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The traditional suction mechanism with an air pump in robotics is difficult to miniaturize. Integrating a piezoelectric pump into a suction cup is an effective method to achieve miniaturization. In this paper, a novel suction cup with a piezoelectric micropump is designed. The micropump is valveless and the suction cup is designed with a laminated structure in order to facilitate miniaturizing and manufacturing. A systematic optimization design method of the suction cup is introduced which addresses the static and dynamic driving characteristics of the piezoelectric actuator and the rectifying efficiency of diffuser/nozzle’s optimization. The design is verified via simulation using an improved equivalent electric network model. Static lumped parameters in this model are calculated by the finite element method instead of the traditional analytic method, and the diffuser/nozzle’s flow resistance is computed by integrating and introducing rectifying efficiency coefficient. Simulation results indicate that the suction cup can generate a stable negative pressure, and the equivalent electric network model can improve the simulation efficiency and accuracy. The maximum steady-state negative pressure of the suction cup can also be effectively improved after optimization.

Suction technology is widely used in robotics. By installing a suction cup at the end of a manipulator, numerous forms of work, such as pickup and handling, can be realized. If the suction device is installed on the mobile mechanism of a robot, the robot can move freely on different walls. Magnetic suction requires that the object or the wall to be suctioned must be composed of a magnetic conducting material, which limits the application scope [

To produce negative pressure in a suction cup, one method is to increase the volume of the suction cup through a mechanical device when the air quantity and temperature in the suction cup is constant, and this is called a passive suction cup. Because there is not a traditional air pump, the suction cup’s size can be miniaturized. Takahiro Matsuno has developed a passive suction cup based on a motor-actuated disc spring [

The other way is to reduce the air quantity in a suction cup under the condition that the volume and temperature of the air in the suction cup are constant. This is the basic principle of using an air pump to extract air from a suction cup to produce negative pressure. T. Takahashi [

If the above thin film micropump can be integrated into a small suction cup, it can overcome the shortcoming of the passive suction cup. At the same time, the volume of the suction cup can be reduced and a stable negative pressure produced. In this paper, a micro negative pressure suction cup integrated with a piezoelectric valveless micropump is designed and its negative pressure response studied by simulation. The negative pressure generation principle of the suction cup is analyzed, and a micro negative pressure suction cup with an integrated valveless piezoelectric pump is designed in detail. Then, the process to optimize the design of the suction cup is presented. Following the optimization process, an equivalent electric network model of the suction cup is formulated, and the suction characteristics of the suction cup are studied via simulation.

To make the micropump have good air transmission characteristics, the pressure difference

In (

To increase the gas volumetric change rate

The micropump in this paper uses a diffuser and a nozzle instead of valves, and the reason is that the valve needs a pressure difference to open, so the pressure in the vibrating cavity will be partially lost. Reliability is reduced due to wear and fatigue of mechanical parts of the valve. The structure of the micropump with valve is also more complex and not easy to manufacture and assemble and is not conducive to reducing the volume size and weight of the micropump suction cup. A valveless micropump overcomes the above shortcoming and has a greater development prospect. Currently most valveless micropumps use cone-shaped tubes to guide the fluid. Compared with the spatial cone-shaped tube, and the manufacturing process of the plane cone tube is simpler and is beneficial to integrate with other microdevices [

Representative geometric dimensions of the gas micropump from the literature [

Geometric sizes of a gas micropump [

Item | Data | |
---|---|---|

Piezoelectric actuator | Piezoelectric material layer radius | 5 |

Piezoelectric material layer thickness | 0.2 | |

Elastic substrates radius | 6 | |

Elastic substrates thickness | 0.15 | |

| ||

Cone tube | Expanding length | 3 |

Minimum section width | 0.12 | |

Maximum section width | 0.64 | |

Expanding angle | 10 | |

Depth | 0.1 | |

| ||

Vibrating cavity | Radius (mm) | 6 |

Depth (mm) | 0.1 |

The suction cup designed in this paper is shown in Figure

Structure diagram of the suction cup with micropump.

Exploded view

Sectional view

There are vent holes on the upper/lower covers and the upper/lower elastic substrates, respectively. The maximum section end of the input cone tube is connected to the vibrating cavity, and then the minimum section end of the input conical tube, lower substrate vent hole, lower cover vent hole, and the suction cavity are connected in series. The upper cover vent hole, the upper elastic substrates vent hole, and the maximum section end of the output conical tube are connected in series. The minimum section end of the output conical tube is connected to the vibrating cavity. The upper cover vent hole is connected to the outside atmosphere.

The working principle of the micropump suction cup is shown in Figure

Working principle of the micropump suction cup.

Supply mode

Pump mode

In the second section, a valveless micropump suction cup which is easy to be processed and has large volumetric change rate is designed. In order to further improve the performance of the micropump suction cup, a systematic optimization design method is introduced in this section, which covers the optimization of static and dynamic driving characteristics of piezoelectric actuators and rectifying efficiency of diffuser/nozzle.

Research shows that the geometric size, material properties, driving voltage, and driving frequency affect the deformation of a piezoelectric actuator. The geometric size and material properties affect static driving characteristics, that is, the relationship between the driving electric field and the deformation, while the driving frequency will affect the dynamic driving characteristics [

The structure of the unimorph circular piezoelectric actuator used in the micropump suction cup is shown in Figure

Schematic diagram of a unimorph circular piezoelectric actuator.

Research shows that there is an optimal radius ratio

When a DC voltage

In (

The constants

In (

By (

According to the analytical solution in (

Static driving characteristics optimization of piezoelectric actuator.

Optimization of radius ratio

Optimization of thickness ratio

In Figure

In order to produce a stable negative pressure, an alternating voltage should be applied on piezoelectric actuators to make it vibrate continuously. In the past, most work on dynamic driving characteristics of piezoelectric actuators used the finite element method to solve for the resonant frequency, and few studies have been done on the dynamic changes of the piezoelectric actuator’s volume change under an alternating electric field. In this section, an equivalent circuit model of piezoelectric actuator based on lumped parameter is formulated to simulate the dynamic driving performance of the piezoelectric actuator and thereby select the best driving frequency. Additionally, it also lays a foundation for the simulation of the negative pressure response of the suction cup with micropump.

If the alternating power is

In (

In (

The constant

According to the definition of (

Because of the direction of the electric field, the deflection direction and the polarization direction of the piezoelectric material are the same, and the equivalent dielectric constant

In order to obtain the two ports’ equivalent circuit model of the piezoelectric actuator, (

In (

Two-port equivalent circuit of the piezoelectric actuator.

Not considering the influence of the inertia

Considering the influence of the inertia

Assuming that the current of the right side of the transformer in Figure

At the fluid domain side

According to (

By comparing (

Substituting (

By comparing (

When the driving frequency is very low, it is not essential to consider the influence of the piezoelectric actuator’s quality on driving characteristics, but when the driving frequency increases, the quality affects the vibration of the piezoelectric actuator [

In (

In order to establish the equivalent circuit model of the piezoelectric actuator in micropump suction cup in detail, lumped parameters should be calculated first. In many studies, the analytic method is used directly in the calculation of the lumped parameters [

Geometric parameters of the piezoelectric actuator before optimization are in Table ^{2}J^{−1}. According to the definition of ^{3}CJ^{−1}. Then the load applied on the finite element model is changed. A unit external pressure load is applied on the finite element model, and the driving voltage is zero. ^{6}J^{−1}; the equivalent inductor ^{2}m^{−6}. Finally, ^{6}J^{−1}, ^{−3}, and ^{2}J^{−1}. The equivalent circuit model can be obtained by replacing the above lumped parameter into Figure

Piezoelectric actuator’s equivalent circuit model.

In order to verify the correctness of the two ports’ equivalent electric network model, the finite element method is used to simulate the transient driving characteristics of the piezoelectric actuator, and the software ANSYS 10.0 is used. The voltage load is applied to the piezoelectric material layer. Then the FULL method in ANSYS is applied to analyze the transient dynamics of the piezoelectric actuator. Because the finite element method for transient dynamic analysis is very time-consuming, the dynamic response just in the first 0.2 ms is analyzed. The displacement along the polarization direction of the piezoelectric material is kept in analysis results, and then the volume change is calculated. Figure

Correctness verification of the two ports’ equivalent electric network model.

Using the equivalent electric network model and the simulation software Multisim 10.0, the steady-state volume change amplitude of the piezoelectric actuator can be obtained at different driving frequencies as shown in Figure

Frequency response curve of the steady-state volume change amplitude.

In Figure

The radius and thickness ratio of curve 4 are not optimized, but the amplitude of the driving voltage is 50 V. The comparison between curve 1 and curve 4 shows that the larger the driving voltage, the larger the volume change. The maximum value of the steady-state volume change at the driving voltage 50 V is approximately 1.9

The air rectifying characteristics of the cone-shaped tube have an extremely important influence on the performance of the micropump suction cup, so the cone tube must be optimized. The rectification efficiency is defined as

As shown in Figure

Structure chart of the plane cone tube.

On the basis of Table

In order to calculate the rectification efficiency, the volume flow must be known, and it can be calculated by the following equation in the finite element model:

In (

To investigate the effect of the minimum section width on the rectification efficiency, the expanding length and expanding angle are fixed at 3 mm and 10 degrees. The minimum section width varies from 0.06 mm to 0.36 mm. The pressure difference between the two ends of the cone tube is 0.5 kPa and 5.0 kPa. Initially, the rectification efficiency is simulated by ANSYS 10.0 in different situations, and then all simulation results are shown in Figure

Relationship between the minimum section width and the rectification efficiency.

To investigate the effect of expanding length on the rectification efficiency, the minimum section width and expanding angle are fixed at 0.12 mm and 10 degrees. The expanding length varies from 0.5 mm to 5.0 mm. The pressure difference between the two ends of the cone tube is 0.5 kPa and 5.0 kPa, and simulation results are shown in Figure

Relationship between the expanding length and the rectification efficiency.

Flow field vector diagram in the conical tube.

Diffuser

Nozzle

To investigate the effect of expanding angle on the rectification efficiency, the minimum section width and expanding length are fixed at 0.12 mm and 3 mm. The expanding angle varies from 6° to 16°. The pressure difference between the two ends of the cone tube is 0.5 kPa and 5.0 kPa, and simulation results are shown in Figure

Relationship between the expanding length and the expanding angle.

After a large number of finite element analyses, it is found that the minimum section width, expanding angle, and expanding length all have the optimal value to make the air rectification efficiency of a plane cone tube the largest when the other parameters are fixed. At the optimal value, the rectification efficiency increases with the increased pressure difference. This is because when the pressure difference is larger, the flow velocity is higher and the kinetic energy and the pressure potential energy are converted more completely, so at the optimal value the rectification efficiency is higher. The volume change rate of the vibrating cavity and the volume change of the piezoelectric actuator should be maximized to obtain a larger pressure difference.

In order to verify the rationality of the design of the micropump suction cup, a model should be established to simulate the negative pressure response. Bourouina has discussed a method of establishing the piezoelectric micropump’s simulation model by equivalent circuit [

Basic components of the micropump suction cup include two unimorph circular piezoelectric actuators, a vibrating cavity, two cone tubes, a suction cavity, and some vents. The equivalent electric network of the piezoelectric actuator has been deduced in Section

Because the geometric sizes of the vibrating cavity and the suction cavity are relatively large, the flow resistance is ignored. When the air pressure in the cavities changes, the air quantity is different, and this means that the vibrating cavity and the suction cavity have flow capacity. Further, the working frequency of the micropump suction cup is high, and the air pressure changes when the air flows at a high speed in the vibrating cavity and suction cavity, which indicates that these two cavities also have flow inductance.

When the mass of the air in the cavity is

Equivalent electric network model of elements.

Vibrating cavity and suction cavity

Cone tube

The cone tube plays a guiding and rectifying effect on the airflow in the micropump suction cup, and the flow resistance of the air along the nozzle is greater than that of the diffuser. The rectifier element in the electrical circuit is diode. Therefore, in this paper, an ideal diode is introduced to the equivalent circuit of the cone tube to characterize the rectifying effect. Because the length of the cone tube is very short, its air capacity is limited, so the flow capacity is negligible. The flow resistance of a rectangular cross-section microchannel is [

Because the cross-sectional area of the plane cone tube is varied, its flow resistance calculation method is different from the traditional fixed section microchannel. As shown in Figure

Calculation of cone tube’s flow resistance.

If the depth of the cone tube is 2c, assuming that the width of an infinitely short cone tube is constant, the flow resistance of this infinitely short cone tube can be obtained,

The diffuser’s flow resistance

According to the definition of the cone tuber’s rectification efficiency, the flow resistance

In (

In (

The flow inductance of nozzle is

The final equivalent electrical network model of the cone tube is shown in Figure

Geometric parameters of each element in the micropump are shown in Table

Suction cavity’s geometric parameters.

Suction cavity | Radius (mm) | 15 |

Height (mm) | 0.2 |

Equivalent electrical network parameters of the micropump suction cup.

Cone tube | Diffuser flow resistance (Jsm^{−6}) | |

Diffuser flow inductance (Js^{2}m^{−6}) | | |

Nozzle flow resistance (Jsm^{−6}) | | |

Nozzle flow inductance (Js^{2}m^{−6}) | | |

| ||

Vibrating cavity | Flow Capacitance (m^{6}J^{−1}) | |

Flow inductance (Js^{2}m^{−6}) | | |

| ||

Suction cavity | Flow Capacitance (m^{6}J^{−1}) | |

Flow inductance (Js^{2}m^{−6}) | |

Equivalent electrical network model of the micropump suction cup.

According to the above model, the pressure in the micropump suction cup’s suction cavity is the voltage value in the equivalent capacitance

Negative pressure response simulation curve.

In Figure

Negative pressure’s frequency response curves.

Figure

Relationship between the negative pressure and the driving voltage’s amplitude.

Figure

Influence of suction cavity on negative pressure response.

Thickness increase

Radius increase

In order to realize the miniaturization of the suction mechanism for robotics and get a stable negative pressure at the same time, design and simulation of a novel suction cup integrated with a valveless piezoelectric micropump are presented in this paper, and the following conclusions are obtained:

The structure design of the micropump suction cup should be easy to be miniaturized and easy to manufacture, and using the valveless micropump and laminated structure can achieve these.

The systematic optimization design method of the suction cup in this paper is effective. To get a larger volumetric change, theoretical model of the piezoelectric actuator can be used to find the actuator’s optimal radius and thickness ratio, and the two ports’ equivalent circuit model of piezoelectric actuator can calculate the actuator’s resonant frequency.

Finite element analysis results show that the minimum section width, cone angle, and expanding length of the diffuser/nozzle influence its rectification efficiency. When the other parameters are constant, all of them have the best value.

A modified equivalent circuit modeling method which can improve the efficiency and accuracy of simulation is presented. In this model, static lump parameters are calculated by finite element method to avoid complex theoretical calculation processes. The computing process of the diffuser/nozzle’s flow resistance and inductance is also improved by integrating and introducing rectifying efficiency coefficient.

Simulation results based on the equivalent circuit model show that the suction cup can produce a stable negative pressure rapidly. The above-mentioned optimization measures can improve the mean value of the steady-state negative pressure.

There are still some problems in this paper. For example, the backpressure of valveless micropump is lower than that of the valve micropump, which limits the maximum negative pressure, and experimental verification is not carried out. Subsequent studies will be carried out in these areas.

All data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This research is partially supported by Shanghai Department of Science and Technology Fund Project for Shanghai Engineering Research Center for Assistive Devices (Grant no. 15DZ2251700).