This paper aims to determine the optimal design parameters for percussive drilling systems considering the bitrock interaction. First, the motion dynamics of a bit impacted by a dropped piston are modeled by impact stress propagation and a rockbreaking mechanism representing the penetration resistance coefficient and unloading constant. Next, the damping vibration behavior of the bit is investigated considering the impact duration and the rock loading/unloading condition. In addition, the proposed dynamics are simplified by adopting two dimensionless parameters representing the bitpiston mass ratio and the rockpiston stiffness ratio. Finally, the drilling efficiency, defined by the energy transmitted from the piston to the rock, is presented in terms of the proposed parameters. The use of optimal design parameters for percussive drilling systems improved the drilling efficiency. These results are applicable to the design and performance estimation of downthehole and tophammer systems.
Drilling equipment is the collective term used for machines that apply impact and rotation forces to drill (for the most part) surfaces and blastholes, and it is classified as tophammer drilling (THD), downthehole (DTH) drilling, and rotary drilling (RD) rigs, depending on the operating method (Figure
Drilling mechanisms of two types of percussive drilling system: (a) tophammer drilling and (b) downthehole drilling (modified from Song et al. [
Simply put, a percussive drilling mechanism utilizes the percussive energy resulting from the repeated impact of the drifter (THD rigs) or the DTH hammer (DTH rigs) and the feed force and rotation force that are transmitted to the drill bit through the drill rod. The energy generated from the repeated impacts is then converted into wave energy, which is transmitted to the rock via the drill bit. Finally, the drill bit, now with enough impact energy for drilling, cuts into and crushes the rock. The rate at which the impactgenerated energy in a percussive drilling system is transmitted (i.e., the drilling efficiency) is determined by complex effects such as drilling rod, coupling sleeve, the compressive strength of the rock, and interactions between the drill bit and the rock. Therefore, certain drilling methods are highly efficient, with high rates of penetration, when drilling soft rock (uniaxial compressive strength, UCS, < 20 MPa) or medium hard rock (UCS 50–120 MPa), but the efficiency decreases when drilling very hard rock (UCS > 200 MPa) [
There are numerous previous studies regarding drill bit, rock drilling, the transmission of impact energy, and drilling efficiency. Hustrulid and Fairhurst [
Chiang and Elias [
The analysis of behavior of drill bit should be performed for the design and manufacturing of a percussive drilling system with high drilling efficiency because the drilling efficiency and the range of rock fracturing depend on movement characteristics of drill bit during percussion and because drill bit also percusses the rock directly, meaning the close relationship with the delivery of percussion energy and drilling efficiency.
This study aimed to identify design parameters that could optimize the drilling efficiency in a percussive drilling system, while taking dynamic drill bitrock interactions resulting from the piston impact into consideration. Drilling dynamic models (i.e., dynamic models of the drill bit) were established by introducing drill bitrock interactions to determine the rockpenetrating properties of the bit. This was done using impact stress wave propagation theory, the penetration resistance coefficient, and the unloading constant in relation to the impacting piston and drill bit. The drilling dynamics was established considering the movement of the drill bit induced by piston impacts and the loading and unloading conditions resulting from the effects of the rock.
The drilling dynamics proposed here employ two dimensionless parameters: the first (
To that end, Section
The energy transmission efficiency via the impact of the percussive drilling system is examined in Section
Figures
Figure
Schematic rock fracture mechanism by percussive drilling (modified from Cho et al. [
The piston mass, length, crosssectional area, descending speed, density, and longitudinal wave velocity are designated as
The following equation expresses the motion of the drill bit resulting from the force applied to it by the piston [
According to the relation between the dynamic stress and velocity of a mass in an elastic body system, the velocity of the contacting end of the bit can be expressed as follows [
Typically, nearly all the percussion impact energy is converted into wave energy. The piston hitting the drill bit generates an incident stress wave (
The secondary incident stress wave in a percussive drilling system has been reported not to contribute to the crushing of rocks [
The interaction between the drill bit and rock (the forcepenetration relationship, Figure
Force versus penetration relationship representing the bit–rock interaction curve.
The duration of the incident stress wave
For the loading condition, we obtain the following equations [
For the unloading condition, the equations can be expressed as follows [
The response characteristics of a drill bit (i.e., the damped characteristics) can be under, critical, or overdamped given its motion equation, that is, (
When loading, the equation of motion for the drill bit is defined as follows:
When unloading, the drillbit equation of motion is defined by (
The dimensionless parameters
As explained earlier, the typical motion of drill bits involves four conditions. However, this study considers six conditions, as listed in Table
Expansion conditions for dynamic drillbit properties for loading, unloading, and stresswave duration,
Case no.  Initial conditions  



 


 
1 
 
2 
 
3 


4 


5 




6 






Table
In summary, in Cases 1 to 5 in Table
Numerical simulations on a dynamic model of drill bit properties were run for the six cases and used the dynamic drill bit properties during induced percussion (Section
Figure
Results of the motion response of the bit for
Case 2 (Figure
Case 5 (Figure
Overall, the longer the duration of
Dynamic drillbit properties for loading, unloading, and
Case no.  Conditions  Damping modes capable of reaching 




 
1 

Over  Over 
Over 
2 

Over  Over 
Critical 
3 

Over  Over 
Under 
4 

Critical  Critical 
Under 
5 

Under  Under 
Under 
6 




Under 
Under  Under 
In Section
In a percussive drilling system, the piston directly hits the drill bit at speed
The initial height
The efficiency,
Which can be expressed as follows through dimensional analysis:
The value
Moreover, for
The initial conditions are
Next, the displacement value
The efficiency of the percussive drilling systems for given
The results of simulations on the drill bitrock interaction model shown in Figure
Damping mode capable of reaching maximum rock fracture displacement
The critical damped mode has
The underdamped mode has
The special underdamped mode refers to the case where
The damped mode of each
Figure
State of reaching drill bit dimensionless penetration
Figure
Dimensionless time capable of reaching
The effect of initial condition on
Section A refers to
In examining
Given the steels generally used to make pistons, the effective range of
Figure
Drilling efficiency of percussive drilling systems with respect to
In Figure
The piston should have twice the mass of the drill bit (i.e.,
This study defined equations for the motion of a drill bit when struck by a piston and expanded the dynamic properties of the drill bit based on the conditions
A percussive drilling system accomplishes its work via the percussion impact of a piston. In the systems studied here,
The main purpose of this study was to examine the impact energy transmission rate and drilling efficiency in a percussive drilling system (Figure
The movement and response characteristics of bit during percussion process,
This study neglected the effects of the secondary incident stress wave and also the effect of buttons embedded in the drill bit. Additionally, for analytical simplification, the piston and drill bit were assumed to be of the same diameter and material, and a rectangular pulse with an incident stress wave of duration
This paper aimed to identify the optimal design parameters for percussive drilling systems by introducing a drill bitrock interaction model that could verify the bit’s motion during percussion and the resulting damping characteristics. The study analyzed drilling efficiency and drew the following conclusions.
Percussive drilling systems have six dynamic drill bit properties that can be expandable. This paper discussed the physical meaning of the dimensionless parameters
Drilling was most efficient in the interval 1
The results indicate that application of a pistontodrill bit mass ratio of 0.5 (i.e., a piston mass twice that of the drill bit mass) to the rocks whose stiffness corresponds to
The authors declare that there are no conflicts of interest.
This paper proposed six conditions for the dynamics of a drill bit struck by a piston impact, as summarized below. The damping conditions for the damping ratios and
First, for the overdamped condition of
Next, we examine the case where
Second, under critical damping where
In this case, assuming the normal state,
The following is the case where
In this case, bit displacement
The second condition of critical damping is defined as
The third condition is underdamping with
The following is the case where
In this case, the drill bit displacement
The third condition is the critically damped mode defined as
Next, the underdamped condition is where
The following case is where conversion is made to unloading after the drill bit reaches its maximum displacement, but the incident stress wave is sustained. Applying the conditions of
Last, this unloading condition is where the incident stress wave is resolved. When unloading the drill bit, using the conditions
In this case, drill bit displacement