CN108984872B - Method for analyzing and evaluating motion of oscillator in casing mud and effect of oscillator on casing - Google Patents

Method for analyzing and evaluating motion of oscillator in casing mud and effect of oscillator on casing Download PDF

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CN108984872B
CN108984872B CN201810702491.2A CN201810702491A CN108984872B CN 108984872 B CN108984872 B CN 108984872B CN 201810702491 A CN201810702491 A CN 201810702491A CN 108984872 B CN108984872 B CN 108984872B
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oscillator
collision
casing
sleeve
equation
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CN108984872A (en
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刘延强
赵德敏
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China University of Petroleum East China
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Abstract

The invention relates to a method for analyzing and evaluating the main motion behavior of an oscillator in casing mud and the effect of the oscillator on a casing, which comprises the following steps of starting the oscillator, calculating and recording the occurrence time t through a motion equation 1 To get solved
Figure DDA0001714804110000011
The movement of the oscillator is the movement of the oscillator before collision and the residual vibration generated by the collision of the sleeve
Figure DDA0001714804110000012
Or
Figure DDA0001714804110000013
Time, calculating the occurrence time t of recording from the time motion equation 2 To get solved
Figure DDA0001714804110000014
To be provided with
Figure DDA0001714804110000015
Or
Figure DDA0001714804110000017
The residual vibration generated by sleeve collision is superposed in the motion equation as an initial condition, and by analogy, the time, initial angular velocity and collision impulse t of each sleeve collision are solved i 、
Figure DDA0001714804110000018
So as to finally obtain a series of oscillator pair sleeves
Figure DDA0001714804110000019
Or
Figure DDA00017148041100000110
Action time and impact impulse t i 、 Ii (ii) a The method has the advantages that the method can effectively analyze and evaluate the main motion behavior of the oscillator in the casing mud and the effect of the oscillator on the casing and provide data support for analyzing the effect of the casing on the cement slurry.

Description

Method for analyzing and evaluating motion of oscillator in casing mud and effect of oscillator on casing
Technical Field
The invention belongs to the technical field of drilling, and relates to a method for analyzing and evaluating the motion of an oscillator in casing mud and the effect of the oscillator on a casing.
Background
During the drilling and completion process, the quality of the cementing solid casing directly influences the working quality of the casing after completion. If the well cementation cement is unevenly distributed and not dense, the sleeve is unevenly stressed and is easy to damage. Therefore, how to achieve uniform and dense effect of the poured cement is always a concern for the completion workers. Therefore, people design different oscillators to be put into the casing, and the casing is shocked by the swinging of the oscillator to excite the casing to vibrate, so that the cement outside the casing is promoted to fluctuate, and the effect of uniform and compact distribution of the well cementation cement is achieved. However, there is no support for theoretical analysis and verification, and the data is rare. This paper attempts to explore an evaluation scheme for analyzing the effect of the vibrator on casing cement consolidation by performing a simulated analysis of the movement of the vibrator in a vertical well casing and the primary behavior of the effect on the casing.
Disclosure of Invention
The invention aims to provide a method for analyzing and evaluating the motion of an oscillator in casing mud and the action of the oscillator on the casing.
The technical scheme adopted by the invention is carried out according to the following steps:
(1) Starting from the start of the oscillator, the equation of motion is given by equation (1) when
Figure BDA0001714804090000011
Or->
Figure BDA0001714804090000012
Time (plus or minus)Depending on the calculation result of equation (1) at this time), the first time t of collision with the casing is calculated from equation (1) 1 The speed after the first collision with the sleeve is obtained by solving the formula (6) and the formula (5)>
Figure BDA0001714804090000013
And a collision impulse I, recorded as>
Figure BDA0001714804090000014
I 1 Angular displacement of ^ 5 upon collision>
Figure BDA0001714804090000015
Or>
Figure BDA0001714804090000016
(2) To be provided with
Figure BDA0001714804090000017
For the initial condition, the equation of motion after the first collision of the oscillator with the casing is equation (7). When +>
Figure BDA0001714804090000018
Or->
Figure BDA0001714804090000019
Time (the positive and negative of which depends on the calculation result of the equation (7)) and the second time of collision with the casing t calculated by the equation (7) 2 The rear angle speed after the second collision with the sleeve is obtained by solving the formula (8) and the formula (5)>
Figure BDA00017148040900000110
And a collision impulse I, recorded as>
Figure BDA00017148040900000111
I 2 Angular displacement of ^ 5 upon collision>
Figure BDA00017148040900000112
Or->
Figure BDA00017148040900000113
(3) And so on. T after obtaining the i-1 st collision i-1 ,
Figure BDA0001714804090000021
I i-1 Then, in order
Figure BDA0001714804090000022
For the initial condition, the equation of motion after the i-1 st collision of the oscillator with the housing is given by (10)>
Figure BDA0001714804090000023
Or->
Figure BDA0001714804090000024
(the positive and negative are determined by the calculation result of the equation (10) at this time) and the equation (10) are solved to obtain the time t elapsed by the ith impacting casing i . Upon impact an angular displacement of->
Figure BDA0001714804090000025
Or->
Figure BDA0001714804090000026
The clearance speed after the ith collision with the sleeve is obtained by solving the formula (11) and the formula (5)>
Figure BDA0001714804090000027
And a collision impulse I, recorded as>
Figure BDA0001714804090000028
I i 。
Finally obtaining the action time and the collision impulse t of a series of oscillators to the sleeve i 、I i (ii) a The effect of the oscillator on the casing, such as impact strength and frequency (by t), is evaluated accordingly i Determining the interval time of each adjacent collision, and then averagely counting the collision period and frequency).
Wherein the movement of the oscillator in the sleeve is limited by the sleeve, when the transverse displacement reaches the difference between the outer radius of the oscillator and the inner radius of the sleeve, the oscillator collides with the sleeve, and when the oscillator collides with the sleeve, the oscillator reaches the maximum angular displacement of the oscillator
Figure BDA0001714804090000029
In the formula, D 1 Is the inner diameter of the sleeve, l is the length of the oscillator, D is the outer diameter of the outer cylinder of the oscillator, l 1 The distance between the top of the oscillator and the suspension point O is shown, and alpha is the included angle between the centroid of the bottom of the oscillator and the connecting line between the contact point of the oscillator and the casing and the suspension point O respectively.
Before the oscillator starts, the oscillator is static and angularly displaced
Figure BDA00017148040900000210
Angular velocity>
Figure BDA00017148040900000211
I.e. initial conditions of
Figure BDA00017148040900000212
The motion equation of the oscillator is
Figure BDA00017148040900000213
Where ξ is the damping ratio of the oscillator system, p is the natural frequency of the oscillator system,
Figure BDA00017148040900000214
is the natural frequency of the oscillator, omega is the angular speed of rotation of the oscillator rotor, alpha 0 Is the initial phase of the steady state response of the oscillator system, and phi is the amplitude of the steady state response of the oscillator system.
If the coefficient of restitution of the oscillator when colliding with the sleeve is k, then
Figure BDA0001714804090000031
In the formula, v 1 、u 1 The velocities of the oscillator and the casing contact point before and after the collision, respectively
Figure BDA0001714804090000032
In the formula (I), the compound is shown in the specification,
Figure BDA0001714804090000033
oscillator in x before and after collision respectively 1 z 1 Angular velocity in the plane, given in equation (2) having
Figure BDA0001714804090000034
K =0.56 was found for the collision recovery coefficient of the oscillator and the bushing, both made of steel.
According to the impulse moment theorem, there are
Figure BDA0001714804090000035
Wherein I is the impulse of the sleeve acting on the oscillator, J O Is the moment of inertia of the oscillator system to the O-axis.
Is obtained by the resolution of the formulas (3) and (4)
Figure BDA0001714804090000036
By
Figure BDA0001714804090000037
Or->
Figure BDA0001714804090000038
And (2) solving by adopting a trial algorithm to obtain the time t for initially impacting the casing for the first time 1 The angular displacement and the angular velocity are respectively equal when the casing pipe is impacted for the first time
Figure BDA0001714804090000039
The angular velocity of the first collision after the formula (5) and the formula (6) are solved
Figure BDA00017148040900000310
And a collision impulse I, marked>
Figure BDA00017148040900000311
I 1 . After the oscillator is subjected to the collision, will be based on->
Figure BDA00017148040900000312
As an initial condition, the equation of motion is
Figure BDA00017148040900000313
By
Figure BDA00017148040900000314
Or->
Figure BDA00017148040900000315
Solving with the formula (7) to obtain the time t for the second impact on the casing 2 The angular displacement and the angular velocity are respectively equal to
Figure BDA00017148040900000316
Figure BDA0001714804090000041
The angular velocity of the second collision is obtained by solving the equations (5) and (8)
Figure BDA00017148040900000415
And a collision impulse I, recorded as>
Figure BDA0001714804090000042
I 2 . After the oscillator is subjected to the second impact, will be based on->
Figure BDA0001714804090000043
For the initial condition, the equation of motion is
Figure BDA0001714804090000044
And so on. T after obtaining the i-1 st collision i-1 ,
Figure BDA0001714804090000045
I i-1 Then, in order
Figure BDA0001714804090000046
For the initial condition, the equation of motion is
Figure BDA0001714804090000047
By
Figure BDA0001714804090000048
Or->
Figure BDA0001714804090000049
Solving with the formula (10) to obtain the time t of the ith impacting casing i The angular displacement and the angular velocity of the ith impact on the sleeve are respectively
Figure BDA00017148040900000410
The ith collision clearance angle velocity is obtained by solving the equations (5) and (11)
Figure BDA00017148040900000411
And a collision impulse I, recorded as>
Figure BDA00017148040900000412
I i . After the oscillator is collided, the signal will be asserted>
Figure BDA00017148040900000413
For the initial condition, the equation of motion is
Figure BDA00017148040900000414
From this, the motion behaviour of the oscillator in the casing and the action conditions on the casing are determined.
Drawings
FIG. 1 is a schematic view of the contact collision of a vibrator with a casing.
Detailed Description
The present invention will be described in detail with reference to the following embodiments.
The movement of the oscillator in the casing is limited by the casing and will collide with the casing when the lateral displacement reaches the difference between the outer radius of the oscillator and the inner radius of the casing (called apparent radius for short). Belonging to the problem of boundary nonlinear vibration. Let the inner diameter of the sleeve be D 1 Fig. 1 shows the case where the oscillator collides with the sleeve.
Figure BDA0001714804090000051
Before the start-up of the oscillator,
Figure BDA0001714804090000052
i.e. is>
Figure BDA0001714804090000053
Figure BDA0001714804090000054
Where ξ is the damping ratio of the oscillator system, p is the natural frequency of the oscillator system,
Figure BDA0001714804090000055
is the natural frequency of the oscillator, omega is the angular speed of rotation of the oscillator rotor, alpha 0 Is the initial phase of the steady state response of the oscillator system, and phi is the amplitude of the steady state response of the oscillator system.
Let k be the coefficient of restitution of the oscillator when colliding with the casing. Considering that the transverse velocity of the impact point on the sleeve before and after the collision is much smaller than that of the impact point of the oscillator, the theory of collision is approximately
Figure BDA0001714804090000056
In the formula, v 1 、u 1 The velocities of the oscillator and the casing contact point before and after the impact, respectively. Then
Figure BDA0001714804090000057
In the formula (I), the compound is shown in the specification,
Figure BDA0001714804090000058
oscillator before and after collision at x 1 z 1 Angular velocity in-plane. Substituted formula (2) is
Figure BDA0001714804090000059
Steel pair capable of taking steel for collision recovery coefficient of oscillator and sleeve 4 K =0.56.
According to the impulse moment theorem, there are
Figure BDA00017148040900000510
Wherein I is the impulse of the sleeve acting on the oscillator, J O Is the moment of inertia of the oscillator system to the O-axis.
Is obtained by the resolution of the formulas (3) and (4)
Figure BDA0001714804090000061
By
Figure BDA0001714804090000062
Or->
Figure BDA0001714804090000063
Solving the formula (1) to obtain the time t for initially impacting the casing for the first time 1 . It is clear that this is a transcendental equation, solved using a trial and error algorithm. Displacement and speed on first impact with a sleeve are ^ respectively>
Figure BDA0001714804090000064
The angular velocity of the first collision after the formula (5) and the formula (6) are solved
Figure BDA0001714804090000065
And a collision impulse I, recorded as>
Figure BDA0001714804090000066
I 1 . After the oscillator is collided, the signal will be asserted>
Figure BDA0001714804090000067
For the initial condition, the equation of motion is
Figure BDA0001714804090000068
By
Figure BDA0001714804090000069
Or->
Figure BDA00017148040900000610
Solving with the trial algorithm of formula (7)From the moment t when the second casing impact is passed 2 The angular displacement and the angular velocity are respectively equal to
Figure BDA00017148040900000611
The angular velocity after the second collision is obtained by solving the equations (5) and (8)
Figure BDA00017148040900000612
And a collision impulse I, recorded as>
Figure BDA00017148040900000613
I 2 . After a second impact on the oscillator, will +>
Figure BDA00017148040900000614
As an initial condition, the equation of motion is
Figure BDA00017148040900000615
And so on. T after obtaining the i-1 st collision i-1 ,
Figure BDA00017148040900000616
I i-1 Then, in order
Figure BDA00017148040900000617
As an initial condition, the equation of motion is
Figure BDA0001714804090000071
By
Figure BDA0001714804090000072
Or->
Figure BDA0001714804090000073
Trial calculation with equation (10)The time t of the ith impacting casing is obtained initially by the method i The angular displacement and the angular velocity at the ith impact on the casing are respectively
Figure BDA0001714804090000074
The ith collision clearance angle velocity is obtained by solving the equations (5) and (11)
Figure BDA0001714804090000075
And a collision impulse I, marked>
Figure BDA0001714804090000076
I i . After the oscillator is collided, the signal will be asserted>
Figure BDA0001714804090000077
For the initial condition, the equation of motion is->
Figure BDA0001714804090000078
......
From this, the motion behaviour of the oscillator in the casing and the action conditions on the casing are determined. The method and the steps for solving the problem of the vibration of the oscillator under the limitation of the boundary are as follows:
(1) Starting from the start of the oscillator, the equation of motion is given by equation (1) when
Figure BDA0001714804090000079
Or>
Figure BDA00017148040900000710
The time (the positive and negative of which depends on the calculation result of the equation (1) at that time), and the first time of collision with the casing t is calculated by the equation (1) 1 The clearance speed after the first collision with the sleeve is obtained by solving the formula (6) and the formula (5)>
Figure BDA00017148040900000711
And a collision impulse I, marked>
Figure BDA00017148040900000712
I 1 Angular displacement of ^ 5 upon collision>
Figure BDA00017148040900000713
Or->
Figure BDA00017148040900000714
(2) To be provided with
Figure BDA00017148040900000715
For the initial condition, the equation of motion after the first collision of the oscillator with the casing is equation (7). When/is>
Figure BDA00017148040900000716
Or>
Figure BDA00017148040900000717
Time (the positive and negative of which depends on the calculation result of the equation (7)) and the second time of collision with the casing t calculated by the equation (7) 2 The rear angle speed after the second collision with the sleeve is obtained by solving the formula (8) and the formula (5)>
Figure BDA00017148040900000718
And a collision impulse I, recorded as>
Figure BDA00017148040900000719
I 2 Angular displacement in case of collision>
Figure BDA00017148040900000720
Or>
Figure BDA00017148040900000721
(3) And so on. T after obtaining the i-1 st collision i-1 ,
Figure BDA00017148040900000722
I i-1 Then, in order
Figure BDA0001714804090000081
For the initial condition, the equation of motion after the i-1 st collision of the oscillator with the housing is given by (10)>
Figure BDA0001714804090000082
Or->
Figure BDA0001714804090000083
(the positive and negative are determined by the calculation result of the equation (10) at this time) and the equation (10) are solved to obtain the time t elapsed by the ith impacting casing i . Upon impact an angular displacement of->
Figure BDA0001714804090000084
Or>
Figure BDA0001714804090000085
The clearance speed after the ith collision with the sleeve is obtained by solving the formula (11) and the formula (5)>
Figure BDA0001714804090000086
And a collision impulse I, recorded as>
Figure BDA0001714804090000087
I i 。
Finally obtaining the action time and the collision impulse t of a series of oscillators on the sleeve i 、I i (ii) a The effect of the oscillator on the casing, such as impact strength and frequency (by t), is evaluated accordingly i Determining the interval time between each two adjacent collisions, and then averagely counting the collision period and frequency).
According to the dynamic and vibration mechanics theory, the invention carries out simulation analysis aiming at the motion of the oscillator in the casing of the vertical well and the action behavior of the oscillator on the casing, determines an evaluation scheme for analyzing the cement consolidation effect of the oscillator on the casing, establishes a motion differential equation of the oscillator in the casing of the vertical well under the excitation of an eccentric rotor, which reflects the main motion characteristics, determines the motion rule of the oscillator, then determines the nonlinear boundary problem generated by the motion limitation of the casing on the oscillator by trial calculation, and evaluates the action rule of the oscillator on the casing by combining with the collision theory, and finally analyzes the casing vibration behavior caused by the oscillator and evaluates the cement consolidation effect of the oscillator on the casing. And a theoretical basis is laid for exploring and evaluating the consolidation effect of the oscillator on the casing cement.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention in any way, and any simple modifications, equivalent variations and modifications made to the above embodiment according to the technical essence of the present invention are within the scope of the technical solution of the present invention.

Claims (1)

1. The method for analyzing and evaluating the motion of the oscillator in the casing slurry and the action of the oscillator on the casing is characterized by comprising the following steps of:
(1) Starting from the start of the oscillator, the equation of motion is as shown in equation (1) when
Figure FDA0001714804080000011
Or->
Figure FDA0001714804080000012
Then, the first time collision time t with the casing is calculated by the formula (1) 1 The clearance speed after the first collision with the sleeve is obtained by solving the formula (6) and the formula (5)>
Figure FDA0001714804080000013
And impact of collision I, recorded as
Figure FDA0001714804080000014
I 1 Angular displacement of ^ 5 upon collision>
Figure FDA0001714804080000015
Or>
Figure FDA0001714804080000016
(2) To be provided with
Figure FDA0001714804080000017
For the initial condition, the equation of motion after the first impact of the oscillator with the casing is equation (7) when
Figure FDA0001714804080000018
Or->
Figure FDA0001714804080000019
Calculating the second collision time t with the casing according to the equation (7) 2 The rear angle speed after the second collision with the sleeve is obtained by solving the formula (8) and the formula (5)>
Figure FDA00017148040800000110
And a collision impulse I, recorded as>
Figure FDA00017148040800000111
I 2 Angular displacement of ^ 5 upon collision>
Figure FDA00017148040800000112
Or->
Figure FDA00017148040800000113
(3) By analogy, t after the i-1 st collision is obtained i-1 ,
Figure FDA00017148040800000114
I i-1 Then, in
Figure FDA00017148040800000115
For the initial condition, the equation of motion after the i-1 st collision of the oscillator with the housing is given by (10)>
Figure FDA00017148040800000116
Or->
Figure FDA00017148040800000117
Solving with the formula (10) to obtain the time t of the ith impacting casing i Angular displacement of ^ 5 upon collision>
Figure FDA00017148040800000118
Or->
Figure FDA00017148040800000119
The clearance speed after the ith collision with the sleeve is obtained by solving the formula (11) and the formula (5)>
Figure FDA00017148040800000120
And impact of collision I, recorded as
Figure FDA00017148040800000121
I i ；
Finally obtaining the action time and the collision impulse t of a series of oscillators to the sleeve i 、I i (ii) a Evaluating the action condition of the oscillator on the sleeve according to the above;
wherein the movement of the oscillator in the sleeve is limited by the sleeve, when the transverse displacement reaches the difference between the outer radius of the oscillator and the inner radius of the sleeve, the oscillator collides with the sleeve, and the inner diameter of the sleeve is set as D 1 When the oscillator collides with the sleeve, the oscillator reaches the maximum angular displacement of
Figure FDA00017148040800000122
In the formula (I), the compound is shown in the specification,
Figure FDA00017148040800000123
is the angle between the axis of the oscillator and the z-axis, D 1 Is the inner diameter of the sleeve, l is the length of the oscillator, D is the outer diameter of the outer cylinder of the oscillator, l 1 The distance between the top of the oscillator and the suspension point O is defined, and alpha is an included angle between the centroid of the bottom of the oscillator and a connecting line between a contact point of the oscillator and the sleeve and the suspension point O respectively;
before the oscillator starts, the oscillator is at rest and at an angular positionMoving device
Figure FDA00017148040800000124
Angular velocity->
Figure FDA00017148040800000125
I.e. an initial condition of->
Figure FDA0001714804080000021
The motion equation of the oscillator is
Figure FDA0001714804080000022
Where ξ is the damping ratio of the oscillator system, p is the natural frequency of the oscillator system,
Figure FDA0001714804080000023
is the natural frequency of the oscillator, ω is the angular speed of rotation of the oscillator rotor, α 0 Is the initial phase of the steady state response of the oscillator system, phi is the amplitude of the steady state response of the oscillator system;
the coefficient of restitution of the collision between the oscillator and the sleeve is set as k,
Figure FDA0001714804080000024
in the formula, v 1 、u 1 The velocities of the oscillator and the casing contact point before and after the collision, respectively
Figure FDA0001714804080000025
In the formula (I), the compound is shown in the specification,
Figure FDA0001714804080000026
oscillator in x before and after collision respectively 1 z 1 Angular velocity in plane, instead ofFormula (2) is
Figure FDA0001714804080000027
For the collision recovery coefficient k =0.56 of the oscillator with the bushing,
according to the impulse moment theorem, there are
Figure FDA0001714804080000028
Wherein I is the impulse of the sleeve acting on the oscillator, J O The moment of inertia of the oscillator system to the O-axis,
is obtained by the resolution of the formulas (3) and (4)
Figure FDA0001714804080000029
By
Figure FDA00017148040800000210
Or->
Figure FDA00017148040800000211
And (2) solving by adopting a trial algorithm to obtain the time t for initially impacting the casing for the first time 1 The angular displacement and the angular velocity are respectively when the casing pipe is impacted for the first time
Figure FDA00017148040800000212
The angular velocity after the first collision is obtained by solving the equations (5) and (6)
Figure FDA00017148040800000213
And a collision impulse I, recorded as>
Figure FDA00017148040800000214
I 1 After the oscillator is collided, the signal is judged to be greater or less than>
Figure FDA0001714804080000031
For the initial condition, the equation of motion is
Figure FDA0001714804080000032
By
Figure FDA0001714804080000033
Or>
Figure FDA0001714804080000034
Solving with the formula (7) to obtain the time t for the second impact on the casing 2 The angular displacement and the angular velocity are respectively equal to
Figure FDA0001714804080000035
The angular velocity after the second collision is obtained by solving the equations (5) and (8)
Figure FDA0001714804080000036
And a collision impulse I, recorded as>
Figure FDA0001714804080000037
I 2 After the oscillator is subjected to the second collision, will be based on->
Figure FDA0001714804080000038
For the initial condition, the equation of motion is
Figure FDA0001714804080000039
By analogy, t after the i-1 st collision is obtained i-1 ,
Figure FDA00017148040800000310
I i-1 Then, in order
Figure FDA00017148040800000311
For the initial condition, the equation of motion is
Figure FDA00017148040800000312
By
Figure FDA00017148040800000313
Or->
Figure FDA00017148040800000314
Solving with the formula (10) to obtain the time t of the ith impacting casing i The angular displacement and the angular velocity of the ith impact on the sleeve are respectively
Figure FDA00017148040800000315
The i-th collision relief angle velocity is obtained by solving the equations (5) and (11)
Figure FDA00017148040800000316
And a collision impulse I, marked>
Figure FDA00017148040800000317
I i After the oscillator is collided, the signal is judged to be greater or less than>
Figure FDA0001714804080000041
As an initial condition, the equation of motion is
Figure FDA0001714804080000042
From this, the motion behaviour of the oscillator in the casing and the action situation on the casing are determined.
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Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2004054836A (en) * 2002-07-24 2004-02-19 Ebara Corp Wall surface impact simulation method for solid-liquid mixed-phase fluid
CN2638030Y (en) * 2003-06-30 2004-09-01 北京兴捷科技发展有限公司 Dynamic regulating type gyroscopic clinometer used in well detection
CN101558174A (en) * 2005-09-23 2009-10-14 Uit有限责任公司 Method of metal performance improvement and protection against degradation and suppression thereof by ultrasonic impact
CN103383298A (en) * 2013-07-11 2013-11-06 冯辅周 Method for analyzing vibration characteristics of solid slab under ultrasonic excitation
CN104747119A (en) * 2013-12-31 2015-07-01 中国石油化工集团公司 Vibration well cementation device and vibration well cementation method
CN105525892A (en) * 2014-09-28 2016-04-27 中国石油化工集团公司 Casing pipe vibrating device
CN106324097A (en) * 2016-10-12 2017-01-11 华侨大学 Method for determining material collision restitution coefficient based on sound wave sensing

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2004054836A (en) * 2002-07-24 2004-02-19 Ebara Corp Wall surface impact simulation method for solid-liquid mixed-phase fluid
CN2638030Y (en) * 2003-06-30 2004-09-01 北京兴捷科技发展有限公司 Dynamic regulating type gyroscopic clinometer used in well detection
CN101558174A (en) * 2005-09-23 2009-10-14 Uit有限责任公司 Method of metal performance improvement and protection against degradation and suppression thereof by ultrasonic impact
CN103383298A (en) * 2013-07-11 2013-11-06 冯辅周 Method for analyzing vibration characteristics of solid slab under ultrasonic excitation
CN104747119A (en) * 2013-12-31 2015-07-01 中国石油化工集团公司 Vibration well cementation device and vibration well cementation method
CN105525892A (en) * 2014-09-28 2016-04-27 中国石油化工集团公司 Casing pipe vibrating device
CN106324097A (en) * 2016-10-12 2017-01-11 华侨大学 Method for determining material collision restitution coefficient based on sound wave sensing

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
Yiyong Yin 等.Vibration characteristics of casing string under the exciting force of an electric vibrator.Natural Gas Industry B.2017,第4卷(第6期),457-462. *
金国光 等.机械臂接触碰撞动力学分析.《农业机械学报》.2016,第47卷(第11期),369-375. *

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