CN104344811A - Online detection system and method for inclination of piston of gas chamber - Google Patents

Abstract

The invention provides an online detection system for the inclination of a piston of a gas chamber. The system comprises a biaxial inclination angle sensor and a converter, which are connected through an RS485 bus, wherein the converter is connected with a conventional control system in a Profibus-DP slave station way through a DP cable, and comprises a UART-to-RS485 (universal asynchronous receiver/transmitter-to-RS485) level conversion chip, a microprocessor, a DP slave station protocol processing chip and a DP bus physical interface chip, which are sequentially connected; the microprocessor is used for calculating an inclination angle of the piston of the gas chamber according to data acquired by the biaxial inclination angle sensor. According to the system, the independently researched and developed converter is adopted, the acquired data is processed in the converter, and then the system is connected to the conventional control system in the Profibus-DP slave station way, so that interfaces are unified in terms of hardware to facilitate connection to control systems of various brands, a user is hardly required to do any programming work in the control system, and mainly displays the data transmitted by the system, and the compatibility is improved.

Description

A kind of gas chamber piston degree of tilt on-line detecting system and method

Technical field

The invention belongs to gas chamber piston condition monitoring field in metallurgy industry, be specially a kind of gas chamber piston degree of tilt on-line detecting system and method.

Background technology

Along with the fast development of steel industry, smelter is more and more paid attention to the comprehensive utilization producing coal gas in smelting process, and therefore large-scale gas chamber obtains increasing widespread use in smelter.Piston is as parts very important in gas chamber, and whether its operation is normal seems particularly important for gas chamber.

During normal operation, piston moves up and down along with the inflation/deflation of gas chamber.Due between piston and whole cabinet without any being rigidly connected, only rely on top wire rope to make it balance, a few kiloton and piston weighs, it is mainly supported by the pressure of coal gas in cabinet, therefore piston may produce inclination to a certain degree in operational process, when acquiring a certain degree, coal gas overvoltage or leakage in piston card rail, cabinet just may occur, also likely rubber diaphragm is torn for rubber diaphragm sealed gas chamber, causes heavy losses.Therefore, in gas chamber operational process, the strict running status detecting piston is needed.

For piston running status, traditional detection mode is the degree of tilt being calculated piston by the oil tank of differential pressure transmitter measure setup around piston or the oil level change carried in oil duct.Along with the inclination of piston, the liquid level in oil tank around also can change thereupon, and after measuring, the liquid level of these three or four points can calculate the degree of tilt of piston.Although this metering system precision can meet the demands, cost of investment is high, construction bothers and later maintenance workload is large.

Summary of the invention

The technical problem to be solved in the present invention is: provide a kind of gas chamber piston degree of tilt on-line detecting system and method, the precision of the degree of tilt in on-line checkingi piston operational process can be improved, and with the existing control system of mode access user of Profibus-DP slave station, cost is low, compatibility is strong.

The present invention for solving the problems of the technologies described above taked technical scheme is: a kind of gas chamber piston degree of tilt on-line detecting system, is characterized in that: it comprises the double-shaft tilt angle sensor and converter that are connected by RS485 bus; Double-shaft tilt angle sensor is for detecting the inclination angle in gas chamber piston plane two vertical direction, and converter accesses existing control system by DP cable in the mode of Profibus-DP slave station;

Described converter comprises the UART connected successively and turns RS485 level transferring chip, microprocessor, DP slave station protocol process chip and DP bus physical interface chip, and the data that microprocessor is used for gathering according to double-shaft tilt angle sensor calculate gas chamber piston angle of inclination and direction.

By said system, described double-shaft tilt angle sensor is arranged in Flameproof box, and Flameproof box is arranged on the piston dam of piston edge, keeps relative level with the piston flat surface after leveling.

The gas chamber piston degree of tilt online test method utilizing above-mentioned gas chamber piston degree of tilt on-line detecting system to realize, is characterized in that: it comprises the following steps:

S1, definition X, Y-axis are orthogonal coordinate axis in piston flat surface, the direction of measurement of double-shaft tilt angle sensor and the direction of X, Y parallel to each other, the former surface level of piston is primary plane β, and the piston center of circle is the intersection point O of X, Y-axis, and piston radius is R, piston is along straight line MN run-off the straight, plane after inclination is γ, in plane γ, if B point be tilt after the peak of piston flat surface, vertical range between it and plane β is H, and ∠ BOB ₁=θ, so θ is X-axis forward and inclination peak direction angle in the counterclockwise direction, i.e. the vergence direction of piston; OB ₁, OB ₂radius after being respectively inclination in X, Y-axis, then its angle ∠ B ₁oB ₂=90 °, it is a ' that obliquity sensor records X-direction top rade, and Y direction top rade is b ';

S2, following algorithm is adopted to carry out filtering process to the raw data collected:

Y _k＝(1-j)*X _k+j*Y _k-1(1)，

J is filter factor in formula (1), its span between 0 ~ 1, X _kfor current sample values, Y _k-1for last filter result, Y _kfor present filter result;

The X-direction top rade a ' recorded and Y direction top rade b ' is carried out filtering respectively through formula (1), obtains filtered X-direction top rade a and filtered Y direction top rade b;

S3, calculate following parameter:

$H=R\sqrt{{\sin }^{2}a+{\sin }^{2}b}$

$\mathrm{\θ}=\arctan \left(\frac{\sin b}{\sin a}\right)$

In formula, for the angle between the plane γ after primary plane β and inclination;

S4, according to X, Y-axis, piston flat surface is divided into four quadrants,

1) if a>0, b>0, then represent that piston peak is at I quadrant, 0 ° of < θ <90 °;

2) if a<0, b>0, then represent that piston peak is at II quadrant, 90 ° of < θ <180 °;

3) if a<0, b<0, then represent that piston peak is at III quadrant, 180 ° of < θ <270 °;

4) if a>0, b<0, then represent that piston peak is at IV quadrant, 270 ° of < θ <360 °;

5) if a=0, b>0, then represent that piston tilts along Y-axis positive dirction, θ=90 °;

6) if a=0, b<0, then represent that piston tilts along Y-axis negative direction, θ=270 °;

7) if b=0, a>0, then represent that piston tilts along X-axis positive dirction, θ=0 °;

8) if b=0, a<0, then represent that piston tilts along X-axis negative direction, θ=180 °;

9) if a=0, b=0, then represent that piston is horizontal, without tilting.

Beneficial effect of the present invention is:

1, present system adopts the converter of independent research, in the converter the data collected are processed, existing control system is accessed again in the mode of Profibus-DP slave station, first on hardware, interface has been unified, present system is facilitated to access PLC or the DCS control system of various brand, secondly user almost without the need to doing any extra programing work in PLC or DCS, only need in PLC or DCS by present system configuration to former control system, and native system uploading data is shown in HMI, improve compatible and convenient and reliable.

2, the inventive method first carries out filtering process to raw data, then adopts specific algorithm to calculate, and can eliminate undesired signal, improve computational accuracy.

Accompanying drawing explanation

Fig. 1 is hardware frame figure.

Fig. 2 is the hardware circuit diagram of converter in Fig. 1.

Fig. 3 is inclination angle algorithm principle figure.

Fig. 4 is X, Y-direction original angle signal graph.

Fig. 5 is X, Y-signal figure after signal transacting.

Fig. 6 is the angle of inclination figure to calculating before and after original data processing.

Fig. 7 is sensor in-site installation schematic diagram.

In figure: 1-piston, 2-double-shaft tilt angle sensor, 3-Flameproof box, 4-1 column.

Embodiment

Below in conjunction with instantiation, the present invention will be further described.

The invention provides a kind of gas chamber piston degree of tilt on-line detecting system, as shown in Figure 1, it comprises the double-shaft tilt angle sensor and converter that are connected by RS485 bus; Double-shaft tilt angle sensor is for detecting the inclination angle in gas chamber piston plane two vertical direction, and converter accesses existing control system by DP cable in the mode of Profibus-DP slave station;

Described converter comprises the UART connected successively and turns RS485 level transferring chip, microprocessor, DP slave station protocol process chip and DP bus physical interface chip, and the data that microprocessor is used for gathering according to double-shaft tilt angle sensor calculate gas chamber piston angle of inclination and direction.Double-shaft tilt angle sensor is the market universal product, and its precision can reach 0.004 °, and Width funtion is powered (DC9 ~ 36V).

Utilize the inclination angle in high-precision dual-axis obliquity sensor on-line checkingi gas chamber piston plane two vertical direction, its output signal is RS485 signal, the converter of signal access independent research, converter has two effects: one is the angle of inclination and the peak vergence direction that calculate whole piston area according to two original dip angle signals, two are to provide Profibus-DP interface, to be equivalent to whole detection system, as a Profibus-DP slave station access user control system, directly give user by final calculation result.So be made with several benefit: 1, be standard P rofibus-DP agreement conventional in industrial control field by the nonstandard protocol conversion of sensor, facilitate detection system to access PLC or the DCS control system of various brand; 2, user almost without the need to doing any programing work in PLC or DCS, mainly shown in PLC or DCS in HMI by detection system forward data.

Converter adopts STM32 series A RM processor as MCU, Profibus-DP communication part adopts VPC3 special communication chip to assist, as shown in Figure 2, the present embodiment adopts the MCU of 32 Cortex-M3 core A RM chip STM32F103ZET6 as whole system of ST company, the ADM2587 of ADI company is adopted to turn RS485 level transferring chip as UART, adopt the VPC3+C/S chip of profichip company as DP slave station protocol process chip, adopt the ADM2486 of ADI company as DP bus physical interface chip.RS485 interface chip ADM2587 and DP interface chip ADM2486 has isolation features, thus ensure that the antijamming capability of whole system in industrial applications, improves the reliability of whole system.

Profibus-DP agreement is applied widely at present, much equipment is all with DP interface, but its underlying protocol is very complicated, if its difficulty of producer's self-developing is quite large by leaving, so Siemens takes the lead in being proposed a asic chip SPC3, Profichip company is proposed again the VPC3 of function and the complete compatible SPC3 of software afterwards, power relative to the 5V of SPC3, the compatible 5V/3.3V of VPC3 powers, its power consumption is lower, be more suitable for current low-voltage power supply trend, therefore we have selected the communication chip of VPC3 chip as converter of Profichip company.

VPC3 follows PROFIBUS standard agreement, and user only needs to understand PROFIBUS standard agreement related content and chip technology content can oneself coding, by control chip to realize the exploitation of slave station.

VPC3 Internal latches/register-bit is in front 21 address locations (00H ~ 15H), and organizational parameter is arranged in the unit of RAM from 16H, and user buffer region is positioned at the unit from 40H.Mode register 0,1,2 and status register, interrupt control register, house dog are all positioned at front 21 address locations.Buffer structure is write based on organizational parameter.In addition, General Parameters setting data (as station address, device id etc.) and state display (as general controls order etc.) are also stored in these unit.Mode register 0 and register 2 must carry out assignment under off-line state, once power on, just can not revise.Some controling parameters of mode register 1 must be modified in application process.

Preferably, described double-shaft tilt angle sensor is arranged in Flameproof box, and Flameproof box is arranged on the piston dam of piston edge, keeps relative level with the piston flat surface after leveling.

According to national regulations, gas chamber piston upper area is 1st district, and double-shaft tilt angle sensor is not intrinsic safety type instrument, therefore needs double-shaft tilt angle sensor to load to have in the Flameproof box of flame proof function, and site operation personnel only need consider the installation of Flameproof box.Flameproof box must be installed after piston flat surface leveling is checked and accepted again, mounting means is that level installs (above uncapping), suggestion is arranged on by the piston dam of the piston edge of cement casting, to prevent piston from shaking the signal disturbing caused, the piston flat surface after simultaneously must ensureing Flameproof box and leveling keeps relative level.It should be noted that native system provides relative zero function to carry out software correction because the very difficult Flameproof box that mechanically adjusts reaches abswolute level.

As shown in Figure 7, wherein slash region representation piston dam on piston 1 limit, Flameproof box 3 is arranged on piston dam, and double-shaft tilt angle sensor 2 is arranged in Flameproof box 3, and Flameproof box 3 Width need align with certain root post of gas chamber (this figure illustrates with No. 1 column 4).Being defined sensing column direction, the center of circle is X-axis forward, and tangential direction is Y-axis, and vergence direction angle represents and X-axis forward angle in the counterclockwise direction, and scope is 0 ~ 360 °.

Because double-shaft tilt angle sensor has feed cable and 485 communication cables, two cables, and the upper and lower stroke of piston reaches tens meters, therefore need establish two cover cable gathering-devices at top land, prevents piston mutual tangled up and knotted between each cable when moving up and down.Cable gathering-device does not have power part, is only to rely on the deadweight of cable to be wound around, so flexible cable must be adopted could to be comparatively easy to be wound into cable gathering-device from piston to this section, gas chamber top cable.

Utilize the gas chamber piston degree of tilt online test method that above-mentioned gas chamber piston degree of tilt on-line detecting system realizes, it comprises the following steps:

S1, definition X, Y-axis are orthogonal coordinate axis in piston flat surface, the direction of measurement of double-shaft tilt angle sensor and the direction of X, Y parallel to each other, the former surface level of piston is primary plane β, and the piston center of circle is the intersection point O of X, Y-axis, and piston radius is R, piston is along straight line MN run-off the straight, plane after inclination is γ, in plane γ, if B point be tilt after the peak of piston flat surface, vertical range between it and plane β is H, and ∠ BOB ₁=θ, so θ is X-axis forward and inclination peak direction angle in the counterclockwise direction, i.e. the vergence direction of piston; OB ₁, OB ₂radius after being respectively inclination in X, Y-axis, then its angle ∠ B ₁oB ₂=90 °, it is a ' that obliquity sensor records X-direction top rade, and Y direction top rade is b '.

S2, following algorithm is adopted to carry out filtering process to the raw data collected:

Y _k＝(1-j)*X _k+j*Y _k-1(1)，

J is filter factor in formula (1), its span between 0 ~ 1, X _kfor current sample values, Y _k-1for last filter result, Y _kfor present filter result.

The X-direction top rade a ' recorded and Y direction top rade b ' is carried out filtering respectively through formula (1), obtains filtered X-direction top rade a and filtered Y direction top rade b;

S3, calculate following parameter:

$H=R\sqrt{{\sin }^{2}a+{\sin }^{2}b}$

$\mathrm{\&theta;}=\arctan \left(\frac{\sin b}{\sin a}\right)$

In formula, for the angle between the plane γ after primary plane β and inclination;

S4, according to X, Y-axis, piston flat surface is divided into four quadrants,

1) if a>0, b>0, then represent that piston peak is at I quadrant, 0 ° of < θ <90 °;

2) if a<0, b>0, then represent that piston peak is at II quadrant, 90 ° of < θ <180 °;

3) if a<0, b<0, then represent that piston peak is at III quadrant, 180 ° of < θ <270 °;

4) if a>0, b<0, then represent that piston peak is at IV quadrant, 270 ° of < θ <360 °;

5) if a=0, b>0, then represent that piston tilts along Y-axis positive dirction, θ=90 °;

6) if a=0, b<0, then represent that piston tilts along Y-axis negative direction, θ=270 °;

7) if b=0, a>0, then represent that piston tilts along X-axis positive dirction, θ=0 °;

8) if b=0, a<0, then represent that piston tilts along X-axis negative direction, θ=180 °;

9) if a=0, b=0, then represent that piston is horizontal, without tilting.

Be below the original angle signal at two days two nights of certain steel mill's continuous acquisition, frequency acquisition is 1Hz, as shown in Figure 4, and 200 points altogether.Upper as can be seen from figure, the fluctuation of upper signal of whole time period is comparatively obvious, main because double-shaft tilt angle sensor precision too high (after radix point 3), when gas chamber runs, piston rocks a little to some extent and output angle will be caused to change, and whole piston diameter reaches nearly 70 meters (150,000 cabinets), top land is spliced by one piece of block plate, and it is even likely because local steel plate vibrates instead of because rocking of whole piston caused that double-shaft tilt angle sensor exports angle change.In figure, the amplitude of the upper and lower saltus step of original angle signal is at about ± 0.02 °, although amplitude is little, because its absolute angle itself is just very little, therefore this saltus step has a great impact result of calculation.And from actual process object analysis, whole piston weight weighs upper kiloton, and can not rock back and forth frequently, its tilting procedure must be a process comparatively slowly.Therefore must process original signal, eliminate undesired signal.

Native system adopts following algorithm to process original signal:

Y _k＝(1-a)*X _k+a*Y _k-1(1)，

In formula (1), a is filter factor, and its span is between 0 ~ 1, and general value is comparatively large, X _kfor current sample values, Y _k-1for last filter result, Y _kfor present filter result.Can find out according to its computing formula, the result of this filtering depends primarily on the output valve of filtering last time, instead of the sampled value of last time, the contribution that this sampled value same exports filtering relative to filtering last time output valve be smaller, but correcting action can be had to Output rusults, simulate the functions of low-pass filter compared with Great inertia.This algorithm has good inhibiting effect to PERIODIC INTERFERENCE, and is applicable to the higher occasion of vibration frequency, but it can cause delayed phase, and its delay degree depends on a value size, and a is larger, and filter result is more delayed.Signal in Fig. 4 is carried out filtering by formula (1), and its result as shown in Figure 5.

Comparison diagram 4 and Fig. 5, after finding filtering, signal becomes level and smooth, eliminates the saltus step up and down of original signal.

Although filtering eliminates shake, the saltus step solving original signal, on the impact of detection system subsequent calculations, equally also can bring the problem of signal lag.Filter factor a is larger, and filter result is more level and smooth, but sensitivity decrease, signal lag is serious; Filter factor a is less, and filter result sensitivity is higher, but shake is severe, therefore must select the filter factor that suitable, take into account the impact of two aspects.

If directly adopt raw data to calculate, its result saltus step is comparatively large, will severe jamming operating personnel to the judgement of piston practical operation situation, as shown in Figure 6, obviously can find out that signal quality obtains larger improvement after the filtering.

Algorithm principle is as follows:

Whole measuring principle as shown in Figure 3, assuming that X, Y are orthogonal coordinate axis in former piston flat surface in figure, the direction of measurement of obliquity sensor and the direction of X, Y parallel to each other.The former surface level of piston is primary plane β, and the piston center of circle is the intersection point O of X, Y-axis, and piston radius is R, piston is along straight line MN run-off the straight, and the plane after inclination is γ, in plane γ, if B point be tilt after the peak of piston flat surface, the vertical range between it and plane β is H, and ∠ BOB ₁=θ, so θ is X-axis forward and inclination peak direction angle in the counterclockwise direction, i.e. the vergence direction of piston; OB ₁, OB ₂radius after being respectively inclination in X, Y-axis, then its angle ∠ B ₁oB ₂=90 °, it is a ' that obliquity sensor records X-direction top rade, and Y direction top rade is b '; The X-direction top rade a ' recorded and Y direction top rade b ' is carried out filtering respectively through formula (1), obtains filtered X-direction top rade a and filtered Y direction top rade b.

Respectively from B ₁, B ₂make vertical line to primary plane β, intersection point is C ₁, C ₂, make h ₁=B ₁c ₁, h ₂=B ₂c ₂, then:

h ₁＝Rsina (2)，

h ₂＝Rsinb (3)，

If primary plane β and tilt after plane γ between angle be namely make a vertical line from B point to plane β, intersection point is C, then in Δ OBC:

In plane γ, from B ₁point is a vertical line B to radius OB ₁b ' ₁, at Δ OB ₁b ' ₁in:

OB′ ₁＝Rcosθ (5)，

Due to MN ⊥ OB, B ₁b ' ₁⊥ OB and therefore MN//B ₁b ' ₁; Simultaneously due to and therefore B ₁b ' ₁// β.Therefore from B ' ₁vertical line B ' is to plane β ₁c ' ₁, intersection point is C ' ₁, then:

h ₁＝B′ ₁C′ ₁(6)，

At Δ OB ' ₁c ' ₁in, oB ' is known again according to formula (5) ₁=Rcos θ, then:

According to formula (2) (6) (7), can obtain that is:

In like manner from B ₂point is a vertical line B to radius OB ₂b ' ₂, then OB ' ₂=Rsin θ, in like manner can obtain:

Can obtain according to (9)/(8):

Formula (3), (4) respectively square summation can obtain:

Therefore finally can obtain conclusion: 1. $H=R\sqrt{{\sin }^{2}a+{\sin }^{2}b}$

②

③ $\mathrm{\&theta;}=\arctan \left(\frac{\sin b}{\sin a}\right)$

Wherein H be tilting of the piston after peak apart from the height of former piston flat surface, for the angle between tilting of the piston plane and primary plane, θ is X-axis forward and inclination peak direction angle in the counterclockwise direction, i.e. the vergence direction of piston.

Because piston may in circumferentially any one angle surface thereof, therefore the angle that obliquity sensor exports in X, Y-axis can just can be born.As shown in Figure 3, whole piston flat surface is divided into four quadrants.X, Y direction angle determination tilting of the piston orientation angle θ measured by obliquity sensor.

1) if a>0, b>0, then represent that piston peak is at I quadrant, 0 ° of < θ <90 °;

2) if a<0, b>0, then represent that piston peak is at II quadrant, 90 ° of < θ <180 °;

3) if a<0, b<0, then represent that piston peak is at III quadrant, 180 ° of < θ <270 °;

4) if a>0, b<0, then represent that piston peak is at IV quadrant, 270 ° of < θ <360 °;

Also have several special circumstances:

5) if a=0, b>0, then represent that piston tilts along Y-axis positive dirction, θ=90 °;

6) if a=0, b<0, then represent that piston tilts along Y-axis negative direction, θ=270 °;

7) if b=0, a>0, then represent that piston tilts along X-axis positive dirction, θ=0 °;

8) if b=0, a<0, then represent that piston tilts along X-axis negative direction, θ=180 °;

9) if a=0, b=0, then represent that piston is horizontal, without tilting.

Above embodiment is only for illustration of Computation schema of the present invention and feature, and its object is to enable those skilled in the art understand content of the present invention and implement according to this, protection scope of the present invention is not limited to above-described embodiment.So all equivalent variations of doing according to disclosed principle, mentality of designing or modification, all within protection scope of the present invention.

Claims (3)

1. a gas chamber piston degree of tilt on-line detecting system, is characterized in that: it comprises the double-shaft tilt angle sensor and converter that are connected by RS485 bus; Double-shaft tilt angle sensor is for detecting the inclination angle in gas chamber piston plane two vertical direction, and converter accesses existing control system by DP cable in the mode of Profibus-DP slave station;

Described converter comprises the UART connected successively and turns RS485 level transferring chip, microprocessor, DP slave station protocol process chip and DP bus physical interface chip, and the data that microprocessor is used for gathering according to double-shaft tilt angle sensor calculate gas chamber piston angle of inclination and direction.

2. gas chamber piston degree of tilt on-line detecting system according to claim 1, it is characterized in that: described double-shaft tilt angle sensor is arranged in Flameproof box, Flameproof box is arranged on the piston dam of piston edge, keeps relative level with the piston flat surface after leveling.

3. the gas chamber piston degree of tilt online test method utilizing the gas chamber piston degree of tilt on-line detecting system described in claim 1 or 2 to realize, is characterized in that: it comprises the following steps:

S1, definition X, Y-axis are orthogonal coordinate axis in piston flat surface, the direction of measurement of double-shaft tilt angle sensor and the direction of X, Y parallel to each other, the former surface level of piston is primary plane β, and the piston center of circle is the intersection point O of X, Y-axis, and piston radius is R, piston is along straight line MN run-off the straight, plane after inclination is γ, in plane γ, if B point be tilt after the peak of piston flat surface, vertical range between it and plane β is H, and ∠ BOB ₁=θ, so θ is X-axis forward and inclination peak direction angle in the counterclockwise direction, i.e. the vergence direction of piston; OB ₁, OB ₂radius after being respectively inclination in X, Y-axis, then its angle ∠ B ₁oB ₂=90 °, it is á that obliquity sensor records X-direction top rade, and Y direction top rade is

S2, following algorithm is adopted to carry out filtering process to the raw data collected:

Y _k＝(1-j)*X _k+j*Y _k-1(1)，

J is filter factor in formula (1), its span between 0 ~ 1, X _kfor current sample values, Y _k-1for last filter result, Y _kfor present filter result;

By the X-direction top rade á that records and Y direction top rade carry out filtering respectively through formula (1), obtain filtered X-direction top rade a and filtered Y direction top rade b;

S3, calculate following parameter:

$H=R\sqrt{{\sin }^{2}a+{\sin }^{2}b}$

$\mathrm{\&theta;}=\arctan \left(\frac{\sin b}{\sin a}\right)$

In formula, for the angle between the plane γ after primary plane β and inclination;

S4, according to X, Y-axis, piston flat surface is divided into four quadrants,

1) if a>0, b>0, then represent that piston peak is at I quadrant, 0 ° of < θ <90 °;

2) if a<0, b>0, then represent that piston peak is at II quadrant, 90 ° of < θ <180 °;

3) if a<0, b<0, then represent that piston peak is at III quadrant, 180 ° of < θ <270 °;

4) if a>0, b<0, then represent that piston peak is at IV quadrant, 270 ° of < θ <360 °;

5) if a=0, b>0, then represent that piston tilts along Y-axis positive dirction, θ=90 °;

6) if a=0, b<0, then represent that piston tilts along Y-axis negative direction, θ=270 °;

7) if b=0, a>0, then represent that piston tilts along X-axis positive dirction, θ=0 °;

8) if b=0, a<0, then represent that piston tilts along X-axis negative direction, θ=180 °;

9) if a=0, b=0, then represent that piston is horizontal, without tilting.