Structural Modeling and Performance Analysis of Rotary Circuit in Directional Drilling Rig Based on Load Sensing Technology

  • Jianwei Wang


Aim at improving the energy saving and transmission efficiency of directional drilling rig, the load sensing technology and constant-pressure variable technique are adopted to enable the system to provide the required pressure and flow rate according to the load variation. In order to research the dynamic characteristics of hydraulic control systems, the background and working principle of the load sensing technology were introduced. The dynamic mathematical model of load sensing system is established based on the hydraulic principle. The directional drilling rig mainly consists of two basic circuits: rotary circuit and feed circuit. The dynamic characteristics of rotary circuit are mainly studied. In addition, the hydraulic system of kilometres directional rig is simulated with the software of AMESim. The simulation results show that the load sensing pump could output its required flow and outlet pressure adapted to the load pressure in real time, thus effectively improving the efficiency of the hydraulic system. Furthermore, to verify the validity of the mathematical model and the simulation analysis, an experimental platform of the load sensing hydraulic system was built. The dynamic performance test of load sensing hydraulic system was performed by using the platform. The experimental results demonstrated that the load sensing hydraulic system could output its required flow and pressure when the working condition changed. Finally, they also illustrate the validity of the proposed approach.


Load sensing Rotary circuit Directional drilling rig Dynamic characteristics Variable pump 

1 Introduction

The gas drainage technology is a very effective means to not only weaken the active forces caused coal seams outburst, but also enhance the ability of resistance the gas outburst disaster. Conventional rotary drilling is the most commonly method used in the coal mine drilling. Conventional rotary drilling relies mainly on the rig drives drill column rotate, then drives drill to cut coal seams and forms the hole. The poor energy efficiency is a big issue in the conventional hydraulic proportional valve controlled drilling rig due to the huge throttling losses and overflow losses. It is very important for hydraulic system to provide the required pressure and flow according to the varying load, thus improve its energy efficiency and transmission efficiency.

With the development of hydraulic technology and the expansion of application field, the higher demands are put forward the hydraulic system design. Traditional methods and techniques cannot meet those requirements. As a result, it is necessary to research the dynamic characteristics of a hydraulic system, and master the dynamic operating characteristics and parameters of system changes, then the working reliability and response characteristics of the system can be further improved [1, 2, 3]. Static characteristics of a hydraulic system is referring to the output state of system from the transient process entering in the steady process, such as the flow of pumps and valves, the velocity of the actuator, efficiency and stability of the system, etc. Dynamic characteristic is referring to the response process (or the transient response) of control system after receiving the input signal, from initial state to a final state, or the variation of parameters with time during the working process of the system. At present, the design of directional drilling rig is focused on the steady state analysis of system, considered mostly how to realize the function of the system, mainly solved the speed range, speed stability, stiffness and system efficiency. However, the disturbance, stability and response speed of system with the change of the external load are seldom considered comparatively [4, 5, 6, 7].

As a power drive and control system, in addition to the general requirements of the drilling process, the hydraulic system of drilling rig must meet some special requirements: (1) within a wide range of step-less speed regulation of actuator to adapt to the changing drilling process, (2) without changing the motion direction of the engine, the implementation mechanism can be quickly and accurately reverse, (3) no pressure and flow interference in the hydraulic system, etc.

Kilometres directional drilling rig adopts pump-controlled system, which includes rotary circuit, feeding circuit and other auxiliary circuit. The rotary circuit provides the rotation power for drilling rig to overcome the load torque. The feeding force and pulling force are provided by the feeding circuit. The load sensing and constant-pressure variable control technology are adopted to use for rotary circuit and feeding circuit of kilometers directional drilling rig respectively. Furthermore, the system can provide the required pressure, flow and power according to the load change, so as to improve its energy saving and transmission efficiency. When the load sensing control system is adopted in rotary circuit, the rotary speed fluctuation and the overflow losses are significantly reduced. In order to further analyse the load sensing effect on the rotary performance of rig, it is very meaningful to analysis the dynamic simulation and its characteristics of rotary circuit.

Researching on the hydraulic system simulation, the commonly used modeling methods mainly include analytical method, state-space method, expert system and bond graph method. When analytical method [8, 9, 10] is adopted to establish the model of the hydraulic system, in order to analyse the elements and the compositions of the system, physics, fluid mechanics, kinematics, dynamics, or the laws of thermodynamics etc. should be applied to build analysing equation, meanwhile taken into account the influence of compressibility, viscous damping and friction. When the researched object is a large-scale complicated system, structural modelling is very difficult. The state-space method [11, 12] is similar with the transfer function method, but the state-space method needs to expand too many nodes, it will result in the combination blast when the dimension increases, so it only suits to solve the simple problem. Attributing to the artificial intelligence and computer technology, expert system [13, 14] can easily finish the system modelling, but it relies on the expert’s knowledge and experience to conduct reasoning and judgment. Bond graph method [15, 16, 17, 18, 19] doesn’t belong to large scale system analysis method, when the complex system wants to analyse, therefore, a large number of state variables should be described.

Due to direct physical connection between modules in different fields, AMESim has become the standard environment for system engineering modelling and simulation in multidisciplinary fields. In this paper, to research the dynamic performance of the system, AMESim software based on power bond graph is applied to modeling and simulation of hydraulic system. AMESim intelligent solver can choose the best algorithm according to the mathematical properties of different models, and adjust the integration step length to improve the simulation accuracy. Furthermore, it has four simulation modules: dynamic simulation, steady state simulation, intermittent simulation and batching simulation. During the process of modeling, the standard application libraries build-in software is adopted to avoid the formulas and programming process, which can improve design applicability and efficiency. The simulation results show the characteristics of the rotary circuit through the output variation of pressure and flow rate.

The remainder of the paper is organized as follows: Sect. 2 describes the operating principles of load sensing hydraulic system. Section 3 introduces a design process of mathematical models of load sensing system. System simulation and analysis are explored in Sect. 4. Section 5 shows the experimental setups, control results and discussion. Finally, conclusions are given in Sect. 6.

2 Load Sensing Principle

A load-sensing system is a novel hydraulic control technology which has attracted the research interests of researchers [20, 21, 22, 23]. Load sensitivity is the variable adjustment mechanism to realize the variable load pressure feedback to the pressure compensation device or hydraulic pump, in order to adapt hydraulic pressure of pump to the load pressure and obtain high control accuracy and low energy losses [24, 25]. Working principle of load sensing hydraulic system is shown as Fig. 1.
Fig. 1

Working principle of load sensing system

The load-sensing system is composed of swashplate piston pump, plunger cylinder with spring variable mechanism, pressure control valve, flow control valve, load-sensing check valve, and so on. As a key component of kilometers directional drilling rig, the performance of the load-sensing system plays an important role in the hydraulic system. When the system pressure below the set pressure of control valve, the right station of pressure control valve will come into play, the load sensing variable pump could adjust the inclination angle of the swashplate according to the required flow and pressure of working load. The outlet pressure of load sensing variable pump is always higher than the certain load stress value. When the system pressure is higher than the setting pressure of pressure control valve, the left station of pressure control valve will come into play, the hydraulic circuit between the flow control valve and the plunger cylinder without spring variable mechanism will be cut off, the high pressure oil output by the load sensing variable pump will flow into the head port of plunger cylinder without spring variable mechanism, the inclination angle of the variable pump swashplate will become gradually small until close to zero degree. The principle of load sensing hydraulic system meets the performance requirement of outputting high pressure and small flow under the condition of the variable pump overload.

The flow of the pump outlet is adjusted by the differential pressure of throttle valve head-end to control load sensing valve, which not only affected by load pressure change. The pump outlet pressure is merely higher certain value than the load pressure. The pump outlet pressure can automatically adapt to the load change under the highest-pressure limit. Hydraulic pump need to offer the pressure and flow matching to hydraulic actuator load; therefore, the hydraulic system cannot produce excess pressure and excess flow. In the hydraulic system, power is equal to the flow multiply by pressure, resulting in the hydraulic pump is only available to match the load pressure (or flow), make the hydraulic system power is close to the load at a level. Consequently, energy saving effect of system is obvious.

3 Mathematical Models of Load Sensing System

A load sensing hydraulic system consists of a load sensing pump, an adjustable throttle valve, a load feedback piping and a hydraulic motor, etc. A load sensing pump is composed of a load sensing valve, a variable cylinder and a variable pump. The assembly of rotary mechanism is shown in Fig. 2. For the sake of simplifying model, ignoring some minor factors without affecting the control system characteristic, the dynamic mathematical model of load sensing system is established as shown in Fig. 3.
Fig. 2

Assembly of rotary mechanism. 1. Motor; 2. planetary reducer; 3. gear mechanism; 4. spindle; 5. chuck

Fig. 3

Simulation model of rotary mechanism

In order to better analyse the performance of the load sensing system, the dynamic mathematical model includes kinetic equations and fluid continuity equations.

3.1 Force Balance Equation of Load Sensing Valve

The flow control valve is the positive overlap dual valve spool. The Force of valve spool is shown as Fig. 4. The force of flow control valve spool includes the driving force, inertia force, viscous damping force and spring force of the oil pressure acting on both ends of the valve spool. By applying Newton’s second law, the kinetic equation is given as follows:
$$ \ddot{x}_{r} = \frac{1}{{m_{r} }}\left( { - \,B_{r} \dot{x}_{r} - k_{r} x_{r} + A_{r} ((P_{s} - P_{Ls} ) - P_{d} )} \right) $$
where \( x_{r} \) is valve spool displacement (m), \( m_{r} \) is valve spool mass (kg), \( B_{r} \) is viscous damping efficient (N s/m), \( k_{r} \) is spring stiffness coefficient (N/m), \( A_{r} \) is cross-sectional area of valve spool (m2), \( P_{s} \) is pump outlet pressure (Pa), \( P_{Ls} \) is load sensing pressure (Pa), \( P_{d} \) is the setting differential pressure of load sensing valve (Pa).
Fig. 4

Schematic diagram of the load sensing system

Due to the steady flow force, the transient flow force and the friction between valve spool and valve bush is very smaller than (Ps − PLs − Pd), they are ignored.

3.2 The Kinetic Equations of the Displacement Control Mechanism of Load Sensing Pump

The displacement control mechanism of load sensing pump is composed the swash plate and control cylinder as shown in Fig. 4. In order to describe the dynamic characteristics of swash plate and variable displacement mechanism, the piston displacement \( x_{y} \) and the swash plate angular displacement \( \theta_{sp} \) are chosen as variables. Owing to the difficulty of measuring the piston displacement, the swash plate angular displacement \( \theta_{sp} \) is taken as only variable. The following kinetic equation is given by Kavanagh in 1987.
$$ J_{sp} \ddot{\theta }_{sp} = - \,B_{sp} \dot{\theta }_{sp} - K_{sp} \theta_{sp} + T_{sp} + K_{pr2} P_{s} - K_{pr3} P_{s} \theta_{sp} - R_{py} A_{y} P_{y} $$
where \( J_{sp} \) is the equivalent moment inertia of pump displacement control mechanism (kg m2), \( \theta_{sp} \) is swash plate angular displacement (rad), \( B_{sp} \) is damping coefficient of control cylinder and swash plate (N s/m), \( K_{sp} \) is equivalent coefficient of spring torque (N m/rad), \( T_{sp} \) is equivalent spring preloading torque (N m), \( K_{pr2} \) is the constant of pressure torque (N m/Pa), \( P_{s} \) is pump outlet pressure (Pa), \( K_{pr3} \) is the constant of pressure torque (N m/Pa), \( R_{py} \) is the distance between control cylinder axis and swash plate rotation center (m), \( A_{y} \) is equivalent effect area of control cylinder (m2), \( P_{y} \) is pressure of control cylinder cavity (Pa).

3.3 Flow Continuity Equation of Displacement Control Cylinder Cavity

Taking account of the volume between load sensing valve and displacement control cylinder and zero-opened load sensing valve, flow continuity equation is given as follow.
$$ \dot{P}_{y} = \frac{\beta }{{V_{y} }}\left( {Q_{r1} - A_{y} \dot{x}_{y} - Q_{r2} } \right) $$
where \( V_{y} \) is the volume of displacement control cylinder cavity (m3), \( \beta \) is elasticity modulus of oil (Pa), \( Q_{r1} \) is inlet flow of load sensing valve (m3/s), \( Q_{r2} \) is outlet flow of load sensing valve (m3/s).
The flow equation through the corresponding proportional directional valves can be expressed as,
$$ Q_{r1} = C_{d} A_{s} (x_{r} )\sqrt {\frac{2}{\rho }(P_{s} - P_{y} )} \quad x_{r} \ge 0 $$
where \( C_{d} \) is flow coefficient of valve port, \( \rho \) is density of hydraulic oil (kg/m3), \( A_{s} (x_{r} ) \) is equivalent area of inlet valve opening (m2).
$$ Q_{r2} = C_{d} A_{T} x_{r} \sqrt {\frac{2}{\rho }P_{y} } \quad x_{r} < 0 $$
where \( A_{T} (x_{y} ) \) is equivalent area of outlet valve opening (m2).

3.4 Flow Supply Equation of Load Sensing Pump

The flow distribution diagram of load sensing pump is shown as Fig. 5. The control oil circuit is denoted by the dotted line.
Fig. 5

Distribution diagram of flow

The flow of pump outlet can be derived by flow continuity equation.
$$ Q_{s} = D_{p} \omega - Q_{r1} $$
where Qs is the flow of pump outlet (m3/s), Dp is pump displacement (m3), which is linear correlation with swash plate angular displacement, \( \omega \) is pump shaft speed (rad/s).
$$ D_{p} = f(\theta_{sp} ) = \frac{{NA_{p} R_{p} \tan \theta_{sp} }}{\pi } $$
where N is number of pistons within pump, Ap is cross section area of pistons (m2), Rp is arm of piston (m).
Then Qs can be expressed as follow.
$$ Q_{s} = \frac{{NA_{p} R_{p} \tan \theta_{sp} }}{\pi } - Q_{r1} $$

3.5 Balance Equation of Pump Inlet Flow

Pump inlet pressure is affected by the pump inlet flow, leakage flow and the load flow, so the equation is given as follows:
$$ \dot{P}_{s} = \frac{\beta }{{V_{p} }}\left( {(Q_{s} - Q_{L} ) - Q_{pl} } \right) $$
where Vp is the closed volume of pump outlet pressure (m3), QL is load flow (m3/s), Qpl is leakage flow (m3/s).

3.6 Flow Equation of Adjustable Throttle Valve

$$ Q = C_{d} Awx\sqrt {\frac{2}{\rho }(P_{s} - P_{L} } ) { } $$
where Q is flow (m3/s), w is width of throttle valve port (m), x is opening of throttle valve port (m), PL is load pressure of throttle valve downstream (Pa).

3.7 Balance Equation of Motor

Flow continuity equation of motor inlet is given as follow.
$$ \dot{P}_{L} = \frac{\beta }{{V_{m} }}( - \,D_{m} \phi + Q_{L} - Q_{ml} ) $$
$$ Q_{ml} = c_{ml} \cdot P_{L} $$
where Qml is leakage flow of motor (m3/s), Vm is the closed volume of motor inlet pressure (m3), Dm is motor displacement (m3/rad), \( \phi \) is motor shaft speed (rad/s), cml leakage coefficient of motor.
Dynamic torque equation of motor spindle can be represented as follow.
$$ \dot{\phi } = \frac{1}{{J_{m} }}( - \,B_{m} \phi + D_{m} P_{L} - T_{mf} ) $$
where Jm is rotational inertia of motor and load (kg m2), Bm is damping coefficient of load, Tmf is load torque (N m).

4 System Simulation and Analysis

Based on analyzing the mathematical model of load sensing system, hydraulic system simulation model of kilometer directional rig is established by adopting Hydraulic library and HCD library of AMESim. The simulation model includes three hydraulic components: the load sensing pump, the constant-pressure variable pump and the multiple directional valves. Aiming to lay the foundation for the whole machine fluid joint simulation, the rotary circuit is chosen to research its dynamic characteristics in this paper.

In the hydraulic system of kilometers directional rig, the maximum displacement and pressure of PD100 are set 100 ml/r and 280 bar respectively. The maximum displacement and pressure of constant-pressure variable pump PV10 are set 10 ml/r and 210 bar respectively. The nominal torque of load sensing system is 6000 N m, the load torque is set 4000–7000 N m. The flow, pressure of relief valve and mass of the main valve are set 34.5 ml/r, 210 bar and 1 kg respectively. Medium density is 850 kg/m3. Bulk modulus is 1700 MPa. Dynamic viscosity is 5.1 × 10−2Pa s. Reference temperature is 40 °C. The stroke of cylinder is 0.02 m. The running simulation time is 15 s.

The simulation results are shown in Figs. 6, 7, 8 and 9. The simulation shows the characteristic of the system through the output variation of pressure and flow rate. Figure 6 shows the random fluctuation curve of load torque. Figure 7 shows the comparison of rotation speed between gyrator and drilling rod. Figure 8 shows the comparison curve of inlet pressure between pump and motor. The change pressure curves of with load torque of pump and motor are shown in Fig. 9.
Fig. 6

Random load torque

Fig. 7

Comparative curves of rotation speed between gyrator and drilling rod

Fig. 8

Comparative curves of inlet pressure between pump and motor

Fig. 9

Change pressure curves with load torque of pump and motor

According to the results obtained, the setting load torque can be random fluctuations within the range between 4000 and 7000 N m as shown in Fig. 6. When load torque is higher than 6000 N m, the sliding phenomenon will appear in the rotary system, the drilling rod speed will decrease, and speed curves of gyrator and drilling rod are separated. When the load torque is less than 6000 N m, the rotary system is smooth running, and speed curves of gyrator, spindle and drilling rod are almost coincided with each other in Fig. 7. Pump inlet pressure fluctuates with the variation of motor inlet pressure, and it reflects better sensitivity, as shown in Fig. 8. Furthermore, Pump inlet pressure also fluctuates with the variation of load torque, but when load torque is greater than 6000 N m, the pump inlet pressure will reach the maximum value 300 bar assigned to the bump. Consequently, the differential pressure of load sensing valve in load sensitive pump will be disappeared, the motor inlet pressure curve is coincided with pump inlet pressure curve, and the load sensitivity is fail. When the load torque declines to below 6000 N m and the pump inlet pressure drops to 300 bars, the load sensitivity is effective in Fig. 9. It realizes the principle of load sensitive.

The simulation results of experiment testify to adequate physical behaviour of model. Figure 6 shows that the simulation model can offer random load torque in the range of acceptable condition, which satisfies the requirement of experiment. Under normal working load (less than 6000 N m), there is good consistency between the gyrator rotation speed and the drilling rig rotation speed as show in Fig. 7. It verifies the stability and tracking performance of the load sensing system. It is established that the relative error of simulation model in this case does not exceed 15% between pump outlet pressure and motor inlet pressure as shown in Figs. 8 and 9. The error range of pressure is controlled within 20 bar which verifies the principle of load sensitive and realizes the energy saving and efficiency improving.

5 Experimental Validation

In order to verify the validity of the mathematical model and the simulation analysis, an experimental platform of the load sensing hydraulic system for kilometres directional drilling rig was established as shown in Fig. 10. Figures 11 and 12 described the installation drawing of pressure, flow and speed sensors in the experimental platform. The dynamic performance test of load sensing hydraulic system was carried out by using the platform.
Fig. 10

Experimental platform of the load sensing hydraulic system

Fig. 11

Installation drawing of flow and pressure sensors. 1. Fixed installation hole; 2. fixed plate; 3. pressure sensors; 4. flow sensors

Fig. 12

Installation drawing of speed sensor. 1. Fixed support; 2. speed sensor; 3. spindle shield

The GPD50 type pressure sensors, which technical parameters are shown in Table 1, are adopted to test the oil circuits’ pressure. The response time of GPD50 type pressure sensor is 20 ms, which meets the requirement of real-time measurement. The GLW15 type turbine flow sensor was used to measure the oil circuit flow. The speed sensor adopted YE0.3/24.4 type digital encode.
Table 1

Technical parameters of pressure sensor



Range (MPa)


Excitation voltage (V)


Output signal (V)


Working temperature (°C)

− 45–85

Accuracy class

± 1%

Overload level


Zero drift

± 0.1%

The information acquisition module is one of the key parts of experimental platform. The signals of pressure, flow and speed acquired by the corresponding sensors can be not only displayed by the hydraulic multi-meter, but also real-time transported to the computer and processed by the LabVIEW program to show the characteristic curves of load sensing hydraulic system as shown in Fig. 13.
Fig. 13

Characteristic curves of load sensing hydraulic system

During the experiment, the load pressure of experimental platform was carried out by the manual control the throttle valve, the step change of the load pressure assigned to increase 0.2 MPa every step per second. When other parameters were stabilized, the system could start to record. According to the characteristic curves of load sensing hydraulic system shown in Fig. 13, it was found that the relations between the pump flow, pump pressure and load pressure were positive correlation, but the relation between the feed pressure and load pressure was negative correlation. With the increase of load pressure, the load sensing control system would consider the drilling process might encounter the stuck drill, so the pump flow and pressure should be increased to enhance the flushing strength according to the torque. The load sensing variable pump can be adapted to the load, effectively improved the drilling efficiency of the hole-bottom and synchronously reduced the feed pressure. Consequently, the possibility of the drilling stem damage accident could be reduced and saved the energy.

The experiment indicated that a typical parameter changed significantly, the load sensing hydraulic control system can control the drilling parameters of drilling rig to make the corresponding adjustment. Compared with the simulation results, the characteristic curves of load sensing hydraulic system could verify the correctness of the mathematical model and the simulation analysis. The load sensing hydraulic system could effectively control the rotary circuit of kilometres directional rig and reliably prove the drilling process. It can be seen from the experimental data that the control system can effectively control the drilling parameters to cope with various holes and lay the foundation for the parameterization and automation of the drilling rig.

Simulation results have a good agreement with the experimentally obtained results for each flow rate and different pressure loads. For both the conditions, as great and small conditions of the pressure of controlled flow rate line and pressure of excess flow rate line cases, simulation results have a good agreement for each flow rate.

6 Conclusion

The study proposed a new structural modelling and performance analysis strategy in the directional drilling rig using load sensing technology. According to the hydraulic control system model and experiments on the kilometres directional drilling rig platform, the following statements could be obtained.
  1. (1)

    Aiming at kilometres directional rig adopted load sensing system, the system mathematical model is established based on analysing the characteristics of rotary circuit. This model accurately describes the performance of load sensing variable pump.

  2. (2)

    The hydraulic characteristics simulation of rotary circuit is realized by using AMESim. The simulation results demonstrate that the variable pump can adjust the angle size of the swash plate in real time according to the varying load to supply the required pressure and flow, and realize the compensation function of pressure and flow. Furthermore, to verify the validity of the mathematical model and the simulation analysis, an experimental platform of the load sensing hydraulic system was built. The characteristic curves outputted by the experimental platform further verified the proposed approach is both effective and feasible.

  3. (3)

    The proposed method can set a reference to design, analysis and optimization on hydraulic pump controlling systems in engineering field.




The authors acknowledge the National Natural Science Foundation of China (Grant: 51275061), the National Natural Science Foundation of China (Grant: 61672121), the Doctoral Scientific Research Foundation of Liaoning Province (Grant: 20141121), Science and Technology Research Foundation of the Educational Department of Liaoning Province (Grant: LS2010006).


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Mechanical EngineeringDalian UniversityDalianChina

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