A method and system for predicting the average value of rotary-yaw coupled cutting force of a multi-toothed milling head

Abstract

The application discloses a kind of multi-tooth milling and digging head rotary-yaw coupling cutting force average prediction method and system, belong to rock breaking technical field.The application is based on Evans cutting theory, introduce rotary-yaw coupling caused cutting thickness time-varying function and the angle of cutting trajectory tangent at the tooth tip of tooth axis, establish single-tooth instantaneous cutting force dynamic model;Based on the assumption that the cutting tooth is evenly distributed in the milling and digging head circumference, the single-tooth cutting force contribution is integrated and superimposed within the rotation angle range of the cutting tooth participating in rock breaking, and an analytical mathematical model is established between the average total cutting force of multiple cutting teeth and the operating parameters such as cutting depth, yaw speed and rotational speed.The application has high prediction accuracy and high calculation efficiency, can reveal the influence law of operating parameters on the average cutting force, provide theoretical guidance for the construction parameter optimization of ecological sensitive area reef cleaning engineering, improve the reef cleaning efficiency and reduce equipment wear.

Description

Technical Field

[0001] This invention relates to the field of rock breaking technology in ecologically sensitive areas, such as reef clearing, tunnel excavation, and mining engineering. Specifically, it relates to a method for predicting the average cutting force of a multi-tooth milling head under rotation-yaw coupling conditions. Background Technology

[0002] The upper reaches of the Yangtze River, a vital waterway, is the world's largest navigable river in mountainous areas. Removing underwater obstructions to navigation is crucial for improving navigation capacity. However, the habitats of rare fish species within this waterway highly overlap with the spatial and temporal distribution of obstructive sections, constituting an ecologically sensitive area. The intense vibrations, noise, dust, and harmful gases generated by traditional drill-and-blast methods pose a significant threat to aquatic ecosystems and nearby structures. In contrast, milling, as a mechanical rock-breaking method, offers significant advantages in terms of environmental indicators such as vibration intensity, noise, dust, harmful gases, and the extent of environmental impact, and is therefore being applied to reef removal projects in sensitive areas.

[0003] Milling relies on rotating cutting teeth to break up rocks. These teeth bear complex dynamic loads under thrust and torque, and the magnitude and fluctuation characteristics of their cutting force directly determine the stability, rock-breaking efficiency, and reliability of the equipment. Engineering practice shows that overload or drastically fluctuating cutting forces can easily lead to milling head jamming, abnormal wear of the cutting teeth, and even breakage, severely restricting the equipment's continuous operation capability and increasing maintenance costs. This has become a key bottleneck hindering the widespread application of this technology. Therefore, in-depth research into the variation law of cutting force during the milling head's rock-breaking process and the establishment of an accurate cutting force prediction model have significant practical significance and engineering value.

[0004] In the study of cutting load characteristics of cutting teeth, Evans first proposed a theoretical model of peak cutting force for pick-type cutting teeth based on the maximum tensile stress criterion. Subsequently, scholars such as Roxborough and Goktan modified and extended Evans' model. Scholars such as Bao and Wang introduced fracture mechanics theory and constructed a cutting force estimation model from the perspective of crack propagation. Hekimoglu established the relationship between measured cutting force and effective area and proposed a geometric calculation method considering the tool spacing. The above theoretical models have initially revealed the mechanical mechanism of rock breaking by cutting teeth, but they all assume linear motion of a single cutting tooth and constant cutting depth, making it difficult to truly reflect the dynamic evolution of cutting force during the cutting process.

[0005] To overcome the limitations of theoretical models, scholars have studied the cutting force characteristics under complex cutting conditions through cutting experiments and numerical simulations. Yasar, Liao Jiubo, and others analyzed the effects of rock strength, tool parameters, cutting thickness, and cutting line spacing on the cutting force. Wang, Cai, and others used discrete element simulation to reveal the influence of different confining pressures, cone angles, angles of attack, and depths of cut on the cutting force. The above studies revealed the characteristics of cutting force variation of a single cutting tooth under complex conditions. However, in the actual rock-breaking process of a milling head, the synergistic effect of multiple teeth, the dynamic changes in cutting thickness, and the complex spatial motion trajectory all affect the cutting force characteristics. The cutting behavior based on a single cutting tooth cannot accurately reflect the cutting force of a multi-tooth milling head.

[0006] In recent years, scholars have begun to focus on the overall load characteristics and prediction models of multi-tooth milling heads. Li, Kao, and others have investigated the effects of factors such as traction speed, rock hardness, and tooth arrangement on cutting force through experiments and simulations. Regarding prediction models, Zhang proposed a stochastic cutting force model, and Li proposed a drum torque estimation method by superimposing the cutting forces of each tooth. Furthermore, machine learning methods have been introduced into this field; Xin, Hadi, Morshedlou, Jian, and others have established cutting force prediction models using BP neural networks, extreme gradient boosting, random forests, and chaotic optimization algorithms, respectively.

[0007] Despite the significant progress made in the aforementioned research, most current findings are still based on simplified theoretical assumptions, focusing on the cutting behavior of a single cutting tooth under straight, constant cutting depth conditions. Existing research has not yet systematically revealed the intrinsic relationship between cutting force and milling and reef-breaking parameters, especially lacking cutting force prediction models applicable to multi-tooth collaborative, variable cutting depth, and complex motion conditions. Furthermore, in calculating the cutting force of multi-tooth cutting, existing methods mostly use the superposition of the cutting forces of each tooth to obtain the total cutting force, which is computationally complex and not conducive to practical engineering applications. While machine learning-based cutting force prediction models perform well under specific conditions, they rely on large-sample, multi-parameter data, making it difficult to obtain sufficient high-quality samples in complex construction environments, thus limiting their applicability and robustness.

[0008] Therefore, there is an urgent need for a cutting force prediction method that has high prediction accuracy, is easy to calculate, and does not rely on large sample data. Summary of the Invention

[0009] In view of this, the purpose of this invention is to provide a method and system for predicting the mean cutting force of a multi-tooth milling head with rotation-yaw coupling. This method uses Evans theory to introduce a time-varying function of the cutting thickness with rotation-yaw coupling, and combines the uniform distribution assumption with integral superposition to construct an analytical model, thus solving the problem of the difficulty in accurately predicting the mean cutting force of a multi-tooth milling head under complex working conditions.

[0010] To achieve the above objectives, the present invention provides the following technical solution: This invention provides a method for predicting the mean cutting force of a multi-tooth milling head with rotation-yaw coupling, comprising the following steps: Step 1: Establish a dynamic model of the instantaneous cutting force of a single cutting tooth. The model is based on Evans cutting theory and introduces the time-varying function of the cutting thickness caused by the rotation-yaw coupling motion of the cutting tooth and the angle between the axis of the cutting tooth and the tangent of the cutting trajectory at the tooth tip to obtain the expression of the instantaneous cutting force of a single cutting tooth changing with time. Step 2: Obtain the structural and operational parameters of the milling head. The structural parameters include the number of cutting lines, the number of cutting teeth on each cutting line, and the cutting radius of the cutting teeth. The operational parameters include the yaw rate, depth of cut, and rotational speed. Step 3: Based on the assumption that the cutting teeth are uniformly distributed in the circumferential direction of the milling head, within the rotation angle range of the cutting teeth involved in rock breaking, the cutting force contribution of a single cutting tooth is integrated and superimposed to establish a mathematical model between the average total cutting force of multiple cutting teeth and the structural parameters and the operating parameters. Step 4: Substitute the obtained rock mechanics parameters, cutting tooth geometric parameters, structural parameters, and operating parameters into the mathematical model to calculate the average predicted cutting force of the milling head under given working conditions.

[0011] Furthermore, in step 1, the instantaneous cutting force of the single cutting tooth The mathematical model for its variation with time t is as follows: In the formula: The tensile strength of the rock; The compressive strength of the rock; The semi-cone angle of the pick-shaped cutting tooth; is the angle between the axis of the cutting tooth and the tangent to the cutting trajectory at the tooth tip; n is the milling head rotation speed; t is the time it takes for the cutting tooth to rotate and cut the rock. Indicates the maximum cut thickness; Furthermore, the equivalent radius The calculation formula is: In the formula, The equivalent radius of the elliptical cross-section of the contact surface between the cutting tooth and the rock; 'a' represents the radius of the pick-shaped cutting tooth when it contacts the rock. The semi-cone angle of the pick-shaped cutting tooth; It is the angle between the axis of the cutting tooth and the tangent to the cutting trajectory at the tooth tip.

[0012] Furthermore, in step 1, the cutting thickness h is expressed as a sine function with respect to time t: In the formula: n is the rotational speed of the cutting tooth; t is the time for the cutting tooth to rotate and cut the rock; hmax is the maximum cutting thickness.

[0013] Furthermore, in step 3, the formula for calculating the cutting force Fm of a single cutting tooth at the maximum cutting thickness is: Where Fm is the maximum cutting force of each cutting tooth on the same cutting line during one rotation of the cutting process, that is, the cutting force of the cutting tooth at the maximum cutting thickness hmax. The tensile strength of the rock; The compressive strength of the rock; The semi-cone angle of the pick-shaped cutting tooth; is the angle between the axis of the cutting tooth and the tangent to the cutting trajectory at the tooth tip; n is the milling head rotation speed; m represents the number of cutting teeth on the same cutting line; This represents the maximum cutting thickness; v is the yaw speed of the milling head.

[0014] Furthermore, in step 3, the rotation angle range of the cutting teeth involved in rock breaking is determined based on the depth of cut and the cutting radius of the cutting teeth: in, The rotation angle range of the cutting teeth involved in rock breaking; d is the depth of cut; R is the cutting radius of the cutting teeth.

[0015] Furthermore, in step 3, the average total cutting force F of the multi-tooth cutting action... T The mathematical model is as follows: in, This represents the cutting force generated per unit rotation angle. The range of rotation angles of the cutting teeth involved in rock breaking; Indicates the rotation angle of the cutting teeth; This represents the maximum cutting force of each cutting tooth on the same section line during one rotation of the cutting process; s is the number of sections of the milling head cutting teeth arrangement; m is the number of cutting teeth on the same section line; d is the depth of cut of the milling head during lateral swing; R is the cutting radius of the milling head cutting teeth.

[0016] Furthermore, Fm and After substituting the expression, the mathematical model of the average total cutting force FT of the multi-tooth cutting teeth expands to: In the formula: s is the number of cut lines arranged in the milling head cutting teeth; The tensile strength of the rock; The compressive strength of the rock; The semi-cone angle of the pick-shaped cutting tooth; denoted by , where is the angle between the axis of the cutting tooth and the tangent to the cutting trajectory at the tooth tip; v is the yaw speed of the milling head; n is the rotational speed of the milling head; m is the number of cutting teeth on the same cutting line; d is the depth of cut during the yaw of the milling head; and R is the cutting radius of the cutting teeth of the milling head.

[0017] This invention provides a system for predicting the average cutting force of a multi-tooth milling head for breaking reefs, used to execute the above method, including: The data acquisition module is used to acquire rock mechanics parameters, cutting tooth geometric parameters, milling head structural parameters and operating parameters. The structural parameters include the number of cutting lines, the number of cutting teeth on each cutting line, and the cutting radius of the cutting teeth. The operating parameters include yaw rate, depth of cut, and rotational speed. The model building module, connected to the data acquisition module, is used to establish a dynamic model of the instantaneous cutting force of a single cutting tooth, and to establish a mathematical model of the average total cutting force of multiple cutting teeth based on the assumption of uniform distribution of cutting teeth and integral superposition. The calculation module, connected to the model building module, is used to substitute the parameters obtained by the data acquisition module into the mathematical model to calculate the average predicted cutting force. The output module, connected to the calculation module, is used to output the average value of the predicted cutting force.

[0018] Furthermore, it also includes a parameter optimization module, which is connected to the calculation module and is used to output an optimized value of at least one of the following parameters: depth of cut, yaw rate, and rotational speed, based on the predicted average cutting force.

[0019] The beneficial effects of this invention are as follows: This invention provides a method and system for predicting the mean cutting force of a multi-tooth milling head with rotation-yaw coupling. Addressing the problem of accurate prediction of cutting force in reef clearing projects, this method, based on Evans cutting theory, introduces a time-varying function of the cutting thickness caused by rotation-yaw coupling, establishing a single-tooth rotational cutting force model. Furthermore, combining the yaw kinematic characteristics and the spatial arrangement parameters of the cutting teeth, a multi-tooth milling head mean cutting force prediction model is constructed based on the "uniform distribution assumption + integral superposition". The model is validated through 3DEC full-scale milling and reef breaking discrete element numerical simulation and indoor experiments. Subsequently, the influence of 20 different reef breaking parameters (cutting depth, yaw speed, and rotational speed) is analyzed. The results show that the cutting force time history curves predicted by the single-tooth model and obtained from simulation agree well; the deviation between the mean cutting force predicted by the multi-tooth model and the simulation results is within 9.8%, significantly better than the prediction accuracy of the traditional Evans model. Studies have shown that the average cutting force increases with increasing depth of cut and yaw rate, and gradually decreases with increasing rotational speed, with the depth of cut having a more significant impact. The model proposed in this study can effectively predict the cutting force, providing theoretical guidance for optimizing reef clearing construction parameters and predicting the cutting force in ecologically sensitive areas, and has significant engineering application value. Compared with existing technologies, the advantages of this invention are as follows: (1) High prediction accuracy and strong engineering applicability. Based on Evans cutting theory, this invention introduces a time-varying function of cutting thickness under the rotation-yaw coupling mechanism to construct a dynamic cutting force model for a single cutting tooth; further, combining yaw kinematics and the spatial arrangement characteristics of multiple cutting teeth, a milling head cutting force mean prediction model under the assumption of uniform distribution of multiple cutting teeth is proposed. Verified by 3DEC discrete element simulation and indoor experiments, when the ratio of cutting depth to cutting radius is in the range of 0.15 to 0.6, the deviation between the predicted value and the simulation result is controlled within 9.8%, which is significantly better than the traditional Evans model, providing a reliable cutting force prediction tool for reef clearing projects in ecologically sensitive areas.

[0020] (2) The model is simple and the calculation is efficient. This invention avoids the tedious calculation of tooth-by-tooth superposition by adopting the strategy of "uniform distribution assumption + integral superposition". It establishes a closed analytical model between the average cutting force and macroscopic operating parameters such as cutting depth, yaw speed and rotation speed, which facilitates rapid evaluation and parameter optimization in engineering field.

[0021] (3) The influence of operating parameters on cutting force is revealed. This invention quantitatively presents the relationship between the average cutting force and the increase of cutting depth and yaw speed, and the decrease of cutting force and the increase of rotation speed, providing a theoretical basis for balanced load control and working stability during construction.

[0022] (4) Guiding the optimization of construction parameters to improve reef clearing efficiency and equipment life. Based on the prediction model of this invention, the cutting depth, yaw speed and rotation speed can be reasonably adjusted to effectively control the cutting force, thereby improving construction efficiency, reducing equipment wear and extending the service life of the milling head, which has important engineering application value.

[0023] The above and other objects, advantages, and features of the present invention will be more fully set forth and demonstrated through the following detailed description of specific embodiments in conjunction with the accompanying drawings. Those skilled in the art, upon referring to the following detailed description and the accompanying drawings, will be able to better understand and realize the above advantages of the present invention. Other objects, features, and advantages of the present invention will become clearer after being described in detail in the detailed description section in conjunction with the accompanying drawings. Attached Figure Description

[0024] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following drawings are provided for illustration.

[0025] Figure 1 Flowchart of the method for predicting the mean cutting force of a multi-tooth milling head with rotation-yaw coupling; Figure 2 Evans's straight-line rock cutting model; Figure 3 Single-tooth rotary rock cutting model; Figure 4 Schematic diagram of the rock-breaking process using a single-tooth cutting tool; Figure 5 Numerical simulation model of single-tooth rotary reef breaking; Figure 6 Comparison of the numerical model calculation results of the cutting force of a single cutting tooth with the theoretical value; Figure 7 Schematic diagram of a milling head swinging horizontally to break a reef; Figure 8 Indoor testing system for milling and breaking reefs; Figure 9 Numerical simulation model for milling and breaking reefs; Figure 10 Uniaxial compression and Brazilian splitting test; Figure 11 Numerical simulation results of uniaxial compression and Brazilian splitting tests; Figure 12 Comparison of stress-strain and load-displacement curves between experiments and numerical simulations; Figure 13 Comparison of time history curves of milling head cutting force from experiments and numerical simulations; Figure 14 Cutting force time history curve calculated by digital model; Figure 15 Comparative verification of the theoretical model of mean cutting force; Figure 16 Comparison of the results of the average cutting force prediction model and the numerical model; Figure 17 Comparison of theoretical cutting force and digital cutting force. Detailed Implementation

[0026] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention. Example 1

[0027] like Figure 1 As shown in the figure, the method for predicting the mean cutting force of a multi-tooth milling head with rotation-yaw coupling provided in this embodiment includes the following steps: Step 1: Establish a dynamic model of the instantaneous cutting force of a single cutting tooth. The model is based on Evans cutting theory and introduces the time-varying function of the cutting thickness caused by the rotation-yaw coupling motion of the cutting tooth and the angle between the axis of the cutting tooth and the tangent of the cutting trajectory at the tooth tip to obtain the expression of the instantaneous cutting force of a single cutting tooth changing with time. Step 2: Obtain the structural and operational parameters of the milling head. The structural parameters include the number of cutting lines, the number of cutting teeth on each cutting line, and the cutting radius of the cutting teeth. The operational parameters include the yaw rate, depth of cut, and rotational speed. Step 3: Based on the assumption that the cutting teeth are uniformly distributed in the circumferential direction of the milling head, within the rotation angle range of the cutting teeth involved in rock breaking, the cutting force contribution of a single cutting tooth is integrated and superimposed to establish a mathematical model between the average total cutting force of multiple cutting teeth and the structural parameters and the operating parameters. Step 4: Substitute the obtained rock mechanics parameters, cutting tooth geometric parameters, structural parameters, and operating parameters into the mathematical model to calculate the average predicted cutting force of the milling head under given working conditions.

[0028] In this embodiment, the instantaneous cutting force of the single cutting tooth in step 1 The mathematical model for its variation with time t is as follows: In the formula: The tensile strength of the rock; The compressive strength of the rock; The semi-cone angle of the pick-shaped cutting tooth; is the angle between the axis of the cutting tooth and the tangent to the cutting trajectory at the tooth tip; n is the milling head rotation speed; t is the time it takes for the cutting tooth to rotate and cut the rock. Indicates the maximum cut thickness; The equivalent radius described in this embodiment The calculation formula is: In the formula, denoted as , where is the equivalent radius of the elliptical cross-section of the contact surface between the pick and the rock; 'a' is the radius of the pick when it contacts the rock. The semi-cone angle of the pick-shaped cutting tooth; It is the angle between the axis of the cutting tooth and the tangent to the cutting trajectory at the tooth tip.

[0029] In this embodiment, the cutting thickness h in step 1 is expressed as a sine function with respect to time t: In the formula: n is the rotational speed of the cutting tooth; t is the time for the cutting tooth to rotate and cut the rock; hmax is the maximum cutting thickness.

[0030] In this embodiment, the formula for calculating the cutting force Fm of a single cutting tooth at the maximum cutting thickness in step 3 is as follows: Where Fm is the maximum cutting force of each cutting tooth on the same cutting line during one rotation of the cutting process, that is, the cutting force of the cutting tooth at the maximum cutting thickness hmax. The tensile strength of the rock; The compressive strength of the rock; The semi-cone angle of the pick-shaped cutting tooth; is the angle between the axis of the cutting tooth and the tangent of the cutting trajectory at the tooth tip; n is the milling head rotation speed; m is the number of cutting teeth on the same cutting line; This represents the maximum cutting thickness; v is the yaw speed of the milling head.

[0031] In this embodiment, the rotation angle range of the cutting teeth involved in rock breaking in step 3 is determined based on the depth of cut and the cutting radius of the cutting teeth: in, The rotation angle range of the cutting teeth involved in rock breaking; d is the depth of cut; R is the cutting radius of the cutting teeth.

[0032] In this embodiment, the average total cutting force F of the multi-tooth cutting force in step 3 is... T The mathematical model is as follows: in, This represents the cutting force generated per unit rotation angle. This represents the maximum cutting force of each cutting tooth on the same section line during one rotation of the cutting process; The range of rotation angles of the cutting teeth involved in rock breaking; The rotation angle of the cutting teeth is represented by s; the number of sections of the cutting teeth arrangement on the milling head is represented by m; the number of cutting teeth on the same section is represented by d; and the cutting radius of the cutting teeth on the milling head is represented by R.

[0033] In this embodiment, Fm and After substituting the expression, the mathematical model of the average total cutting force FT of the multi-tooth cutting teeth expands to: In the formula: s is the number of cut lines arranged in the milling head cutting teeth; The tensile strength of the rock; The compressive strength of the rock; The semi-cone angle of the pick-shaped cutting tooth; denoted by , where is the angle between the axis of the cutting tooth and the tangent to the cutting trajectory at the tooth tip; v is the yaw speed of the milling head; n is the rotational speed of the milling head; m is the number of cutting teeth on the same cutting line; d is the depth of cut during the yaw of the milling head; and R is the cutting radius of the cutting teeth of the milling head.

[0034] In this embodiment, the rock mechanical parameters include the rock's tensile strength and compressive strength. The results were obtained through indoor uniaxial compression tests and Brazilian splitting tests.

[0035] In this embodiment, after step 4, the method further includes: assessing the safety of the current construction parameters based on the predicted average cutting force, and using the results to optimize at least one of the cutting depth, yaw speed, and rotation speed to control the cutting force.

[0036] This embodiment provides a multi-tooth milling head reef breaking average cutting force prediction system, used to execute the above method, including: The data acquisition module is used to acquire rock mechanics parameters, cutting tooth geometric parameters, milling head structural parameters and operating parameters. The structural parameters include the number of cutting lines, the number of cutting teeth on each cutting line, and the cutting radius of the cutting teeth. The operating parameters include yaw rate, depth of cut, and rotational speed. The model building module, connected to the data acquisition module, is used to establish a dynamic model of the instantaneous cutting force of a single cutting tooth, and to establish a mathematical model of the average total cutting force of multiple cutting teeth based on the assumption of uniform distribution of cutting teeth and integral superposition. The calculation module, connected to the model building module, is used to substitute the parameters obtained by the data acquisition module into the mathematical model to calculate the average predicted cutting force. The output module, connected to the calculation module, is used to output the average value of the predicted cutting force.

[0037] This embodiment also includes a parameter optimization module, which is connected to the calculation module and is used to output an optimized value of at least one of the following parameters: depth of cut, yaw rate, and rotational speed, based on the predicted average cutting force. Example 2

[0038] This embodiment details a method and system for predicting the mean cutting force of a multi-tooth milling head with rotation-yaw coupling. The specific process is as follows: I. In the process of establishing a calculation model for the average cutting force of multi-tooth milling excavation for reef breaking, 1. Establish a dynamic model of the instantaneous cutting force of a single cutting tooth. The specific process is as follows: Analysis of the assumptions and limitations of the Evans model: Domestic and international scholars have conducted extensive research on the rock-breaking cutting force of pick-shaped cutting teeth, among which the peak cutting force calculation model proposed by Evans is widely used. This model assumes that the cutting teeth penetrate the rock mass vertically and with uniform thickness, and considers that rock fracturing mainly stems from the tensile stress caused by the intrusion of the cutting teeth exceeding its tensile strength. The formula for calculating the cutting force is as follows: (1) In the formula, This represents the instantaneous cutting force of a single cutting tooth; The tensile strength of the rock is given in MPa. The compressive strength of the rock is expressed in MPa. The semi-cone angle of the pick-shaped cutting teeth, h represents the cutting thickness of the pick-shaped cutting teeth, in meters (m).

[0039] like Figure 2 As shown, Figure 2 The Evans model for straight-line rock cutting is used, but in actual milling and rock breaking processes, the operating conditions of the cutting teeth differ significantly from the "straight-line, uniform-thickness cutting" assumed by the Evans model. Specifically, under rotary cutting conditions, the cutting thickness *h* changes in real time with the movement of the cutting teeth and is not a constant value. Furthermore, due to the angle between the cutting tooth axis and the tangent of the cutting trajectory, the stress distribution in the contact area between the cutting tooth and the rock is no longer circumferentially uniform. These factors limit the applicability of the Evans model and make it difficult to accurately predict the cutting force under complex actual working conditions. Therefore, it is necessary to reasonably modify its geometric relationships and the law of cutting thickness variation.

[0040] 2. Derivation of the instantaneous cutting force model for a single cutting tooth: Under rotary cutting conditions, the contact surface between the cutting tooth and the rock is elliptical, and its geometric relationship is as follows: Figure 3 As shown. To solve the total cutting force by integrating the distributed load on the contact surface within the Evans theoretical framework, the elliptical cross-section needs to be reasonably simplified. Since the analytical expression for the arc length of an elliptical infinitesimal element is complex, direct integration is difficult. Therefore, the elliptical cross-section is equivalent to a circular cross-section with radius a0 to simplify the integration process. The circumference of the ellipse can be approximated as L=(a1+a2), where a1 and a2 are the semi-major and semi-minor axes of the ellipse, respectively. Accordingly, the radius of the equivalent circle can be taken as a0=(a1+a2) / 2. Based on geometric relationships, the semi-axis length of the ellipse can be expressed as: , (2) Substituting into the above equation, we can obtain the expression for the equivalent radius a0 as follows: (3) In the formula, a0 is the equivalent radius of the elliptical cross-section of the contact surface between the cutting tooth and the rock; a1 is the minor semi-axis of the elliptical cross-section; a2 is the major semi-axis of the elliptical cross-section; and a is the radius of the cutting tooth when it contacts the rock. Figure 3 As shown, Figure 3 Single-tooth rotary rock cutting model; The semi-cone angle of the pick-shaped cutting tooth; It is the angle between the axis of the cutting tooth and the tangent to the cutting trajectory at the tooth tip.

[0041] When attack angle When, substituting into equation (3), we get a0 = a, which degenerates exactly into the circular contact radius in Evans' original model. This verifies the rationality of the equivalent formula in theoretical extension.

[0042] Based on Evans theory and using differential methods, the expression for the cutting force of a single cutting tooth in a rotating state is derived as follows: (4) In the formula, denoted as the tensile strength of the rock, MPa; a0 is the equivalent radius of the elliptical cross-section of the contact surface between the cutting tooth and the rock; h is the cutting thickness of the pick-type cutting tooth, m. The semi-cone angle of the pick-shaped cutting teeth, .

[0043] Further consideration is that there is an angle between the axis of the cutting tooth and the tangent of the trajectory during the actual cutting process. That is, the angle of intrusion (Not zero), and satisfies the rock compressive strength condition at the tip of the cutting tooth. The corrected cutting force model is obtained: (5) In the formula: The compressive strength of the rock is expressed in MPa. The angle between the axis of the cutting tooth and the tangent to the cutting trajectory at the tooth tip. .

[0044] Furthermore, during the rotary rock breaking process, the cutting thickness h dynamically changes with the angle and position of the cutting teeth (e.g., Figure 4 Initially, h is relatively small, reaching its maximum value hmax as the cutting tooth rotates to its lowest point, and then gradually decreases. Based on motion trajectory analysis, h can be approximated as a sine function of the rotation angle: (6) In the formula: n is the milling head rotation speed, r / min; t is the time for the cutting tooth to rotate and cut the rock, s; hmax is the maximum cutting thickness, m; hmax for a single cutting tooth is the rotation speed of the cutting tooth. The cutting thickness at that time.

[0045] like Figure 4 As shown, Figure 4 Schematic diagram of the rock-breaking process using a single-tooth cutting tool.

[0046] Substituting equation (5) into equation (4) yields the rock-breaking cutting force of a single-tooth cutting tooth. The expression for how it changes with time t: (7) In the formula: The tensile strength of the rock is given in MPa. The compressive strength of the rock is expressed in MPa. The semi-cone angle of the pick-shaped cutting teeth, ; The angle between the axis of the cutting tooth and the tangent to the cutting trajectory at the tooth tip. n is the milling head rotation speed, r / min; t is the time for the cutting teeth to rotate and cut the rock, s; 3. Validation of the single-tooth cutting force model: To verify the accuracy of equation (6) in predicting the cutting force during the single-tooth rotation rock breaking process, a numerical simulation model of single-tooth rotation rock breaking was established based on the 3DEC discrete element platform to simulate the process of rock breaking by the rotating tooth in half a cycle, as shown in the figure. In the numerical simulation model, the tooth model is set as a rigid body element, and the rock model is discretized into several deformable tetrahedral block elements, and its mechanical behavior is described by a linear elastic constitutive model. The contact relationship between the blocks is simulated by the Coulomb slip model to reflect the slip and separation characteristics of the contact surface. The mechanical parameters of the rock mass in the model are all calibrated based on the results of indoor rock sample physical and mechanical tests, and the specific parameter values ​​are summarized in Table 1. In terms of boundary conditions, the bottom of the reef model is completely fixed (ux=uy=uz=0), and the lateral boundary is subject to normal displacement constraint (un=0) to simulate the constraint effect of infinite rock mass on the core fracture zone.

[0047] Table 1 Macroscopic and microscopic mechanical parameters of the reef model like Figure 5 As shown, Figure 5 Numerical simulation model of single-tooth rotary reef breaking. The cutting radius R of the cutting tooth is 0.34m, and the semi-cone angle of the cutting tooth is taken as... The rotational speed n of the fixed milling head is 60 r / min. The drilling speed u of the downward movement of the cutting teeth is taken as four different drilling speeds: 0.05 m / s, 0.1 m / s, 0.15 m / s, and 0.2 m / s. The time history curve of the cutting force is recorded during the simulation, and the same parameters are substituted into equation (6) to calculate the theoretical value, and compared with the simulation results.

[0048] like Figure 6 As shown, Figure 6 Comparison of the numerical model calculation results of the cutting force of a single cutting tooth with the theoretical value. Figure 6 The comparison between the cutting force time history curve obtained from the 3DEC simulation and the theoretical calculation result of Equation (6) is shown. From the overall trend, the simulation results are basically consistent with the theoretical prediction, both showing a single-peak shape of first rising and then falling, and reaching the peak when the cutting tooth rotates to the middle position (corresponding to the maximum cutting thickness).

[0049] Further analysis revealed that when the drilling speed was relatively low (u=0.05m / s, 0.1m / s), the simulation results deviated significantly from the theoretical calculations. Figure 6 (a)(b)); however, under higher drilling speeds (u=0.15m / s, 0.2m / s), the agreement between the two is significantly improved. Figure 6 (c)(d) in the text). Observation. Figure 6 As can be seen from the cutting force curves in (a) and (b), there is a significant sudden drop in load before reaching the peak value. This phenomenon is closely related to the energy accumulation and release mechanism during the rock crushing process: in the initial stage, the cutting teeth compress the rock to form a dense core, energy continues to accumulate, and the cutting force increases accordingly; when the microcracks inside the rock extend to the free surface, the rock undergoes brittle fracture, the accumulated energy is suddenly released, and the cutting force drops sharply.

[0050] Under low drilling speed conditions, due to the small cutting thickness, the load drops rapidly after the reef undergoes brittle fracture, while the next round of fracture requires a long energy accumulation time, resulting in a discontinuous fracturing process and significant fluctuations in cutting force. Figure 6 (a) and (b) in the model are the main reasons for the discrepancy between the theoretical model and the simulation results. In contrast, at higher drilling speeds, the cutting teeth maintain continuous contact with the reef, and immediately enter a new energy accumulation stage after brittle fracture. Figure 6 In (c) and (d), the energy accumulation rate is fast, and the load response is more stable, thus making the theoretical predictions closer to the numerical results. Figure 6 In the example, (a) drilling speed u = 0.05 m / s; (b) drilling speed u = 0.10 m / s; (c) drilling speed u = 0.15 m / s; (d) drilling speed u = 0.20 m / s; II. Calculation Model for Average Cutting Force of Multi-Tooth Cutting While a single-tooth cutting force model can effectively describe the mechanical behavior of a single cutting tooth during rotary rock breaking, actual engineering milling heads typically have multiple sets of cutting teeth arranged according to specific patterns. During operation, multiple teeth simultaneously participate in the synergistic effect of rock breaking. Therefore, the single-tooth model has limitations in predicting the overall cutting force of the milling head and struggles to reflect the intrinsic relationship between the overall load and operating parameters of the milling head under complex working conditions. Therefore, it is necessary to further develop a milling head cutting force calculation model suitable for multi-tooth synergistic effects.

[0051] Equation (6) shows that, under given operating parameters (drilling speed u, rotational speed n), the cutting force Fc of a single cutting tooth has a sinusoidal relationship with time t. Considering the rotation angle of the cutting tooth... With time t The relationship can be expressed as Fc about The function, that is: (8) For a multi-tooth milling head, when it rotates once to cut rock, the maximum cutting thickness hmax of each tooth on the same cutting line satisfies the following relationship: (9) In the formula: v is the yaw speed of the milling head, m / s; n is the rotational speed of the milling head, r / min; m is the number of cutting teeth on the same section line.

[0052] In this embodiment, the cutting teeth are mounted on the milling head, so the two rotate coaxially, and the milling head rotation speed n is the cutting tooth rotation speed n.

[0053] Substituting equation (8) into equation (7) yields: (10) Further simplifying the above equation, let: (11) Here, Fm is equivalent to the maximum cutting force of each cutting tooth on the same cutting line during one rotation, that is, the cutting force of the cutting tooth at the maximum cutting thickness hmax. Substituting equation (10) into equation (9) yields the cutting force of each cutting tooth on a cutting line at the relative position angle: (12) in, This represents the cutting force at the relative position angle of each cutting tooth; like Figure 7 As shown, Figure 7 Schematic diagram of milling head horizontal swing breaking reef. According to... Figure 7The schematic diagram of the milling head cross-section shows that when the milling head performs lateral cutting on the rock with a depth of cut d and a lateral speed v, each cutting tooth needs to rotate a certain angle after penetrating the rock. Only then can the crushing process be completed. At this point, the total cutting force of the entire milling head can be considered as being at this angle. The total cutting force is the sum of the cutting forces of all the cutting teeth involved in rock breaking within the specified range. When the number of cutting teeth in a milling head is small, the total cutting force can be obtained by calculating the cutting force of each tooth at its corresponding position and summing them up. However, in actual engineering, milling heads are usually equipped with a large number of cutting teeth. If the method of summing teeth one by one is still used, it is not only difficult to accurately obtain the real-time position of each cutting tooth, but the calculation process is also extremely cumbersome and not suitable for efficient prediction of actual cutting force. Therefore, in order to effectively estimate the total cutting force of a milling head under specific operating parameters, it is necessary to reasonably simplify and assume its structural layout and mechanical action mechanism.

[0054] Typically, a milling head has several cutting lines arranged circumferentially around the hub. Each cutting line has multiple cutting teeth arranged at equal intervals, with the teeth on adjacent cutting lines staggered. Now, assume a milling head has a total of s cutting lines, with m cutting teeth evenly installed on each line. If the positional differences of the cutting teeth along the axial direction of the hub are ignored, then it can be considered that there are a total of... The cutting teeth are evenly distributed circumferentially on the surface of the milling head. At this time, the circumferential spacing angle between adjacent cutting teeth is... Based on this uniform distribution assumption, the cutting force generated per unit rotation angle along the cut can be expressed as: (13) Integrating equation (12), the entire milling head can be measured within the range of rotational cutting angles. The total cutting force inside is: (14) in, This represents the cutting force generated per unit rotation angle. This represents the maximum cutting force of each cutting tooth on the same section line during one rotation of the cutting process; The range of rotation angles of the cutting teeth involved in rock breaking; The rotation angle of the cutting teeth is represented by s; the number of sections of the cutting teeth arrangement on the milling head is represented by m; the number of cutting teeth on the same section is represented by d; and the cutting radius of the cutting teeth on the milling head is represented by R.

[0055] in, Can be combined Figure 7 The geometric positional relationship between the milling head and the rock is obtained as follows: (15) Finally, substituting equations (10) and (14) into equation (13), we get: (16) It is worth noting that Equation (15) establishes a calculation model for the average cutting force during the multi-tooth reef breaking process of the milling head, which is fundamentally different from the aforementioned single-tooth instantaneous cutting force model, Equation (6). This model reveals the intrinsic relationship between the average cutting force FT of the milling head and key reef breaking parameters (depth of cut d, yaw rate v, and milling head rotation speed n), enabling engineers to directly estimate the corresponding average cutting load based on a specific combination of reef breaking parameters.

[0056] III. Milling and Reef Breaking Test and Numerical Simulation 1. Indoor test of milling and breaking reefs like Figure 8 As shown, Figure 8 The image shows a milling and reef-breaking test system, mainly consisting of a power control system (…). Figure 8 (a) of the hydraulic drive system Figure 8 (c) and milling and reef breaking equipment ( Figure 8 It consists of three parts (e). The power control system includes a control center, power supply and controller; the hydraulic drive system includes a hydraulic pump, hydraulic tank, pressure gauge and related hydraulic pipelines; the milling and reef breaking equipment includes key components such as a horizontal milling head, hydraulic motor, horizontal and vertical hydraulic cylinders, reaction frame and base.

[0057] The test system controls the hydraulic pump via a controller. Figure 8 (b)(c) in the text), the hydraulic motor that drives the hydraulic oil to be delivered to the milling head through the oil pipe ( Figure 8 (d)). After entering the motor, the hydraulic oil drives its internal rotor or gear set to rotate, which in turn drives the external milling head to rotate. After flowing through the hydraulic motor, the hydraulic oil returns to the hydraulic oil tank, forming a complete circuit. The power control system can control the hydraulic oil flow by adjusting the power of the hydraulic pump, thereby adjusting the rotational power of the milling head; at the same time, by controlling the hydraulic pump, the flow of hydraulic oil in the horizontal and vertical hydraulic cylinders can be adjusted to achieve precise movement of the milling equipment along the horizontal or vertical guide rails. Figure 8 (f)). The cutting force experienced by the milling head during operation can be reflected by the pressure inside the hydraulic cylinder. Therefore, a pressure sensor is installed in the hydraulic cylinder and connected to a data acquisition system to achieve real-time recording of the cutting force during the milling and reef-breaking test. Figure 8 (g) in the middle.

[0058] Based on a systematic survey of the rock mechanical properties of major navigational obstruction reefs in the upper reaches of the Yangtze River, statistical results of the uniaxial compressive strength of field rock samples show an average value of approximately 33.6 MPa, with a main distribution range of 27–36 MPa. Therefore, to better simulate the mechanical properties of the field reefs in laboratory tests, C30 concrete with a uniaxial compressive strength characteristic value of 30 MPa was selected as the simulation material. Its strength level is basically consistent with the statistical average value of the field reefs and is highly representative. The specimen size was 170 cm (length). (Width) (High). During the test, the rock specimen to be excavated was placed in a trench below the milling equipment, while the remaining specimens were placed on both sides of the equipment as counterweights to prevent the equipment from tipping over during milling and to ensure that the milling head continuously breaks the rock under stable conditions. Figure 8 As shown in (e) in the diagram.

[0059] To investigate the reef-breaking behavior of the milling head at different cutting depths, four cutting depth conditions were set up in the experiment: d = 0.05 m, 0.10 m, 0.15 m, and 0.20 m. During the experiment, the hydraulic pump was first started and put into standby mode; after adjusting the milling head to an airborne position, rotation was initiated; once the rated speed was reached, the vertical hydraulic cylinder was operated to uniformly lower the milling head for vertical drilling and breaking. When the preset cutting depth was reached, the horizontal hydraulic cylinder was switched to allow the milling head to uniformly break the reef laterally; once the lateral breaking range reached the preset value, the milling head was stopped, and it was lifted and reset using the vertical hydraulic cylinder. During the experiment, the cutting force of the milling head was recorded, and the degree of breakage of the reef specimen was measured and analyzed.

[0060] 2. Numerical Model Establishment and Validation To further explore the variation law of the cutting force of the milling head with various operating parameters during the reef breaking process, and to verify the rationality of the average cutting force model (Equation (15)) established by this method, this embodiment uses 3DEC discrete element software to construct a numerical simulation model to simulate the lateral swing reef breaking process of the milling head.

[0061] (1) Geometric model Based on the actual structure of the milling head, a 3D model was created using Rhino 6 software. The model milling head has a radius R of 0.34m and is arranged with 6 cutting lines (s=6). Each cutting line is evenly equipped with 12 cutting teeth (m=12), and the geometric parameters of the cutting teeth are consistent with the aforementioned single cutting tooth model. The dimensions of the rock model are set as follows: To improve overall computational efficiency while maintaining computational accuracy in the core region, the model employs a gradual mesh generation strategy. Based on previous mesh independence verification results, a fine mesh of 0.02m is set in the core region where the milling head contacts the rock, gradually transitioning to a coarser mesh of 0.2m towards the periphery. The specific mesh generation is as follows: Figure 9As shown, Figure 9 Numerical simulation model for milling and breaking reefs.

[0062] (2) Material parameters In the numerical model, the milling head is set as a rigid body element, and the rock block elements adopt a linear elastic constitutive model and are set as deformable bodies to accurately simulate the formation process of the dense core of the reef under the extrusion of the cutting teeth. The contact behavior between blocks is simulated using the Coulomb slip model. The blocks are bonded together through the contact surface, and failure occurs when the contact stress exceeds their bond strength. The mechanical parameters of the rock in the numerical model are set as shown in Table 1.

[0063] like Figure 10 As shown, Figure 10 Uniaxial compression and Brazilian splitting tests; where (a) RTM-150C rock mechanics testing system, (b) UCS, (c) BTS; Figure 11 As shown, Figure 11 Numerical simulation results of uniaxial compression and Brazilian splitting strength tests; where (a) UCS, (b) BTS; To ensure that the mechanical behavior of the reef in the numerical model is consistent with the indoor test results, the numerical rock mass parameters were systematically calibrated and verified. First, standard indoor mechanical tests were carried out on the rock specimens used in the experiment, including uniaxial compressive strength (UCS) test and Brazilian splitting strength (BTS) test. The test used an RTM-150C rock mechanics testing system, and the loading rate was set to 1 kN / s, such as Figure 10 As shown in (a) above. Based on the 3DEC platform, a discrete element numerical model with dimensions completely consistent with the indoor test was established, and the same loading rate was used for simulation. The physical test results show that compressive-shear cracks are distributed on the surface of the UCS specimen. Figure 10 (b) In this case, the BTS specimen broke into two halves along the diameter direction. Figure 10 c). Numerical simulation results ( Figure 11 a) and b) in the model successfully reproduced the above-mentioned failure modes, indicating that the numerical model can capture the main failure modes of rocks well.

[0064] To further verify the accuracy of the material mechanical behavior in the numerical model, the mechanical response curves obtained from physical experiments and numerical simulations were compared. For example... Figure 12 As shown, Figure 12 Comparison of stress-strain and load-displacement curves from experiments and numerical simulations: (a) UCS, (b) BTS; where (a) under uniaxial compression conditions, the stress-strain curve obtained from numerical simulation matches the physical test results well in the elastic stage and at the peak strength. Figure 12(b) shows that the load-displacement curves obtained from the numerical simulation under Brazilian splitting conditions are in good agreement with the physical test results in the initial elastic segment, peak strength, and post-peak softening stage. The calibrated numerical model can accurately reflect the mechanical behavior of rock under uniaxial compression and Brazilian splitting loading, and its key indicators such as compressive strength, tensile strength, and failure mode are all consistent with the physical test results.

[0065] 3. Simulation Working Condition Design To systematically reveal the variation law of cutting force during the lateral swing of the milling head to break reefs, and to verify the predictive ability of the multi-tooth cutting force calculation model (Equation (15)), this study designed 20 sets of numerical simulation conditions with different parameter combinations (see Table 2) to test whether the model can accurately characterize the intrinsic relationship between the average cutting force and key operating parameters (depth of cut d, lateral swing speed v and milling head rotation speed n).

[0066] Table 2. Parameter Combination Table for Yaw Conditions IV. Results and Discussion like Figure 13 As shown, Figure 13 A comparison of the cutting force time history curves of the milling head obtained from experiments and numerical simulations, and further comparison of the cutting force time history curves during the drilling and reef-breaking process of the milling head. Figure 13 It can be observed that the cutting forces obtained from the experiments and numerical simulations show good consistency in their overall trend, both exhibiting periodic fluctuations and a gradual increase. Compared to the numerical simulation results, the time history curves of the cutting forces measured in the experiments show more significant fluctuations due to the material heterogeneity of the rock specimens used in the experiments. However, the average cutting force obtained from the experiments is 174.6 kN, while the average cutting force calculated by the numerical simulation is 159.3 kN, with a deviation of 8.78%. In the numerical simulation of the highly nonlinear problem of rock breaking, this deviation level is within an acceptable range, indicating that the established numerical simulation model can reflect the macroscopic cutting force response during the rock breaking process of the milling head well.

[0067] In summary, the established numerical model can effectively simulate the reef-breaking process of the milling head, and the simulation results agree well with the experimental data, verifying the reliability of the numerical method. Therefore, subsequent simulations will be conducted based on this model under various combinations of operating parameters of the milling head to systematically analyze the variation law of cutting force under different operating conditions.

[0068] To compare the results of the numerical simulation with the theoretical value calculated by the milling head multi-tooth cutting force calculation model (15), the parameter combination corresponding to working condition 14 set in the numerical simulation, the structural parameters of the milling head, and the mechanical parameters of the rock were substituted into equation (15) to calculate the theoretical value of the average cutting force FT of the milling head under this working condition. The result was then plotted with the numerical simulation results. Figure 14 A comparative analysis was conducted. Figure 14 Cutting force time history curve calculated by digital model; Figure 14 The cutting force time history curve for working condition 14 is shown. The average cutting force in the numerical simulation is 62.6 kN, and the average cutting force calculated using equation (15) is 55.5 kN. The comparison shows that the calculated value of the theoretical model is 7.1 kN lower than that of the numerical simulation, but the two are in good agreement in terms of magnitude, indicating that the established average cutting force model has reasonable predictive ability.

[0069] Furthermore, to further verify the theoretical model, the average cutting force at different cutting depths (d=0.05 m, 0.10 m, 0.15 m, 0.20 m) in the milling and reef-breaking test was compared with the numerical simulation results and the theoretical model predictions. Figure 15 As shown, Figure 15 Comparative verification of the theoretical model for the average cutting force: The results show that the experimentally measured average cutting force and the numerical simulation results exhibit good consistency in both magnitude and trend. The experimental value is slightly higher than the numerical simulation value, mainly due to the randomness of the rock material and the inherent additional resistance of the experimental system. Meanwhile, the experimental results also show good consistency with the theoretical model calculations; the trend of the average cutting force with cutting depth matches the theoretical model prediction, further verifying the effectiveness of the established theoretical model.

[0070] To further reveal the intrinsic relationship between cutting force and milling head operating parameters, the average cutting force under other numerical simulation conditions was extracted, and the theoretical predicted value under the corresponding parameter combination was calculated using Equation (15). Figure 16 The results of numerical simulations are presented in a systematic comparison with the predictions of theoretical models. Figure 16 Figure (a) shows the variation of the mean cutting force FT with yaw speed v at different depths of cut d under a fixed rotational speed (n=60 r / min). The results show that the mean cutting force FT increases with both the depth of cut d and the yaw speed v; and the greater the depth of cut d, the more significant the increase of FT with yaw speed. Figure 16 Figure (b) shows the relationship between the mean cutting force FT and the rotational speed n under the conditions of fixed cutting depth (d=0.2m) and yaw speed (v=0.05m / s). It can be seen that the mean cutting force FT gradually decreases as the rotational speed n increases.

[0071] like Figure 16 As shown, Figure 16 Comparison of the cutting force mean prediction model and the numerical model results: (a) the relationship between FT and d, v; (b) the relationship between FT and n. Figure 16The numerical simulation results show good agreement with the theoretical predictions of Equation (15), and the theoretical model accurately reflects the overall trend of the average cutting force FT as a function of various operating parameters (d, v, n). The theoretical model of Equation (15) also provides a reasonable explanation for the phenomena observed in the numerical simulation. The average cutting force exhibits a quadratic function relationship with the yaw rate v and the rotational speed n, which stems from the dynamic change of the cutting thickness h; while the complex functional relationship between FT and the cutting depth d reflects the influence mechanism of the milling head-rock contact area on the cutting resistance.

[0072] To evaluate the advantages of the model provided in this embodiment compared to the traditional Evans model in predicting the average cutting force of multiple cutting teeth, the average cutting force was calculated using the theoretical model, the Evans model, and numerical simulation under different working conditions of the milling head. In the Evans model, the total cutting force of the milling head is obtained by the linear superposition of the independent forces of each cutting tooth, and the force of each cutting tooth is calculated using the original Evans formula. The calculation results of the three methods are compared, as follows... Figure 17 As shown, Figure 17 This is a comparison between the theoretical cutting force and the digital cutting force. Figure 17 The comparison between the predicted values ​​of the model provided in this embodiment, the Evans model, and the numerical simulation results under 20 cutting conditions is presented. It can be seen that the predicted values ​​of the established multi-tooth cutting force mean model are closer to the numerical simulation results, with a fitted line slope of 0.913, close to the ideal slope y=x; while the fitted slope of the Evans model's predicted values ​​is only 0.565, showing a significant deviation from the actual situation. This improvement is due to the introduction of a dynamic variation function of cutting thickness, yaw kinematics, and a multi-tooth synergistic mechanism into the Evans model, making the model more closely reflect the force characteristics of the milling head in actual engineering.

[0073] It is worth noting that at lower oscillation speeds, the single-tooth cutting process exhibits a significant discrete characteristic of "energy accumulation - brittle fracture - complete release" (Energy accumulation - brittle fracture - complete release). Figure 6 (a and b in the text) This instantaneous deviation will propagate to the prediction of the multi-tooth average cutting force model, causing the prediction accuracy of the model to decrease under extreme working conditions such as extremely low oscillation speed or extremely thin cutting thickness.

[0074] Overall, the predicted values ​​of the model provided in this embodiment are slightly lower than the numerical simulation results, with an average deviation of 9.8%. This deviation mainly stems from the fact that the theoretical model has not fully considered the effects of friction at the cutter-rock interface and the rock mass clamping effect. Nevertheless, the model demonstrates good engineering applicability in terms of both prediction trends and numerical accuracy. By reasonably adjusting the depth of cut, yaw rate, and rotational speed, the cutting force can be effectively controlled, thereby improving construction efficiency, reducing equipment wear, and extending the service life of the milling head, providing a theoretical basis for optimizing milling and reef clearing construction parameters.

[0075] The above-described embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A method for predicting the average cutting force of a multi-tooth milling head with rotation-yaw coupling, characterized in that, Includes the following steps: Step 1: Establish a dynamic model of the instantaneous cutting force of a single cutting tooth. The model is based on Evans cutting theory and introduces the time-varying function of the cutting thickness caused by the rotation-yaw coupling motion of the cutting tooth and the angle between the axis of the cutting tooth and the tangent of the cutting trajectory at the tooth tip to obtain the expression of the instantaneous cutting force of a single cutting tooth changing with time. Step 2: Obtain the structural and operational parameters of the milling head. The structural parameters include the number of cutting lines, the number of cutting teeth on each cutting line, and the cutting radius of the cutting teeth. The operational parameters include the yaw rate, depth of cut, and rotational speed. Step 3: Based on the assumption that the cutting teeth are uniformly distributed in the circumferential direction of the milling head, within the rotation angle range of the cutting teeth involved in rock breaking, the cutting force contribution of a single cutting tooth is integrated and superimposed to establish a mathematical model between the average total cutting force of multiple cutting teeth and the structural parameters and the operating parameters. Step 4: Substitute the obtained rock mechanics parameters, cutting tooth geometric parameters, structural parameters, and operating parameters into the mathematical model to calculate the average predicted cutting force of the milling head under given working conditions.

2. The method for predicting the average cutting force of a multi-tooth milling head with rotation-yaw coupling as described in claim 1, characterized in that, In step 1, the instantaneous cutting force of the single cutting tooth The mathematical model for its variation with time t is as follows: In the formula: The tensile strength of the rock; The compressive strength of the rock; The semi-cone angle of the pick-shaped cutting tooth; θ is the angle between the axis of the cutting tooth and the tangent of the cutting trajectory at the tooth tip; n is the milling head rotation speed of the cutting tooth; t is the time it takes for the cutting tooth to rotate and cut the rock. This indicates the maximum cut thickness.

3. The method for predicting the average cutting force of a multi-tooth milling head with rotation-yaw coupling as described in claim 2, characterized in that, The equivalent radius The calculation formula is: In the formula, denoted as , where is the equivalent radius of the elliptical cross-section of the contact surface between the pick and the rock; 'a' is the radius of the pick when it contacts the rock. The semi-cone angle of the pick-shaped cutting tooth; It is the angle between the axis of the cutting tooth and the tangent to the cutting trajectory at the tooth tip.

4. The method for predicting the average cutting force of a multi-tooth milling head with rotation-yaw coupling as described in claim 2, characterized in that, In step 1, the cutting thickness h is expressed as a sine function with respect to time t: In the formula: n is the rotational speed of the milling head; t is the time for the cutting teeth to rotate and cut the rock; hmax is the maximum cutting thickness.

5. The method for predicting the average cutting force of a multi-tooth milling head with rotation-yaw coupling as described in claim 1, characterized in that, In step 3, the formula for calculating the cutting force Fm of a single cutting tooth at the maximum cutting thickness is: Where Fm is the maximum cutting force of each cutting tooth on the same cutting line during one rotation of the cutting process, that is, the cutting force of the cutting tooth at the maximum cutting thickness hmax. The tensile strength of the rock; The compressive strength of the rock; The semi-cone angle of the pick-shaped cutting tooth; is the angle between the axis of the cutting tooth and the tangent to the cutting trajectory at the tooth tip; n is the milling head rotation speed; m represents the number of cutting teeth on the same cutting line; This represents the maximum cutting thickness; v is the yaw speed of the milling head.

6. The method for predicting the average cutting force of a multi-tooth milling head with rotation-yaw coupling as described in claim 5, characterized in that, In step 3, the rotation angle range of the cutting teeth involved in rock breaking is determined based on the depth of cut and the cutting radius of the cutting teeth: in, The rotation angle range of the cutting teeth involved in rock breaking; d is the depth of cut; R is the cutting radius of the cutting teeth.

7. The method for predicting the average cutting force of a multi-tooth milling head with rotation-yaw coupling as described in claim 6, characterized in that, In step 3, the average total cutting force F of the multi-tooth cutting teeth T The mathematical model is as follows: in, This represents the cutting force generated per unit rotation angle. This represents the maximum cutting force of each cutting tooth on the same section line during one rotation of the cutting process; The range of rotation angles of the cutting teeth involved in rock breaking; The rotation angle of the cutting teeth is represented by s; the number of sections of the cutting teeth arrangement on the milling head is represented by m; the number of cutting teeth on the same section is represented by d; and the cutting radius of the cutting teeth on the milling head is represented by R.

8. The method for predicting the average cutting force of a multi-tooth milling head with rotation-yaw coupling as described in claim 7, characterized in that, Fm and After substituting the expression, the mathematical model of the average total cutting force FT of the multi-tooth cutting teeth expands to: In the formula: s is the number of cut lines arranged in the milling head cutting teeth; The tensile strength of the rock; The compressive strength of the rock; The semi-cone angle of the pick-shaped cutting tooth; denoted by , where is the angle between the axis of the cutting tooth and the tangent to the cutting trajectory at the tooth tip; v is the yaw speed of the milling head; n is the rotational speed of the milling head; m is the number of cutting teeth on the same cutting line; d is the depth of cut during the yaw of the milling head; and R is the cutting radius of the cutting teeth of the milling head.

9. A system for predicting the average cutting force of a multi-tooth milling head with rotation-yaw coupling, used to perform the method as described in any one of claims 1-8, characterized in that, include: The data acquisition module is used to acquire rock mechanics parameters, cutting tooth geometric parameters, milling head structural parameters and operating parameters. The structural parameters include the number of cutting lines, the number of cutting teeth on each cutting line, and the cutting radius of the cutting teeth. The operating parameters include yaw rate, depth of cut, and rotational speed. The model building module, connected to the data acquisition module, is used to establish a dynamic model of the instantaneous cutting force of a single cutting tooth, and to establish a mathematical model of the average total cutting force of multiple cutting teeth based on the assumption of uniform distribution of cutting teeth and integral superposition. The calculation module, connected to the model building module, is used to substitute the parameters obtained by the data acquisition module into the mathematical model to calculate the average predicted cutting force. The output module, connected to the calculation module, is used to output the average value of the predicted cutting force.

10. The multi-tooth milling head rotation-yaw coupling cutting force mean prediction system as described in claim 9, characterized in that, It also includes a parameter optimization module, which is connected to the calculation module and is used to output an optimized value of at least one of the following parameters: depth of cut, yaw rate, and rotational speed, based on the predicted average cutting force.

Images