Electromagnetically excited torsional vibration to rock drilling support

Abstract

During a serious underground incident the most important things are the lives of miners and the time necessary for the rescue team to find victims of the accident. The paper presents the concept of a new drilling system that uses torsional vibrations in the drilling process. In the article formulating mathematical models of a drilling rig is one of the tasks of the INDIRES (INformation Driven Incident RESponse) project implemented as a part of the European Research Fund for Coal and Steel. The INDIRES project is dedicated to the task of conducting a rescue operation after accidents in mines.

Keywords

Electromagnetic field finite element method FEM torque generator mathematical modelling

1. Introduction

The article presents the concept of a new drilling system that uses torsional vibrations excited electromagnetically in the drilling process. Formulating mathematical models of a drilling rig is one of the tasks of the INDIRES (INformation Driven Incident RESponse) project implemented as part of the European Research Fund for Coal and Steel in years 2017–2020. The INDIRES project is dedicated to the task of conducting a rescue operation after accidents in mines. One of the tasks is to develop a new drilling method that eliminates the disadvantages of impact drilling – exposure to landslide dumping. The use of torsional vibrations with frequencies close or equal to the natural frequency of the material to be worked on can be a safe drilling method. The advantage of torsional vibrations in the drilling process compared to hammer drilling or drilling without assistance, are reduced cutting forces and smaller transverse vibrations of the drill [1]. The transport of the developed material in this drilling technique using torsional vibrations is also facilitated. But torsional vibrations can also be undesirable, as is the case in deep hole drilling, e.g. in oil and gas mining [8,14]. The new drilling rig system consists of three electromechanical transducers: a torsional vibration generator, an induction torque converter [2] and a drive motor. Higher harmonics of the magnetic field in the air gap of the torsional vibration generator are used to create torsional vibrations. These harmonics are the result of a discrete distribution of the stator and rotor windings in the slots, so parameters such as the number of rotor cage bars and the number of pole pairs have a key impact on the amplitude of the generated torque. The electromagnetic torsional vibration generator described in this article generates torsional torque at several different frequencies as opposed to mechanical generators. An inductive torque converter transfers the main drive torque from the drive motor to the electromagnetic torsional vibration generator and drilling head, but also limits the propagation of torsional torque transfer towards the main drive motor. The new construction of the drilling rig exhibits the features of a mechatronic device due to the synergistic interaction of three different electromechanical transducers in the drilling process without hammering.

2. The theory. Principle of operation of drilling rig

The construction of a new drilling rig that uses torsional vibrations in the drilling process can be presented in a demonstrative way in the form of a block diagram shown in Fig. 1. The drilling rig consists of its drive system with three main components: main driving motor (MDM) [3], induction torque converter (ITC) [2], electromagnetic torsional vibration generator (TVG) [5,12].

Fig. 1.

Block schema representing drilling rig components. 1 – main driving motor, 2 – induction torque converter, 3 – electromagnetic torsional vibration generator, 4 – drilling head.

The drilling rig system can be divided taking into consideration the operating speed of its components due to the high-speed area and variable speed area. The main drive motor (MDM) works in the area of high speed, it generates the main drive torque for the cutting head and at the same time it drives the internal screw conveyor. The induction torque converter (ITC) operates between areas of large and variable speed and is responsible for the non-contact transfer of the drive torque for the torsional vibration generator (TVG) and cutting head. In the area of variable speed there operates the torsional vibration generator (TVG) coupled with the cutting head.

The torque flow diagram for the whole drilling rig is presented in Fig. 2. The main driving motor (MDM) delivers the fundamental driving torque T_eM, for indirect drive of the cutting head by the torque component T_eC and direct drive of the internal screw conveyor by the torque component T_eS. The internal screw conveyor is responsible for the transfer of the mined rock from the cutting head across the whole drilling rig, through the internal channel – all the drilling rig components are made as a hollow shaft. The internal conveyor rotates with the same speed as the main driving motor (MDM). The torque component T_eC, which is an input torque for the induction torque converter (ITC), is transferred by ITC, but the output torque T_ed1 is lower than T_eC because a part of torque T_ev1 is consumed for the ventilation and cooling system of ITC.

Fig. 2.

Torque flow in drilling rig.

The output torque T_ed₁ of ITC becomes the input torque for the electromagnetic torsional vibration generator (TVG). TVG produces two additional torque components: T_eg₁ and T_eg₂. The first one is a residual torque with asynchronous nature (not alternating) – it helps drive the cutting head in a desired direction. But the other one is an alternating torque which forces the cutting head to the torsional vibration, perpendicular to the rock surface. Finally, the torque T_eH exerted on the cutting head consists of three components, two of a continuous nature T_ed₁and T_eg₁, and one alternating T_eg₂. Such composition of torques gives a very wide range of possibilities to control the drilling process. It ensures, independently of the driving torque T_ed₁, settings of amplitudes and frequencies of the alternating torque T_eg₂. Even when the cutting head is locked, after transporting the mined material by the internal screw conveyor, all T_eM torque may be transferred by ITC to the cutting head. The main driving motor (MDM) will never be locked, because ITC transfers the torque in a contactless manner. That gives a chance to unlock the cutting head by changing frequencies and amplitudes of the alternating torque T_ed₂ generated by TVG. Locked cutting head states during a drilling process may happen very often and all the drilling rig components may affect a strong current and thermal load. It is necessary to show a power flow diagram with indication of power losses sources. Such a flow diagram for the drilling rig is presented in Fig. 3.

Fig. 3.

Power flow in drilling rig.

As indicated in Fig. 3, the input power of MDM is spread over power P₁ transferred to ITC and power losses ΔP_cu1 and ΔP_m1, which represent respectively losses generated by flowing currents in motor windings and mechanical losses arising in bearings and the internal screw conveyor. In a similar way the power flow in ITC may be expressed: the input power P₁ is spread into power P₂ transferred to TVG and power losses in the windings ΔP_cu2 and mechanical power losses ΔP_m2 in bearings and the ventilation (cooling) system. When the cutting head is locked, all input power P₁ is dispersed into power losses in windings ΔP_cu2, resulting in heat generation and temperature rising, which should be dispersed by the cooling system. The maximal torque is transferred from MDM and a high mechanical tension is applied on the locked TVG and cutting head. TVG is adding an alternating torque – power P_avr, which periodically increases and decreases the tension exerted by the cutting head on the mined rocks – it helps to unlock the cutting head. The continuous power P_as component superposes an additional constant tension over the mined rocks. The mechanical power losses ΔP_m31 and ΔP_m32 of TVG are relatively small, and they are related to the incoming power P₂ and P_avr, P_as respectively. The power losses ΔP_cu32 in the windings of TVG are related directly to the input powers components P_avr and P_as. The power losses ΔP_cu31 in the windings of TVG are related indirectly to the input power P₂ and to the angular rotation speed of the TVG shaft; they appear only when the stator windings of TVG are supplied. In the next chapter the mathematical models of all the drilling rig components are shown.

3. The methods. Mathematical modelling of drilling rig components

To formulate a mathematical model of each component of the drilling rig, standard Kirchhoff and Lagrange methods were used. These mathematical models were supplemented by the results of the calculation of electromagnetic fields distribution in the air-gap of an induction torque converter. For this purpose, the FEM methods were used. The final models of all the components will be presented as a set of ordinary differential equations, convenient for fundamental properties of drilling rig investigations. In Section 3.1 the mathematical model of the electromagnetic torsional vibration generator (TVG) is shown. The mathematical models of the induction torque converter (ITC), the main drive motor (MDM) and drilling rig kinematic chain are presented in Sections 3.2 and 3.3 respectively.

3.1. Mathematical model of electromagnetic torsional vibration generator

It is possible to modify the construction of a squirrel cage induction machine that will generate torsional torque with very large amplitudes (comparable to the pull out torque value of the machine). It turns out that in some cases of mutual relation of the number of rotor slots and the number of pole pairs, the use of straight rotor slots leads to the generation of torsional torque with high amplitudes – sufficient to determine the natural frequency of the propulsion systems [4–6]. The induction machine modified in this way will be referred to as the electromagnetic torsional vibration generator (TVG). This machine may be equipped with two sets, separately wound and separately placed stator 3-phase windings. Such a set of stator windings allows us to influence the values of an asynchronous (not alternating) torque generated by TVG, by setting the angular shift between sets of windings. In our further consideration we assume a single set of stator windings. The rotor of TVG consists of cage windings with straight rotor U-shaped bars (in cross section) [4]. The rotor of TVG is equipped with a hollow shaft providing space for the internal conveyor. A thorough analysis of the mechanism of generating torsional torque indicates that they can have their synchronous speeds (at which they assume constant values), in three different regions of induction machine operation (i.e. in regions of motor, brake and stopped rotor operation). The torsional torque can therefore be divided into three groups, and the division criterion can be the range of machine operation at which the alternating moments change into a constant value (i.e. they pass into synchronous moments). Thus, we are dealing with a group of torsional torque in the field of engine operation (engine group), in the field of brake operation (brake group) and with the rotor stopped (starting group). Whether all or some groups of torsional torque will be present in a given machine depends solely on the number of pole pairs, the number of stator and rotor slots and the type of stator winding. Such relations of rotor slots and the number of pole pairs are possible, at which only torsional torque belonging to one group (starting, motor or braking) as well as to all these groups will be generated. The mathematical model expressed in the natural 3-phase coordinate system for the stator and Q_r-phase rotor, in the case of Q_r = 28 rotor bars for rotor windings, gives a set of 31 first order ordinary differential equations. The number of equations may be reduced by transforming the set of equations into a new 2-phase 𝛼𝛽-coordinate system fixed with a stator and 2-phase dq-coordinate system fixed with a rotor [6], but this dq-coordinate system rotates with the TVG rotor. The mathematical model of the electromagnetic part of TVG, taking also into consideration higher magnetomotive space force (MMF) harmonics, within a new 𝛼𝛽-dq system (this is a combination of the previously mentioned 𝛼𝛽 and dq coordinate systems) can be expressed in the following matrix form: $\begin{eqnarray}\displaystyle {\displaystyle \frac{d}{dt}}\left[\begin{array}{@{}c@{}}\mathbf{i}_{s}^{{\alpha}{\beta}}\\ \mathbf{i}_{r}^{dq}\end{array}\right]\text{} & =\text{} & \displaystyle \left[\begin{array}{@{}cc@{}}\mathbf{L}_{{\sigma}s}^{{\alpha}{\beta}}+\mathbf{M}_{ss}^{{\alpha}{\beta}} & \mathbf{M}_{sr}^{{\alpha}{\beta}dq}({\vartheta})\\ \mathbf{M}_{sr}^{{\alpha}{\beta}dq}({\vartheta})^{T} & \mathbf{L}_{{\sigma}r}^{dq}+\mathbf{M}_{rr}^{dq}\end{array}\right]^{-1}\nonumber\\ \displaystyle \text{} & \text{} & \displaystyle \cdot \left(\left[\begin{array}{@{}c@{}}\mathbf{u}_{s}^{{\alpha}{\beta}}\\ 0\end{array}\right]-\left(\left[\begin{array}{@{}cc@{}}\mathbf{R}_{s}^{{\alpha}{\beta}} & 0\\ 0 & \mathbf{R}_{r}^{dq}\end{array}\right]+p{\omega}_{m}\left[\begin{array}{@{}cc@{}}0 & {\displaystyle \frac{\partial }{\partial {\vartheta}}}\mathbf{M}_{sr}^{{\alpha}{\beta}dq}({\vartheta})\\ {\displaystyle \frac{\partial }{\partial {\vartheta}}}\mathbf{M}_{sr}^{{\alpha}{\beta}dq}({\vartheta})^{T} & 0\end{array}\right]\right)\left[\begin{array}{@{}c@{}}\boldsymbol{ i}_{s}^{{\alpha}{\beta}}\\ \mathbf{i}_{r}^{dq}\end{array}\right]\right)\end{eqnarray}$ (1) where $\mathbf{i}_{s}^{{\alpha}{\beta}}$ , $\mathbf{i}_{r}^{dq}$ – vector of stator and rotor currents in 𝛼𝛽 and dq coordinate systems, $\mathbf{u}_s^{\alpha\beta}$ – vector of generator supply voltages in 𝛼𝛽 coordinate system, $\mathbf{M}_{ss}^{{\alpha}{\beta}}$ – matrix of stator self-inductances, $\mathbf{L}_{{\sigma}s}^{{\alpha}{\beta}}$ – matrix of stator leakage inductances, $\mathbf{M}_{sr}^{{\alpha}{\beta}dq}({\vartheta})$ – matrix of mutual inductances, $\mathbf{M}_{rr}^{dq}$ – matrix of rotor self-inductances, $\mathbf{L}_{{\sigma}r}^{dq}$ – matrix of rotor leakage inductances, $\mathbf{R}_{s}^{{\alpha}{\beta}}$ – matrix of stator resistances, $\mathbf{R}_{r}^{dq}$ – matrix of rotor resistances, 𝜗 – angular rotor displacement, ω_m – angular speed of the rotor, p – number of pole pairs. The electromagnetic torque generated by TVG can be written as follows: $\begin{eqnarray}\displaystyle T_{e}=\mathbf{i}_{s}^{{\alpha}{\beta}^{T}}{\displaystyle \frac{\partial }{\partial {\vartheta}}}\mathbf{M}_{sr}^{{\alpha}{\beta}dq}({\vartheta})\mathbf{i}_{r}^{dq}. & & \displaystyle\end{eqnarray}$ (2) The simplest possible variant of a mathematical model of TVG expressed by Eqs ((1)) and ((2)) allows us to analyse only the selected MMF space harmonics [4,11,12] for shaping the amplitudes and frequencies of the torsional (pulsating) torque. For the following combination of parameters, like p = 2, Q_r = 28, the set of MMF space harmonics (in general an infinite set) contains harmonics with orders: p, 13p, 29p, 41p, 43p… ect. [5,12]. A characteristic feature of such a mathematical model is also generation, apart from the asynchronous torque, a torsional (pulsating) torque [4–7,11,12] generated by the pairs of the following harmonics $\{p,13p\}$ , $\{p,29p\}$ , $\{p,41p\}$ , $\{p,43p\}$ . The relation describing frequencies of the torsional (pulsating) torque versus the angular rotating speed of the TVG rotor can be presented in the form of a so-called torque – speed characteristic, an exemplary characteristic is presented in Fig. 4.

Fig. 4.

Torque-speed charateristics of pulsating torque generated by TVG.

The torque-speed characteristics shown in Fig. 4 can be expressed in the following formulas: $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle f_{({\nu},{\rho})}=\left|{\displaystyle \frac{{\rho}\pm {\nu}}{2{\pi}}}{\Omega}_{m}\mp 2f_{0}\right|\end{eqnarray}$ (3) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle f_{({\nu},{\rho})}=\left|{\displaystyle \frac{{\rho}\pm {\nu}}{2{\pi}}}{\Omega}_{m}\right|\end{eqnarray}$ (4) where 𝛺_m – angular speed of generator shaft (in steady state), f₀ – frequency of supply network, 𝜌, 𝜈 – orders of MMF space harmonics in air – gap producing chosen torsion torque. The sign plus/minus in Eqs (3) and (4) depends on the rotation direction of MMF space harmonics [4–6,11,12].

3.2. Mathematical model of induction torque converter

The induction torque converter is an electromagnetic device consisting of two main components [2]: excitation circuit – built from two disks containing sets of permanent magnets, forming a ring close to the external edge of a disk, receiving circuit – built from three phase windings, forming a disk inserted between the disks of the excitation circuit. The main task of the induction torque converter is to transfer the external torque (power) without mechanical contact. The mathematical model of ITC can be formulated in two steps: step 1 – in this step it is necessary to calculate the averaged values of the magnetic flux density in the air-gap, this result will be needed to calculate the so-called induced voltage and torque coefficient, step 2 – in this step the partial differential equation will be formulated for winding of the receiving circuit formulated as the so-called circuit model. At the beginning of step 1 the geometry of the exiting circuit was implemented in COMSOL Multiphysics 3.5 program. The implemented geometry was limited to one quarter part of the whole geometry due to symmetry features, as it is shown in Fig. 5.

Fig. 5.

Quarter part of geometry of excitation circuit of induction torque converter. 1 – denotes magnetic yokes of excitation circuit, 2 – denotes permament magnets, 3 – denotes air-gap.

In Table 1 there are summarized basic geometrical dimensions of the induction torque converter.

Table 1

Fundamental dimension of ITC

No.	Name of parameter	Symbol	Value
1	Internal radius of permament magnets	r ₁	53 mm
2	Thickness of permament magnets	h _pm	6 mm
3	Length of permament magnets	l	30 mm
4	Number of permament magnets	—	16
5	Air-gap length	δ	15 mm
6	Yoke thickness	h _yoke	3 mm

After generating the mesh, the mathematical model of ITC consists of 47,938 tetrahedrons and it gives the total number of degrees of freedom equal to 68,124, with 10,618 boundary elements. The calculated module of magnetic flux density in the middle of the air-gap is presented in Fig. 6, as well the generated mesh. The maximal value of the module of magnetic flux density equals 0.585 T. The calculated values of the magnetic flux density B_z component were averaged in the volume of one side of winding of the receiving circuit at a different angular position. The resultant curve is presented in Fig. 7 and this distribution will be used for calculating the induced voltage and torque in the circuit model of excitation circuit.

Fig. 6.

Colour map presenting modulus of magnetic flux density distribution in middle of air-gap length in quarter part of ITC (left) and its mash wireframe (right).

Fig. 7.

Averaged value of magnetic flux density B_z component.

Only the four harmonics have significant values, the average amplitude value of the fundamental harmonics is 0.482 T, the third harmonics – −0.058 T, the fifth harmonics – 0.0066 T and the seventh harmonics – −0.0014 T. It is possible to reconstruct the plot of the magnetic flux density using only these four harmonics. For this purpose, we used the combination of transformation matrices consisting of rotation around z-axes and transformation from the 2-phase into the 3-phase coordinate system, as follows: $\begin{eqnarray}\displaystyle \begin{array}{@{}l@{}}\left[\begin{array}{@{}c@{}}B_{1}\\ B_{2}\\ B_{3}\end{array}\right]=\sqrt{{\displaystyle \frac{2}{3}}}\left[\begin{array}{@{}ccc@{}}\cos 0 & \sin 0 & {\displaystyle \frac{1}{\sqrt{2}}}\\ \cos {\displaystyle \frac{2{\pi}}{3}} & \sin {\displaystyle \frac{2{\pi}}{3}} & {\displaystyle \frac{1}{\sqrt{2}}}\\ \cos {\displaystyle \frac{4{\pi}}{3}} & \sin {\displaystyle \frac{4{\pi}}{3}} & {\displaystyle \frac{1}{\sqrt{2}}}\end{array}\right]\left[\begin{array}{@{}ccc@{}}\cos {\vartheta} & -\sin {\vartheta} & 0\\ \sin {\vartheta} & \cos {\vartheta} & 0\\ 0 & 0 & 1\end{array}\right]\left[\begin{array}{@{}c@{}}B\\ 0\\ 0\end{array}\right]\\ {\vartheta}=2{\pi}\int f_{0}dt\end{array} & & \displaystyle\end{eqnarray}$ (5) where B – amplitude of harmonics, 𝜗 – rotation angle, f₀ – rotating frequency. Equation (5) will be used as many times as the magnetic flux density harmonics are taken into consideration, in each case it is necessary to change the amplitude – B and angle 𝜗 – should be multiplied by the harmonics order. The receiving winding is considered as the 3-phase, and any single-phase circuit consists of inductances, resistances and induced voltage.

The system of the 3-phase winding can be presented in the equation: $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle {\displaystyle \frac{d}{dt}}\mathbf{i}_{k}=\mathbf{L}^{-1}(-\mathbf{R}\mathbf{i}_{k}-({\omega}_{1e}-{\omega}_{2r})\mathbf{k}_{ek}({\vartheta}))\end{eqnarray}$ (6) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle T_{epm}=-\mathop{\sum }_{k=1}^{3}i_{k}k_{tk}({\vartheta})\end{eqnarray}$ (7) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle k_{ek}({\vartheta})=k_{tk}({\vartheta})=N_{k}B_{k}({\vartheta})(2r_{1}l+l^{2})\end{eqnarray}$ (8) where L – 3 × 3 full square matrix of inductances of windings, R – 3 × 3 diagonal matrix of windings resistances, i_k – 3 × 1 vector of phase currents, ω_1e, ω_2r – angular speeds of receiving circuit and of excitation circuit, 𝜗 – angular displacement of excitation circuit, k_ek – 3 × 1 vector of coefficient of induced voltage, k_tk – coefficient of torque, N_k – number of winding turns, B_k(𝜗) – synthetized magnetic flux distribution.

3.3. Mathematical model of main driving motor and kinematic chain of drilling rig

As the main drive source of a drilling rig there can be used an induction squirrel cage motor with a hollow shaft. The equation as an ordinary differential equation of a simple induction motor can be derived from Eqs ((1)) and ((2)), taking into consideration only the fundamental MMF space harmonics. The kinematic chain of a drilling rig consists of five lumped inertial masses representing the mass moment J₁ of MDM rotor [3], the mass moment of inertia of the excitation circuit J_2e (in the form of a disc), the receiving circuit J_1r (in the form of a disc), the mass moment of inertia of the TVG rotor J₂ and the drilling head J₃ mass moment of inertia. The kinematic chain is presented in Fig. 8. In this figure there are indicated stiffnesses of shafts k₁, k₂ and k₃, rotating speeds of lumped inertial masses ω₁, ω_1e, ω_2r, ω₂ and ω₃ and also the appropriate torque.

Fig. 8.

Kinematic chain of drilling rig.

The mathematical model of the kinematic chain of a drilling rig presented in Fig. 8, according to its mechanical part, was formulated using the standard Lagrange method. This model was formulated under the assumption of rigidity of the rotors of all the components and flexibility of the linking shafts. The following equations present the mathematical model of the drilling rig: $\begin{eqnarray}\displaystyle \left.\begin{array}{@{}l@{}}J_{1}\ddot{{\vartheta}}_{1}+k_{1}({\vartheta}_{1}-{\vartheta}_{1e})=T_{1}\\ J_{1e}\ddot{{\vartheta}}_{1e}+k_{1}(-{\vartheta}_{1}+{\vartheta}_{1e})=-T_{epm}\\ J_{2r}\ddot{{\vartheta}}_{2r}+k_{2}({\vartheta}_{2r}-{\vartheta}_{2})=T_{epm}\\ J_{2}\ddot{{\vartheta}}_{2}+k_{2}(-{\vartheta}_{2r}+{\vartheta}_{2})+k_{3}({\vartheta}_{2}-{\vartheta}_{3})=T_{2}\\ J_{3}\ddot{{\vartheta}}_{3}+k_{3}(-{\vartheta}_{2}+{\vartheta}_{3})=T_{3}\end{array}\right. & & \displaystyle\end{eqnarray}$ (9) where 𝜗₁, 𝜗_1e, 𝜗_2r, 𝜗₂, and 𝜗₃ – represent angular displacement of appropriate inertial masses.

4. New results. Experimentation with the new drilling rig

In Fig. 9 there is presented the implemented in Matlab/Simulink mathematical model of all drilling rig components, such as: the torsional vibration generator (TVG – denoted by number 5), the induction torque converter (ITC – denoted by number 3), the main driving motor (MDM – denoted by number 1) [3] and the model of a kinematic chain (denoted by number 4).

Fig. 9.

Block schema of drilling rig mathematical model implemented in Matlab/Simulink.

Power supply to the main driving motor is denoted by number 2 in Fig. 9, whereas power supply to the torsional vibration generator is denoted by 6. The MDM can be supplied from the 3-phase network or PWM inverter, but TVG is supplied from the PWM inverter. The load acting on the cutting/loading head is represented by three step functions – denoted by number 7 in Fig. 9. This mathematical model allows us to investigate transient states occurring in a drilling rig during the start and after a load change. It is possible to change the power supply frequency of TVG and change the output torque frequencies amount. In Fig. 10 there is presented an exemplary drilling test made with the help of the previously manufactured within the project [6] torsional vibration generator in KOMAG Institute of Mining Technology (the INDIRES project participant with headquarters in Gliwice, Poland) laboratory facility. In this picture the region denoted by 1 represents the drilling process supported by the torsional vibration, region 2 represents drilling without the torsional vibration support. More effective drilling was observed at the rotating speed near 425 rpm and with the torsional vibration support. The load of the drilling head was simulated by a direct interaction over torsional vibration generator, gradually increases from 10, 20–40 Nm for time periods 2–4 s. In Fig. 11 there is presented the rotating speed of TVG under a load change. Finally, the rotating speed of TVG stabilizes near 425 rpm. The torque generated at this rotating speed and the same frequency of power supply as in the real experimentation (equal to 41.5 Hz) is presented in Fig. 12. As we can observe, the amplitudes of torsional vibration increase as the rotating speed decreases. To check the number of harmonics of the torsional vibration torque, the last 1 s of the torque plot presented in Fig. 12 was analyzed by FFT. The results of the FFT analysis are presented in Fig. 13. The number of harmonics of the torsional vibration torque for the last 1 s of the load torque is seven in a wide spectrum up to 1250 Hz, but significant due to the values of the torque amplitude being only up to 500 Hz.

Fig. 10.

Speed of drilling head (red line) and sandstone rock penetration (green line), when TVG is operating (1), when only MDM is operating (2). Results obtained from real measurements at KOMAG’s laboratory facility.

Fig. 11.

Speed of drilling head under different load – simulation results.

Fig. 12.

Torque generated by TVG under different load – simulation results.

Fig. 13.

FFT from the last 1 s of electromagnetic torque generated by TVG – simulation results.

Fig. 14.

Range of change of torque harmonics generated by TVG under rotating speed change within 400–450 rpm – simulation results.

In Fig. 14 there is presented the result of torsional torque frequencies change during the experiment of drilling process. In the experiment a torsional generator and typical drill bit were used for drilling in sandstone (a rock with high hardness, 6–8 in the Mohs scale [16,17]). The red lines, within the yellow rectangle, show how the frequencies of harmonics of the torsional torque change during the experiment.

5. Summary

The concept of using electromagnetically excited torsional vibrations in the drilling process was originally analyzed using numerical methods. The model of the motor – induction torque converter – a torsional vibration generator system, built in the MATLAB environment, allowed us to simulate the operation of the drilling system.

The mathematical model of the drilling rig allows testing its properties under various operating conditions including loads, with different power supply variants. The drilling rig is powered from the generator and the drive motor. Taking into account the dependence of the generated torsional torques on the frequency of the voltage supplying the generator and the rotor speed, we obtain wide possibilities of setting both the amplitude and, above all, the frequency of the torsional torque. The frequency of the torsional torque can be maintained at the desired level regardless of changes in the rotational speed of the drilling head, which is only a matter of proper power supply and control. The formulation of a dedicated power supply and control system will constitute a further stage of research work. It is possible for complex drilling system consisted with combination of rotary motion and longitudinal vibration or longitudinal-torsional vibration developing the successful working control system [13,15]. We hope that for presented in this article drilling rig idea similar method may be used [15].

As part of the experimental work, sandstone walls were drilled. The obtained results initially confirmed the correctness of the operation of the numerical model and the concept of using torsional vibrations in the drilling process.

The real experiment was simulated using formulated mathematical models of all drilling rig components. As can be seen at a lower rotational speed (around 425 rpm), the actual test bench was drilled faster than at a higher rotational speed (around 450 rpm). The simulation experiment carried out and the results presented in Fig. 12 explain why this happened – at a lower rotational speed, the generator generates torsional torque of greater amplitudes. Moreover, the lower rotational speed also means torsional torque with a lower frequency, which in this case could have been closer to the natural frequency of the rock being drilled. Figure 14 shows the range of frequency changes of the generated torsional torque at rotational speed changes in the range of 400–450 rpm. Torsional torque frequency change took place between the following ranges: 717–810 Hz, 560–630 Hz, 404–450 Hz and 157–180 Hz.

Improvement of the model and optimization of the system require further theoretical and experimental work, including the torsional vibration generator, induction torque converter and the drilling tool itself.

Footnotes

Acknowledgements

Scientific work financed from financial resources for science in the years 2017–2020 granted for the implementation of an international co-financed project. This project has received funding from the Research Fund for Coal and Steel under grant agreement no. 748632 (acronym INDIRES).

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, Stone in Architecture: Properties, Durability, Springer Science & Business Media, 2011.