# Modeling and Dynamic Performance Analysis of Hydraulic Top Drive Main Transmission System with Long Hydraulic Pipelines

Authors: Yuanling Shi; Pingsong Zhang
Journal: Geofluids
 (2022)

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## Abstract

Hydraulic top drive is the main power component used to drive drilling tools rotating to drill a hole for drilling rigs. Its main transmission system was built with hydraulic power source and hydraulic actuators. During the drilling procession, the hydraulic top drive is mounted on a derrick, and moving along its vertical guide rails. The hydraulic power station is usually placed on the drilling platform or the ground. In that way, long pipelines are needed to connect the hydraulic pumps and hydraulic motors. Thus, the effects on the performance of hydraulic top drive should not be neglected. A mathematical model of hydraulic top drive main transmission with differential equation of hydraulic units and state space equation of hydraulic long pipelines was deduced in this research. A simulation model was built using the AMESim software. And field drilling test of the hydraulic top drive was carried out in Songliao Basin Drilling Project (SK-II) well site. To verify and modify the virtual model, a comparison analysis was performed by setting the parameters and load of the three methods at the same values. The result of comparison shows that the simulation results are very close to the theoretical results and field drilling test data. Thus, the dynamic characteristics could be analyzed by this simulation model. Dynamic characteristics of the hydraulic top drive with different length and various diameters of pipelines were studied. The simulation results demonstrate that pipeline lengths and pipeline diameters affect the system in different laws, and it needs to comprehensively consider the system response speed, overshoot, and steady-state characteristics when choosing the size of pipelines for hydraulic top drive.


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## Body

## 1. Introduction

Top drive is the main power component used to drive drilling tools rotating on the drilling rigs [1, 2]. Compared with the oil and gas drilling rigs, most of the rigs for geological exploration have not been equipped with top drive, the automation of which needs to be improved urgently. The top drive system drives drilling tools rotating and penetrating rocks, while it travels along its vertical guide rails up and down. According to the power supply, the widely used top drive at present mainly includes electric top drive and hydraulic top drive. In hydraulic top drive, hydraulic power components and hydraulic actuators are used to construct the main transmission system. Electro-hydraulic control technology is usually applied to regulate the output parameters of hydraulic top drive, such as the speed and the torque [3]. Currently, electro-hydraulic system is more and more widely used in industry machine and automation process, whose advantages are glaringly obvious for the occasions requiring fast response speed, high positioning accuracy, and large load. It is mainly because of the convenient speed regulating, great ratio of power to volume, and smooth operation that the electro-hydraulic system can provide, comparing with the DC or AC motors [4–6].To insure power supply of the hydraulic top drive system, an independent hydraulic power station is often equipped, which can be placed on the drilling floor or on the ground. Considering that the hydraulic top drive moves up and down along its guide rail installed on the derrick, no matter where the hydraulic power station is put, long hydraulic pipelines are needed to connect the hydraulic pumps and hydraulic motors, shown as Figure1. And the length of hydraulic pipelines can reach to tens of meters, which will lead to the pressure and flow rate inconsistent between hydraulic pumps and hydraulic motors. In other words, the long hydraulic pipelines have a significant impact on the output performance of top drive. Especially when hydraulic top drive is stopped suddenly or sticking accidents happen during drilling, the load acted on the top drive will change rapidly, which will result in huge pressure shock on hydraulic components, and even result in noise, vibration, and fatigue failure of hydraulic pipelines. Thus, when analyzing the performance of the hydraulic top drive, long hydraulic pipelines should not be neglected.Figure 1
Pipelines form when top drive working. (a) The lowest operation position of hydraulic top drive. (b) The middle operation position of hydraulic top drive. (c) The highest operation position of hydraulic top drive.Analysis of performance and dynamic characteristic of hydraulic system have been investigated by numerous researchers in various fields [7–10], such as the air-craft, construction machinery, and mining mechanics. However, in most of the research, hydraulic pipelines are neglected in modelling and analysis. Since the 1950s, pipeline dynamics have been studied widely [11]. A host of in-depth researches has been done in developing the transient models globally, and both frequency domain model [12] and time domain model [13] have been gained. For investigating the dynamic behaviors of fluid networks [14–17], different modelling approaches, impedance method, transmission line method, and bond graph method for instance, have been found its way. And frequency method, characteristic line method, distributed parameter method, lumped parameter method, etc., are often used in pipeline analysis. N. Nedi’c et al. [18] present a mathematical model with lumped parameters to study a pump-controlled motor system, where the long transmission line is divided into several segments. In literature [19], new bond graphs are put forward by using rational transfer functions and separation of variables techniques, and simulation results with different pipelines are analyzed. In literature [20], bond graph representations for hydraulic pipelines were constructed based on the one-dimensional bond graph structures and modal approximation techniques, and a comparison was made for lossless, 1-D linear fluid friction, and 2-D fluid friction models. In literature [11], a wave energy converter with long pipelines was studied, and transient pressure pulsations and pipelines influence were investigated by using a dynamic model with pipeline modal approximation models [21, 22]. To investigate the dynamic output performance of hydraulic top drive, hydraulic components, such as hydraulic pumps and hydraulic motors, were modeled by means of differential equations. For combining the model of hydraulic components and hydraulic pipelines, the modal approximation model of hydraulic pipelines presented by means of state equation was adopted in this paper.Due to the advantages, such as convenient modeling, high calculation accuracy, low hardware requirement, and low time consumption, computer simulation analysis is highly applied in various disciplines [23–25]. For a top drive, with high cost of manufacturing, it is a long period from design to application, and field test is not easy to be carried out. It is an economical and efficient technical means for this kind of equipment to build a simulation model, analyzing its performance before manufacturing, predicting faults, and optimizing parameters in the process of application. Based on simulation methods, it will help to improve the design efficiency of top drive, and scan for potential problems comprehensively and accurately without relying on a product. Meanwhile, simulation models can also be used for hydraulic top drive system optimization and drilling parameter selection, during the hydraulic top drive drills as well. Thus, a simulation model will be built in this research in the AMESim software.This paper is organized as follows: in the second section, the configuration of hydraulic top drive main drive system was introduced, then a mathematical model of which was built with differential equation for hydraulic components and modal approximation model for hydraulic pipelines. In the third section, a simulation model was built using AMESim, and drilling experiment in Songliao Basin Drilling Project (SK-II well site) is described. In the last part of this paper, comparative analysis of mathematical results, simulation results, and drilling experiments results is performed, and then dynamic characteristics of hydraulic top drive is investigated with various pipelines considered.


## 2. Configuration and Mathematical Modelling of the System

### 2.1. System Configuration

As the hydraulic top drive is mainly used to drive drilling tools rotating, its main transmission system can be regarded as the most important unit, including the main gearbox, hydraulic system, and control system, as shown in Figure2. For the main gearbox, multi-stage structure is adopted to realize the function of high speed and large torque. During drilling process, the top drive main shaft, mounted in the center of the gearbox, is connected directly with the drill pipe through tread. A large center gear is used to fix the top drive main shaft, outside of which four pinions are engaged. At the top side of each pinion, a small planetary gearbox, a disc brake, and a hydraulic motor are connected sequentially. The disc brakes are used for braking, and planetary gearboxes are used for slowdown and increase torsion. The hydraulic motors provide power to the top drive for rotating.Figure 2
Configuration of top drive main hydraulic system. 1 Prime mover. 2 Variable displacement hydraulic pump. 3 Supplementary circuit. 4 Overload protective circuit. 5 Flush circuit. 6 Long hydraulic pipelines. 7 Variable displacement hydraulic motor. 8 Planetary gearbox. 9 Top drive gear box. 10 Top drive main shaft.For the hydraulic system, two hydraulic variable displacement pumps are selected as the power units, and four variable hydraulic displacement motors are chosen as the actuator units. The hydraulic motors are mounted on the body of top drive, and the hydraulic pumps are placed on the ground in the hydraulic power station. Several sections of hydraulic pipelines are used to connect the motors and pumps. What’s more, to ensure the system operation, supplementary circuit, overload protective circuit, flush circuit, and other necessary units are equipped.Electro-hydraulic proportional control technology is adopted to regulate the speed and torque. The displacements of hydraulic pumps and motors are varied with the pilot hydraulic proportional control mode, with a pressure limiting variable pump offering hydraulic control signals. An electromagnetic proportional pressure relief valve is connected with the variable pump and the variable motor displacement control mechanism. When current signals are input, electromagnetic proportional pressure relief valve converts it into hydraulic signals; thus, the displacement of variable pumps and the displacement of variable motors are adjusted.


### 2.2. Mathematical Model of Hydraulic Top Drive Main Transmission

A closed loop volumetric speed regulation system is adopted to control and drive the main gearbox of the hydraulic top drive, which includes two hydraulic variable pumps and four hydraulic variable motors. When the mathematical model is developed, the following hypotheses are made.(1)
In order to simplify the model, the two hydraulic pumps are combined into one, and the four hydraulic motors are equivalent to one(2)
The moment of inertia of top drive main shaft is regarded as a constant value(3)
The leakage of hydraulic pump and hydraulic motor remains unchanged, and the leakage mode is laminar flow leakage(4)
The input speed of hydraulic pumps remains unchanged(5)
The pressure on the low pressure side of the system remains constant, thus ignoring the dynamic fluctuation of the pressure at this side(6)
Only the high side pressure is determined by loads


#### 2.2.1. Hydraulic Pump Model

Two axial piston variable pumps are adopted in the hydraulic top drive, and the input speed remains constant. The flow rate outflowing from the hydraulic pumps is equal to that incoming the hydraulic pipelines. Flow equation of the hydraulic pump is as follows:(1)Q1=Dpωp−CipP1−Pc−CepP1−VpβeṖ1,where Q1 is the flow rate of the pump, Dp is the displacement of the pump, m3/rad; ωp is the angular velocity of the pump, rad/s; P1 is the outlet pressure of the hydraulic pump, Pa; Pc is the supplementary pressure, Pa; Cip is the internal leakage coefficient of the pump, m3/s/Pa; and Cep is the external leakage coefficient of the pump, m3/s/Pa.


#### 2.2.2. Hydraulic Motor Model

Four axial piston variable motors are applied in the hydraulic top drive. And the flow rate flowing into the hydraulic motors is equal to that flowing out of the hydraulic pipelines. The flow equation of the variable displacement hydraulic motor is as follows:(2)Q2−CimP2−Pc−CemP2=Dmωm+VmβeṖ2,where Q2 is the flow rate flowing into hydraulic motor;P2 is the inlet pressure of hydraulic motor,Pa; Cim is the internal leakage coefficient of the motor, m3/s/Pa; Cem is the external leakage coefficient of the motor, m3/s/Pa; Dm is the motor displacement, m3/rad; ωm is the angular velocity of the motor, rad/s; Vm is the average volume of the hydraulic motor, m3; and βe is the effective bulk modulus of the system, N/m2/Pa.The torque on the hydraulic motor is balanced, and the balance equation is(3)Tg=DmP2−Pc=Jω̇m+Bmωm+TL,where Tg is the theory torque on the motor, N∙m; J is the total inertia of the motor, kg∙m2; Bm is the vicious damping coefficient, N∙m/rad/s; and TL is the load torque, N∙m.


#### 2.2.3. Mathematic Model of Long Hydraulic Pipelines

Regarding the fluid transmission line as a distributed parameter system, an accurate model of it is established [26, 27]. There are four possible sets of boundary conditions for the one-dimensional distributed parameter model of the fluid transmission line, and each boundary condition corresponds to an input-output configuration. The above four possible boundary condition configurations are Pup,Pdown, Qup,Qdown, Pup,Qdown, or Pdown,Qup as inputs, respectively. Generally, when both ends of the pipelines are connected to valves, the flow rate inputs model Qdown,Qup will be applied, while when both ends of the pipelines are connected to volumes, the pressure inputs model Pup,Pdown is usually adopted. Considering that for the hydraulic top drive, long pipelines are connected to hydraulic pumps and hydraulic motors, which all can be regarded as volumes, the pressure inputs model is applied in this paper. The hydraulic pipelines model is expressed as follows:
(4)Q1Q2=coshГsZcssinhГs−1ZcssinhГs1ZcssinhГs−coshГsZcssinhГsP1P2,where P1 and P2 are the upstream pressure and downstream pressure of the pipelines, respectively; and Q1 and Q2 are the upstream flow rate and downstream flow rate, respectively.The fluid performance in transmission line is dominated by the characteristic impedanceZc and the propagation operator Гs. Because there are several basic model for pipelines, such as the lossless model, the linear friction model, and the dissipative model, the expressions for the line characteristic impedance and the propagation operator is different when different basic model is selected. For the linear friction model, these two parameters are defined as follows:
(5)Гs¯=Dns¯1+8/s¯1/2,Zcs¯=Z01+8/s¯1/2,where s¯ is the normalized Laplace operator, which is given as s¯=s/ωc; ωc is the viscosity frequency, which is given as ωc=v0/r2; rh is the inner radius of the pipe;Dn is the dissipation number; and Z0 is the line impedance constant. The last two parameters are defined as follows:
(6)Dn=lv0cr2,Z0=ρcAp,where l is the length of the pipelines; ν0 is the kinematic viscosity of the working fluid; c is the acoustic velocity, which is defined as c=βe/ρ; βe is the effective bulk modulus of working fluid; ρ is the density of the oil; and Ap is the cross-sectional area of the pipe.Considering that the hydraulic system of the top drive is a nonlinear system, it cannot be easy to calculate and analyze in frequency domain. To integrate the hydraulic pump model, hydraulic motors model, and hydraulic pipeline model, an approximate model of hydraulic pipelines proposed in the literature [11, 20, 22] is adopted in this paper. The approximate model can be regarded as a finite dimensional state space model:
(7)1ωcẊ=AX+Bu,Y=CX,where
(8)X=Q10Q20Q11Q21⋯Q1nQ2nT,u=P1P2T,Y=Q1Q2T,A=diagA0,A1,⋯,An,B=B0,B1,⋯,BnT,C=I0,I1,⋯,In,with
(9)A0=−800−8,B0=1Z0Dn1−11−1,I0=1001,Ai=0−λsi21−8,Bi=2Z0Dn001−−1i,Ii=010−1i,where i=1,2,3⋯,n; λsi is root indices, which is defined as λsi=πi/Dn. Other parameters are defined as above.Table1 shows the values of the above mathematical model parameters for the top drive hydraulic system.Table 1
Main parameter of the hydraulic top drive mathematical model.
ParametersValueDpmax2.5e-4m3/radωp50πrad/skrv3/65bar/mAa3±0.5 barb11±0.5 barDmmax2.5e-4m3/radCt5.0e-12m3/s/PaVpm02.53e-2m3βe7.0e8N/m2/PaJ20kg∙m2Bm0.3N∙m/rad/sc1000m/sρ0.85e+3kg/m3v05.0e-5m2/s


## 2.1. System Configuration

As the hydraulic top drive is mainly used to drive drilling tools rotating, its main transmission system can be regarded as the most important unit, including the main gearbox, hydraulic system, and control system, as shown in Figure2. For the main gearbox, multi-stage structure is adopted to realize the function of high speed and large torque. During drilling process, the top drive main shaft, mounted in the center of the gearbox, is connected directly with the drill pipe through tread. A large center gear is used to fix the top drive main shaft, outside of which four pinions are engaged. At the top side of each pinion, a small planetary gearbox, a disc brake, and a hydraulic motor are connected sequentially. The disc brakes are used for braking, and planetary gearboxes are used for slowdown and increase torsion. The hydraulic motors provide power to the top drive for rotating.Figure 2
Configuration of top drive main hydraulic system. 1 Prime mover. 2 Variable displacement hydraulic pump. 3 Supplementary circuit. 4 Overload protective circuit. 5 Flush circuit. 6 Long hydraulic pipelines. 7 Variable displacement hydraulic motor. 8 Planetary gearbox. 9 Top drive gear box. 10 Top drive main shaft.For the hydraulic system, two hydraulic variable displacement pumps are selected as the power units, and four variable hydraulic displacement motors are chosen as the actuator units. The hydraulic motors are mounted on the body of top drive, and the hydraulic pumps are placed on the ground in the hydraulic power station. Several sections of hydraulic pipelines are used to connect the motors and pumps. What’s more, to ensure the system operation, supplementary circuit, overload protective circuit, flush circuit, and other necessary units are equipped.Electro-hydraulic proportional control technology is adopted to regulate the speed and torque. The displacements of hydraulic pumps and motors are varied with the pilot hydraulic proportional control mode, with a pressure limiting variable pump offering hydraulic control signals. An electromagnetic proportional pressure relief valve is connected with the variable pump and the variable motor displacement control mechanism. When current signals are input, electromagnetic proportional pressure relief valve converts it into hydraulic signals; thus, the displacement of variable pumps and the displacement of variable motors are adjusted.


## 2.2. Mathematical Model of Hydraulic Top Drive Main Transmission

A closed loop volumetric speed regulation system is adopted to control and drive the main gearbox of the hydraulic top drive, which includes two hydraulic variable pumps and four hydraulic variable motors. When the mathematical model is developed, the following hypotheses are made.(1)
In order to simplify the model, the two hydraulic pumps are combined into one, and the four hydraulic motors are equivalent to one(2)
The moment of inertia of top drive main shaft is regarded as a constant value(3)
The leakage of hydraulic pump and hydraulic motor remains unchanged, and the leakage mode is laminar flow leakage(4)
The input speed of hydraulic pumps remains unchanged(5)
The pressure on the low pressure side of the system remains constant, thus ignoring the dynamic fluctuation of the pressure at this side(6)
Only the high side pressure is determined by loads


### 2.2.1. Hydraulic Pump Model

Two axial piston variable pumps are adopted in the hydraulic top drive, and the input speed remains constant. The flow rate outflowing from the hydraulic pumps is equal to that incoming the hydraulic pipelines. Flow equation of the hydraulic pump is as follows:(1)Q1=Dpωp−CipP1−Pc−CepP1−VpβeṖ1,where Q1 is the flow rate of the pump, Dp is the displacement of the pump, m3/rad; ωp is the angular velocity of the pump, rad/s; P1 is the outlet pressure of the hydraulic pump, Pa; Pc is the supplementary pressure, Pa; Cip is the internal leakage coefficient of the pump, m3/s/Pa; and Cep is the external leakage coefficient of the pump, m3/s/Pa.


### 2.2.2. Hydraulic Motor Model

Four axial piston variable motors are applied in the hydraulic top drive. And the flow rate flowing into the hydraulic motors is equal to that flowing out of the hydraulic pipelines. The flow equation of the variable displacement hydraulic motor is as follows:(2)Q2−CimP2−Pc−CemP2=Dmωm+VmβeṖ2,where Q2 is the flow rate flowing into hydraulic motor;P2 is the inlet pressure of hydraulic motor,Pa; Cim is the internal leakage coefficient of the motor, m3/s/Pa; Cem is the external leakage coefficient of the motor, m3/s/Pa; Dm is the motor displacement, m3/rad; ωm is the angular velocity of the motor, rad/s; Vm is the average volume of the hydraulic motor, m3; and βe is the effective bulk modulus of the system, N/m2/Pa.The torque on the hydraulic motor is balanced, and the balance equation is(3)Tg=DmP2−Pc=Jω̇m+Bmωm+TL,where Tg is the theory torque on the motor, N∙m; J is the total inertia of the motor, kg∙m2; Bm is the vicious damping coefficient, N∙m/rad/s; and TL is the load torque, N∙m.


### 2.2.3. Mathematic Model of Long Hydraulic Pipelines

Regarding the fluid transmission line as a distributed parameter system, an accurate model of it is established [26, 27]. There are four possible sets of boundary conditions for the one-dimensional distributed parameter model of the fluid transmission line, and each boundary condition corresponds to an input-output configuration. The above four possible boundary condition configurations are Pup,Pdown, Qup,Qdown, Pup,Qdown, or Pdown,Qup as inputs, respectively. Generally, when both ends of the pipelines are connected to valves, the flow rate inputs model Qdown,Qup will be applied, while when both ends of the pipelines are connected to volumes, the pressure inputs model Pup,Pdown is usually adopted. Considering that for the hydraulic top drive, long pipelines are connected to hydraulic pumps and hydraulic motors, which all can be regarded as volumes, the pressure inputs model is applied in this paper. The hydraulic pipelines model is expressed as follows:
(4)Q1Q2=coshГsZcssinhГs−1ZcssinhГs1ZcssinhГs−coshГsZcssinhГsP1P2,where P1 and P2 are the upstream pressure and downstream pressure of the pipelines, respectively; and Q1 and Q2 are the upstream flow rate and downstream flow rate, respectively.The fluid performance in transmission line is dominated by the characteristic impedanceZc and the propagation operator Гs. Because there are several basic model for pipelines, such as the lossless model, the linear friction model, and the dissipative model, the expressions for the line characteristic impedance and the propagation operator is different when different basic model is selected. For the linear friction model, these two parameters are defined as follows:
(5)Гs¯=Dns¯1+8/s¯1/2,Zcs¯=Z01+8/s¯1/2,where s¯ is the normalized Laplace operator, which is given as s¯=s/ωc; ωc is the viscosity frequency, which is given as ωc=v0/r2; rh is the inner radius of the pipe;Dn is the dissipation number; and Z0 is the line impedance constant. The last two parameters are defined as follows:
(6)Dn=lv0cr2,Z0=ρcAp,where l is the length of the pipelines; ν0 is the kinematic viscosity of the working fluid; c is the acoustic velocity, which is defined as c=βe/ρ; βe is the effective bulk modulus of working fluid; ρ is the density of the oil; and Ap is the cross-sectional area of the pipe.Considering that the hydraulic system of the top drive is a nonlinear system, it cannot be easy to calculate and analyze in frequency domain. To integrate the hydraulic pump model, hydraulic motors model, and hydraulic pipeline model, an approximate model of hydraulic pipelines proposed in the literature [11, 20, 22] is adopted in this paper. The approximate model can be regarded as a finite dimensional state space model:
(7)1ωcẊ=AX+Bu,Y=CX,where
(8)X=Q10Q20Q11Q21⋯Q1nQ2nT,u=P1P2T,Y=Q1Q2T,A=diagA0,A1,⋯,An,B=B0,B1,⋯,BnT,C=I0,I1,⋯,In,with
(9)A0=−800−8,B0=1Z0Dn1−11−1,I0=1001,Ai=0−λsi21−8,Bi=2Z0Dn001−−1i,Ii=010−1i,where i=1,2,3⋯,n; λsi is root indices, which is defined as λsi=πi/Dn. Other parameters are defined as above.Table1 shows the values of the above mathematical model parameters for the top drive hydraulic system.Table 1
Main parameter of the hydraulic top drive mathematical model.
ParametersValueDpmax2.5e-4m3/radωp50πrad/skrv3/65bar/mAa3±0.5 barb11±0.5 barDmmax2.5e-4m3/radCt5.0e-12m3/s/PaVpm02.53e-2m3βe7.0e8N/m2/PaJ20kg∙m2Bm0.3N∙m/rad/sc1000m/sρ0.85e+3kg/m3v05.0e-5m2/s


## 2.2.1. Hydraulic Pump Model

Two axial piston variable pumps are adopted in the hydraulic top drive, and the input speed remains constant. The flow rate outflowing from the hydraulic pumps is equal to that incoming the hydraulic pipelines. Flow equation of the hydraulic pump is as follows:(1)Q1=Dpωp−CipP1−Pc−CepP1−VpβeṖ1,where Q1 is the flow rate of the pump, Dp is the displacement of the pump, m3/rad; ωp is the angular velocity of the pump, rad/s; P1 is the outlet pressure of the hydraulic pump, Pa; Pc is the supplementary pressure, Pa; Cip is the internal leakage coefficient of the pump, m3/s/Pa; and Cep is the external leakage coefficient of the pump, m3/s/Pa.


## 2.2.2. Hydraulic Motor Model

Four axial piston variable motors are applied in the hydraulic top drive. And the flow rate flowing into the hydraulic motors is equal to that flowing out of the hydraulic pipelines. The flow equation of the variable displacement hydraulic motor is as follows:(2)Q2−CimP2−Pc−CemP2=Dmωm+VmβeṖ2,where Q2 is the flow rate flowing into hydraulic motor;P2 is the inlet pressure of hydraulic motor,Pa; Cim is the internal leakage coefficient of the motor, m3/s/Pa; Cem is the external leakage coefficient of the motor, m3/s/Pa; Dm is the motor displacement, m3/rad; ωm is the angular velocity of the motor, rad/s; Vm is the average volume of the hydraulic motor, m3; and βe is the effective bulk modulus of the system, N/m2/Pa.The torque on the hydraulic motor is balanced, and the balance equation is(3)Tg=DmP2−Pc=Jω̇m+Bmωm+TL,where Tg is the theory torque on the motor, N∙m; J is the total inertia of the motor, kg∙m2; Bm is the vicious damping coefficient, N∙m/rad/s; and TL is the load torque, N∙m.


## 2.2.3. Mathematic Model of Long Hydraulic Pipelines

Regarding the fluid transmission line as a distributed parameter system, an accurate model of it is established [26, 27]. There are four possible sets of boundary conditions for the one-dimensional distributed parameter model of the fluid transmission line, and each boundary condition corresponds to an input-output configuration. The above four possible boundary condition configurations are Pup,Pdown, Qup,Qdown, Pup,Qdown, or Pdown,Qup as inputs, respectively. Generally, when both ends of the pipelines are connected to valves, the flow rate inputs model Qdown,Qup will be applied, while when both ends of the pipelines are connected to volumes, the pressure inputs model Pup,Pdown is usually adopted. Considering that for the hydraulic top drive, long pipelines are connected to hydraulic pumps and hydraulic motors, which all can be regarded as volumes, the pressure inputs model is applied in this paper. The hydraulic pipelines model is expressed as follows:
(4)Q1Q2=coshГsZcssinhГs−1ZcssinhГs1ZcssinhГs−coshГsZcssinhГsP1P2,where P1 and P2 are the upstream pressure and downstream pressure of the pipelines, respectively; and Q1 and Q2 are the upstream flow rate and downstream flow rate, respectively.The fluid performance in transmission line is dominated by the characteristic impedanceZc and the propagation operator Гs. Because there are several basic model for pipelines, such as the lossless model, the linear friction model, and the dissipative model, the expressions for the line characteristic impedance and the propagation operator is different when different basic model is selected. For the linear friction model, these two parameters are defined as follows:
(5)Гs¯=Dns¯1+8/s¯1/2,Zcs¯=Z01+8/s¯1/2,where s¯ is the normalized Laplace operator, which is given as s¯=s/ωc; ωc is the viscosity frequency, which is given as ωc=v0/r2; rh is the inner radius of the pipe;Dn is the dissipation number; and Z0 is the line impedance constant. The last two parameters are defined as follows:
(6)Dn=lv0cr2,Z0=ρcAp,where l is the length of the pipelines; ν0 is the kinematic viscosity of the working fluid; c is the acoustic velocity, which is defined as c=βe/ρ; βe is the effective bulk modulus of working fluid; ρ is the density of the oil; and Ap is the cross-sectional area of the pipe.Considering that the hydraulic system of the top drive is a nonlinear system, it cannot be easy to calculate and analyze in frequency domain. To integrate the hydraulic pump model, hydraulic motors model, and hydraulic pipeline model, an approximate model of hydraulic pipelines proposed in the literature [11, 20, 22] is adopted in this paper. The approximate model can be regarded as a finite dimensional state space model:
(7)1ωcẊ=AX+Bu,Y=CX,where
(8)X=Q10Q20Q11Q21⋯Q1nQ2nT,u=P1P2T,Y=Q1Q2T,A=diagA0,A1,⋯,An,B=B0,B1,⋯,BnT,C=I0,I1,⋯,In,with
(9)A0=−800−8,B0=1Z0Dn1−11−1,I0=1001,Ai=0−λsi21−8,Bi=2Z0Dn001−−1i,Ii=010−1i,where i=1,2,3⋯,n; λsi is root indices, which is defined as λsi=πi/Dn. Other parameters are defined as above.Table1 shows the values of the above mathematical model parameters for the top drive hydraulic system.Table 1
Main parameter of the hydraulic top drive mathematical model.
ParametersValueDpmax2.5e-4m3/radωp50πrad/skrv3/65bar/mAa3±0.5 barb11±0.5 barDmmax2.5e-4m3/radCt5.0e-12m3/s/PaVpm02.53e-2m3βe7.0e8N/m2/PaJ20kg∙m2Bm0.3N∙m/rad/sc1000m/sρ0.85e+3kg/m3v05.0e-5m2/s


## 3. Simulation Model and Field Test

### 3.1. Simulation Model

In Section2, the mathematical model of hydraulic top drive has been established, which contains a series of differential equations. Based on the above model, it is difficult to obtain the analytical solution and analyze the dynamic characteristics of the system under different conditions. To analyze the dynamic characteristics of the hydraulic top drive with long pipelines, a simulation model is built in AMESim platform, shown as Figure 3. The hydraulic system of the top drive includes two parallel hydraulic pumps, which drive four parallel hydraulic motors. For a simulation model, setting the number of hydraulic pumps and motors according to the real configuration of the hydraulic top drive will lead to the simulation model jumbled and complex, not conducive to debugging and calculation. Thus, on the premise of not affecting the simulation results, the two hydraulic pumps and four hydraulic motors are equivalent to one pump and one motor, respectively, in the simulation model, to simplify model and improve calculation speed. The maximum displacement of the hydraulic pump in simulation model is the sum of the maximum displacement of the two hydraulic pumps in the real configuration system, and so is the hydraulic motor. So, the simulation model contains a hydraulic pump and its variable displacement mechanism, a hydraulic motor and its variable displacement mechanism, long hydraulic pipelines, supplementary circuit, overload protective circuit, flush circuit, loading part, top drive gear transmission part, control signals, and other necessary parts.Figure 3
Simulation model of hydraulic top drive with long pipelines.


### 3.2. Field Test

Thanks to the deep continental scientific drilling project, field test of the top drive was carried out in Songliao Basin Drilling Project well site. As one of the key automation devices of the CRUST-I 10000m scientific drilling rig, the hydraulic top drive drove drilling tools to cutting rocks while travelling along a special guide mounted in the derrick of the rig. The hydraulic power station was placed on the ground, shown in Figure4. The hydraulic components, such as prime motor, hydraulic pumps, hydraulic oil tank, control cabinet, and hydraulic valves, are included in the power station. Table 2 lists the type and quantity of hydraulic units of the top drive. Figure 5 shows the hydraulic top drive in drilling experiment. The hydraulic motors and several control valves were installed on the hydraulic top drive.Figure 4
Hydraulic power station of the top drive.Table 2
Hydraulic units information of the top drive.
ElementTypeMakerQuantityHydraulic piston pump90-R250-HFSAUER-DANFOSS2Hydraulic piston motor51 V250-A-F2-N-HSSAUER-DANFOSS4Pressure-limited variable pumpLRR-030-DPCSAUER-DANFOSS1Pressure reducing valveEHPR98-T38-0-N-24ERHYDRA-FORCE2Incremental encoderBEI-HS35F-100BEI-SENSOR1Hydraulic pipelineF38VIEATON80 mFigure 5
Hydraulic top drive in drilling experiment.There are five sections of hydraulic pipelines used to connect the hydraulic pumps and hydraulic motors. The configuration of the five sections hydraulic pipelines is detailed in Table3. Eaton’s Triple Crown GH493-16 hose is selected to connect the hydraulic pumps and hydraulic motors, whose inner diameter is 25.4 mm, outer diameter is 37.6 mm, maximum operating pressure is 350 bar, and operating temperature is in the range of -40°C to 127°C. For the CRUST-I drilling rig, the height of its derrick is 48 m, and the height of its drilling floor is 12 m. The maximum distance that the hydraulic top drive travels is 36.5 m. Thus, the total length of hydraulic pipelines used in the drilling experiment is 80 m.Table 3
Pipeline configuration of the top drive.
Pipeline sectionLength/mmInner diameter/mmPump A and B to circuit block50025.4Circuit block to HYDAC filter50025.4HYDAC filter to drill floor circuit block200025.4Drill floor circuit block to derrick circuit block250025.4Derrick circuit block to top drive motor240025.4The field trail site is located in Anda, Heilongjiang, China. The purpose of the Songliao Basin Drilling Project is to penetrate the Cretaceous continental stratum and get the complete sedimentary records of the whole Cretaceous continental stratum. The design depth of the SK-II well is 6400 m, and finally the well was completed with the depth of 7018 m.Drilling experiments were implemented in two phases. The first phase was performed from the depth of 2800 m to the depth of 3628 m. During this stage, sweeping borehole was carried out by the top drive from the depth of 2800 m to the depth of 3100 m, and then core drilling was conducted from the depth of 3100 m to the depth of 3628 m. Totally, the hydraulic top drive ran for 66 days, and 28 barrels of core were obtained. Besides, the longest core was obtained with the length of 30.49 m between the depth of 3675.59 m and 3706.08 m, and coring rate reached to 100%. Based on the stratum histogram of the SK-II well, the stratum from 2840 m to 3320 m is Yingcheng Formation, and from 3320 m to 5670 m is Shahezi Formation. The upper part of the Yingcheng Formation is mainly green gray coarse sandstone, conglomerate and glutenite, purple and mottled purple tuff with thin layer of conglomerate, thick mottled and gray conglomerate with thin layer of purple mudstone; the lower part is a very thick layer of tuff, thick layers of green and gray tuff mixed with gray andesite basalt. The Shahezi Formation is mainly composed of black mudstone intercalated with black coal line, intercalated with thin layers of gray fine sandstone, dark gray siltstone and argillaceous siltstone; the bottom is interbedded with gray sandy conglomerate, coarse sandstone and gray black mudstone. Figure6 shows cores obtained when the hydraulic top drive drilled the hole. The second stage of drilling experiment was carried out from the depth of 6769.77 m to the depth of 7108.88 m. During this period, the hydraulic top drive drilled the cement plug, with totally 5 trips and a total trip of about 62000 m.Figure 6
Cores obtained by the hydraulic top drive.


## 3.1. Simulation Model

In Section2, the mathematical model of hydraulic top drive has been established, which contains a series of differential equations. Based on the above model, it is difficult to obtain the analytical solution and analyze the dynamic characteristics of the system under different conditions. To analyze the dynamic characteristics of the hydraulic top drive with long pipelines, a simulation model is built in AMESim platform, shown as Figure 3. The hydraulic system of the top drive includes two parallel hydraulic pumps, which drive four parallel hydraulic motors. For a simulation model, setting the number of hydraulic pumps and motors according to the real configuration of the hydraulic top drive will lead to the simulation model jumbled and complex, not conducive to debugging and calculation. Thus, on the premise of not affecting the simulation results, the two hydraulic pumps and four hydraulic motors are equivalent to one pump and one motor, respectively, in the simulation model, to simplify model and improve calculation speed. The maximum displacement of the hydraulic pump in simulation model is the sum of the maximum displacement of the two hydraulic pumps in the real configuration system, and so is the hydraulic motor. So, the simulation model contains a hydraulic pump and its variable displacement mechanism, a hydraulic motor and its variable displacement mechanism, long hydraulic pipelines, supplementary circuit, overload protective circuit, flush circuit, loading part, top drive gear transmission part, control signals, and other necessary parts.Figure 3
Simulation model of hydraulic top drive with long pipelines.


## 3.2. Field Test

Thanks to the deep continental scientific drilling project, field test of the top drive was carried out in Songliao Basin Drilling Project well site. As one of the key automation devices of the CRUST-I 10000m scientific drilling rig, the hydraulic top drive drove drilling tools to cutting rocks while travelling along a special guide mounted in the derrick of the rig. The hydraulic power station was placed on the ground, shown in Figure4. The hydraulic components, such as prime motor, hydraulic pumps, hydraulic oil tank, control cabinet, and hydraulic valves, are included in the power station. Table 2 lists the type and quantity of hydraulic units of the top drive. Figure 5 shows the hydraulic top drive in drilling experiment. The hydraulic motors and several control valves were installed on the hydraulic top drive.Figure 4
Hydraulic power station of the top drive.Table 2
Hydraulic units information of the top drive.
ElementTypeMakerQuantityHydraulic piston pump90-R250-HFSAUER-DANFOSS2Hydraulic piston motor51 V250-A-F2-N-HSSAUER-DANFOSS4Pressure-limited variable pumpLRR-030-DPCSAUER-DANFOSS1Pressure reducing valveEHPR98-T38-0-N-24ERHYDRA-FORCE2Incremental encoderBEI-HS35F-100BEI-SENSOR1Hydraulic pipelineF38VIEATON80 mFigure 5
Hydraulic top drive in drilling experiment.There are five sections of hydraulic pipelines used to connect the hydraulic pumps and hydraulic motors. The configuration of the five sections hydraulic pipelines is detailed in Table3. Eaton’s Triple Crown GH493-16 hose is selected to connect the hydraulic pumps and hydraulic motors, whose inner diameter is 25.4 mm, outer diameter is 37.6 mm, maximum operating pressure is 350 bar, and operating temperature is in the range of -40°C to 127°C. For the CRUST-I drilling rig, the height of its derrick is 48 m, and the height of its drilling floor is 12 m. The maximum distance that the hydraulic top drive travels is 36.5 m. Thus, the total length of hydraulic pipelines used in the drilling experiment is 80 m.Table 3
Pipeline configuration of the top drive.
Pipeline sectionLength/mmInner diameter/mmPump A and B to circuit block50025.4Circuit block to HYDAC filter50025.4HYDAC filter to drill floor circuit block200025.4Drill floor circuit block to derrick circuit block250025.4Derrick circuit block to top drive motor240025.4The field trail site is located in Anda, Heilongjiang, China. The purpose of the Songliao Basin Drilling Project is to penetrate the Cretaceous continental stratum and get the complete sedimentary records of the whole Cretaceous continental stratum. The design depth of the SK-II well is 6400 m, and finally the well was completed with the depth of 7018 m.Drilling experiments were implemented in two phases. The first phase was performed from the depth of 2800 m to the depth of 3628 m. During this stage, sweeping borehole was carried out by the top drive from the depth of 2800 m to the depth of 3100 m, and then core drilling was conducted from the depth of 3100 m to the depth of 3628 m. Totally, the hydraulic top drive ran for 66 days, and 28 barrels of core were obtained. Besides, the longest core was obtained with the length of 30.49 m between the depth of 3675.59 m and 3706.08 m, and coring rate reached to 100%. Based on the stratum histogram of the SK-II well, the stratum from 2840 m to 3320 m is Yingcheng Formation, and from 3320 m to 5670 m is Shahezi Formation. The upper part of the Yingcheng Formation is mainly green gray coarse sandstone, conglomerate and glutenite, purple and mottled purple tuff with thin layer of conglomerate, thick mottled and gray conglomerate with thin layer of purple mudstone; the lower part is a very thick layer of tuff, thick layers of green and gray tuff mixed with gray andesite basalt. The Shahezi Formation is mainly composed of black mudstone intercalated with black coal line, intercalated with thin layers of gray fine sandstone, dark gray siltstone and argillaceous siltstone; the bottom is interbedded with gray sandy conglomerate, coarse sandstone and gray black mudstone. Figure6 shows cores obtained when the hydraulic top drive drilled the hole. The second stage of drilling experiment was carried out from the depth of 6769.77 m to the depth of 7108.88 m. During this period, the hydraulic top drive drilled the cement plug, with totally 5 trips and a total trip of about 62000 m.Figure 6
Cores obtained by the hydraulic top drive.


## 4. Result and Discussion

### 4.1. Comparison of Mathematical Results, Simulation Results, and Experiment Data

During the drilling test, the top drive operated continuously 24 hours a day. All parameters of top drive operation, such as speed, torque, and pressure, were recorded every 2 seconds. Some of the speed and torque obtained in drilling experiment are shown in Figure7. From the curve, it can find that the load applied on top drive shaft fluctuates randomly all time. And the pressure at outlet of hydraulic pumps varied with the load applied on the top drive. The pressure at the inlet of hydraulic pumps was remained at 1.57 MPa, which was the supplementary pressure of the system. As can be seen from Figure 7, the operating speeds of top drive were at 9 rpm, 11 rpm, 20 rpm, and 30 rpm, respectively. Though the output speed fluctuated randomly for the influence of load, the fluctuation was less than 2 rpm. In other words, at each running stage, the speed could be maintained at its setting value.Figure 7
Experiment data when top drive drilling in SK-II at the depths of 3436.92 m to 3447.52 m.To verify and modify the mathematical model and simulation model built in this paper, a comparison analysis between the above three methods was performed. In the comparison, parameters of hydraulic pumps, hydraulic motors, and hydraulic pipelines were set at the same values for the three methods. Based on the measured torque of the field test, the load applied on the mathematical mode and simulation model is determined. From Figure7, it can be found that it was not easy to find out the change rules of load on top drive and describe it with mathematical equations. So, a section of relative stable load was selected to be applied on the mathematical model and simulation model.As shown in Figure8, the blue curve represented the drilling experiment data measured in drilling experiment, the average value and fluctuation of which were 8000 N∙m and 500 N∙m, respectively. The green curve represented load applied on simulation model, and the purple curve represented the load applied on the mathematical model. Both the load applied on simulation model and mathematical model were divided into two stages. From the beginning to the third second, the system was in the state of no-load; from the third second to the end of the calculation, a random fluctuate torque was applied on the system, with an average value of 8000 N∙m and fluctuating amplitude of 500N∙m.Figure 8
Loads applied on the hydraulic top drive.Figure9 shows the pressure difference of hydraulic motor obtained from the mathematical model, simulation model, and drilling experiment. From Figure 9, it could be found that, in the mathematical model, there was an overshoot of 6 MPa at the beginning stage of the system. Fluctuation of pressure losses decreased gradually, and the pressure loss reached to steady state in 0.5 second. In the simulation result, an overshoot of 1 MPa emerged at the beginning stage of simulation, and then the pressure difference of hydraulic motors oscillated with damping and reached to the steady state at 0.5 s. In the transient stage, the amplitude and frequency of vibration gained from mathematical model were both bigger than those gained from simulation model. At the 3rd second, the pipe pressure loss gained from mathematical model and simulation model both increased rapidly, with the overshoot of 7.51 MPa and 8.31 MPa, respectively. Then, the amplitude of pressure loss decreased, and the system reached to steady state within 1 second. The reason for the result difference between mathematical model and simulation model was that an approximate model derived from pipe four-ports distributed parameter model was used in mathematical model, while pipe lump parameter model was applied in simulation model.Figure 9
Pressure difference of hydraulic motor.When the system reached to steady state, the pressure loss of pipelines in mathematical model, simulation model, and drilling experiment all fluctuate with the load applied on hydraulic top drive shaft. In the mathematical model, the pressure loss changed around 5.51 MPa, with the fluctuation of 0.1 MPa; in simulation model, the pressure loss fluctuated around 5.85 MPa with the fluctuation of 0.2 MPa; in drilling experiment, the pressure loss fluctuated around 6.07 MPa with the fluctuation of 0.3 MPa. The cause of the difference in the steady-state output results of the above three methods was that several factors, the frictions of hydraulic motor and top drive shaft for example, are not considered in the mathematical model and simulation model.Setting the speed of top drive at 30 rpm and applying loads as Figure8 shown to the mathematical model and simulation model, the output speed is shown in Figure 10. The blue curve represented the speed measured in drilling experiment, the green cure represented the simulation results, and the purple curve represented the calculate results obtain from mathematical model. From the figure, it could be found that in the mathematical model, there was an overshoot of 52 rpm at the beginning of calculation, and then the system oscillated with fluctuation decreasing and reached to steady state within 1 second; at the 3rd second when load was began to be applied to the system, top drive speed dropped rapidly and then reached to steady state in 0.5 second. From the simulation result, it could be found that there was an overshoot of 7 rpm at the beginning of the simulation, and then the system oscillated with fluctuation decreasing and reached to steady state within 1 second; at the 3rd second when load was applied to the system, top drive speed dropped rapidly and then reached to steady state within 0.5 second. In the steady state, the mathematical result, simulation result and experiment result all fluctuated around 30 rpm, and the fluctuations were all less than 1 rpm. The results gained from the three methods coincided very well.Figure 10
Output speed of the hydraulic top drive.It can be seen from the comparative analysis that the mathematical model results, simulation results, and experimental data are basically consistent. The simulation model established in this paper can be used to study the dynamic characteristics of top drive with long hydraulic pipelines.


### 4.2. Output Characteristic of Hydraulic Top Drive with Different Hydraulic Pipe Length

When the set speed is 30 rpm and torque applied on the shaft is set to fluctuate between 7500N∙m and 8500 N∙m, the output speed of top drive is shown in Figure 11 with the length of long pipelines of 50 m, 80 m, and 110 m, respectively. For clear observation of the dynamic response of the speed, Figure 11(b) and Figure 11(c) illustrate the top drive speed from the beginning to the 3rd second and from the 29th second to the 30th second, respectively. From the figure, it could be found that with the increase of the length of the pipelines, the responses of hydraulic top drive speed slowed down, and the overshoots decreased. When the system reached to steady state, the steady-state value of hydraulic top drive speed fluctuated around the setting value of 30 rpm and the fluctuations increased with the length of pipelines increasing.Figure 11
Top drive shaft speed with different pipe length. (a) Speed from the beginning to the 30th second. (b) Speed from the beginning to the 3rd second. (c) Speed from the 29th second to the 30th second.
(a)(b)(c)Figure12 shows the inlet pressure of hydraulic motors. As can be seen from the figure, with the length of hydraulic pipelines increasing, fluctuations and the response speed of the pressure at the beginning decreased. When the system reached steady state, steady-state value of the pressure increased with the length of pipelines increasing, while the fluctuations decreased.Figure 12
Hydraulic motor inlet pressure of the top drive with different pipe length. (a) Pressure from the beginning to the 30th second. (b) Pressure from the beginning to the 5th second. (c) Pressure from the 25th second to the 30th second.
(a)(b)(c)Figure13 illustrates the pressure loss of high-pressure line of hydraulic top drive with different pipe length. It can be concluded from the plots that with the increase of hydraulic pipelines length, response of pressure loss slowed down. When the system reached to the steady state, the pressure loss and its fluctuation increased with the length of hydraulic pipeline increasing.Figure 13
Pressure loss of the long pipelines with different length. (a) Pressure loss from the beginning to the 30th second. (b) Pressure loss from the beginning to the 3rd second.
(a)(b)


### 4.3. Output Characteristic of Hydraulic Top Drive with Different Pipe Diameters

When the setting speed of top drive was 30 rpm, and fluctuating load between 7500N∙m and 8500 N∙m was applied on the top drive shaft, the output speed with different pipelines diameters is shown in Figure 14. From the figure, it could be found that with the increase of pipe diameter, the response of hydraulic top drive speed slowed down and the overshoot of hydraulic top drive speed increased. When the system reached to steady state, the hydraulic top drive speed fluctuated around the setting value of 30 rpm, but with the diameter of pipelines increasing, the fluctuation increased.Figure 14
Top drive speed with different pipe diameter. (a) Speed from the beginning to the 30th second. (b) Speed from the beginning to the 5th second. (c) Speed from the 29th second to the 30th second.
(a)(b)(c)Figure15 shows the inlet pressure of hydraulic motors with different diameters of hydraulic pipes. From the figure, it could be found that with the diameter decreasing, the fluctuation at the beginning decreased. When the system reached steady state, the steady-state value of inlet pressure and its fluctuation increased with the decrease of pipe diameters.Figure 15
Hydraulic motor inlet pressure of the top drive with different pipe diameter. (a) Pressure from the beginning to the 30th second. (b) Pressure from the beginning to the 5th second. (c) Pressure from the 25th second to the 30th second.
(a)(b)(c)The pressure loss of hydraulic pipelines in high-pressure side with different diameters of hydraulic pipeline is shown in Figure16. From the figure, it could be found that with the diameters decreasing, the pressure loss and its fluctuation both increased. When the diameters of hydraulic pipelines reached to 40 mm, the pressure loss would be very low.Figure 16
Pressure loss of the long hydraulic pipelines with different diameter.


## 4.1. Comparison of Mathematical Results, Simulation Results, and Experiment Data

During the drilling test, the top drive operated continuously 24 hours a day. All parameters of top drive operation, such as speed, torque, and pressure, were recorded every 2 seconds. Some of the speed and torque obtained in drilling experiment are shown in Figure7. From the curve, it can find that the load applied on top drive shaft fluctuates randomly all time. And the pressure at outlet of hydraulic pumps varied with the load applied on the top drive. The pressure at the inlet of hydraulic pumps was remained at 1.57 MPa, which was the supplementary pressure of the system. As can be seen from Figure 7, the operating speeds of top drive were at 9 rpm, 11 rpm, 20 rpm, and 30 rpm, respectively. Though the output speed fluctuated randomly for the influence of load, the fluctuation was less than 2 rpm. In other words, at each running stage, the speed could be maintained at its setting value.Figure 7
Experiment data when top drive drilling in SK-II at the depths of 3436.92 m to 3447.52 m.To verify and modify the mathematical model and simulation model built in this paper, a comparison analysis between the above three methods was performed. In the comparison, parameters of hydraulic pumps, hydraulic motors, and hydraulic pipelines were set at the same values for the three methods. Based on the measured torque of the field test, the load applied on the mathematical mode and simulation model is determined. From Figure7, it can be found that it was not easy to find out the change rules of load on top drive and describe it with mathematical equations. So, a section of relative stable load was selected to be applied on the mathematical model and simulation model.As shown in Figure8, the blue curve represented the drilling experiment data measured in drilling experiment, the average value and fluctuation of which were 8000 N∙m and 500 N∙m, respectively. The green curve represented load applied on simulation model, and the purple curve represented the load applied on the mathematical model. Both the load applied on simulation model and mathematical model were divided into two stages. From the beginning to the third second, the system was in the state of no-load; from the third second to the end of the calculation, a random fluctuate torque was applied on the system, with an average value of 8000 N∙m and fluctuating amplitude of 500N∙m.Figure 8
Loads applied on the hydraulic top drive.Figure9 shows the pressure difference of hydraulic motor obtained from the mathematical model, simulation model, and drilling experiment. From Figure 9, it could be found that, in the mathematical model, there was an overshoot of 6 MPa at the beginning stage of the system. Fluctuation of pressure losses decreased gradually, and the pressure loss reached to steady state in 0.5 second. In the simulation result, an overshoot of 1 MPa emerged at the beginning stage of simulation, and then the pressure difference of hydraulic motors oscillated with damping and reached to the steady state at 0.5 s. In the transient stage, the amplitude and frequency of vibration gained from mathematical model were both bigger than those gained from simulation model. At the 3rd second, the pipe pressure loss gained from mathematical model and simulation model both increased rapidly, with the overshoot of 7.51 MPa and 8.31 MPa, respectively. Then, the amplitude of pressure loss decreased, and the system reached to steady state within 1 second. The reason for the result difference between mathematical model and simulation model was that an approximate model derived from pipe four-ports distributed parameter model was used in mathematical model, while pipe lump parameter model was applied in simulation model.Figure 9
Pressure difference of hydraulic motor.When the system reached to steady state, the pressure loss of pipelines in mathematical model, simulation model, and drilling experiment all fluctuate with the load applied on hydraulic top drive shaft. In the mathematical model, the pressure loss changed around 5.51 MPa, with the fluctuation of 0.1 MPa; in simulation model, the pressure loss fluctuated around 5.85 MPa with the fluctuation of 0.2 MPa; in drilling experiment, the pressure loss fluctuated around 6.07 MPa with the fluctuation of 0.3 MPa. The cause of the difference in the steady-state output results of the above three methods was that several factors, the frictions of hydraulic motor and top drive shaft for example, are not considered in the mathematical model and simulation model.Setting the speed of top drive at 30 rpm and applying loads as Figure8 shown to the mathematical model and simulation model, the output speed is shown in Figure 10. The blue curve represented the speed measured in drilling experiment, the green cure represented the simulation results, and the purple curve represented the calculate results obtain from mathematical model. From the figure, it could be found that in the mathematical model, there was an overshoot of 52 rpm at the beginning of calculation, and then the system oscillated with fluctuation decreasing and reached to steady state within 1 second; at the 3rd second when load was began to be applied to the system, top drive speed dropped rapidly and then reached to steady state in 0.5 second. From the simulation result, it could be found that there was an overshoot of 7 rpm at the beginning of the simulation, and then the system oscillated with fluctuation decreasing and reached to steady state within 1 second; at the 3rd second when load was applied to the system, top drive speed dropped rapidly and then reached to steady state within 0.5 second. In the steady state, the mathematical result, simulation result and experiment result all fluctuated around 30 rpm, and the fluctuations were all less than 1 rpm. The results gained from the three methods coincided very well.Figure 10
Output speed of the hydraulic top drive.It can be seen from the comparative analysis that the mathematical model results, simulation results, and experimental data are basically consistent. The simulation model established in this paper can be used to study the dynamic characteristics of top drive with long hydraulic pipelines.


## 4.2. Output Characteristic of Hydraulic Top Drive with Different Hydraulic Pipe Length

When the set speed is 30 rpm and torque applied on the shaft is set to fluctuate between 7500N∙m and 8500 N∙m, the output speed of top drive is shown in Figure 11 with the length of long pipelines of 50 m, 80 m, and 110 m, respectively. For clear observation of the dynamic response of the speed, Figure 11(b) and Figure 11(c) illustrate the top drive speed from the beginning to the 3rd second and from the 29th second to the 30th second, respectively. From the figure, it could be found that with the increase of the length of the pipelines, the responses of hydraulic top drive speed slowed down, and the overshoots decreased. When the system reached to steady state, the steady-state value of hydraulic top drive speed fluctuated around the setting value of 30 rpm and the fluctuations increased with the length of pipelines increasing.Figure 11
Top drive shaft speed with different pipe length. (a) Speed from the beginning to the 30th second. (b) Speed from the beginning to the 3rd second. (c) Speed from the 29th second to the 30th second.
(a)(b)(c)Figure12 shows the inlet pressure of hydraulic motors. As can be seen from the figure, with the length of hydraulic pipelines increasing, fluctuations and the response speed of the pressure at the beginning decreased. When the system reached steady state, steady-state value of the pressure increased with the length of pipelines increasing, while the fluctuations decreased.Figure 12
Hydraulic motor inlet pressure of the top drive with different pipe length. (a) Pressure from the beginning to the 30th second. (b) Pressure from the beginning to the 5th second. (c) Pressure from the 25th second to the 30th second.
(a)(b)(c)Figure13 illustrates the pressure loss of high-pressure line of hydraulic top drive with different pipe length. It can be concluded from the plots that with the increase of hydraulic pipelines length, response of pressure loss slowed down. When the system reached to the steady state, the pressure loss and its fluctuation increased with the length of hydraulic pipeline increasing.Figure 13
Pressure loss of the long pipelines with different length. (a) Pressure loss from the beginning to the 30th second. (b) Pressure loss from the beginning to the 3rd second.
(a)(b)


## 4.3. Output Characteristic of Hydraulic Top Drive with Different Pipe Diameters

When the setting speed of top drive was 30 rpm, and fluctuating load between 7500N∙m and 8500 N∙m was applied on the top drive shaft, the output speed with different pipelines diameters is shown in Figure 14. From the figure, it could be found that with the increase of pipe diameter, the response of hydraulic top drive speed slowed down and the overshoot of hydraulic top drive speed increased. When the system reached to steady state, the hydraulic top drive speed fluctuated around the setting value of 30 rpm, but with the diameter of pipelines increasing, the fluctuation increased.Figure 14
Top drive speed with different pipe diameter. (a) Speed from the beginning to the 30th second. (b) Speed from the beginning to the 5th second. (c) Speed from the 29th second to the 30th second.
(a)(b)(c)Figure15 shows the inlet pressure of hydraulic motors with different diameters of hydraulic pipes. From the figure, it could be found that with the diameter decreasing, the fluctuation at the beginning decreased. When the system reached steady state, the steady-state value of inlet pressure and its fluctuation increased with the decrease of pipe diameters.Figure 15
Hydraulic motor inlet pressure of the top drive with different pipe diameter. (a) Pressure from the beginning to the 30th second. (b) Pressure from the beginning to the 5th second. (c) Pressure from the 25th second to the 30th second.
(a)(b)(c)The pressure loss of hydraulic pipelines in high-pressure side with different diameters of hydraulic pipeline is shown in Figure16. From the figure, it could be found that with the diameters decreasing, the pressure loss and its fluctuation both increased. When the diameters of hydraulic pipelines reached to 40 mm, the pressure loss would be very low.Figure 16
Pressure loss of the long hydraulic pipelines with different diameter.


## 5. Conclusions

Hydraulic top drive is mainly used to drive drilling tools rotating to drill a hole, whose main transmission system mainly consists of main gearbox, hydraulic system, and control system. For the hydraulic system, hydraulic variable displacement pumps are selected as the power units, and variable hydraulic displacement motors are chosen as the actuator units. In well site, the hydraulic power station is generally placed on the drilling floor or on the ground, while the body of hydraulic top drive is mounted on the derrick and travels up and down during drilling process. Thus, long hydraulic pipelines are needed to connect the hydraulic top drive and the hydraulic power station, which will influence the performance and dynamic characteristic of the hydraulic top drive. To study the dynamic performance, a mathematical model was developed by integrating the differential model of hydraulic units and approximate model of hydraulic pipelines. A simulation model based on the AMESim software was built. What’s more, field drilling test of the hydraulic top drive was carried out in the Songliao Basin Drilling Project well site.To verify and modify the mathematical model and simulation model built in this paper, a comparison analysis was performed by setting the parameters and load of the three methods at the same values. From the comparative analysis, it can be seen that the mathematical model results, simulation results, and experimental data are basically consistent. The simulation model established in this paper can be used to study the dynamic characteristics of top drive with long hydraulic pipelines.Output characteristics of hydraulic top drive with different length and diameters of pipelines were studied in this paper. With the increase of the length of pipelines, the response speed of hydraulic top drive speed and the pressure loss in the high-pressure side pipelines slow down, while the response speed of hydraulic motor inlet pressure decreases at the beginning. When the system reaches to the steady state, the fluctuations of the hydraulic top drive speed and the pressure loss in the high-pressure side pipelines increase, while the fluctuations of the hydraulic motor inlet pressure decrease. As the diameters of hydraulic pipelines increase, the response of hydraulic top drive speed slows down, while the overshoot of hydraulic top drive speed and the fluctuations when the system reaches to steady state both increase. With increasing diameters, the steady-state value of inlet pressure and its fluctuation, the pressure loss of hydraulic pipelines in high-pressure side and its fluctuation both reduce.Because the characteristics of hydraulic top drive speed and pressure output in very different laws with pipeline lengths and pipeline diameters change, it needs to comprehensively consider the system response speed, overshoot, and steady-state characteristics when choosing the size of pipelines for the hydraulic top drive. In order to reduce impacts of speed and pressure, the pipelines connecting hydraulic pumps and hydraulic motors would be not any longer than necessary.



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*Source: 1304176-2022-04-16.xml*