A method for calculating and analyzing drilling of a diamond-impregnated drill bit

Abstract

This invention provides a calculation and analysis method for impregnated diamond drill bits, belonging to the technical field of impregnated diamond drill bits for geological drilling. The method includes the following steps: obtaining drill bit parameters and rock parameters; based on engineering practice, obtaining parameters relating the drill bit's mechanical drilling speed to the drilling pressure per unit area; obtaining parameters relating the drill bit's life to the footage per revolution; establishing a calculation model for the footage per revolution; determining the equivalent depth of rock breaking per diamond grain; constructing a parameter curve function relationship on the same coordinate system; and determining... δ , ε , ε δ and F The interrelationships between these parameters are determined through efficient drilling calculations using impregnated diamond drill bits. Based on engineering practice, this invention obtains parameters related to the feed per revolution (PDR) and drill pressure per unit area, and establishes a calculation model for the relationship between PDR and drill bit parameters, drilling parameters, and rock parameters. By optimizing and improving drill bit and drilling parameters, the PDR can be calculated and determined, thereby increasing both PDR and mechanical drilling speed.

Claims

1. A method of analysis of drilling with impregnated diamond bits, characterized in that: The method includes the following steps: Step 1: Obtain drill bit parameters and rock parameters, and based on engineering practice, obtain the relationship parameters between drill bit mechanical drilling speed and drilling pressure per unit area, and the relationship parameters between drill bit life and footage per revolution; Step 2: Establish a calculation model for the advance per drill bit revolution; Step 3: Determine the equivalent rock-breaking depth of each diamond penetrating the rock; Step 4: Drill pressure per unit area on the same coordinate system. F The x-axis represents the advance per revolution. δ, Coefficient of variation of contact area between diamond and rock ε and ε δ Establish a y-axis as the vertical axis. ε δ - F straight line, δ - F curve, ε - F Determine the relationship between the curve functions. δ , ε , ε δ and F The interrelationship between them; Step 5: Calculation and Determination of High-Efficiency Drilling with Impregnated Diamond Bits. After obtaining relevant drilling parameters for impregnated diamond bits through engineering practice, it is necessary to optimize and improve the bit parameters or drilling parameters. The specific process for determining the relevant parameters is as follows: First, determine the interrelationships between the parameters; second, increase the feed per revolution. δ, Third, improve the lifespan of impregnated diamond drill bits. H Fourth, ensure that the impregnated diamond drill bit is self-sharpening to prevent the diamond from being polished. Fifth, pursue higher advance per revolution in deep hole drilling. δ This helps to prevent the lifespan of the drill bit from being reduced.

2. The drilling calculation and analysis method for impregnated diamond drill bits according to claim 1, characterized in that, The specific process of step 1 is as follows: Step 1.1: Based on engineering practice, obtain the relevant parameters of the mechanical drilling rate of impregnated diamond drill bits. Under the same conditions of encountering rock and rotating speed n, use different pressure per unit area. F 1. F 2. Drilling depth to obtain the corresponding hourly efficiency. v 1. v 2. Drilling pressure per unit area F 1. F The value range of 2 should ensure that the impregnated diamond drill bit can operate normally, and that the diamond does not fall out abnormally. F 2 and F The ratio of 1 should be controlled between 1.00 and 1.20; The advance per revolution δ of a diamond-tipped drill bit is calculated using the following formula: ； In the formula, δ is the footage per revolution, v is the drill bit hourly efficiency, and n is the drill bit rotation speed; Step 1.2: Based on engineering practice, obtain the parameters relating the lifespan of impregnated diamond drill bits to the depth per revolution. Under essentially the same rock conditions, using impregnated diamond drill bits with identical parameters from the same batch, and at essentially the same rotational speed... n and different drilling pressure per unit area F 1. F 2. F 3. F 4. Drilling depth to obtain the corresponding average hourly efficiency. v 1. v 2. v 3. v 4. Obtain the corresponding drill bit life. H 1. H 2. H 3. H 4. Calculate the corresponding average advance per revolution. δ 1. δ 2. δ 3. δ 4; Drilling pressure per unit area F 1. F 2. F 3. F 4. To meet the requirement of obtaining the average advance per revolution δ 1 = 0.35 d ~0.4 d , δ 2 = 0.4 d ~0.45 d , δ 3 = 0.45 d ~0.5 d , δ 4 = 0.5 d ~0.6 d Drilling pressure per unit area F The value of 4 satisfies the condition of abnormal diamond detachment, and also affects drill bit life. H 4< H 3.

3. The drilling calculation and analysis method for impregnated diamond drill bits according to claim 1, characterized in that, The specific process of step 2 is as follows: advance per revolution δ Determined total number of diamonds per revolution penetrating the rock N Calculate using the following formula: ； In the formula: N The number of diamond grains that penetrate the rock per revolution. S C The contact area between the drill bit lip and the rock. δ For each revolution, the advance is 1 inch. C Diamond concentration, d The average diamond particle size; To make the drill bit's torque shear force equal to the frictional resistance, the drilling pressure... P The combined force of the torque and shear force determines the number of diamond particles that penetrate the rock per revolution. N Calculate using the following formula: ； In the formula: This is the resultant force coefficient of drilling pressure and torque shear force; ； f Let be the coefficient of friction between the drill bit and the rock. P For drill bit pressure; ； F The drilling pressure per unit area of ​​the drill bit. P K For the indentation hardness of diamond in rocks, S d This refers to the area of ​​contact between each diamond and the rock. ； h The equivalent depth to which each diamond cuts into the rock; By equivalence between equations (2-1) and (2-2), we obtain the advance per revolution. δ Calculation formula: ； make: ； In the formula: ε This is the coefficient of variation of the contact area between diamond and rock. S dS The equivalent surface area of ​​each diamond compression core that cuts into the rock in contact with the fractured rock. ； ； h S The equivalent depth to which each diamond breaks through the rock; Substituting equations (2-4), (2-7), and (2-8) into equation (2-6), we obtain the advance per revolution. δ Calculation formula: 。 4. The drilling calculation and analysis method for impregnated diamond drill bits according to claim 3, characterized in that, The specific process of step 3 is as follows: The equivalent depth of rock breaking per diamond grain penetrating the rock h S It is based on the average volume of rock broken per revolution of each diamond penetrating the rock. q S Average rock cutting distance per drill revolution L r Calculate the average rock-breaking area per revolution of each diamond grain penetrating the rock. A S Then establish a diameter of d Height is h S The arc area of ​​the circle A Sr The calculation formula, then let A Sr = A S Calculate the equivalent depth of rock fracture for each diamond grain penetrating the rock. h S ; The volume of rock broken per revolution of the drill bit Q r Calculate using the following formula: ； In the formula: Q r This represents the volume of rock broken per drill revolution. D h The outer diameter of the drill bit. d h The inner diameter of the drill bit; The number of diamond grains per revolution penetrating the rock, as given by equation (2-1). N The determined average volume of rock broken per revolution per diamond penetrating the rock. q S Calculate using the following formula: ； In the formula, q S The average volume of rock broken per revolution per diamond penetrating the rock, and the average rock-breaking area per revolution per diamond penetrating the rock. A S Calculate using the following formula: ； ； In the formula, A S This represents the average rock-breaking cutting area per revolution of each diamond grain penetrating the rock. L r This represents the average distance the diamond cuts the rock per revolution. Diameter d Height is h S The area of ​​the arc-shaped bow A Sr Calculate using the following formula: ； A Sr For diameter is d Height is h S The area of ​​the arc-shaped curve, α S For diameter is d Height is h S The half-angle of the included arc at the center, in radians; Since equation (3-5) is equal to equation (3-3), that is... A Sr = A S The approximation method is used to obtain α S The equivalent depth of rock breaking per revolution of each diamond grain cutting into the rock. h S Calculate using the following formula: 。 5. The drilling calculation and analysis method for impregnated diamond drill bits according to claim 3, characterized in that, The specific process of step 4 is as follows: Step 4.1: Establish ε δ - F The linear function, rewritten from equation (2-10), is: ； ； In the formula, K εδ for ε δ - F Slope of a linear function ε δ and F The relationship is a straight line passing through the origin of the coordinate system; Step 4.2: Establish δ - F Curve function, advance per revolution δ With drilling pressure per unit area F It improves with the increase, and advances the foot per revolution. δ The increase ratio is greater than the drilling pressure per unit area. F Increase the multiplier, δ and F The relationship is a curve passing through the origin of the coordinate system; make δ - F The curve function is: ； a is δ - F The coefficients of the curve function are determined by engineering practice parameters, where m is... δ - F The exponent of the curve function is determined by parameters from engineering practice; Based on engineering practice ( δ 1, F 1), ( δ 2, F 2) Two points with coordinate parameters, δ - F The exponent m of a curve function is calculated using the following formula: ； δ - F The coefficient 'a' of the curve function is calculated using the following formula: ； Step 4.3: Establish ε - F The curve function, by substituting equation (4-3) into equation (4-1), yields... ε - F Curve function: ； ε along with F The increase and decrease, when F When it approaches 0, then ε Approaching infinity, when F When it approaches infinity, then ε Approaching infinity, ε and F The relationship is that the curve does not intersect with either the vertical or horizontal coordinates; Step 4.4: Analysis δ , ε , ε δ and F Relationship within the same coordinate system δ - F curve and ε δ - F Among the critical parameters for the intersection of straight lines, δ - F curve and ε δ - F Since all lines pass through the origin, they must intersect at some point, and the intersection point must satisfy the following condition: ε δ = δ Then there must be ε = 1.0, the fixed-point parameters are called critical parameters, and the corresponding parameters are marked with the subscript L, i.e. F L , δ L , ε L =1.0, and has ; δ - F curve and ε - F Among the parameters of the intersection point of the curves, δ - F curve and ε - F If curves intersect at a certain point, the intersection point must satisfy... ε = δ The fixed-point parameters are called intersection parameters, and the corresponding parameters are marked with the subscript J, i.e. F J , δ J = ε J , and have ; ε - F curve and ε δ - F Among the far-crossing parameters of intersecting straight lines, ε - F curve and ε δ - F If two straight lines intersect at a certain point, the intersection point must satisfy the following condition: ε δ = ε Then there must be δ =1.0, the fixed-point parameter is called the outcrossing parameter, and the corresponding parameter is marked by the subscript x, i.e. F x , δ x =1.0、 ε x ; In the far point parameters, when F Increase to Time, that is, corresponding ε δ - F straight line ε δ =1.0, the fixed-point parameter is called the far-point parameter, and the corresponding parameter is marked by the subscript y, i.e. , ε y δ y =1.

0.

6. The drilling calculation and analysis method for impregnated diamond drill bits according to claim 3, characterized in that, The specific process for determining the interrelationships of the parameters in step 5 is as follows: Step 5.1.1: Determine the coefficient of variation ε of the contact area between the diamond and the rock. ε The value reflects the strength of the diamond compression core's ability to break rocks, and increases the drilling pressure per unit area. F If the diamond core's ability to compress and break rocks is enhanced, then... ε The value decreases. ε Value and F The relationship between the values ​​is calculated using the following formula: ； ε The value reflects the amount of diamond worn per revolution. δ d Amount of wear per revolution of the tire body δ T The relationship, when ε When =1.0, h = h S Diamond compression cores are ineffective at breaking rocks; the rock-breaking effect is extremely poor, with only a small advance per revolution. δ The value is relatively low, so we can assume that the correspondence is relatively low. δ d = δ T To determine the critical parameter value for whether a drill bit can self-sharpen, when ε When <1.0, δ d < δ T The drill bit can sharpen itself when ε When >1.0, δ d = δ T Drill bits cannot sharpen themselves, therefore, when ε When ≤ 1.0, diamond wear per revolution δ d Amount of wear per revolution of the tire body δ T The ratio of them is calculated using the following formula: ； ε The value is related to the abrasion resistance of the matrix of impregnated diamond drill bits, and the drilling pressure per unit area. F Under certain conditions, the amount of wear per revolution of the tire body δ T It is inversely proportional to the carcass hardness HRC value, which represents the carcass's wear resistance. ε The relationship between the value and the HRC value is calculated using the following formula: ； ε Value and drilling speed n Related, increase speed n If the diamond core's ability to compress and break rocks weakens, then... ε The value increases. ε Value and n The relationship between the values ​​is calculated using the following formula: ； Drilling pressure per unit area F Unchanged, rotational speed n Too high, leading to ε If the value is ≥1.0, the drill bit cannot sharpen itself. Step 5.1.2: Equivalent rock-breaking depth per revolution of each diamond penetrating the rock h S , h S The value is related to the average diamond grain size. d Diamond concentration C Related to the drill bit lip size, the average diamond particle size d Diamond concentration C And if the drill bit lip size remains unchanged, then h S The value remains constant, meaning the average volume of rock broken per revolution per diamond penetrating the rock. q S Unchanged, increase drilling pressure per unit area F This increased the number of diamond grains per revolution penetrating the rock. N This increases the volume of rock broken per drill revolution. Q r Increase the advance per revolution δ ; Reduce diamond concentration C or increase the average diamond grain size d Both increased the equivalent depth of rock breaking per diamond grain penetrating the rock. h S ,and, h S The increase factor is greater than d The increase factor; Increase diamond concentration C or reduce the average diamond grain size d Both increased the total equivalent surface area of ​​diamond in drill bits for wear resistance. S B This improves the wear resistance of the diamond in the drill bit and reduces the wear rate per revolution. δ d However, when drilling encounters rock, the hardness (HRC) of the drill bit matrix, and the drilling speed... n If the diamond core's ability to break rock remains constant, then the drilling pressure per unit area will remain constant. F corresponding ε The value remains unchanged, therefore, C value or d The change in value will not lead to ε Changes in value; Step 5.1.3: ε δ - F slope of a linear function K εδ ， K εδ The magnitude of the value reflects ε δ Value and drilling pressure per unit area F The relationship also reflects the strength of the wear resistance of the diamond in the drill bit, and increasing the diamond concentration... C Or reduce the average diamond particle size d All of these enhance the wear resistance of diamond. K εδ The values ​​all decrease accordingly, aiming for a inch advance per revolution. δ The ability to reduce the number of bits decreases, while the ability to increase the lifespan of the drill bit increases, and vice versa. Step 5.1.4: δ - F Curve function The index m, the magnitude of which reflects the drilling pressure per unit area of ​​the impregnated diamond drill bit. F Under these conditions, pursue advance per revolution δ The capability also reflects the advance per revolution. δ Change ratio, and drilling pressure per unit area F The relationship between the variation ratio and the drilling pressure is as follows: the larger the value of m, the greater the drilling pressure per unit area. F Under varying magnification conditions, the advance per revolution δ A larger change factor is more conducive to increasing the advance per revolution. δ ; For different rocks, there are different m values. For impregnated diamond bits that can self-sharpen and form cutting edges, through calculation and analysis, it is found that δ - F the exponential m value of the curve function is between 1.0 < m ≤ 2.0; Drilling pressure per unit area F If the diamond concentration remains unchanged, but is reduced... C Or increase the average diamond particle size d This increases the advance per revolution. δ, However, for drill bits with the same matrix properties and the same type of rock, the diamond compression core has the same effect on rock breaking, resulting in the same drilling pressure per unit area. F corresponding ε If the values ​​are the same, it is considered that δ Value change factor and F The relationship between the rate of change of values ​​remains basically unchanged, therefore, C value or d The value of m can be assumed to remain unchanged regardless of the change in the value. Step 5.1.5: δ - F Curve function The coefficient 'a', the magnitude of 'a', reflects the strength of the wear resistance of the diamond in the drill bit, and also reflects the strength of the wear resistance of the drill bit matrix. When drilling encounters rock, the drill bit matrix hardness (HRC) and drilling speed are considered. n If the diamond core's ability to break rock remains constant, then the drilling pressure per unit area will remain constant. F corresponding ε If the diamond concentration remains unchanged, but the diamond concentration is increased... C Or reduce the average diamond particle size d ,but ε δ - F slope of a linear function K εδ As it decreases, the coefficient a The value also decreases accordingly, and vice versa, according to equation (4-6). a Value and K εδ The relationships between the values ​​are as follows: ； if ε δ - F slope of a linear function K εδ With the value remaining constant, increasing the hardness HRC of the drill bit matrix increases the coefficient of variation of the contact area between the diamond and the rock. ε This enhances the wear resistance of the drill bit matrix, and the coefficient 'a' decreases accordingly. According to equations (4-6) and (5-3), the value of 'a' is related to... ε The relationship between the HRC value and the HRC value is as follows: ； Step 5.1.6: Lifespan of Impregnated Diamond Bits H， When the diamond in the drill bit wears down normally and does not fall out abnormally, the lifespan of a padded diamond drill bit is... H With each revolution, the advance is... δ Increased by increasing the drilling pressure per unit area F Pursuing higher advance per revolution δ When the diamond in the drill bit falls out abnormally, the wear resistance of the diamond cannot be fully utilized, thus reducing the drill bit's lifespan. H The lifespan is reduced, therefore, there is a maximum value for drill bit life. H max There exists a corresponding maximum drilling pressure per unit area. F max There is a corresponding advance limit value per revolution. δ max Per revolution advance limit value δ max The inclusion force of the matrix on the diamond, and the average diamond size d Related, increase d Value, then δ max Increase; when H 1< H 2< H 3, and H 4< H At time 3, the corresponding maximum drilling pressure per unit area F max exist F 3~ F Between 4, if F 4 and F The difference of 3 is relatively small, so we can calculate it using the following formula. F max value: ； Will F max Substituting into equation (4-3), the corresponding advance limit value per revolution is calculated. δ max The maximum cutting coefficient of diamond per revolution is calculated using the following formula. k max : ； H max value, F max value, δ max value, K max Value, also known as the limit parameter; The cutting force distributed per diamond per revolution F dt When the cutting force is too high, the diamond in the drill bit will undergo shear failure, and the cutting force distributed to each diamond per revolution will be reduced. F dt Calculate using the following formula: ； In the formula: F dt The cutting force distributed per diamond per revolution, where g is the acceleration due to gravity, and to prevent diamond shear failure in the drill bit, the required compressive strength of a single diamond is... F dσ Calculate using the following formula: ； In the formula, F dσ This represents the compressive strength of a single diamond. K df For the safety factor of diamond cutting per revolution, take medium-hard rock K df ≥ 6.0, rock containing coarse-grained sandstone. K df ≥ 8.0; Hard rock sampling K df ≥ 8.0; Hard rock sample K df ≥ 10.0; k τσ The coefficient relating the shear strength to the compressive strength of a single diamond is taken as... k τσ =0.08; When encountering rock and the required safety factor per diamond cutting per revolution. K df At the same time, the compressive strength value of a single diamond F dσ The relationship with the relevant parameters is as follows: ； When the average diamond particle size is increased d Increase matrix hardness (HRC) and reduce diamond concentration. C In such cases, the diamond grade should be increased accordingly, and the compressive strength of a single diamond should be improved. F dσ .

7. The drilling calculation and analysis method for impregnated diamond drill bits according to claim 3, characterized in that, In step 5, increase the advance per revolution. δ The specific process is as follows: Step 5.2.1: Increase drilling pressure per unit area F Increase the advance per revolution δ The depth of drilling per revolution δ and the drilling pressure per unit area F The relationship is calculated using the following formula: ； Each revolution advances a foot δ The increase in magnification, and the drilling pressure per unit area F The increase in multiplier exhibits an exponential m-order relationship; Step 5.2.2: Reduce diamond concentration C Or increase the average diamond particle size d Increase the advance per revolution δ ; Reduce diamond concentration C Or increase the average diamond particle size d All improved ε δ - F slope of a linear function K εδ ,improve δ - F Curve function The coefficient 'a' value is used to increase the advance per revolution. δ ; If the drill bit matrix hardness is HRC, the drilling pressure per unit area is... F And the rock encountered during drilling remains unchanged, when the diamond concentration changes from C =100% reduced to C =75%, the advance per revolution δ increased by 1.099 times, when the average diamond particle size increased from d =0.3275mm increased to d When the diameter is 0.3900mm, the advance per revolution δ increases by 1.059 times; Step 5.2.3: Reduce the hardness (HRC) of the drill bit matrix to increase the feed per revolution. δ , δ - F Curve function The coefficient a value, and ε The value is inversely proportional to the drill bit matrix hardness (HRC), and nearly inversely proportional to the drilling pressure per unit area. F When the time remains unchanged, the advance per revolution is [missing information]. δ It has an almost inverse relationship with the hardness HRC of the drill bit matrix; If the diamond concentration C Average diamond particle size d Drilling pressure per unit area F And the drilling encountered no change in the rock, and the advance per revolution was [missing information]. δ The increase ratio is close to the decrease ratio of the drill bit matrix hardness HRC.

8. The drilling calculation and analysis method for impregnated diamond drill bits according to claim 3, characterized in that, Step 5 improves the lifespan of impregnated diamond drill bits. H The specific process is as follows: when the depth of advance per revolution of the impregnated diamond drill bit... δ Not greater than the maximum cutting coefficient per revolution of diamond k max With average diamond particle size d The accumulation, that is, increasing the height of the working layer of the drill bit diamond when the diamond wears normally and no abnormal loss occurs, assuming a high diamond grade and no shearing failure of the drill bit diamond. H Z Or increase diamond concentration C or reduce the average diamond particle size d Increasing the matrix hardness (HRC) or improving the hardness of the drill bit body both improve drill bit life. H .

9. The drilling calculation and analysis method for impregnated diamond drill bits according to claim 3, characterized in that, Step 5, which ensures that the impregnated diamond drill bit is self-sharpening and prevents the diamond from being polished, involves the following steps: Step 5.4.1: Drilling pressure per unit area F It should be greater than the critical drilling pressure per unit area. F L To prevent the drill bit diamond from being polished, the coefficient of variation of the contact area between the diamond and the rock is... ε At a value of 1.0, the diamond wear per revolution δ d Amount of wear per revolution of the tire body δ T When the diamond bit is polished, the corresponding drilling pressure per unit area is called the critical drilling pressure per unit area. F L Critical drilling pressure per unit area F L Calculate using the following formula: ； Drilling pressure per unit area F > F L This effectively prevents the diamond in the drill bit from being polished. Step 5.4.2: Increase the rotational speed n To pursue higher mechanical drilling speed, avoid polishing of the drill bit diamond, reduce rotational resistance in shallow hole drilling, and increase rotational speed; If in terms of rotational speed n 1. Drilling pressure per unit area F 1. Drilling depth, the corresponding coefficient of change of contact area between diamond and rock is: ε 1. When the drilling pressure per unit area F 1 remains unchanged, increase the speed to n At time 2, to prevent the drill bit diamond from being polished, the coefficient of variation of the contact area between the diamond and the rock should meet the following requirements. ε 2 ≤ 1.0, permissible increase in rotational speed n 2. Calculate using the following formula: ； Step 5.4.3: Increase the rotational speed n、 Drilling pressure per unit area F To achieve higher mechanical drilling speeds and prevent the drill bit diamond from being polished, if the rotational speed is... n 1. Drilling pressure per unit area F 1. Drilling depth, the corresponding coefficient of change of contact area between diamond and rock is: ε 1. Requires increasing the rotational speed to n At 2 o'clock, to prevent the diamond bit from being polished, the drilling pressure per unit area should be increased to 2. F 2. The coefficient of variation of the contact area between the corresponding diamond and the rock. ε 2 ≤ 1.0, drilling pressure per unit area F 2. Determine using the following formula: 。 10. The drilling calculation and analysis method for impregnated diamond drill bits according to claim 3, characterized in that, Step 5 in deep hole drilling aims to achieve higher progress per revolution. δ The specific process to avoid reducing drill bit life is as follows: Deep hole drilling involves high rotational resistance, making it impossible to increase the rotational speed or pursue a higher mechanical drilling speed. Instead, the drilling pressure per unit area is typically increased. F Pursuing higher advance per revolution δ To increase the mechanical drilling speed, when pursuing the footage per revolution δ Greater than the maximum cutting coefficient per revolution of diamond k max With average diamond particle size d When diamonds accumulate, they may abnormally detach from the drill bit, preventing it from fully utilizing their anti-wear properties and thus shortening the drill bit's lifespan. H The diamond's average particle size was significantly reduced, thus increasing its size. d This improves the maximum cutting coefficient of diamond per revolution. k max This increased the advance limit per revolution. δ max This prevents the drill bit's lifespan from being reduced.

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