CN109635448B - Method for calculating critical whirling speed of slewing device - Google Patents

Abstract

A method for calculating the critical whirling speed of rotator features that the centrifugal force (mu) per unit length is used to calculate the dynamic effect of rotator ₁ ω ² y represents that the critical vortex motion speed under the condition of the simple support-simple support boundary is calculated, and the critical vortex motion speed under the condition of the simple support-simple support boundary is obtained by calculating the shape curve of the device, the bending strain energy, the work done by the external force P, the centrifugal force of unit length and the total energy of the system; critical whirling velocity under the boundary condition of clamped-clamped; the boundary conditions of solid branch-solid branch are: the invention can deduce the critical whirling speed formula according to the constraint conditions at two ends of the revolving body structure, and substitute the structure parameters into the critical rotational speed formula of the sleeve whirling, thus the critical whirling speed can be calculated quantitatively, the rotational speed of the sleeve during drilling can be guided according to the calculation result, and the damage of the whirling phenomenon can be avoided.

Description

Method for calculating critical whirling speed of slewing device

Technical Field

The invention relates to the technical field of oil and gas well exploitation, in particular to a method for calculating a critical whirl velocity of a slewing device.

Background

In petroleum drilling, in order to reduce the non-production time and reduce the loss of drilling fluid, a casing drilling method is proposed. Due to the restriction of the borehole, the casing is quite complex to move during drilling, and the phenomenon of whirl of the drill string occurs similarly to conventional drilling. At present, the research on the whirl phenomenon mostly focuses on the research on the whirl mechanism and law of the drill string. Since the sixty-seven decades of the last century, drill string dynamics research and practice have confirmed that the lower drill string has a common whirl phenomenon in the borehole (meaning that the drill string revolves around the axis of the borehole in addition to rotating); the lower drill string is usually in a reverse whirl (counter-rotation direction) state, while the forward whirl (forward rotation direction) is relatively less; reverse whirl of a lower drill string easily induces fatigue damage of a drilling tool, early damage of a drill bit and the like. For the reasons, the research on the whirl mechanism and the law of the lower drill string is very important at home and abroad. With the development of casing drilling technology, the damage caused by the casing whirl phenomenon is increasingly prominent, and how to accurately calculate the critical whirl speed when the casing rotates, so as to guide the rotating speed selection during construction and avoid the whirl phenomenon when the casing is drilled is more important.

At present, the research on the whirl phenomenon mostly focuses on the research on the whirl mechanism and the whirl rule of the drill string, and the method is also mostly limited to indoor test simulation. On one hand, the method is high in cost and time consumption, on the other hand, the method is too strong in pertinence, only suitable for a specific structure and a specific boundary, and the universality is lacked.

Disclosure of Invention

In order to overcome the defects of the prior art, the invention aims to provide a method for calculating the critical whirling speed of a slewing device. The rotating speed of the casing during drilling can be guided according to the calculation result, and the damage of the vortex phenomenon is avoided.

In order to achieve the purpose, the invention adopts the technical scheme that:

a method for calculating the critical whirling speed of a slewing device comprises the following steps;

based on the d 'Alembert's principle, the dynamic effect of the rotating device is realized by the centrifugal force mu with a unit length ₁ ω ² y represents; the method comprises the following steps of calculating the critical whirling speed under the condition of a simple support-simple support boundary and calculating the critical whirling speed under the condition of a fixed support-fixed support boundary, wherein:

the calculation steps of the critical whirling speed under the condition of the simple support-simple support boundary are as follows:

(1) For simple-simple support, the boundary conditions are as follows:

y = y "= 0 (at x =0 and x = l)

(2) The shape curve of the device is:

wherein L is the distance between the two support points, and the differential is taken from the formula (1) to obtain: .

(3) Bending strain energy U _b Comprises the following steps:

(4) Work W done by external force P ₁ Comprises the following steps:

(5) The centrifugal force per unit length is:

dT＝μ ₁ dxω ² y (6)

work W done by centrifugal force ₂ Comprises the following steps:

(6) The total energy of the system is as follows:

(7) When the total potential energy is minimum at the critical vortex speed, the first order differential of the total energy of the system should be 0, that is:

further obtaining:

after finishing to obtain

Wherein the content of the first and second substances,

is euler buckling load at the simple-simple boundary,

then

Namely the critical whirling speed under the condition of a simple support-simple support boundary;

the calculation steps of the critical whirling speed under the boundary condition of the fixed branch and the fixed branch are as follows:

(1) The boundary conditions of solid branch-solid branch are:

y = y' =0 (at x =0 and x = l)

(2) The shape curve of the device is:

(3) Bending strain energy U _b Comprises the following steps:

(4) Work W done by external force P ₁ Comprises the following steps:

(5) Work W done by centrifugal force ₂ Comprises the following steps:

and (3) obtaining the following conditions after sorting according to the analogy simple support-simple support boundary conditions:

wherein the content of the first and second substances,

is euler bending load of clamped-clamped

I.e. the critical whirling speed in the case of a solidus-solidus boundary.

The invention has the beneficial effects that:

the invention can make up the defects of the experimental method adopted by the conventional whirling law research institute, and has the characteristics of time saving, cost saving and strong applicability. According to the constraint conditions at two ends of the revolving body structure, the actual structure parameters are substituted into the critical rotational speed formula of the sleeve whirl, so that the critical whirl speed of the sleeve during rotation can be accurately calculated, the rotational speed of the sleeve during drilling is further guided, and the damage of the whirl phenomenon is avoided.

Drawings

Fig. 1 is a schematic view of a rotating device rotating at an angular velocity ω under a pressure P.

Detailed Description

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

A method for calculating the critical whirling speed of a slewing device comprises the following steps;

based on the d 'Alembert's principle, the dynamics problem can be converted into dynamics problem by using the centrifugal force mu with unit length for the dynamics effect of the rotating device ₁ ω ² y, from which the schematic shown in fig. 1 can be built to describe this problem.

Critical whirl velocity under simple-simple boundary condition

(1) For simple-simple support, the boundary conditions are as follows:

y = y "= 0 (at x =0 and x = l)

(2) The shape curve of the device is:

wherein L is the distance between the two support points, and the differential is taken from the formula (1) to obtain:

(3) Bending strain energy U _b Comprises the following steps:

(4) Work W done by external force P ₁ Comprises the following steps:

(5) The centrifugal force per unit length is:

dT＝μ ₁ dxω ² y (6)

work W done by centrifugal force ₂ Comprises the following steps:

(6) The total energy of the system is as follows:

(7) When the total potential energy is minimum at the critical vortex speed, the first order differential of the total energy of the system should be 0, that is:

further obtaining:

after finishing to obtain

Wherein the content of the first and second substances,

euler buckling load at the simple-simple boundary,

then the

Namely the critical whirling speed under the condition of a simple support-simple support boundary;

critical vortex velocity at clamped-clamped boundary condition

(1) The boundary conditions of solid branch-solid branch are:

y = y' =0 (at x =0 and x = l)

(2) The shape curve of the device is:

(3) Bending strain energy U _b Comprises the following steps:

(4) Work W done by external force P ₁ Comprises the following steps:

(5) Work W done by centrifugal force ₂ Comprises the following steps:

analogy simple-simple boundary conditions, after sorting, we obtain:

wherein the content of the first and second substances,

is euler bending load of clamped-clamped

I.e. the critical whirling speed in the case of a solidus-solidus boundary.

According to the constraint conditions at two ends of the revolving body structure, the structural parameters are substituted into a casing whirl critical rotating speed formula, so that the critical whirl speed can be quantitatively calculated, the rotating speed of the casing during drilling can be guided according to the calculation result, and the harm of the whirl phenomenon is avoided.

Claims (1)

1. A method for calculating the critical whirling speed of a rotating device is characterized in that,

based on the d 'Alembert's principle, the dynamic effect of the rotating device is realized by the centrifugal force mu with a unit length ₁ ω ² y represents; the method comprises the following steps of calculating the critical whirling speed under the condition of a simple support-simple support boundary and calculating the critical whirling speed under the condition of a fixed support-fixed support boundary, wherein:

the calculation steps of the critical whirling speed under the condition of the simple support-simple support boundary are as follows:

(1) For simple-simple support, the boundary conditions are as follows:

y = y "= 0 (at x =0 and x = l)

(2) The shape curve of the device is:

wherein L is the distance between the two support points, and the differential is taken from the formula (1) to obtain: .

(3) Bending strain energy U _b Comprises the following steps:

(4) Work W done by external force P ₁ Comprises the following steps:

(5) The centrifugal force per unit length is:

dT＝μ ₁ dxω ² y (6)

work W done by centrifugal force ₂ Comprises the following steps:

(6) The total energy of the system is as follows:

(7) When the total potential energy is minimum at the critical vortex speed, the first order differential of the total energy of the system should be 0, that is:

further obtaining:

after finishing to obtain

Wherein, the first and the second end of the pipe are connected with each other,

is euler buckling load at the simple-simple boundary,

then the

I.e. the critical whirl velocity in the case of a simple-simple boundary.

The calculation steps of the critical whirling speed under the condition of the clamped-clamped boundary are as follows:

(1) The boundary conditions of solid branch-solid branch are:

y = y' =0 (at x =0 and x = l)

(2) The shape curve of the device is:

(3) Bending strain energy U _b Comprises the following steps:

(4) Work W done by external force P ₁ Comprises the following steps:

(5) Work W done by centrifugal force ₂ Comprises the following steps:

analogy simple-simple boundary conditions, after sorting, we obtain:

wherein the content of the first and second substances,

is euler buckling load of clamped-clamped

I.e. the critical whirling speed in the case of a solidus-solidus boundary.

Images