Performance Investigation of a Low-Speed High Torque Hydromotor Drive System Used in Blast Hole Drill Machine Under Varying Load Conditions

Abstract

In this article, a performance investigation of a low-speed high torque hydromotor drive system used in blast hole drilling machine is carried out for varying load conditions. Blast hole drill machines are widely used in drilling operations in open-pit mines to drill hole in rocks. During such operation, the varying strength of rocks results in variable load on hydromotor, which decreases its speed and it may lead to fluctuations in speed as well as torque. A high torque low-speed hydromotor is used to fulfill the requirement of operation, which has lower volumetric efficiency than its counterpart. As a result, such hydromotors have more leakage losses with an increase in the load on it. Therefore, a constant speed of the drill bit of said machine is needed for smooth operation. In the present work, a PI controller is used to vary the pump displacement that manipulates the supply flow to the hydromotor in order to maintain a constant drive speed irrespective of load. In this respect, a Simulink model of the drive is developed, and a test rig is fabricated to validate the system responses. The test rig consists of a loading unit that replicates similar varying load conditions on hydromotor as it experiences with the variation in the strength of the drilled rock. The obtained results indicate an improved performance of the hydromotor drive used in the blast hole drilling operations by implementing the said controller.

1 Introduction

Hydrostatic drive system is commonly employed in mobile machinery because of its various advantages over its counterpart [1]. It provides one of the best alternatives, where the primary focus is to control drive speed with varying loads. A number of applications demand constant speed for better control performance and smooth operation. One of such application is blast hole drilling operation. Blast holes are drilled in order to fill explosives for the removal of overburden from the opencast mine surfaces through blasting. Here, hydrostatic drives play a major role since they can provide high torque by a small size hydraulic motor when compared to electric motor size of same required torque rating. Therefore, the overall weight of the mast is reduced so that it becomes easily mobile, while traveling from one hole to another and compared to a mechanical system hydrostatic transmission system is more flexible in transmitting power. Therefore, the hydrostatic drive has its upper hold [2].

In the blast hole drilling process, the varying overburden density of the formation changes the load torque requirement which result decreased drill bit speed due to increased leakage losses [3]. The drive performance is negatively impacted by variations in load torque and speed, which also reduce the dependability of system components [4]. Three commonly used control schemes to deal with decreasing speed are pump speed control, pump displacement control, and controlled flow supplied through the valve. The pump displacement control is a better solution compared to others in terms of response time and cost (valve adds extra cost to drive). Thus, the drive speed is maintained constant through pump displacement control mode using a PI controller. PI controller is simple in design, cheaper, and has a good control performance [5].

This paper investigates the dynamic performance of a low-speed, high-torque closed-loop speed-controlled hydromotor motor by controlling the pump displacement speed of varying loading conditions. In this respect, the modeling of the hydrostatic drive system is done using MATLAB Simulink environment and is validated using the experimental setup. This paper focuses on maintaining a constant drill bit speed of a hydrostatic-driven blast hole drilling machine using a PI controller.

2 Physical System

Figure 1 represents the circuit diagram of a hydromotor drive system integrated with pump displacement control. In the experimental setup, a variable displacement pump (1) driven by fixed displacement motor (2) supplies a variable flow to the hydromotor. PI controller is used to vary the displacement of the pump results in varying hydromotor speed. The hydromotor (6) is driving the loading unit which consists of a gear unit (9), loading pump (11), and proportional pressure relief valve (4). The pressure at the outlet of the loading pump is varied by changing the supplied command voltage signal to the PPRV (4) that varies the load torque on the hydromotor motor. Due to low-capacity loading pump, a 20:1 gearbox is connected in between hydromotor motor and loading pump which amplify the load torque on hydromotor.

Fig. 1

a Schematic diagram of the physical system. b Experimental test rig

In this test setup, the system pressure, discharge flow given to the motor, and the motor speed is shown by the sensors. A data logger the sensor data for further study. This article focuses on maintaining the drive at a constant speed in order to drill holes in formation.

3 Physical System Modeling

For predicting the system response, it’s modeled in a MATLAB^® Simulink platform. It is commonly utilized to simulate multi-energy domain systems like a hydro-mechanical system. Some assumptions are taken while creating the model:

• Newtonian hydraulic fluid is taken that has invariant fluid properties with respect to pressure and temperature.

• The formation properties are assumed to continuum for different types of rocks; thus, the load torque changes with a change in rock strength.

• The losses of the gearbox unit are neglected.

• Multi-piston dynamics of the pump and the motor is not considered.

Figure 2 depicts the mathematical modeling of the hydromotor drive system which is taken into account in the current analysis. In the model, the variable flow (Q^p) is supplied by the pump to a hydromotor through changing the displacement of the pump through a PI controller. The controller compares the hydromotor speed with the desired speed, and a command signal is generated corresponding to the error signal to vary the pump displacement. TF block represents the transfer function of pump displacement for the given command signal. The lookup tables are used to consider the leakage and torque losses of hydromotor and pumps. Their characteristics are established in the parameter identification section. A part of the pump supply flow goes to the tank as flow passing through PRV, external leakage of pump and hydromotor. Thus, the flow loss due to compressibility can be estimated using the flow balance equation, which is used to obtain the hydromotor inlet pressure.

Fig. 2

Simulink model of the physical system

Similarly, the torque balance equation is used to predict the hydromotor speed. The torque available at the hydromotor is driving the load torque and the inertial torque of the hydromotor. The set pressure of PPRV and mechanical efficiency is used to estimate the load torque.

4 System Equations

Referring the model given in Fig. 2, the pump flow $(Q^{{\text{p}}} = D^{{\text{p}}} \omega^{{\text{p}}} + Q_{{\text{l}}}^{{\text{p}}} )$ supplied to the hydromotor ($Q_{{\text{i}}}^{{\text{m}}}$) and a part its flow passes through PRV ($Q^{{{\text{prv}}}}$) to maintain the set pressure. The flow loss due to compressibility at the hydromotor inlet is

$$Q_{{\text{m}}}^{{\text{c}}} = D^{{\text{p}}} \omega^{{\text{p}}} - Q_{{\text{l}}}^{{\text{p}}} - Q_{{\text{i}}}^{{\text{m}}} - Q^{{{\text{prv}}}} .$$

(1)

The variation of pump displacement on the given command signal to it, pump $(Q_{{\text{l}}}^{{\text{p}}} )$ and hydromotor leakage losses $(Q_{{\text{i}}}^{{\text{m}}} )$ are characterized and shown in Sect. 5.

The flow passing through PRV is obtained by

$$Q^{{{\text{prv}}}} = \left\{ {\begin{array}{*{20}c} {0\quad {\text{if}}\;(P^{{\text{S}}} \le 200)} \\ {C_{{\text{D}}} A^{{{\text{prv}}}} \sqrt {\frac{{2(P^{{\text{S}}} - 100)}}{\rho }} } \\ \end{array} \quad {\text{if}}\quad (P^{S} > 200)} \right\}.$$

(2)

In Eq. (1), the flow supplied ($Q_{{\text{i}}}^{{\text{m}}}$) to hydromotor is calculated by

$$Q_{{\text{i}}}^{{\text{m}}} = D^{{\text{m}}} \omega^{{\text{m}}} + Q_{{\text{l}}}^{{\text{m}}} .$$

(3)

Hydromotor inlet pressure is given by

$$P_{{\text{i}}}^{{\text{m}}} = K^{{\text{m}}} \int {Q_{{\text{m}}}^{{\text{c}}} \, } {\text{d}}t,$$

(4)

where the fluid column in the motor plenum is equal to the bulk stiffness.

$$K^{{\text{m}}} = \frac{K}{{V^{{\text{m}}} }}.$$

The torque available at the motor is driving the inertial load ($I$) and loading torque ($\tau^{{\text{l}}}$). The motor torque can be written as

$$\tau^{{\text{m}}} = J^{{\text{m}}} \frac{{{\text{d}}\omega^{{\text{m}}} }}{{{\text{d}}t}} + \tau^{{\text{l}}} ,$$

(5)

where the motor and loading torque are

$$\tau^{{\text{m}}} = \eta_{{{\text{mech}}}}^{{\text{m}}} P_{{\text{i}}}^{{\text{m}}} D^{{\text{m}}} ,$$

(6)

$$\tau^{{\text{l}}} = \frac{{P^{{\text{l}}} D_{{\text{l}}}^{{\text{p}}} }}{{\eta_{{{\text{mech}}}}^{{\text{l}}} }}*N.$$

(7)

In Eqs. (6) and (7), $P^{{\text{l}}} ,D_{{\text{l}}}^{{\text{p}}} ,N,\eta_{{{\text{mech}}}}^{{\text{m}}} ,\eta_{{{\text{mech}}}}^{{\text{l}}} ,N$ represent the load of the pressure pump, Volumetric Displacement, Gear ratio, mechanical efficiency of hydromotor, and loading pump, respectively. Stating the given value of $\tau^{{\text{l}}}$ and $\tau^{{\text{m}}}$ from Eqs. (6) and (7) in Eq. (5), the speed ($\omega^{{\text{m}}}$) of the motor is represented by

$$\frac{{{\text{d}}\omega^{{\text{m}}} }}{{{\text{d}}t}} = \frac{{\left( {\eta_{{{\text{mech}}}}^{{\text{m}}} D^{{\text{m}}} P_{{\text{l}}}^{{\text{m}}} - \frac{{P^{{\text{l}}} D_{{\text{l}}}^{{\text{p}}} }}{{\eta_{{\text{l}}}^{{\text{m}}} }}} \right)}}{I}.$$

(8)

Using Eq. (8), the motor speed ($\omega^{{\text{m}}}$) is predicted.

5 Parameter Identification

The characteristic curve of the main hydraulic components used in the fabrication of the test rig is shown in Fig. 3. The leakage loss of variable displacement pump with variation in pressure and command signal is shown in Fig. 3a, whereas hydromotor leakage loss (Fig. 3b) is characterized for its constant speed and varying pressure. With the increase in pressure, hydromotor speed and command voltage signal, leakage losses increase. The torque loss of hydromotor and loading pump is shown in terms of mechanical efficiencies in Fig. 3c and d. The change is pump displacement for the different commands signal are shown in Fig. 3e. Figure 3f shows the pressure setting of the PPRV with respect to the supplied command signal to it. Table 1 shows the simulation parameters used to predict the hydromotor speed.

Fig. 3

Characteristic curve of the main hydraulic components of the test rig

Table 1 Component’s parameters

6 Model Validation and Result Discussion

Simulink model discussed so far is validated using the experimental test setup as shown in Fig. 1. The experimental response from setup validates the model by comparing the obtained simulation response with test results for the varying load. The load torque requirement for the drilling operation with variation in rock strength is shown in Fig. 5a. To replicate the said torque on the hydromotor, the pressure of the loading pump is varied by changing the command signal applied to the PPRV.

Figure 5 shows the hydromotor drive system responses obtained by deploying PI controller to drive the motor at 100 rpm for the given load (Fig. 4). At no load condition, hydromotor at 100 rpm is driven by a 5.69 V volt control signal which is supplied to the pump. As the load torque increases, the hydromotor inlet pressure surges due to rise in viscous load on the hydromotor. At 16.52 s, the load torque rises to 241.1 Nm from 223.5 Nm, which increases the system pressure from 82.2 bar to 88.43 bar. The simulated and experimental pressure response is shown in Fig. 5b. Estimation of the fitness in the pressure response is done by Russell’s error method in order to compare the experimental responses with the simulation response. It is estimated 3.1% for the hydromotor inlet pressure response that shows a good agreement with the said responses and thereby validates the model. The hydromotor needs more supply flow to compensate the increased leakage losses. The rise in leakage flow with increase in the pressure is visualized from Fig. 3a and b. Thus, the pump displacement is controlled to supply the needed flow to drive the hydromotor at a constant speed. Figure 5a shows the said control signal (PI controller) where it requires 5.601 V signal to drive the system at no load condition and its control signal increases to 5.781 for 241.1 Nm load. The controlled hydromotor speed is shown in Fig. 5b that shows good controlled speed response. The Russell’s error for the speed response is estimated below 3%.

Fig. 4

Pressure setting of the PPRV for step loading of the hydromotor

Fig. 5

Constant speed drive system responses rotating at 100 rpm achieved by the pump displacement control

7 Conclusion

The dynamic performance of high torque low-speed hydromotor to maintain its constant speed for varying load condition using PI controller is being studied in this article. The model of the system is made in Simulink, and it is validated experimentally. The principal feature of this drive concept is that the drive speed is maintained at constant speed through pump displacement control for the step-rise in the load. The obtained speed responses show a constant speed of 100 rpm which is maintained irrespective of the load on the hydromotor motor. The test and predicted response are in in close agreement as Russell’s error between them is less than 4%. Small deviations in the predicted results and in the measured values need further refinement of the model and better data acquisition system with sensors of higher sampling rate.