A speedless blade tip timing measurement method based on a dynamically variable reference blade

Abstract

A speed-free blade tip timing measurement method based on a dynamic variable reference blade is disclosed. The method includes calculating the average speed of the entire circle and the local average speed of each blade between adjacent sensors according to the measured arrival time of the blade at the blade tip timing sensor, assuming that there is random detuning between the rotor blades, and determining the vibration of each blade in the circle by comparing the deviation value between the local average speed of each blade and the average speed of the entire circle. A target blade is selected, and the blade with the smallest vibration in the circle is used as the reference blade, and the vibration displacement of the target blade in the circle is calculated according to the relative angle relationship between the target blade and the reference blade. Similarly, a reference blade in each circle is selected and the vibration displacement of the target blade is calculated, and finally non-contact online monitoring of the vibration of the rotating blade without a speed signal reference is realized.

Description

Technical Field

[0001] The invention relates to the technical field of non-contact measurement of rotating blades of rotating machinery, and in particular to a speedless blade tip timing measurement method based on a dynamic variable reference blade. Background Art

[0002] Rotor blades are one of the key components of aircraft engines. However, their working environment is harsh, and complex alternating loads often cause blade vibration. If the blade vibration is too large, it may cause excessive stress in a specific area of ​​the blade, resulting in high-cycle fatigue cracks, fractures and other damage, which seriously threatens the operation safety of the aircraft engine. Therefore, during the operation of the aircraft engine, real-time online monitoring of the vibration state of the rotor blade can effectively evaluate its full-field stress state, which is of great significance for the prediction of the high-cycle fatigue life of the blade.

[0003] Traditional blade tip timing technology requires a reference speed signal to achieve vibration measurement of rotor blades. Once the speed signal fails, the entire blade tip timing measurement system may fail. However, in real aircraft engines, speed sensors are often difficult or even impossible to install. Therefore, the present invention provides a blade vibration measurement method based on blade tip timing technology without speed signal reference, which can achieve accurate measurement of rotor blade tip vibration displacement, and then monitor the vibration condition of rotor blades online.

[0004] The above information disclosed in this Background section is only for enhancement of understanding of the background of the invention and therefore it may contain information that does not form the prior art that is already known to a person of ordinary skill in the art. Summary of the invention

[0005] In view of the deficiencies in the prior art, the purpose of the present invention is to provide a speed-free blade tip timing measurement method based on a dynamically variable reference blade, which solves the problem that traditional blade tip timing technology requires a speed signal reference. By finding the reference blade through the deviation between the local average speed of each circle and the average speed of the entire circle and performing simple calculations, the vibration displacement of the rotor blade can be measured, thereby realizing online monitoring of the vibration state of the rotor blade.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] A method for measuring blade tip timing at zero speed based on a dynamic variable reference blade of the present invention comprises:

[0008] The first step S1 is to install s blade tip timing sensors along the circumference of the engine casing to obtain the measured time series of the arrival of the blades of the entire stage of rotor at the blade tip timing sensors under variable speed conditions;

[0009] In the second step S2, based on the time series, the average rotation speed of the rotor blades in a whole circle and the local average rotation speed of each blade between adjacent sensors are calculated to determine the target blade;

[0010] In the third step S3, assuming that there is random detuning between the rotor blades, the deviation between the local average speed of each blade and the average speed of the entire circle is calculated, and the reference blade of the circle is selected;

[0011] The fourth step S4, calculating the vibration displacement of the target blade under the circle according to the relative angle relationship between the target blade and the reference blade;

[0012] In the fifth step S5, similarly, a reference blade in each circle is selected and the vibration displacement of the target blade is calculated, thereby finally realizing online vibration monitoring of the rotating blade without a speed signal reference.

[0013] In the method, in the first step S1, the number of the blade tip timing sensors is not less than 2, that is, s≥2.

[0014] In the method described above, in the first step S1, the measured time series refers to the time when the blade actually reaches each blade tip timing sensor. Among them, t s，b，n It represents the time when the bth blade in the nth sensor circle arrives at the sth blade tip timing sensor, n∈[1,N],s∈[1,S],b∈[1,B],B,S,N represent the number of blades, the number of blade tip timing sensors and the total number of circles respectively.

[0015] In the method described above, in the second step S2, the average rotation speed of the rotor blade in the pth circle is expressed as: The local average rotation speed of each blade between adjacent sensors can be expressed as Among them, Ω b，i，p represents the local average speed of the bth blade in the pth cycle between the tip timing sensors i and i+1, represents the circumferential installation angle of the i-th blade tip timing sensor.

[0016] In the method, in the second step S2, the target blade refers to a designated blade whose vibration displacement needs to be calculated.

[0017] In the method described, in the third step S3, the random detuning refers to the random deviation between the blades of the entire rotor stage caused by factors such as manufacturing errors, material unevenness and blade wear. This deviation may cause the natural frequencies of different blades of the entire rotor stage to be different, and then cause the blades of the entire stage to reach the resonance state non-simultaneously under variable speed conditions.

[0018] In the method described, in the third step S3, the deviation value of the local average speed of each blade and the average speed of the whole circle is expressed as follows: It represents the deviation between the local average speed of blade b in the pth circle between adjacent blade tip timing sensors and the average speed of the entire circle. This value represents the speed fluctuation caused by blade vibration. The larger the value, the greater the vibration of the blade.

[0019] In the method described, in the third step S3, the reference blade is selected according to the formula Determine, where R p The reference blade of the pth circle, that is, the blade with the smallest vibration is selected as the reference blade. The blade with the smallest vibration in each circle may be different, so the reference blade in each circle may change dynamically.

[0020] In the method, the fourth step S4 comprises:

[0021] S401: Assume the target leaf is B T , reference blade is B R , the angle between the two blades in the initial state is α. The target blade is at a blade tip timing sensor S i The vibration angle under the condition is θ, then the vibration displacement of the target blade can be expressed as y T =R·θ, where R is the rotor radius;

[0022] S402: In the pth round, the target blade and the reference blade arrive at the blade tip timing sensor S i The arrival times are t i，T，p and t i，R，p , assuming that the target blade does not vibrate, then at time t i，T，p ~t i，R，p The ideal angular displacement of the reference blade is equal to the angle α between the two blades in the initial state; however, due to the vibration of the target blade, the actual angular displacement of the reference blade is β = 2πΩ p ·(t i，R，p -t i，T，p ),Ω p is the average rotation speed of the whole circle;

[0023] S403: The vibration angle of the target blade can be expressed as θ=β-α=2πΩ p ·(t i，R，p -t i，T，p )-α;

[0024] S404: The tip vibration displacement of the target blade can be expressed as y T =Rθ=R(2πΩ p ·(t i，R，p -t i，T，p )-α).

[0025] In the method described, in the fifth step S5, the expression of the target blade vibration displacement under each circle is: n represents the nth circle, Ω(n) represents the average rotation speed of the nth circle, α(n) represents the initial angle between the reference blade and the target blade of the nth circle, t i，T (n) and t i，R (n) respectively represent the target blade and the reference blade reaching the blade tip timing sensor S in the nth round i Arrival time.

[0026] Beneficial Effects

[0027] The present invention adopts a blade that hardly vibrates in the entire stage of rotor blades as a reference blade to calculate the vibration displacement of a target blade, thereby avoiding the limitation of the traditional blade tip timing technology that requires a reference speed signal; the deviation between the local average speed of the rotor blade between the blade tip timing sensors and the average speed of the entire circle is used to screen out the reference blade, and the process is simple; the present invention uses the blade as a reference object to calculate the vibration displacement of the target blade, which can effectively eliminate the trend item caused by blade deformation under variable speed conditions.

[0028] The above description is only an overview of the technical solution of the present invention. In order to make the technical means of the present invention clearer and to enable those skilled in the art to implement it according to the contents of the specification, and to make the above and other purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are described below by way of example. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present invention. For ordinary technicians in this field, other drawings can also be obtained based on these drawings.

[0030] By reading the detailed description of the preferred specific embodiments below, various other advantages and benefits of the present invention will become clear to those of ordinary skill in the art. The drawings in the specification are only for the purpose of illustrating the preferred embodiments and are not considered to be limitations of the present invention. Obviously, the drawings described below are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can also be obtained based on these drawings without creative work. Moreover, the same reference numerals are used to represent the same components throughout the drawings.

[0031] In the attached picture:

[0032] Figure 1 A schematic flow chart of a method for measuring zero-speed blade tip timing based on a dynamically variable reference blade provided by an embodiment of the present invention;

[0033] Figure 2 Schematic diagram of a rotor blade dynamics model established in one embodiment of the present invention; wherein k i 、m i 、c i (i=1, 2, 3, 4, 5) represent the stiffness, mass and damping of the i-th blade respectively;

[0034] Figure 3 A schematic diagram of the circumferential angle layout of blade tip timing sensors provided by one embodiment of the present invention;

[0035] Figure 4 A schematic diagram of a dynamic variable reference blade selection process provided by an embodiment of the present invention; wherein, Ω RMSEi (i=1, 2, 3, 4, 5) represents the deviation between the local average speed of the i-th blade and the average speed of the whole circle;

[0036] Figure 5(a) to Figure 5(e) A schematic diagram of the comparison of the vibration displacement of each blade with and without the speed reference calculation under the blade tip timing sensor No. 3 provided for an embodiment of the present invention; wherein, Figure 5(a) is the vibration displacement comparison result of blade No. 1, Figure 5(b) is the vibration displacement comparison result of blade No. 2, Figure 5(c) is the vibration displacement comparison result of blade No. 3, Figure 5(d) is the vibration displacement comparison result of blade No. 4, and Figure 5(e) is the vibration displacement comparison result of blade No. 5.

[0037] The present invention is further explained below in conjunction with the accompanying drawings and embodiments. DETAILED DESCRIPTION

[0038] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described in combination with the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0039] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0040] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not require further definition and explanation in subsequent drawings.

[0041] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", "clockwise", "counterclockwise" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the referred device or element must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present invention.

[0042] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.

[0043] In the present invention, unless otherwise clearly specified and limited, the terms "installed", "connected", "connected", "fixed" and the like should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be directly connected or indirectly connected through an intermediate medium, it can be the internal connection of two elements or the interaction relationship between two elements. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0044] In the present invention, unless otherwise clearly specified and limited, a first feature being "above" or "below" a second feature may include that the first and second features are in direct contact, or may include that the first and second features are not in direct contact but are in contact through another feature between them. Moreover, a first feature being "above", "above" and "above" a second feature includes that the first feature is directly above and obliquely above the second feature, or simply indicates that the first feature is higher in level than the second feature. A first feature being "below", "below" and "below" a second feature includes that the first feature is directly below and obliquely below the second feature, or simply indicates that the first feature is lower in level than the second feature.

[0045] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be further described in detail below in conjunction with the accompanying drawings, and each of the accompanying drawings does not constitute a limitation on the embodiments of the present invention.

[0046] A method for measuring zero-speed blade tip timing based on a dynamically variable reference blade includes:

[0047] In the first step S1, s blade tip timing sensors are installed along the circumference of the engine casing to obtain the measured time series of the arrival of the blades of the entire stage of rotor at the blade tip timing sensors under the variable speed condition;

[0048] In the second step S2, the average rotation speed of the rotor blades in a whole circle and the local average rotation speed of each blade between adjacent sensors are calculated based on the time series to determine the target blade;

[0049] In the third step S3, assuming that there is random detuning between the rotor blades, the deviation between the local average speed of each blade and the average speed of the entire circle is calculated, and the reference blade of the circle is selected;

[0050] In the fourth step S4, the vibration displacement of the target blade under the circle is calculated according to the relative angle relationship between the target blade and the reference blade;

[0051] In the fifth step S5, similarly, a reference blade in each circle is selected and the vibration displacement of the target blade is calculated, thereby finally realizing online vibration monitoring of the rotating blade without a speed signal reference.

[0052] In a preferred implementation manner of the method, in the first step S1, the number of the blade tip timing sensors is not less than 2, that is, s≥2.

[0053] In a preferred embodiment of the method, in the first step S1, the measured time series refers to the time when the blade actually reaches each blade tip timing sensor. Among them, t s，b，n It represents the time when the bth blade in the nth sensor circle arrives at the sth blade tip timing sensor, n∈[1,N],s∈[1,S],b∈[1,B],B,S,N represent the number of blades, the number of blade tip timing sensors and the total number of circles respectively.

[0054] In a preferred embodiment of the method, in the second step S2, the average rotational speed of the rotor blade in the pth circle is expressed as The local average rotation speed of each blade between adjacent sensors can be expressed as Among them, Ω b，i，p represents the local average speed of the bth blade in the pth cycle between the tip timing sensors i and i+1, represents the circumferential installation angle of the i-th blade tip timing sensor.

[0055] In a preferred embodiment of the method, in the second step S2, the target blade refers to a designated blade whose vibration displacement needs to be calculated.

[0056] In a preferred embodiment of the method, in the third step S3, the random detuning refers to the random deviation between the blades of the entire rotor stage caused by factors such as manufacturing errors, material unevenness and blade wear. This deviation may cause the natural frequencies of different blades of the entire rotor stage to be different, and thus cause the blades of the entire stage to reach the resonance state non-simultaneously under variable speed conditions.

[0057] In a preferred embodiment of the method, in the third step S3, the deviation value of the local average speed of each blade and the average speed of the whole circle is expressed as follows: It represents the deviation between the local average speed of blade b in the pth circle between adjacent blade tip timing sensors and the average speed of the entire circle. This value represents the speed fluctuation caused by blade vibration. The larger the value, the greater the vibration of the blade.

[0058] In a preferred embodiment of the method, in the third step S3, the reference blade is selected according to the formula Determine, where R p The reference blade of the pth circle, that is, the blade with the smallest vibration is selected as the reference blade. The blade with the smallest vibration in each circle may be different, so the reference blade in each circle may change dynamically.

[0059] In a preferred embodiment of the method, the fourth step S4 comprises:

[0060] S401: Assume the target leaf is B T , reference blade is B R , the angle between the two blades in the initial state is α. The target blade is at a blade tip timing sensor S i The vibration angle under the condition is θ, then the vibration displacement of the target blade can be expressed as y T =R·θ, where R is the rotor radius;

[0061] S402: In the pth round, the target blade and the reference blade arrive at the blade tip timing sensor S i The arrival times are t i，T，p and t i，R，p , assuming that the target blade does not vibrate, then at time t i，T，p ~t i，R，p The ideal angular displacement of the reference blade is equal to the angle α between the two blades in the initial state; and due to the vibration of the target blade, the actual angular displacement of the reference blade is β = 2πΩ p ·(t i，R，p -t i，T，p ),Ω p is the average rotation speed of the whole circle;

[0062] S403: The vibration angle of the target blade can be expressed as θ=β-α=2πΩ p·(t i，R，p -t i，T，p )-α;

[0063] S404: The tip vibration displacement of the target blade can be expressed as y T =Rθ=R(2πΩ p ·(t i，R，p -t i，T，p )-α).

[0064] In a preferred embodiment of the method, in the fifth step S5, the expression of the target blade vibration displacement under each circle is: n represents the nth circle, Ω(n) represents the average rotation speed of the nth circle, α(n) represents the initial angle between the reference blade and the target blade of the nth circle, t i，T (n) and t i，R (n) respectively represent the target blade and the reference blade reaching the blade tip timing sensor S in the nth round i Arrival time.

[0065] In order to further understand the present invention, Figure 1 to Figure 5(e) A specific simulation example is used to further describe the present invention instead of the experimental example, and to illustrate the relationship between the transfer ratio and the crack length and the rotation speed. It should be emphasized that the following description is merely exemplary, and the application of the present invention is not limited to the following example.

[0066] Figure 1 This is a flow chart of the speed-free blade tip timing measurement method based on dynamic variable reference blades completed by the present invention. After selecting the target blade, the method first obtains the measured arrival time series of the rotor blades under the variable speed condition through the circumferentially installed blade tip timing sensor, and further calculates the average speed of the rotor blades in the whole circle and the local average speed of each blade between adjacent sensors based on the time series. Assuming that there is random detuning between the rotor blades, the reference blade of the circle can be selected by calculating the deviation value between the local average speed of each blade and the average speed of the whole circle. Then, the vibration displacement of the target blade in the circle is calculated based on the relative angle relationship between the target blade and the reference blade. Finally, the reference blade in each circle is selected and the vibration displacement of the target blade is calculated in the same way, and finally the online vibration monitoring of the rotating blade without the reference of the speed signal is realized.

[0067] The specific steps are as follows:

[0068] 1. Establish an uncoupled five-blade dynamic model, such as Figure 2 As shown, k i 、m i 、c i(i=1, 2, 3, 4, 5) respectively represents the stiffness, mass and damping of the i-th blade, and the stiffness detuning of the blade is simulated by setting different stiffness values. The natural frequencies of the five blades after detuning are set to B1=143.2Hz, B2=139.6Hz, B3=146.8Hz, B4=141.8Hz, and B5=144.7Hz.

[0069] 2. Simulate and set up 5 blade tip timing sensors to simulate blade tip timing sampling to obtain the actual blade arrival time series. The installation angle θ = [0° 18.9° 37.7° 55.8° 267°], and the layout is as follows: Figure 3 As shown, a uniform speed-increasing swept frequency excitation is applied to the rotor blades to obtain the time series of the entire stage of rotor blades reaching the blade tip timing sensor under variable speed conditions;

[0070] 3. Calculate the average rotation speed of the rotor blades throughout the entire revolution and the local average rotation speed of each blade between adjacent sensors to determine the target blade;

[0071] 4. Calculate the deviation between the local average speed of each blade and the average speed of the whole circle, and select the reference blade of the circle, such as Figure 4 As shown, it can be seen that due to the resonance of the blades, the deviation values ​​of the local average speed of different blades and the average speed of the whole circle have reached extreme values ​​one after another. In addition, around the 1200th circle, the reference blade changed from blade No. 5 to blade No. 2, which reflects the advantage of the "dynamic variable reference" of the present invention;

[0072] 5. Calculate the vibration displacement of the target blade in the circle according to the relative angle between the target blade and the reference blade. Similarly, select the reference blade in each circle and calculate the vibration displacement of the target blade. Taking the blade tip timing sensor No. 3 as an example, the blade vibration displacement value set by the simulation is recorded as "with speed reference", and the blade vibration displacement calculated by the method provided by the present invention is recorded as "without speed reference". The two displacement results are compared. Figure 5(a) to Figure 5(e) As shown, it can be seen that the method provided by the present invention can accurately calculate the vibration displacement of the blade without a speed reference.

[0073] Although the embodiments of the present invention are described above in conjunction with the accompanying drawings, the present invention is not limited to the above specific embodiments and application fields, and the above specific embodiments are only illustrative and instructive, rather than restrictive. A person of ordinary skill in the art can also make many forms under the guidance of this specification and without departing from the scope of protection of the claims of the present invention, all of which belong to the protection of the present invention.

Claims

1. A method for measuring blade tip timing without speed based on a dynamic variable reference blade, characterized in that: It includes the following steps: The first step S1 is to install the engine casing circumferentially A blade tip timing sensor is used to obtain the measured time series of the arrival of the blade tip timing sensor of the entire stage of rotor blades under variable speed conditions; In the second step S2, based on the time series, the average rotation speed of the rotor blades in a whole circle and the local average rotation speed of each blade between adjacent sensors are calculated to determine the target blade; In the third step S3, assuming that there is random detuning between the rotor blades, the deviation between the local average speed of each blade and the average speed of the entire circle is calculated, and the reference blade of the circle is selected; The fourth step S4, calculating the vibration displacement of the target blade under the circle according to the relative angle relationship between the target blade and the reference blade; In the fifth step S5, similarly, a reference blade in each circle is selected and the vibration displacement of the target blade is calculated, and finally online vibration monitoring of the rotating blade is realized without a speed signal reference; In the second step S2, the rotor blades The average speed of a full circle is expressed as , and the local average rotation speed of each blade between adjacent sensors can be expressed as ,in, Indicated in Circle Blade tip timing sensor and The local average speed between Indicates The circumferential mounting angle of the blade tip timing sensor; The fourth step S4 comprises, S401: Assume that the target leaf is , the reference leaf is , the angle between the two blades in the initial state is , the target blade is at a blade tip timing sensor The vibration angle is , then the vibration displacement of the target blade is expressed as ,in, is the rotor radius; S402: The target blade and the reference blade reach the blade tip timing sensor The arrival times are and , assuming that the target blade does not vibrate, then at time The ideal angular displacement of the reference blade is equal to the angle between the two blades in the initial state. ; In fact, due to the vibration of the target blade, the actual angular displacement of the reference blade is , is the average rotation speed of the whole circle; S403: The vibration angle of the target blade can be expressed as ; S404: The tip vibration displacement of the target blade can be expressed as .

2. The method according to claim 1, characterized in that In the first step S1, the number of blade tip timing sensors is not less than 2, that is, .

3. The method according to claim 1, characterized in that In the first step S1, the measured time series refers to the time when the blade actually reaches each blade tip timing sensor ,in, Indicates the sensor Circle The leaves reach The time of the blade tip timing sensor, They represent the number of blades, the number of blade tip timing sensors and the total number of revolutions respectively.

4. The method according to claim 1, characterized in that: In the second step S2, the target blade refers to a designated blade whose vibration displacement needs to be calculated.

5. The method according to claim 1, characterized in that: In the third step S3, the random detuning refers to the random deviation between the blades of the entire rotor stage due to factors such as manufacturing errors, material unevenness and blade wear. This deviation may cause the natural frequencies of different blades of the entire rotor stage to be different, and then cause the blades of the entire stage to reach the resonance state non-simultaneously under variable speed conditions.

6. The method according to claim 1, characterized in that In the third step S3, the deviation value of the local average speed of each blade and the average speed of the whole circle is expressed as follows: , which indicates the Inner blade The deviation between the local average speed between adjacent blade tip timing sensors and the average speed of the entire circle indicates the speed fluctuation caused by blade vibration. The larger the value, the greater the vibration of the blade.

7. The method according to claim 1, characterized in that In the third step S3, the reference blade is selected according to the formula Determine, among which, Indicates The reference blade of a circle, that is, the blade with the smallest vibration, is selected as the reference blade. The blade with the smallest vibration in each circle may be different, so the reference blade in each circle may change dynamically.

8. The method according to claim 1, characterized in that In the fifth step S5, the expression of the target blade vibration displacement in each circle is: , Indicates lock up, Indicates Average speed of the whole circle, Indicates The initial angle between the reference blade and the target blade, and Respectively represent the target leaf and the reference leaf in Circle reaches the blade tip timing sensor Arrival time.

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