Comparison of the steady-state performance of hydrostatic drives used in the rotary head of the drill machine

Abstract

This article presents a comparative analysis of steady-state behavior of hydrostatic drives of a drill machine used in mining application. Usually, a closed-circuit hydrostatic drive rotates the cutter head (drill bit) of a drill machine through its rotary head. In this respect, performance investigation of two such alternative drives is carried out through modeling, simulation and experimentation. One of the drives comprises a variable displacement pump and two high speed low torque (HSLT) bent axis motors with a gear reducer, whereas another one consists of an identical pump and a low speed high torque (LSHT) radial piston motor. To simulate the hydrostatic drives, the bondgraph models are made, where various losses are considered as resistive elements. Considering the characteristics of the losses obtained experimentally, the predicted performances of the systems obtained through simulation are validated with the test data. The dependencies of the losses on the pump displacement and the load torque on the drives are also analyzed. The characteristics of the drives with respect to the operating speed range of the drill machine used in mining operation are studied at different torque levels. On the basis of the results obtained, suitability of the hydrostatic drives for the rotary head of the drill machine is also discussed for different rock characteristics.

Appendices

Appendix 1

From the characteristics shown in Figs. 7, 8, 9, 10, 11, 12, 13 and 14, the empirical relations that express the variation of R _pl , R _pd , R _vih , R _vil , R _elh , R _ell , R _eqh and R _eql with β _pd are given below (for, 0 ≤ β _pd ≤ 1 and 340 Nm ≤ T _ld ≤ 540 Nm):

$$R_{pl} \, \times 10^{ - 11} = \,x\, \times \,\beta_{pd}^{2} \, + \,y\,\, \times \,\beta_{pd} + \,z$$

(43)

where $x\, = \, - 1 \times 10^{ - 6} T_{ld}^{2} + \,0.0035T_{ld} - 0.4514$, $y\, = \, - 9 \times 10^{ - 6} T_{ld}^{2} \, + \,0.0064T_{ld} - 0.366$ and $z\,\, = \,7 \times 10^{ - 6} T_{ld}^{2} \, - 0.0122T_{ld} + 8.5502$

$$R_{pd} \times 10^{2} = \,x \times \,\beta_{pd} \, + \,y$$

(44)

where $x = \,9 \times 10^{ - 7} T_{ld}^{2} - 0.0023T_{ld} + \,1.0659$ and $y = \, - 1 \times 10^{ - 6} T_{ld}^{2} \, + 0.004T_{ld} - 0.427$

$$R_{vih} \times 10^{ - 8} = \,x\, \times \,\,\beta_{pd}^{2} \, + \,y\, \times \,\beta_{pd} \, + \,\,z$$

(45)

where $x\,\, = \, - 2 \times 10^{ - 5} \,T_{ldh}^{2} + 0.0107T_{ldh} + 23.313$, $y\,\, = \,\,2 \times 10^{ - 6} T_{ldh}^{2} - 0.0169T_{ldh} - 30.049$ and $z\, = \,3 \times 10^{ - 5} \,T_{ldh}^{2} + 0.0199T_{ldh} + 6.6242$

$$R_{vil} \times 10^{ - 8} = \,x\beta_{pd} \, + \,y$$

(46)

where $x = \,0.0001T_{ldl}^{2} - 0.1044T_{ldl} + 10.43$ and $y = \,0.1084T_{ldl} + 21.98$

$$R_{elh} \times 10^{ - 11} = \,x\, \times \,\beta_{pd}^{2} \, + \,y\,\, \times \,\,\beta_{pd} \, + \,\,z$$

(47)

where $x\,\, = \,0.0001T_{ldh}^{2} - 0.1262T_{ldh} + 35.028$,$y\,\, = \, - 0.0001T_{ldh}^{2} + 0.1749T_{ldh} - 60.644$ and $z\, = \,2 \times 10^{ - 5} T_{ldh}^{2} - 0.0646T_{ldh} + 32.808$

$$R_{ell} \times 10^{ - 11} = \,x\beta_{pd} + y$$

(48)

where $x\, = \,3 \times 10^{ - 6} T_{ldl}^{2} - 0.002T_{ldl} + 0.0693$ and $y = \, - 0.0099T_{ldl} + 18.441$

$$R_{eqh} \times 10^{ - 12} = \,x\, \times \,\,\beta_{pd} \, + \,\,y$$

(49)

where $x\, = \,1 \times 10^{ - 7} T_{ldh}^{2} \, - \,0.0001T_{ldh} + \,0.0228$ and $y = \,2 \times 10^{ - 8} T_{ldh}^{2} - 8 \times 10^{ - 5} T_{ldh} + 1.1205$

$$R_{eql} \times 10^{ - 12} = x\beta_{pd} + y$$

(50)

where $x\, = \,5 \times 10^{ - 6} T_{ldl}^{2} - 0.0042T_{ldl} + 0.6008$ and $y\, = \,2 \times 10^{ - 6} T_{ldl}^{2} - 0.0043T_{ldl} + 9.3417$

Appendix 2

The predicted rotational speed and the pump torque of the HSLT and the LSHT drives are:

$$N_{mph} \,\, = \,\,\frac{{D_{p} \,\,N_{p} }}{{2\,D_{mh} }}\,\left( {1\,\, - \,\,\frac{{R_{vih} }}{{R_{vih} \, + \,2\,R_{pl} }}} \right)\,\, - \,\,\frac{{T_{ldh} }}{{2\,D_{mh}^{2} }}\,\left( {\frac{1}{{R_{vih} \, + \,2\,R_{pl} }}\,\, + \,\,\frac{1}{{R_{eqh} }}\,\, + \,\,\frac{1}{{R_{elh} }}} \right)$$

(51)

$$N_{mpl} \,\, = \,\,\frac{{D_{p} \,N_{p} }}{{D_{ml} }}\,\left( {1\,\, - \,\,\frac{{R_{vil} }}{{R_{vil} \, + \,R_{pl} }}} \right)\,\, - \,\,\frac{{T_{ldl} }}{{D_{ml}^{2} }}\,\left( {\frac{1}{{R_{vil} \, + \,R_{pl} }}\,\, + \,\,\frac{1}{{R_{eql} }}\,\, + \,\,\frac{1}{{R_{ell} }}} \right)$$

(52)

$$T_{pph} \,\, = \,\,N_{p} \,R_{pd} \,\, + \,\,\left( {\frac{{D_{p} }}{{D_{mh} }}} \right)\,\frac{{R_{pl} }}{{R_{vih} \, + \,2\,R_{pl} }}\,\left( {D_{p} \,D_{mh} \,N_{p} \,R_{vih} \,\, + \,\,T_{ldh} } \right)$$

(53)

$$T_{ppl} \,\, = \,\,N_{p} \,R_{pd} \,\, + \,\,\left( {\frac{{D_{p} }}{{D_{ml} }}} \right)\,\frac{{R_{pl} }}{{R_{vil} \, + \,\,R_{pl} }}\,\left( {D_{p} \,D_{ml} \,N_{p} \,R_{vil} \,\, + \,\,T_{ldl} } \right)$$

(54)

Appendix 3

The coefficients α ₁ through α ₉ of Eqs. (40) and (41) are given below:$a_{1} \,\, = \,\,\frac{{N_{p} }}{{2\,D_{mh} }}\,\left( {1\,\, - \,\,\frac{{R_{vih} }}{{R_{vih} \,\, + \,\,2\,R_{pl} }}} \right)$ $a_{2} \,\, = \,\,\frac{1}{{2\,D_{mh}^{2} }}\,\left( {\frac{1}{{R_{vih} \,\, + \,\,2\,R_{pl} }}\,\, + \,\,\frac{1}{{R_{eqh} }}\,\, + \,\,\frac{1}{{R_{elh} }}} \right)$; $a_{3} \,\, = \,\,\frac{{N_{p} }}{{D_{mh} }}\,\left( {\frac{{R_{pl} }}{{R_{vih} \,\, + \,\,2\,R_{pl} }}} \right)$; $a_{4} \,\, = \,\,N_{p}^{2} \,\left( {\frac{{R_{vih} \,R_{pl} }}{{R_{vih} \,\, + \,\,2\,R_{pl} }}} \right)$; $a_{5} \,\, = \,\,N_{p}^{2} \,R_{pd}$; $a_{6} \,\, = \,\,\frac{{N_{p} }}{{D_{ml} }}\,\left( {1\,\, - \,\,\frac{{R_{vil} }}{{R_{vil} \,\, + \,\,R_{pl} }}} \right)$; $a_{7} \,\, = \,\,\frac{1}{{D_{ml}^{2} }}\,\left( {\frac{1}{{R_{vil} \,\, + \,\,R_{pl} }}\,\, + \,\,\frac{1}{{R_{eql} }}\,\, + \,\,\frac{1}{{R_{ell} }}} \right)$; $a_{8} \,\, = \,\,\frac{{N_{p} }}{{D_{ml} }}\,\left( {\frac{{R_{pl} }}{{R_{vil} \,\, + \,\,R_{pl} }}} \right)$; $\quad a_{9} \,\, = \,\,N_{p}^{2} \,\left( {\frac{{R_{vil} \,R_{pl} }}{{R_{vil} \,\, + \,\,R_{pl} }}} \right)$

Appendix 4: Experimental test-rig

Figures 23 and 24 give the schematic and pictorial representations of the experimental test-rig of the hydrostatic drives and their specifications are indicated in Table 1.

Fig. 23

Experimental test-rig of the hydrostatic drives

Fig. 24

Pictorial representation of the experimental test-rig of the hydrostatic drives

Referring to Figs. 23 and 24, the main features of the experimental test-rig are as follows:

• 1. An electric motor (1) drives a variable displacement pump (2) at constant speed. The pump (2) supplies pressurized fluid to the bent axis hydro-motors M1, M2 for the HSLT drive and radial piston hydro-motor M3 for the LSHT drive.

• 2. The hydro-motors (5, 12) drive the pump (7) of the loading circuit.

• 3. The loading circuit provides mainly the viscous load on the hydro-motors (5, 12) that is made by adjusting the pressure setting of the proportional pressure relief valve (8) or displacement of the pump (7) of the loading circuit.

• 4. The signal voltages that varies from 0 to 10 V dc sent from the control panel varies the swash plate angle of the pumps (2, 7) and adjusts the set pressure of the relief valve (8). Thus, the load on the motor shaft is controlled.

• 5. The sensors along with the digital indicators are provided to record the parameters as pressure, flow, rotational speed and torque.

• 6. The fluid used in the experiment is of ISO 32 grade mineral oil, the viscosity, bulk modulus and the density of which are 0.025 Ns/m², 1.8 × 10⁹ N/m² and 850 kg/m³, respectively. By providing suitable oil cooler, the oil temperature was maintained at 50 ± 2 °C during experiment, and thus the viscosity of the fluid has been kept constant with reasonable accuracy.