Novel Intelligent Autonomous Control Method and Control System for Vertical Hydraulic Turbulent Flow Mill
By using multi-speed control and an embedded DSP system, the rotational speed of the vertical mill is monitored and adjusted in real time, solving the problems of starting current surge and low grinding efficiency, and achieving efficient and safe operation of the vertical mill, adapting to various environments.
Patent Information
- Application Number
- CN202310883000.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-07-19
- Publication Date
- 2025-11-14
- Estimated Expiration
- 2043-07-19
AI Technical Summary
Existing vertical mills have large starting current surges, large voltage fluctuations, low power factor, and low grinding efficiency. They are difficult to achieve uniform grinding over a wide speed range and are prone to resonance or reverse crushing.
A multi-speed control method is adopted, which combines multi-dimensional sensors and an embedded DSP control system to monitor and adjust the speed of the high-speed motor in real time. The mill status is monitored by displacement, pressure and noise sensors, and the motor is controlled to operate within a reasonable range. Segmented speed adjustment is used to achieve the best grinding effect.
It improves the grinding efficiency and safety of vertical mills, reduces energy consumption, broadens the application range of motors, adapts to harsh environments, and improves grinding accuracy and system stability.
Smart Images

Figure CN116871040B_ABST
Abstract
Description
Technical fields:
[0001] This invention belongs to the technical field of powder grinding equipment, specifically relating to a novel intelligent autonomous control method and control system for a vertical hydraulic turbulent mill. Background technology:
[0002] Early vertical mills used asynchronous motors as the drive system, mainly employing autotransformer reduction, soft start, and frequency converters for starting. The autotransformer reduction starting method resulted in a starting current of 6 to 7 times the motor's rated current. Later soft start methods resulted in a starting current of 4 to 5 times the motor's rated current. Currently, frequency converter starting is the most commonly used method, with a starting current of 2 to 3 times the motor's rated current. These starting methods place too much impact on the transformer and power grid, causing large voltage fluctuations, a decrease in power factor, excessive starting power consumption, and accelerating the aging of contactors in the starter cabinet and mechanical transmission facilities in the vertical mill.
[0003] Currently, vertical mills primarily use a constant-speed method to grind materials. After a period of grinding, only a small portion of materials within the narrower particle size distribution band achieves good grinding, while the majority of the material is poorly ground. If the mill speed could be adjusted to a wider range, allowing for thorough grinding of all materials, the grinding efficiency could be significantly improved. However, improper adjustment of the mill's operating speed—too high, potentially causing system resonance and operational accidents; too low, significantly impacting mill efficiency and possibly leading to reverse crushing—is problematic. Therefore, this invention provides a novel intelligent autonomous control method and control system for vertical hydraulic turbulence mills to address these issues. Summary of the Invention:
[0004] The purpose of this invention is to address the shortcomings of existing technologies by providing a novel intelligent autonomous control method and control system for vertical hydraulic turbulent mills. This system solves the problems of excessive impact from motor startup on the turbulent mill and large voltage fluctuations leading to a decrease in power factor. At the same time, it adopts multi-speed control to improve the grinding efficiency of the turbulent mill, save energy, and enable the entire system to operate in the optimal state.
[0005] The present invention adopts the following technical solution:
[0006] (I) A novel intelligent autonomous control method for a vertical hydraulic turbulent mill, comprising the following steps:
[0007] S1. Based on the working conditions of the turbulent mill, set the turbulent mill to three grinding states: high-speed grinding, medium-high-speed grinding, and medium-speed grinding. The initial mode is medium-speed grinding.
[0008] S2. Set the starting speed of medium-speed grinding to V1 and the running time to T1; the starting speed of medium-high speed grinding to V2 and the running time to T2; the starting speed of high-speed grinding to V3 and the running time to T3; and the allowable speed of high-speed grinding to V4.
[0009] S3. Set the initial operating speed of the high-speed motor to V0, and set the starting slope of the high-speed motor to k. Then, the instantaneous reference speed during the starting process is V. * =kV0t, where t is time, and the value of k is in the range of 0 < k < 1;
[0010] S4. Start the high-speed motor. The high-speed motor will operate at the reference speed V. * Based on the baseline, soft start operation is performed. When the speed reaches the medium-speed grinding start speed V1, the high-speed motor drives the turbulent mill to work in the medium-speed grinding state.
[0011] S5. In medium-speed grinding mode, the high-speed motor runs at a variable speed according to V=V1+[(V2-V1) / T1]t. When the speed reaches V2, it can be switched to medium-high speed grinding mode or the current grinding mode can be maintained according to actual needs.
[0012] S6. In medium-high speed grinding mode, the high speed motor runs at a variable speed according to V=V2+V2 / T2·t. When the speed reaches V3, it can be switched to high speed grinding mode or the current grinding mode can be maintained according to actual needs.
[0013] S7. In high-speed grinding mode, the high-speed motor operates at a speed of V = V3 + [(V3-V2) / T3]t, and the high-speed motor operating speed is controlled between V3 and V4.
[0014] Furthermore, in S1, when the ratio of the excitation frequency to the first-order natural frequency is greater than 0.5, it is a high-speed grinding state.
[0015] Furthermore, in S2, V3 is the speed when the ratio of the excitation frequency to the first-order natural frequency is equal to 0.5, and V4 is the maximum safe speed at which all parameters meet the requirements.
[0016] Furthermore, since the excitation frequency is positively correlated with the motor speed, the excitation frequency differs significantly from the natural frequency under medium-speed and medium-high-speed grinding conditions, thus preventing resonance. However, during high-speed grinding, to improve grinding efficiency, the speed needs to be controlled within a certain range, namely between V3 and V4, to ensure that the ratio of the excitation frequency to the natural frequency remains within a certain range. Therefore, when the high-speed motor speed is below V3, an acceleration process is implemented; when the high-speed motor speed is above V4, which is the maximum safe speed that meets the requirements of all parameters, a deceleration process is implemented.
[0017] Furthermore, when the turbulent mill system is in a high-speed grinding state, i.e., when the ratio of the excitation frequency to the first-order natural frequency is greater than 0.5, the excitation frequency is the same as or very close to the natural frequency of the turbulent mill system. That is, when the excitation frequency f is close to the natural frequency f... 固 When the ratio of the excitation frequency to the first natural frequency is 1, the system will resonate. To ensure the safe operation of the turbulent mill, the frequency ratio must be controlled within a certain range. Since the excitation frequency is positively correlated with the motor speed, controlling the speed within a certain range is sufficient. Because the turbulent mill has multiple degrees of freedom, the system possesses multiple natural frequencies, the lowest of which is the first natural frequency. The effect is best when the ratio of the excitation frequency to the first natural frequency is greater than 0.5 and less than 0.8. However, since pressure and noise parameters need to be kept within safe ranges, the excitation frequency should be the primary parameter, with pressure and noise as secondary parameters. That is, the permissible high-speed grinding speed V4 must simultaneously meet the following conditions:
[0018]
[0019]
[0020] Where f is the excitation frequency, f 固 L is the first natural frequency of the turbulent mill; L is the real-time system noise intensity. max P is the maximum permissible system noise level; P is the real-time pressure at the top of the turbulent grinding cylinder. max The maximum allowable pressure at the top of the turbulent grinding cylinder is given. When f, L, and P meet the conditions of equations (1) and (2), the motor accelerates. When any equation is not met, the motor decelerates, so that the parameters are always controlled within a reasonable range, which ensures both the efficiency and safety of high-speed grinding.
[0021] Furthermore, the real-time pressure P is monitored in real time by a pressure sensor installed on the top of the turbulent mill cover cylinder; the real-time system noise intensity L is monitored in real time by a noise sensor; and the excitation frequency f is calculated by combining the displacement of the turbulent mill monitored in real time by a displacement sensor with the time relationship.
[0022] Furthermore, in S7, when the advance detection indicates that V4 is 2 seconds away, a graded deceleration is performed within 2 seconds. In the first second of the graded deceleration, the speed is reduced by 5% of the current speed, and in the last second, the speed is reduced by 10% of the current speed.
[0023] (II) This invention also provides a novel intelligent autonomous control system for a vertical hydraulic turbulent mill, comprising: a vertical hydraulic turbulent mill body, a data acquisition card, a high-speed motor, a multi-dimensional sensor module, and a DSP controller. The multi-dimensional sensor module and the data acquisition card are signal-connected to the DSP controller, and the DSP controller is signal-connected to the high-speed motor. The high-speed motor controls the operation of the vertical hydraulic turbulent mill body. The multi-dimensional sensor module includes a displacement sensor, a pressure sensor, and a noise sensor. The displacement sensor is installed on the vertical hydraulic turbulent mill body to monitor the displacement of the turbulent mill. The DSP controller calculates the excitation frequency by combining the displacement with the time relationship. The pressure sensor is installed on the top of the cover cylinder of the turbulent mill body to monitor the pressure on the top. The noise sensor is used to monitor the intensity of system noise generated during the operation of the turbulent mill.
[0024] Furthermore, the multi-dimensional sensor module monitors the system noise intensity, system vibration displacement, and pressure signal on the top of the cover cylinder of the turbulent mill. After amplification, the monitoring signals are input to the embedded DSP controller via the data acquisition card. After processing by the built-in analysis program of the embedded DSP controller, the data acquisition card inputs the control signal to the high-speed motor, thereby controlling the turbulent mill to perform efficient and safe grinding within a controllable range.
[0025] The beneficial effects of this invention are:
[0026] 1. Based on the changes in the operation of the mill, the mill operates in multiple speed stages from coarse grinding to fine grinding, so that the grinding media and the material can achieve sufficient friction in each grinding stage, thus achieving the most ideal production process, greatly improving the grinding efficiency of the ball mill, and realizing energy-saving operation.
[0027] 2. This invention can adjust the grinding speed and grinding time of the turbulent mill according to the type and fineness of the material, so that the material is fully ground, which can meet the grinding requirements of high fineness, greatly reduce the grinding time, and improve the grinding efficiency of the turbulent mill.
[0028] 3. This invention uses an embedded DSP control system and a multi-dimensional sensor module to process the high-speed operation of the turbulent mill in real time, enabling it to process signals transmitted from various sensors at high speed and adjust the speed of the high-speed motor in real time according to the collected parameters.
[0029] 4. This invention uses a high-speed motor to drive the turbulent mill. High-speed motors are simple, robust, and reliable, featuring high speed, low noise, high power density, and high fault tolerance. They can adapt to harsh environments such as high speed and heavy load, and have an extremely wide adjustable operating speed range. Ordinary motors are limited by bearings, resulting in lower speed and power ratings and extremely limited applicability. This invention significantly increases the motor's speed and power rating, broadening its application range and ensuring stable operation in harsh environments such as high temperatures and high dust levels. While increasing the speed, it effectively improves the grinding accuracy of the turbulent mill, completely solving the drawbacks of low speed and frequent damage. Attached image description:
[0030] Figure 1 This is a flowchart of the speed-up method in an embodiment of the present invention;
[0031] Figure 2 This is a block diagram of the control system structure in an embodiment of the present invention. Detailed implementation method:
[0032] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.
[0033] Example 1
[0034] Reference Figure 2 This invention provides a novel intelligent autonomous control method for a vertical hydraulic turbulent mill, comprising the following steps:
[0035] S1. Based on the working conditions of the turbulent mill, set the turbulent mill to three grinding states: high-speed grinding, medium-high-speed grinding, and medium-speed grinding. The initial mode is medium-speed grinding. When the ratio of the excitation frequency to the first-order natural frequency is greater than 0.5, it is in the high-speed grinding state.
[0036] S2. Set the starting speed of medium-speed grinding to V1, which is a fixed speed of 10000 rpm, and the running time to T1. Set the starting speed of medium-high speed grinding to V2, which is a fixed speed of 15000 rpm, and the running time to T2. Set the starting speed of high-speed grinding to V3, which is the speed when the ratio of the excitation frequency to the first-order natural frequency is 0.5, and the running time to T3. Set the allowable speed of high-speed grinding to V4, which is the maximum safe speed that meets the requirements of all parameters.
[0037] S3. Set the initial operating speed of the high-speed motor to V0, and set the starting slope of the high-speed motor to k. Then, the instantaneous reference speed during the starting process is V. * =kV0t, where t is time, and the value of k is in the range of 0 < k < 1;
[0038] S4. Start the high-speed motor. The high-speed motor will operate at the reference speed V. * Perform a soft-start operation as a baseline, V * The speed is 5000 rpm. When the speed reaches the starting speed V1 of medium-speed grinding, the high-speed motor drives the turbulent mill to work in medium-speed grinding mode. It can be switched to medium-speed grinding mode or maintained in the current grinding mode according to actual needs.
[0039] S5. In medium-speed grinding mode, the high-speed motor runs at a variable speed according to V=V1+[(V2-V1) / T1]t. When the speed reaches V2, it can be switched to medium-high speed grinding mode or the current grinding mode can be maintained according to actual needs.
[0040] S6. In medium-high speed grinding mode, the high speed motor runs at a variable speed according to V=V2+V2 / T2·t. When the speed reaches V3, it can be switched to high speed grinding mode or the current grinding mode can be maintained according to actual needs.
[0041] S7. In high-speed grinding, the high-speed motor operates at a variable speed according to V = V3 + [(V3 - V2) / T3]t. Since the excitation frequency is positively correlated with the motor speed, the excitation frequency differs significantly from the natural frequency in medium-speed and medium-high-speed grinding, thus preventing resonance. However, in high-speed grinding, to improve grinding efficiency, the speed must be controlled within a certain range, i.e., between V3 and V4, to ensure that the ratio of the excitation frequency to the natural frequency remains within a certain range. Therefore, when the high-speed motor speed is below V3, an acceleration process is implemented; when the high-speed motor speed is above V4, which is the maximum safe speed that meets all parameters, a deceleration process is implemented.
[0042] In this embodiment of the invention, after the turbulent mill runs at a given speed, the control system judges the grinding state based on the working parameters collected by the multi-dimensional sensor module, and controls the high-speed motor to adjust the speed up or down. The multi-dimensional sensor module includes a displacement sensor, a pressure sensor, and a noise sensor. The turbulent mill has obvious differences in vibration, noise, and pressure under the same rotation speed and different working conditions. The grinding state of the turbulent mill is judged based on the data analysis of the three aspects.
[0043] Specifically, after the turbulent mill starts running at a given speed, the multi-dimensional sensor module and the embedded DSP control system begin operation. First, initialization begins. During initialization, the turbulent mill runs at the given speed, and it is necessary to check whether each sensor, communication module, and functional module is working properly. After initialization, amplitude, noise, and pressure are collected. The displacement sensor collects vibration data of the entire turbulent mill system, the noise sensor collects system noise during operation, and the pressure sensor collects pressure data at the top of the cover cylinder. All of this data is then transmitted to the embedded DSP control system.
[0044] When the turbulent mill system is in high-speed grinding mode, that is, when the ratio of the excitation frequency to the first-order natural frequency is greater than 0.5, the excitation frequency is the same as or very close to the natural frequency of the turbulent mill system. When the excitation frequency f and the natural frequency f 固 When the frequency ratio is 1, the system will resonate. To ensure the safe operation of the turbulent mill, the frequency ratio must be controlled within a certain range. Since the excitation frequency is positively correlated with the motor speed, controlling the speed within a certain range is sufficient. The displacement sensor detects the displacement of the turbulent mill, and the DSP controller determines the excitation frequency based on the displacement-time relationship. Because the turbulent mill has multiple degrees of freedom, the system has multiple natural frequencies, the lowest of which is the first natural frequency. The effect is better when the ratio of the excitation frequency to the first natural frequency is greater than 0.5 and less than 0.8. However, since the pressure and noise parameters need to be kept within a safe range, the excitation frequency should be the primary parameter, with pressure and noise as auxiliary parameters. That is, the allowable high-speed grinding speed V4 requires the excitation frequency f, pressure P, and noise intensity L to simultaneously meet the following conditions:
[0045]
[0046]
[0047] Where f is the excitation frequency, f 固 L is the first natural frequency of the turbulent mill; L is the real-time system noise intensity. max P is the maximum permissible system noise level; P is the real-time pressure at the top of the turbulent grinding cylinder. max The maximum allowable pressure at the top of the turbulent grinding cylinder is given. When f, L, and P meet the conditions of equations (1) and (2), the motor accelerates. When any equation is not met, the motor decelerates or accelerates, so that the parameters are always controlled within a reasonable range, which ensures both the efficiency and safety of high-speed grinding.
[0048] In this embodiment of the invention, considering the possibility of speed exceeding the limit during the grinding process, this situation should be taken into account in the program. For speed exceeding the limit, adjustments need to be made in advance. If the speed is lower than the set lower limit, the turbulent mill is operating in an inefficient state, which does not meet actual production needs, and speed increase processing is required. If the speed is higher than the set upper limit, to avoid damage to the turbulent mill due to high-speed operation, speed reduction should be performed in advance. Since the speed of the turbulent mill is ultra-high speed, it is necessary to determine in advance whether the speed will exceed the maximum speed, and simultaneously detect the time required to exceed the maximum speed. When it is detected that only 2 seconds remain before reaching the maximum speed, speed reduction begins. The specific process is as follows: when it is detected that 30,000 rpm is reached with 2 seconds remaining, a 2-second staged speed reduction is prepared, that is, the speed is reduced by 5% in the first second of the staged speed reduction, and the speed is reduced by 10% in the last second.
[0049] Example 2
[0050] This invention provides a novel intelligent autonomous control system for a vertical hydraulic turbulent mill, comprising: a power supply, a vertical hydraulic turbulent mill body, a data acquisition card, a high-speed motor, a multi-dimensional sensor module, and a DSP controller. The power supply is connected to the high-speed motor via a power line, enabling the high-speed motor to drive the turbulent mill for grinding operations. The structure of the vertical hydraulic turbulent mill body is described in the invention patent application number 2021103315291, entitled "A High-Efficiency Vertical Hydraulic Turbulent Mill for Ultrahard and Ultrafine Powders," and will not be described in detail here.
[0051] The multidimensional sensor module, data acquisition card, and DSP controller are connected by signal. The DSP controller is connected by signal to the high-speed motor, which controls the operation of the vertical hydraulic turbulent mill body. The multidimensional sensor module includes a displacement sensor, a pressure sensor, and a noise sensor. The displacement sensor is installed on the vertical hydraulic turbulent mill body to monitor the displacement of the turbulent mill. The DSP controller calculates the excitation frequency by combining the displacement with the time relationship. The pressure sensor is installed on the top of the cover cylinder of the turbulent mill body to monitor the pressure on the top of the cover cylinder. The noise sensor is used to monitor the system noise intensity generated during the operation of the turbulent mill.
[0052] The multidimensional sensor module monitors the system noise intensity, system vibration displacement, and pressure signal on the top of the cover cylinder of the turbulent mill. After amplification, the monitoring signals are input to the embedded DSP controller via the data acquisition card. After processing by the built-in analysis program of the embedded DSP controller, the data acquisition card inputs the control signal to the high-speed motor. The high-speed motor controls the turbulent mill to change speed, so that the turbulent mill is always in a high-efficiency operating state.
[0053] The speed adjustment method is as follows: When the working mode is in medium-speed or medium-high-speed grinding state, the embedded DSP control system issues a speed adjustment command and adjusts the speed according to a determined speed-time relationship. When the working mode is in high-speed grinding state, safety hazards such as resonance and excessive pressure may occur. By collecting data on the vibration, noise, and pressure at the top of the cover cylinder of the turbulent mill through multi-dimensional sensors, the system comprehensively judges whether it is in a safe state. Based on this, the embedded DSP control system issues a speed adjustment command, which ultimately changes the rotation speed of the turbulent mill through the high-speed motor, controlling the rotation speed of the turbulent mill to always be in the optimal state, effectively ensuring the grinding efficiency of the turbulent mill.
[0054] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions that fall within the scope of the present invention are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principle of the present invention should be considered within the scope of protection of the present invention.
Claims
1. A novel intelligent autonomous control method for vertical hydraulic turbulent flow mills, characterized in that, Includes the following steps: S1. Set the turbulent mill to three grinding states: high-speed grinding, medium-high-speed grinding, and medium-speed grinding. The initial mode is medium-speed grinding. S2, Set the starting speed of medium-speed grinding to... The running time is The starting speed for medium-high speed grinding is The running time is The starting speed of high-speed grinding is The running time is The permissible rotational speed for high-speed grinding is ; S3. Set the starting operating speed of the high-speed motor to... If the starting slope of the high-speed motor is set to k, then the instantaneous reference speed during the starting process is: t is time, and the value of k is in the range of 0 < k < 1; S4. Start the high-speed motor, which operates at the instantaneous reference speed. Soft start operation is performed based on the reference speed, and the speed reaches the starting speed of medium-speed grinding. At that time, the high-speed motor drives the turbulent mill to work in medium-speed grinding mode; S5. In medium-speed grinding mode, the high-speed motor operates at the following speed: Variable speed operation is performed; when the speed reaches... When necessary, switch to medium-high speed grinding mode or maintain the current grinding mode according to actual needs; S6. In medium-high speed grinding mode, the high-speed motor operates at the following speed: Variable speed operation is performed; when the speed reaches... When needed, switch to high-speed grinding mode or maintain the current grinding mode, depending on the actual requirements. S7. In high-speed grinding mode, the high-speed motor operates at the following speed: Variable speed operation is performed, with the high-speed motor operating speed controlled between V3 and V4; The The following conditions must be met simultaneously: (1) (2) Where f is the excitation frequency, f 固 L is the first natural frequency of the turbulent mill; L is the real-time system noise intensity. max P is the maximum permissible system noise level; P is the real-time pressure at the top of the turbulent grinding cylinder. max This is the maximum allowable pressure at the top of the turbulent grinding cylinder.
2. The novel intelligent autonomous control method for vertical hydraulic turbulent mill according to claim 1, characterized in that, In S1, when the ratio of the excitation frequency to the first-order natural frequency is greater than 0.5, it is in high-speed grinding state.
3. The novel intelligent autonomous control method for vertical hydraulic turbulent mill according to claim 1, characterized in that, In S2, The velocity is defined as the ratio of the excitation frequency to the first natural frequency being equal to 0.
5. The maximum safe speed that meets the requirements of each parameter.
4. The novel intelligent autonomous control method for vertical hydraulic turbulent mill according to claim 1, characterized in that, The real-time pressure P is monitored in real time by a pressure sensor installed at the top of the turbulent grinding cylinder. The real-time system noise intensity L is monitored in real time by a noise sensor; The excitation frequency f is calculated by combining the displacement of the turbulent mill monitored in real time by the displacement sensor with the time relationship.
5. The novel intelligent autonomous control method for vertical hydraulic turbulent mill according to claim 1, characterized in that, In S7, when the timer detects that there are 2 seconds remaining before arrival... When the speed is reduced in stages within 2 seconds, the speed is reduced by 5% of the current speed in the first second of the staged speed reduction, and by 10% of the current speed in the last second.
6. A control system according to any one of claims 1 to 5, Its features are, It includes: a vertical hydraulic turbulence mill body, a data acquisition card, a high-speed motor, a multi-dimensional sensor module and a DSP controller. The multi-dimensional sensor module and the data acquisition card are connected to the DSP controller, and the DSP controller is connected to the high-speed motor. The high-speed motor controls the operation of the vertical hydraulic turbulence mill body. The multidimensional sensor module includes a displacement sensor, a pressure sensor, and a noise sensor; The displacement sensor is installed on the vertical hydraulic turbulent mill body to monitor the displacement of the turbulent mill. The excitation frequency is calculated by combining the displacement with the time relationship through the DSP controller. The pressure sensor is installed on the top of the turbulent mill body cover cylinder to monitor the pressure on the top. The noise sensor is used to monitor the intensity of system noise generated during the operation of the turbulent mill.
7. The control system according to claim 6, characterized in that, The multidimensional sensor module monitors the system noise intensity, system vibration displacement, and pressure signal on the top of the cover cylinder of the turbulent mill. After amplification, the monitoring signals are input to the embedded DSP controller via the data acquisition card. After processing by the built-in analysis program of the embedded DSP controller, the data acquisition card inputs the control signal to the high-speed motor, thereby controlling the turbulent mill to perform grinding within a controllable range.
Citation Information
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