CN116909185A - Micro-vibration active control system and method based on pneumatic drive - Google Patents

Abstract

The application relates to the field of vibration control in civil engineering, and provides a micro-vibration active control system and method based on pneumatic drive, wherein the micro-vibration active control system comprises a vibration absorber, a monitoring subsystem, a feedback subsystem and a control subsystem; the vibration absorber comprises a cylinder, an air source and a mass block; a piston is arranged in the cylinder; the air source is used for inflating or exhausting; the mass block and the piston synchronously move; the monitoring subsystem is used for monitoring the speed of the structure in real time; the feedback subsystem calculates a target control force required by the mass block and a target pressure difference required by two cavities of the cylinder; the control subsystem brings the actual pressure differential across the two chambers of the cylinder to a target pressure differential to achieve a desired target control force applied to the mass. The micro-vibration active control system based on air pressure driving has the advantages of smaller energy consumption, higher reaction speed, higher control precision, no pollution to the environment caused by an air source, low cost and higher economical efficiency.

Description

Micro-vibration active control system and method based on air pressure drive

Technical field

The invention belongs to the technical field of vibration control in civil engineering, and specifically relates to an active micro-vibration control system and method based on air pressure drive.

Background technique

The production equipment in electronic factories is sophisticated and is often used to manufacture and test sub-micron process products. The equipment structure is often required to have high standards of anti-microvibration. Micro-vibration requires very fine control. Structural vibration active control technology is a kind of An effective means to control the micro-vibration response of structures. The so-called structural vibration control refers to using some method to control the dynamic response of the structure within the allowable range of the project. There are many types of active structural vibration control. Currently, the most typical ones include active tuned mass damper AMD and active cable system ATS. Active tuned mass dampers are generally installed on the top floor of a building. When a structure equipped with active tuned mass dampers is subjected to seismic loads or strong wind loads, the structure will produce corresponding dynamic responses, and AMD's sensors will monitor the structure's response (including displacement) in real time. , speed or acceleration), and according to Kati's closed-loop control theory, the computer will receive the information from the sensor and obtain the real-time control force through calculation. Then the driver of the AMD system drives the mass block to make the mass block move, and the inertial force of the mass block is It is equal to the control force exerted by the control system on the structure. The direction of the inertial force of the mass block is opposite to the direction of the movement of the structure. The mass block acts on the structure through springs, dampers and actuators, thereby attenuating and controlling the dynamic force of the structure under the action of earthquake loads. Compared with the uncontrolled structure, AMD can reduce the seismic response by 50% to 80%, and the effect is quite significant. The working principle of the active cable system ATS is similar to that of the active tuned mass damper AMD. The real-time structural response is monitored by the computer and the actual control force is calculated. The driver then applies the control force to the active cable through the active cable. structurally, thus reducing the dynamic response of the structure. During the use of active control technology, the input of external energy is required, and it is necessary to ensure that the external energy cannot be cut off when subjected to dynamic loads.

Currently, the common structural vibration active control technologies are hydraulic drive and electromagnetic drive control technologies. The control instructions control the oil pressure or current to achieve the required control force effect. The control effect is more significant and the stability is higher than the passive control technology. Therefore, it has attracted the attention of the majority of civil engineering researchers.

However, the current common hydraulic drive or electromagnetic drive active control technologies still have many shortcomings: First, due to the high viscosity of the filled oily liquid, the electromagnetic induction has a phase difference, which causes a significant time lag between hydraulic drive and electromagnetic drive active control technologies. phenomenon may fail in actual work; secondly, hydraulic drive and electromagnetic drive control technology consumes a lot of energy and operation; finally, the liquid filled in hydraulic drive technology may cause pollution to the environment, and the cost of electromagnetic drive equipment is high.

Contents of the invention

The purpose of the present invention is to overcome the shortcomings of the existing technology and propose a micro-vibration active control system and method based on air pressure drive to solve the problem of low control accuracy and energy consumption of existing micro-vibration active control devices using hydraulic drive or electromagnetic drive. Big question.

In a first aspect, the present invention provides a micro-vibration active control system based on air pressure drive, including: a vibration absorber, a monitoring subsystem, a feedback subsystem and a control subsystem; the vibration absorber includes a cylinder, an air source and a mass block; A piston is provided in the cylinder, and the piston divides the internal cavity of the cylinder into two cavities; the air source is connected to the two cavities of the cylinder respectively, and is used for inflating or pumping the two cavities. ; The mass block moves synchronously with the piston; the monitoring subsystem is used to monitor the speed of the structure in real time and convert it into an electrical signal; the feedback subsystem calculates the required weight of the mass block based on the electrical signal The target control force and the target pressure difference required by the two cavities of the cylinder; the control subsystem is used to control the air source to inflate or pump the two cavities according to the target pressure difference, so that the The actual pressure difference between the two cavities of the cylinder reaches the target pressure difference to obtain the required target control force applied to the mass block.

Further, the monitoring subsystem includes a speed sensor and a data converter, the speed sensor is used to obtain the speed of structural vibration, and the data converter is used to convert the speed into an electrical signal.

Further, the feedback subsystem includes a microcontroller, which calculates the target control force required for the mass block based on the electrical signal:

F _k =-n·cv

In the formula, F _k is the target control force, n is the control coefficient, c is the structural damping, and v is the speed of structural vibration monitored by the speed sensor at a certain moment;

The microcontroller calculates the additional acceleration of the mass block of the vibration absorber at the same time:

Δa＝F _k /m＝-n·2ξωv/μ

In the formula, Δa is the additional acceleration of the mass block, m is the mass of the mass block, ξ is the structural damping ratio, ω is the natural vibration frequency of the structure, and μ is the mass ratio;

The microcontroller calculates the target pressure difference required for the two cavities of the cylinder based on the additional acceleration of the mass block:

ΔP＝mΔa/S＝-n·2mξωv/μS

In the formula, ΔP is the target pressure difference required between the two cavities of the cylinder, Δa is the additional acceleration of the mass block, m is the mass of the mass block, and S is the cross-sectional area of the piston.

Further, the vibration absorber further includes an electronic proportional valve connected between the air source and the cylinder; the control subsystem controls the valve opening of the electronic proportional valve to realize the air source inflating the two cavities or Pump.

Further, the cylinder is equipped with a barometer; the barometer is used to monitor the real-time pressure difference between the two cavities of the cylinder; the control subsystem adjusts the valve opening of the electronic proportional valve to adjust the real-time pressure difference. The pressure difference is the target pressure difference.

Further, a magnetic attraction device is provided inside the piston, and the magnetic attraction device is used to absorb the mass block.

Further, a slide rail is provided outside the cylinder, and the mass block is provided on the slide rail; the length direction of the slide rail is parallel to the movement direction of the piston.

Further, connectors are provided on both sides of the cylinder, and the connectors connect the cylinder and the structure and are used to transmit vibration energy of the structure.

In a second aspect, the present invention also proposes a control method for a micro-vibration active control system driven by air pressure, which includes the following steps:

Utilize the monitoring subsystem to monitor the speed of the structure in real time and convert it into electrical signals;

Using a feedback subsystem to calculate the target control force required by the mass and the target pressure difference required by the two cavities of the cylinder based on the electrical signal;

The control subsystem is used to control the air source to inflate or pump air into the two cavities according to the target pressure difference, so that the actual pressure difference between the two cavities of the cylinder reaches the target pressure difference to obtain The desired target control force is applied to the mass.

Further, the step of using the feedback subsystem to calculate the target control force required by the mass block and the target pressure difference required by the two cavities of the cylinder based on the electrical signal includes:

The microcontroller using the feedback subsystem calculates the target control force required for the mass block based on the electrical signal:

F _k =-n·cv

In the formula, F _k is the target control force, n is the control coefficient, c is the structural damping, and v is the speed of structural vibration monitored by the speed sensor at a certain moment;

Use the microcontroller to calculate the additional acceleration of the mass block of the vibration absorber at the same time:

Δa＝F _k /m＝-n·2ξωv/μ

In the formula, Δa is the additional acceleration of the mass block, m is the mass of the mass block, ξ is the structural damping ratio, ω is the natural vibration frequency of the structure, and μ is the mass ratio;

Using the microcontroller based on the additional acceleration of the mass block, the target pressure difference required for the two cavities of the cylinder is calculated:

ΔP＝mΔa/S＝-n·2mξωv/μS

In the formula, ΔP is the target pressure difference required between the two cavities of the cylinder, Δa is the additional acceleration of the mass block, m is the mass of the mass block, and S is the cross-sectional area of the piston.

The beneficial effects of the present invention include:

1. By monitoring the speed of the structure, calculate the target control force required by the mass block and the target pressure difference of the cylinder, and control the air source to inflate or pump the two cavities of the cylinder to achieve the actual pressure of the two cavities of the cylinder. The difference reaches the target pressure difference to obtain the required target control force applied to the mass block to achieve vibration control of the structure. Compared with the existing hydraulic drive or electromagnetic drive methods, the micro-vibration active control system based on pneumatic drive of the present invention consumes less energy, has faster response speed, has higher control accuracy, and the air source will not cause pollution to the environment. , low cost and high economy.

2. The control system of the present invention has strong flexibility. Its core lies in the active control strategy of the microcontroller. The control effect changes with the customized "control coefficient". The larger the "control coefficient" n is, the higher the vibration absorption effect is, making the active control The strategy can be flexibly adjusted according to actual needs and has excellent application prospects.

3. The present invention has good control effect on micro-vibration and high control accuracy. It is especially suitable for controlling micro-vibration in electronic factories.

4. The control system of the present invention includes a vibration absorber, a monitoring subsystem, a feedback subsystem and a control subsystem. It has a clear structure and strong fault tolerance.

Description of the drawings

Figure 1 is a schematic structural diagram of the micro-vibration active control system based on air pressure drive of the present invention.

Figure 2 is an enlarged structural diagram of the cylinder in Figure 1.

Fig. 3 is a schematic side cross-sectional structural view of the cylinder of Fig. 2.

FIG. 4 is a schematic top structural view of the cylinder in FIG. 2 .

Figure 5 is a schematic flowchart of the control method of the micro-vibration active control system based on air pressure drive according to the present invention.

In the picture, 1-cylinder; 2-piston; 3-air source; 4-electronic proportional valve; 5-magnetic device; 6-mass block; 7-slide; 8-barometer; 9-connector; 10- Monitoring subsystem; 11-speed sensor; 12-data converter; 13-data receiver; 14-single chip microcomputer; 15-signal output device; 16-control subsystem.

Detailed ways

The present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments.

The micro-vibration active control system based on air pressure drive as shown in Figure 1 includes: vibration absorber, monitoring subsystem 10, feedback subsystem and control subsystem 16.

As shown in Figures 2, 3, and 4, the vibration absorber includes a cylinder 1, an air source 3, and a mass block 6; a piston 2 is provided in the cylinder 1, and the piston 2 divides the internal cavity of the cylinder 1 into two cavities; the air source 3 is connected to the two cavities of the cylinder 1 respectively, and is used for inflating or pumping the two cavities; the mass block 6 moves synchronously with the piston 2. The gas source 3 is used to provide pressurized gas, and the gas of the gas source 3 can be air, nitrogen or helium.

The vibration absorber also includes an electronic proportional valve 4 connected between the air source 3 and the cylinder 1 . The air source 3 and the two cavities of the cylinder 1 are respectively connected through pipelines, and an electronic proportional valve 4 is provided on the pipelines.

Cylinder 1 is provided with a barometer 8; the barometer 8 is used to monitor the real-time pressure difference between the two cavities of cylinder 1 in real time. An air pressure sensor is also provided in the cylinder 1 for monitoring the air pressure values of the two cavities.

A magnetic attraction device 5 is provided inside the piston 2 , and the magnetic attraction device 5 is used to absorb the mass block 6 . Mass block 6 is a metal block.

A slide rail 7 is provided outside the cylinder 1, and a mass block 6 is provided on the slide rail 7; the length direction of the slide rail 7 is parallel to the movement direction of the piston 2. Under the action of the slide rail 7 and the magnetic attraction device 5 , the mass block 6 slides along the length direction of the slide rail 7 .

Connectors 9 are provided on both sides of the cylinder 1. The connectors 9 connect the cylinder 1 and the structure and are used to transmit the vibration energy of the structure. The connector 9 includes threaded holes provided on both sides of the cylinder 1 and bolts mated with the threaded holes, and the bolts are also connected to the structure.

After the internal cavity of the cylinder 1 is divided into two cavities by the piston 2, the two cavities have good air tightness and do not leak from each other. The inner wall of the cylinder 1 has a circular tubular structure, the piston 2 has a cylindrical structure, and the diameter of the piston 2 is the same as the diameter of the inner wall of the cylinder 1. Piston 2 can be a rubber plug, plastic plug or glass plug.

The monitoring subsystem 10 is used to monitor the speed of the structure in real time and convert it into electrical signals. The monitoring subsystem 10 includes a speed sensor 11 and a data converter 12. The speed sensor 11 is arranged on the structure. The speed sensor 11 is used to obtain the speed of structural vibration and submit the speed signal to the data converter 12. The data converter 12 is used to convert The speed signal acquired by the speed sensor 11 is converted into an electrical signal, and the electrical signal is amplified, filtered, compensated, and then transmitted to the feedback subsystem.

The feedback subsystem calculates the target control force required by the mass 6 and the target pressure difference required by the two cavities of the cylinder 1 based on the electrical signal.

The feedback subsystem includes a data receiver 13, a microcontroller 14 and a signal output device 15.

The data receiver 13 is used to receive electrical signals transmitted by the data converter 12 of the monitoring subsystem 10 . and feeds back the received electrical signal to the microcontroller 14. The active control strategy of the single-chip computer 14 is established based on the speed signal of the structure. The input signal of the single-chip computer 14 is the electrical signal representing the structure speed received by the data receiver 13. The output signal of the single-chip computer 14 is the target required by the two cavities of the cylinder 1. pressure difference. The signal output device 15 transmits the output signal of the microcontroller 14 to the control subsystem 16 .

The control subsystem 16 is used to control the air source 3 to inflate or pump air into the two cavities according to the target pressure difference, so that the actual pressure difference between the two cavities of the cylinder 1 reaches the target pressure difference to obtain the required target control force. applied to mass 6. The control subsystem 16 controls the valve opening of the electronic proportional valve 4 to realize the air source 3 inflating or pumping the two cavities. The control subsystem 16 adjusts the valve opening of the electronic proportional valve 4 to adjust the real-time pressure difference as the target pressure difference, or to make the real-time pressure difference close to the target pressure difference. The control subsystem 16 includes a controller, which is connected to the electronic proportional valve 4 and electrical signals. The signal output device 15 transmits the output signal of the single chip microcomputer 14 to the controller. The controller controls the valve opening of the electronic proportional valve 4 based on the output signal of the single chip microcomputer 14 .

The barometer 8 monitors the real-time pressure difference between the two cavities of the cylinder 1 in real time. The control subsystem 16 compares the real-time pressure difference with the target pressure difference. If the two are equal, an instruction is sent to the electronic proportional valve 4 to close the valve and stop. Inflate or pump air; if the two are not equal, an instruction is sent to the electronic proportional valve 4 to continue to inflate or pump air, and adjust the pressure difference between the two chambers until the real-time pressure difference is equal to the target pressure difference.

The active control strategy of the microcontroller 14 of the present invention is as follows:

Based on the electrical signal, the microcontroller 14 calculates the target control force required for the mass block 6:

F _k =-n·cv

In the formula, _Fk is the target control force, n is the customized control coefficient, and the control coefficient is an integer greater than or equal to 1. In this embodiment, the value of n is 5, c is the structural damping, and v is the speed of structural vibration monitored by the speed sensor 11 at a certain moment.

The microcontroller 14 calculates the additional acceleration of the mass 6 of the vibration absorber at the same time:

Δa＝F _k /m＝-n·2ξωv/μ

In the formula, Δa is the additional acceleration of mass block 6, m is the mass of mass block 6, ξ is the structural damping ratio, ω is the natural vibration frequency of the structure, and μ is the mass ratio.

The microcontroller 14 calculates the target pressure difference required for the two cavities of the cylinder 1 based on the additional acceleration of the mass 6:

ΔP＝mΔa/S＝-n·2mξωv/μS

In the formula, ΔP is the target pressure difference required between the two cavities of cylinder 1, Δa is the additional acceleration of mass block 6, m is the mass of mass block 6, and S is the cross-sectional area of piston 2.

The present invention uses pneumatic drive to replace the traditional hydraulic drive and artificially determines the active control strategy, thereby realizing real-time control of the pressure difference between the two cavities of the cylinder 1 and providing core technical support for the application of control force. The invention has clear components, significant energy dissipation and vibration reduction effect, and high stability. The gas filled by the pneumatic drive technology has lower viscosity, faster inflation and pumping speed, and higher precision. It can effectively reduce the time lag phenomenon and is more conducive to vibration control, thereby achieving higher stability; at the same time, the filling gas is easy to It is available and economical, and the cost is low. Even if the equipment leaks, it will not cause pollution or damage to the environment, and has good green and environmental protection.

Based on the same inventive concept, as shown in Figure 5, the present invention also proposes a control method for the above-mentioned micro-vibration active control system based on air pressure drive, which includes the following steps:

Step S1: Use the monitoring subsystem 10 to monitor the speed of the structure in real time and convert it into an electrical signal;

Step S2: Use the feedback subsystem to calculate the target control force required by the mass block 6 and the target pressure difference required by the two cavities of the cylinder 1 based on the electrical signal;

Step S3: Use the control subsystem 16 to control the air source 3 to inflate or pump air into the two cavities according to the target pressure difference, so that the actual pressure difference between the two cavities of the cylinder 1 reaches the target pressure difference to obtain the required target. Control force is exerted on mass 6.

Among them, step S2 specifically includes the following steps:

Step S21: Use the microcontroller 14 of the feedback subsystem to calculate the target control force required for the mass block 6 based on the electrical signal:

F _k =-n·cv

In the formula, _Fk is the target control force, n is the control coefficient, c is the structural damping, v is the speed of structural vibration monitored by the speed sensor 11 at a certain moment; n is a self-defined control coefficient, and the control coefficient is greater than or equal to 1 integer. The value of n in this embodiment is 5. The larger the control coefficient n, the higher the vibration absorption effect.

Step S22: Use the microcontroller 14 to calculate the additional acceleration of the mass 6 of the vibration absorber at the same time:

Δa＝F _k /m＝-n·2ξωv/μ

In the formula, Δa is the additional acceleration of mass block 6, m is the mass of mass block 6, ξ is the structural damping ratio, ω is the natural vibration frequency of the structure, and μ is the mass ratio;

Step S23: Use the microcontroller 14 to calculate the target pressure difference required for the two cavities of the cylinder 1 based on the additional acceleration of the mass 6:

ΔP＝mΔa/S＝-n·2mξωv/μS

In the formula, ΔP is the target pressure difference required between the two cavities of cylinder 1, Δa is the additional acceleration of mass block 6, m is the mass of mass block 6, and S is the cross-sectional area of piston 2.

Step S3 specifically includes:

The control subsystem 16 compares the target pressure difference with the real-time pressure difference between the two cavities of the cylinder 1 monitored by the barometer 8 in real time:

If the two are equal or the difference is within the allowable range, a first command is sent to the electronic proportional valve 4 to close the valve and stop inflation or pumping.

If the two are not equal or the difference exceeds the allowed range, a second command is issued to the electronic proportional valve 4 to continue inflating or pumping to adjust the pressure difference between the two chambers until the real-time pressure difference is equal to the target pressure difference or the real-time pressure difference. The difference between the pressure difference and the target pressure difference is within the allowable range to obtain the required target control force applied to the mass block 6 .

The above are only preferred embodiments of the present invention. The protection scope of the present invention is not limited to the above-mentioned embodiments. All technical solutions that fall under the idea of the present invention belong to the protection scope of the present invention. It should be pointed out that for those of ordinary skill in the art, several improvements and modifications without departing from the principles of the present invention should also be regarded as the protection scope of the present invention.

Claims (10)

1. A micro-vibration active control system based on air pressure drive, characterized by including: a vibration absorber, a monitoring subsystem, a feedback subsystem and a control subsystem; The vibration absorber includes a cylinder, a gas source and a mass block; a piston is provided in the cylinder, and the piston separates the internal cavity of the cylinder into two cavities; the gas source and the two cavities of the cylinder They are respectively connected for inflating or pumping the two cavities; the mass block and the piston move synchronously; The monitoring subsystem is used to monitor the speed of the structure in real time and convert it into electrical signals; The feedback subsystem calculates the target control force required by the mass block and the target pressure difference required by the two cavities of the cylinder based on the electrical signal; The control subsystem is used to control the air source to inflate or pump air into the two cavities according to the target pressure difference, so that the actual pressure difference between the two cavities of the cylinder reaches the target pressure difference, so as to Obtain the desired target control force applied to the mass. 2. The micro-vibration active control system based on air pressure drive according to claim 1, characterized in that the monitoring subsystem includes a speed sensor and a data converter, and the speed sensor is used to obtain the speed of structural vibration, and the A data converter is used to convert the speed into an electrical signal. 3. The micro-vibration active control system based on air pressure drive according to claim 2, characterized in that the feedback subsystem includes a single-chip computer, and the single-chip computer calculates the target control force required for the mass block based on the electrical signal: F _k =-n·cv In the formula, F _k is the target control force, n is the control coefficient, c is the structural damping, and v is the speed of structural vibration monitored by the speed sensor at a certain moment; The microcontroller calculates the additional acceleration of the mass block of the vibration absorber at the same time: Δa＝F _k /m＝-n·2ξωv/μ In the formula, Δa is the additional acceleration of the mass block, m is the mass of the mass block, ξ is the structural damping ratio, ω is the natural vibration frequency of the structure, and μ is the mass ratio; The microcontroller calculates the target pressure difference required for the two cavities of the cylinder based on the additional acceleration of the mass block: ΔP＝mΔa/S＝-n·2mξωv/μS In the formula, ΔP is the target pressure difference required between the two cavities of the cylinder, Δa is the additional acceleration of the mass block, m is the mass of the mass block, and S is the cross-sectional area of the piston. 4. The micro-vibration active control system based on air pressure drive according to claim 1, characterized in that the vibration absorber further includes an electronic proportional valve connected between the air source and the cylinder; the control subsystem controls the The valve opening of the electronic proportional valve enables the air source to inflate or pump air into the two cavities. 5. The micro-vibration active control system based on air pressure drive according to claim 4, characterized in that the cylinder is provided with a barometer; the barometer is used to monitor the real-time pressure difference between the two cavities of the cylinder in real time; The control subsystem adjusts the valve opening of the electronic proportional valve to adjust the real-time pressure difference to the target pressure difference. 6. The micro-vibration active control system based on air pressure drive according to claim 1, characterized in that a magnetic attraction device is provided inside the piston, and the magnetic attraction device is used to absorb the mass block. 7. The micro-vibration active control system based on air pressure drive according to claim 1, characterized in that a slide rail is provided outside the cylinder, and the mass block is provided on the slide rail; the length of the slide rail The direction is parallel to the direction of movement of the piston. 8. The micro-vibration active control system based on air pressure drive according to claim 1, characterized in that connectors are provided on both sides of the cylinder, and the connectors connect the cylinder and the structure for transmitting The vibrational energy of the structure. 9. A control method for a micro-vibration active control system based on air pressure drive as claimed in claim 1, characterized in that it includes the following steps: Utilize the monitoring subsystem to monitor the speed of the structure in real time and convert it into electrical signals; Using a feedback subsystem to calculate the target control force required by the mass and the target pressure difference required by the two cavities of the cylinder based on the electrical signal; The control subsystem is used to control the air source to inflate or pump air into the two cavities according to the target pressure difference, so that the actual pressure difference between the two cavities of the cylinder reaches the target pressure difference to obtain The desired target control force is applied to the mass. 10. The control method of a micro-vibration active control system based on air pressure drive according to claim 9, characterized in that the feedback subsystem uses the feedback subsystem to calculate the target control force required for the mass block and the The steps to achieve the required target pressure difference between the two chambers of the cylinder include: The microcontroller using the feedback subsystem calculates the target control force required for the mass block based on the electrical signal: F _k =-n·cv In the formula, F _k is the target control force, n is the control coefficient, c is the structural damping, and v is the speed of structural vibration monitored by the speed sensor at a certain moment; Use the microcontroller to calculate the additional acceleration of the mass block of the vibration absorber at the same time: Δa＝F _k /m＝-n·2ξωv/μ In the formula, Δa is the additional acceleration of the mass block, m is the mass of the mass block, ξ is the structural damping ratio, ω is the natural vibration frequency of the structure, and μ is the mass ratio; Using the microcontroller based on the additional acceleration of the mass block, the target pressure difference required for the two cavities of the cylinder is calculated: ΔP＝mΔa/S＝-n·2mξωv/μS In the formula, ΔP is the target pressure difference required between the two cavities of the cylinder, Δa is the additional acceleration of the mass block, m is the mass of the mass block, and S is the cross-sectional area of the piston.