectively, to study the vibration reduction and isolation effect of the sandwich-constrained damping gasket.As shown in Figure 4(a), when studying the vibration characteristics of the system without SCDGs, the base and rigid bench are directly fixed together by bolts.In this case, the purpose of the vibration characteristic experiment is to get the vibration response as the blank control group, which provides a reference basis for the subsequent evaluation of vibration reduction and isolation performance of SCDGs.
As shown in Figure 4(b) and Figure 4(c), during the analysis of the vibration reduction and isolation efficacy of SCDGs, four sandwich-constrained damping gaskets will be installed at positions 1-4 between the base and the rigid bench.In this case, the purposes of the vibration characteristic experiment are to study whether the vibration response of the diaphragm air pump system meets the use requirements after installing the SCDGs and to study the influence of the damping layer thickness on the vibration response of the diaphragm air pump system.

Coordinate system.
In the stable working environment of the diaphragm air pump, the circular motion of the eccentric wheel is the main cause of vibration.As shown in Figure 5a, when the eccentric body rotates around the rotation axis, periodic harmonic forces will be generated in the radial direction of the eccentric body.In addition, a certain vibration response will also occur in the direction of the rotation axis due to the existence of the rolling element in the bearing.To ensure the consistency of subsequent vibration tests, it is necessary to unify the coordinate direction of the diaphragm air pump system.
Using the diaphragm air pump as the reference, the origin was set at the center point on the lower surface of its left end (Figure 5b).The y-axis was aligned with the main axis, while the z-axis was normal to the bottom surface during installation.The x-axis was then selected perpendicular to both the z-axis and y-axis (Figure 5c).

Experiments on vibration reduction characteristics.
During the study of vibration-damping characteristics, the vibration severity was used to evaluate the vibration response of the diaphragm air pump body, with the help of a three-axis acceleration sensor.According to the use requirements, 4 test points were selected, and an acceleration sensor was installed on each test point.These 4 test points were respectively the left body of the diaphragm air pump, the pump foot, the connection between the pump body and the motor, and the power box of the motor (Figure 6).The frequency band used for testing during this study was 10-1000 Hz.

Experiments on vibration isolation characteristics.
As shown in Figure 7, four uniaxial acceleration sensors were used in the experiment, which were installed on the rigid bench and near the installation positions of the blue base.The test directions of all four sensors were in the z direction of the system.The frequency band used during this study on the vibration isolation effect of SCDG was 10-8000 Hz.
During the research of vibration isolation characteristics, the vibration acceleration level (AL) and isolation amount (IA) were used as the evaluation index.The IA is equal to the difference in AL of each test point with and without installation of SCDGs.
The vibration acceleration level La (dB) is defined with the formula as follows: where RMS is the effective value of vibration acceleration, in m/s 2 ; a0 is the reference acceleration, which is generally taken as 1 E-6 m/s 2 .The vibration AL along the z direction at each test point was obtained through two steps.First, the time domain data obtained by the acceleration sensor shall be converted into frequency domain data through a fast Fourier transform (FFT).Then the AL at each test point was calculated with the formula as follows: where A10, …, and A8000 are the peak values of acceleration at different frequencies, in m/s 2 .

Vibration reduction performance analysis
The total vibration severity of the diaphragm air pump body and the vibration severities at each measuring point along the three test directions are shown in Table 1.From these data, the corresponding phenomena can be analyzed.

Influence of damping layer thickness on the vibration reduction.
The total vibration severity of the diaphragm air pump body is 12.31 mm/s without installing the SCDG.After the installation, the vibration severities at each test point along each direction and the total vibration severity of the diaphragm air pump body are significantly reduced.At the same time, it can be observed that the thicker the damping layer is, the greater the total vibration severity is, indicating that the damping effect of the SCDGs decreases.
As shown in Figure 8, a local coordinate system is established for SCDG.h is the height of the damping layer.and are the lengths of SCDG along the x and y directions in the local coordinate system, respectively.Then the calculation formulas of relevant parameters of SCDGs are as follows: of the damping layer is: The free surface area of the damping layer is: The ratio of the working area to the free surface area can be calculated as follows: The Japanese Mechanical Society proposed that the formulas of vertical shape coefficient (perpendicular to the bearing surface), longitudinal shape coefficient , and transverse shape coefficient for parallel shear are as follows [7]: According to the above formulas, the vertical stiffness of SCDG is： = where is the Young's modulus of the rubber material used in the damping layer.The longitudinal stiffness and lateral stiffness can be also calculated through the following formulas: where is the shear modulus of the rubber, which can be calculated by the following formula: where is the Poisson ratio of the rubber.Since solid rubber is an incompressible material, its Poisson ratio is generally taken as 0.45-0.5 [8].
According to Formula 9-11, it can be observed that as the thickness of the damping layer increases, the stiffness of the SCDG decreases in three directions.Similar studies have shown that the stiffness of the isolator helps to reduce the vibration of the hydraulic piston pump body.Therefore, an increase in the thickness of the damping layer leads to a decrease in the stiffness, resulting in a weakened damping effect and enhancement in the vibration severity of the system.

Vibration reduction mechanisms of SCDGs.
The contribution of SCDG to reducing the vibration severity of the system mainly depends on its damping mechanism.This mechanism can be further divided into two sub-mechanisms: on the one hand, the internal friction between molecular chains in the damping layer of the gasket allows some of the vibrational mechanical energy to be converted into heat and then dissipated (this is the main mechanism of vibration reduction in the z direction of system); on the other hand, there is a shear effect between the damping layer and constrained layers during vibration, which leads to shear deformation of the damping layer for the feasible energy conversion and dissipation.This is the main mechanism of vibration reduction in the x and y directions [9].
From Table 1, it is observed that after installing the SCDG, the vibration severity for test points is the same whether it is along the x direction or the y direction, except for test point 4. In addition, no matter at which test point, the vibration severity along the z direction is always less than that in the other two directions.This can be explained from two aspects: firstly, it can be observed that in the absence of SCDG, the vibration excitation of the system along the x direction is greater than that in the z direction; secondly, it is mainly because the stiffness of the SCDG in the z direction is relatively high.Taking the stiffness ratio between the x and z directions as an example (Formula 13), the ⁄ part is greater than 1 (Formula 3-8).It can also be found from Formula 12 that Young's modulus of the damping layer material is about 3 times its shear modulus .Therefore, the stiffness of the SCDG along the z direction should be at least 3 times greater than that along the x direction.

Analysis of vibration isolation performance
Firstly, after installing the SCDGs, the vibration AL of each test point decreases, which also proves the vibration isolation effect of these gaskets.Furthermore, as the damping layer thickness of the SCDGs increases, both the AL at individual test points and the average AL show a decreasing trend, indicating an improvement in the vibration isolation effect.However, at a damping layer thickness of 30 mm, the IA stabilizes without further changes with subsequent increases in the damping layer thickness.The experimental data are shown in Table 2.
The method of protecting a fixed foundation by reducing the force transmitted by vibration sources to the foundation is defined as active vibration isolation.Therefore, the research on reducing the transmission of vibration from the diaphragm air pump to the rigid workbench should be considered as active vibration isolation.In this study, the vibration isolation effect of the SCDG can be explained by the transmission rate . . of the vibration isolation system, which is defined as follows :

Figure 3 .
Figure 3. Schematic diagram of vibration performance testing system.

Figure 4 .
Figure 4. Schematic diagram of a testing system (a) with and (b) without installation of SCDGs; (c) installation position of SCDGs.

Figure 5 .
Figure 5. (a) Simplified diagram of an eccentric system, (b) Front view, and (c) Side view of the diaphragm air pump used to display the coordinate system established in this study.

Figure 6 .
Figure 6.Arrangement of acceleration sensors for the experiments on vibration reduction characteristics, 1 to 4 indicate the installation positions of the sensors.

Figure 7 .
Figure 7.The arrangement of acceleration sensors for the experiments on vibration isolation characteristics, 1 to 4 indicate the installation positions of the sensors.

Figure 8 .
Figure 8. Schematic diagram of SCDGs and local coordinate system.The load-bearing area (also known as the actual working area)of the damping layer is:

Table 1 .
The vibration severities at each measuring point and the total vibration severities of the system.

Table 2 .
The AL and IA data of each test point after the installation of SCDG.