Tension roller set dynamic load distribution method based on slipping mechanism

Abstract

The invention discloses a tension roller set dynamic load distribution method based on a slipping mechanism, and particularly relates to the field of dynamic load distribution. According to the method, a model is established by calculating tension loss and a tension roller inlet / outlet actual tension value and combining elastic deformation and geometric parameters; dividing the winding angle of the strip steel into micro-arc sections, analyzing the tension change in a critical sliding state, constructing a normal and tangential stress balance equation, and considering the influence of friction and gravity; according to the limit tension amplification coefficient of each tension roller, proportionally distributing the total tension ratio, initially assuming that the scale factors of each roller are equal, solving a common scale factor through iteration, and calculating the tension difference of each roller; further calculating transmission power and torque, comprehensively considering tension amplification, friction loss and bending loss, and checking with the capability of a driving motor; and if yes, adjusting the proportion of the upstream and downstream tension rollers, preferentially reducing the tension difference of the overrun rollers, and gradually optimizing until the power and torque of all the rollers meet the requirements.

Description

Technical Field

[0001] The present invention relates to the technical field of dynamic load distribution, and more specifically, to a dynamic load distribution method for a tension roll group based on a slip mechanism. Background Art

[0002] During the continuous strip production process, the dynamic load distribution of the tension roll group is a key technology to ensure the stable operation of the strip and product quality; during commissioning, the control of the tension roll group is mainly based on the speed of the No. 1 exit tension roll. The speed loops of other tension roll motors are saturated, and at the same time, the same torque ratio as the speed reference motor is given for torque control to achieve the tension control purpose and the ideal strip yield strength.

[0003] However, in actual use, there are still some disadvantages. For example, traditional load distribution methods often rely on static analysis and do not fully consider the friction and slip mechanisms under dynamic conditions, resulting in unstable working conditions of the roll group, material damage, and increased energy consumption. Summary of the Invention

[0004] In order to overcome the above-mentioned defects of the prior art, an embodiment of the present invention provides a dynamic load distribution method for a tension roll group based on a slip mechanism to solve the problems raised in the above background art.

[0005] To achieve the above object, the present invention provides the following technical solutions: Step A1: Calculate the tension loss and the actual tension values at the inlet and outlet of the tension roll. Step A2: Divide the wrap angle of the strip on the tension roll into multiple micro-arc segments, perform a force analysis on each micro-arc segment, and calculate the tension change under the critical sliding state. Step A3: According to the ultimate tension amplification factor of each tension roll, evenly distribute the tension ratio that the tension roll group needs to increase or decrease to each tension roll. Step A4: Calculate the required transmission power and torque of each tension roll according to the tension difference borne by each tension roll, and check according to the power and torque of the drive motor. Step A5: If the power or torque of a tension roll exceeds the capacity of the drive motor, adjust the tension amplification ratio of the upstream and downstream tension rolls until the power and torque of all tension rolls meet the requirements.

[0006] Preferably, in the step A1, when the strip is wrapped around the tension roll, elastic deformation and plastic deformation will occur inside it, resulting in tension loss. The calculation method of the tension loss caused by the elastic bending of the strip at the inlet and outlet of the tension roll is specifically: , where represents the tension loss caused by the elastic bending of the strip at the inlet and outlet, \(\sigma_s\) represents the yield strength of the strip, \(h\) represents the thickness of the strip, \(b\) represents the width of the strip, and \(R\) represents the bending radius of the strip, which is about 1.1 - 1.2 times the radius of the tension roll.

[0007] Preferably, in the step A2, for the strip wrapped around the tension roll, the normal force on it needs to satisfy the centripetal force balance condition; the strip within the actual wrap angle is evenly divided into \(n\) micro - arc segments. For the \(i\) - th micro - arc segment, the normal - force equation of the strip is: , where \(T_i\) represents the tension of the \(i\) - th micro - arc segment; \(\theta_i\) represents the central angle corresponding to the \(i\) - th micro - arc segment, \(\Delta T_i\) represents the difference between the tension near the outlet side and the tension near the inlet side on the \(i\) - th micro - arc segment, \(N_i\) represents the normal pressure of the \(i\) - th micro - arc segment on the surface of the tension roll, \(\alpha_i\) represents the angle between the \(i\) - th micro - arc segment and the perpendicular bisector, \(m_i\) represents the mass of the \(i\) - th micro - arc segment, and \(g\) represents the acceleration due to gravity, \(v\) represents the moving speed of the strip, and \(R\) represents the radius of the tension roll; For the inclined - installed tension roll or the vertical - motion component of the strip, the gravity changes the contact force between the strip and the tension roll, affecting the frictional force. Then the tangential - force equation is: , where \(T_i\) represents the tension of the \(i\) - th micro - arc segment; \(\theta_i\) represents the central angle corresponding to the \(i\) - th micro - arc segment, \(\Delta T_i\) represents the difference between the tension near the outlet side and the tension near the inlet side on the \(i\) - th micro - arc segment, \(F_{fi}\) represents the frictional force between the \(i\) - th micro - arc segment and the surface of the tension roll, \(\alpha_i\) represents the angle between the \(i\) - th micro - arc segment and the perpendicular bisector, \(m_i\) represents the mass of the \(i\) - th micro - arc segment, and \(g\) represents the acceleration due to gravity, \(v\) represents the moving speed of the strip, and \(R\) represents the radius of the tension roll.

[0008] Preferably, in the step A3, the tension - roll group is composed of \(N\) tension rolls. According to the geometric position of the strip wrapped around each tension roll, the cross - sectional dimensions of the strip, the speed of the unit, the acceleration and deceleration conditions, and combining with the friction coefficient at each tension roll, the ultimate - tension amplification factor of each roll under the current working conditions is obtained ; The calculation method of the ultimate - tension amplification factor is specifically: , where \(K\) represents the ultimate - tension amplification factor, It is expressed as the actual outlet tension of the strip on the tension roll after considering the tension loss, It is expressed as the actual inlet tension of the strip on the tension roll after considering the tension loss, It is expressed as the elastic bending of the strip at the inlet and outlet , where, It is expressed as the limit tension amplification coefficient, It is expressed as the actual outlet tension of the strip on the tension roll after considering the tension loss, It is expressed as the actual inlet tension of the strip on the tension roll after considering the tension loss, It is expressed as the tension loss caused by the elastic bending of the strip at the inlet and outlet; According to the actual tension amplification ability of each roll, the tension ratio that the tension roll group needs to expand or shrink is evenly distributed to each tension roll; when initially calculating, it is assumed that the ratio of the actual tension amplification ratio of each tension roll to the corresponding limit tension amplification coefficient is equal; that is: , where, 、 , ……, , ……, It is expressed as the proportionality factors of the 1st, 2nd, …… k …… Nth tension rolls, It is expressed as the common proportionality factor; Then the calculation method of the total tension ratio of the tension roll group is specifically: , where, It is expressed as the tension at the outlet of the tension roll group, It is expressed as the tension at the inlet of the tension roll group, 、 , ……, , ……, It is expressed as the proportionality factors of the 1st, 2nd, …… k …… Nth tension rolls, It is expressed as the common proportionality factor, N represents the number of tension rolls, It is expressed as the limit tension amplification coefficient.

[0009] Preferably, in the step A4, the driving power required for the kth tension roll consists of three parts. Preferably, in the step A4, the driving power required for the kth tension roll consists of three parts 、friction loss of the transmission shaft 、bending loss of the strip ; Then the calculation method of the power required for tension amplification is specifically: , where, It is expressed as the power required for tension amplification, It is expressed as the tension change of the kth tension roll, It is expressed as the running speed of the strip, Denoted as mechanical transmission efficiency; The calculation method of the friction loss of the transmission shaft is specifically as follows: , where Denoted as the friction loss of the transmission shaft, Denoted as the friction coefficient at the tension roll bearing, Denoted as the sum of the inlet and outlet tensions of the tension roll, Denoted as the running speed of the strip steel, Denoted as mechanical transmission efficiency; The calculation method of the bending loss of the strip steel is specifically as follows: , where Denoted as the bending loss of the strip steel, Denoted as the yield strength, Denoted as the strip width, Denoted as the strip thickness, Denoted as the running speed of the strip steel, Denoted as the radius, Denoted as mechanical transmission efficiency; Then the transmission power required for the k-th tension roll is: , where Denoted as the transmission power required for the k-th tension roll, Denoted as the power required for tension amplification, Denoted as the friction loss of the transmission shaft, Denoted as the bending loss of the strip steel.

[0010] Preferably, in step A5, when the power or torque required by more than one tension roll exceeds the power or torque of the corresponding drive motor, it is necessary to adjust the tension values at the inlet and outlet of this tension roll according to the exceeding ratio of this tension roll, the surplus of the tension amplification ability of the upstream and downstream tension rolls, and the surplus of the power and torque of the drive motor, so as to give full play to the ability of the tension roll group as much as possible and meet the production requirements; When the torque required by the k-th tension roll exceeds the maximum torque provided by the drive motor, according to the calculation formula of the torque required by the tension roll, it can be seen that reducing the torque required by the current roll mainly depends on reducing the tension difference between the inlet and outlet of the current roll; at this time, it is necessary to adjust the outlet tension of the (k - 1)-th tension roll and the inlet tension of the (k + 1)-th tension roll; respectively adjust the of the (k - 1)-th tension roll and the Set it to 1, recalculate the power and torque required for each tension roll, and conduct a check. If the torque required for the k-th tension roll still exceeds the maximum torque provided by the drive motor, continue to adjust the amplification ratios of the upstream and downstream tension rolls until the power and torque required for all tension rolls meet the requirements; if all upstream and downstream tension rolls have been adjusted but the torque still does not meet the requirements, it is determined that the set inlet and outlet tension values of the tension roll group exceed the adjustment capacity of the current equipment, and the process personnel adjust the inlet / outlet tension values according to the actual requirements of the upstream and downstream processes.

[0011] Technical effects and advantages of the present invention: The present invention realizes the accurate check and optimized adjustment of the tension roll group by establishing a tension loss model, a force balance equation for the micro-arc section, and critical slip conditions, combined with the limit tension amplification coefficient and equipment capacity constraints, thereby improving the stability of the production process and the equipment life. Description of the drawings

[0012] Figure 1 It is a schematic flow chart of the method of the present invention.

[0013] Figure 2 It is a schematic diagram of the force analysis of the present invention. Detailed implementation manners

[0014] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0015] Please refer to Figure 1 As shown, the present invention provides a dynamic load distribution method for a tension roll group based on a slipping mechanism, including the following steps: Step A1: Calculate the tension loss and the actual tension values at the inlet and outlet of the tension roll; In the step A1, when the strip steel is wrapped around the tension roll, elastic deformation and plastic deformation will occur inside it, resulting in tension loss. The calculation method for the tension loss caused by the elastic bending of the strip steel at the inlet and outlet of the tension roll is specifically as follows: , where represents the tension loss caused by the elastic bending of the strip at the inlet and outlet, represents the yield strength of the strip, h represents the thickness of the strip, b represents the width of the strip, and R represents the bending radius of the strip, which is about 1.1 to 1.2 times the radius of the tension roll; The tension loss affects the actual tension values at the inlet and outlet of the tension roller. The specific calculation method for the actual tension value at the inlet of the tension roller is as follows: , where represents the front tension after considering the tension loss at the outlet, represents the outlet tension value, represents the tension loss caused by the elastic bending of the strip at the inlet and outlet; The specific calculation method for the actual tension value at the outlet of the tension roller is as follows: , where represents the back tension after considering the tension loss at the inlet, represents the inlet tension value, represents the tension loss caused by the elastic bending of the strip at the inlet and outlet.

[0016] Step A2: Divide the wrapping angle of the strip on the tension roller into multiple micro-arc segments, analyze the force on each micro-arc segment, and calculate the tension change under the critical sliding state; In the above step A2, for the strip wrapped on the tension roller, the normal force needs to satisfy the centripetal force balance condition; the strip within the actual wrap angle is evenly divided into n micro-arc segments. For the i-th micro-arc segment, the normal force equation of the strip is: , where represents the tension of the i-th micro-arc segment; represents the central angle corresponding to the i-th micro-arc segment, represents the difference between the tension on the outlet side and the tension on the inlet side of the i-th micro-arc segment, represents the normal pressure of the i-th micro-arc segment on the surface of the tension roller, represents the angle between the i-th micro-arc segment and the perpendicular bisector, represents the mass of the i-th micro-arc segment, g represents the acceleration due to gravity, represents the moving speed of the strip, and R represents the radius of the tension roller; For the inclined tension roller or the vertical motion component of the strip, the gravity changes the contact force between the strip and the tension roller, affecting the friction force. Then the tangential force equation is: , where represents the tension of the i-th micro-arc segment; represents the central angle corresponding to the i-th micro-arc segment, represents the difference between the tension on the outlet side and the tension on the inlet side of the i-th micro-arc segment, represents the friction force between the i-th micro-arc segment and the surface of the tension roller, represents the angle between the i-th micro-arc segment and the perpendicular bisector, Denoted as the mass of the $i$-th micro-arc segment, $g$ is denoted as the acceleration due to gravity, Denoted as the moving speed of the strip steel, $R$ is denoted as the radius of the tension roll; When the strip steel of this micro-arc segment and the tension roll are in a critical sliding state, according to the law of sliding friction, the following relationship is satisfied: , where, Denoted as the frictional force, Denoted as the normal pressure of the $i$-th micro-arc segment on the surface of the tension roll; The outlet tension of the $i$-th micro-arc segment Is equal to the inlet tension of the $(i + 1)$-th micro-arc segment , that is, the calculation method is specifically: (1) Where, Denoted as the tension of the $(i + 1)$-th micro-arc segment; Denoted as the tension of the $i$-th micro-arc segment; Denoted as the difference between the tension near the outlet side and the tension near the inlet side on the $i$-th micro-arc segment; The angle between the $i$-th micro-arc segment and the vertical bisector And the angle between the $(i + 1)$-th micro-arc segment and the vertical bisector Has the following relationship: (2) Where, Denoted as the angle between the $(i + 1)$-th micro-arc segment and the vertical bisector; Denoted as the angle between the $i$-th micro-arc segment and the vertical bisector; Denoted as the angle between the $i$-th micro-arc segment and the vertical bisector; Denoted as the angle between the $(i + 1)$-th micro-arc segment and the vertical bisector; The inlet tension of the first micro-arc segment Is equal to the back tension of the tension roll , that is: (3) Combining (1), (2), and (3) to obtain a finite difference calculation model for the limit tension amplification coefficient of the tension roll considering elastic-plastic loss, centripetal force, gravity, and acceleration / deceleration conditions, that is: (4) Specifically: In the formula: Is the coefficient of the inlet tension in the equation of the $i$-th micro-arc segment, ; Is the constant term in the equation of the $i$-th micro-arc segment, ; The coefficient matrix of the system of equations (4) is obviously invertible, and the solution to the above problem can always be expressed as ; From this, the front tension after considering the tension loss at the outlet of the tension roll can be obtained; Among them, It is expressed as the maximum front tension that the tension roll can provide when the back tension at the inlet is

[0017] Step A3: According to the limit tension amplification coefficients of each tension roll, evenly distribute the tension ratio that the tension roll group needs to expand or contract to each tension roll; In the said step A3, the tension roll group consists of N tension rolls. According to the geometric position of the strip steel winding at each tension roll, the cross-sectional dimension of the strip steel, the speed of the unit, the acceleration and deceleration conditions, and combined with the friction coefficient at each tension roll, the limit tension amplification coefficient of each roll under the current working conditions is obtained ; The specific calculation method of the limit tension amplification coefficient is: , among which, It is expressed as the limit tension amplification coefficient, It is expressed as the actual outlet tension of the strip steel on the tension roll after considering the tension loss, It is expressed as the actual inlet tension of the strip steel on the tension roll after considering the tension loss, It is expressed as the tension loss caused by the elastic bending of the strip at the inlet and outlet; Evenly distribute the tension ratio that the tension roll group needs to expand or contract to each tension roll according to the actual tension amplification ability of each roll; When initially calculating, it is assumed that the ratio of the actual tension amplification ratio of each tension roll to the corresponding limit tension amplification coefficient is equal; that is: , among which, , , ……, , ……, It is expressed as the proportionality factors of the 1st, 2nd, …… k …… Nth tension rolls, It is expressed as the common proportionality factor; Then the specific calculation method of the total tension ratio of the tension roll group is: , among which, Table , among which, It is expressed as the tension at the outlet of the tension roll group, It is expressed as the tension at the inlet of the tension roll group, , , ……, , ……, It is expressed as the proportionality factors of the 1st, 2nd, …… k …… Nth tension rolls, is expressed as the common scale factor, and N is expressed as the number of tension rollers. is expressed as the ultimate tension amplification coefficient; Solve the calculation formula of the tension roller group to obtain the load distribution that only considers the tension amplification ability of each tension roller. The specific calculation method is as follows: , where is expressed as the common scale factor, and N is expressed as the number of tension rollers. is expressed as the front tension after considering the tension loss at the outlet, is expressed as the reference tension, is expressed as the ultimate tension amplification coefficient; According to the load distribution calculation formula of the tension amplification ability of the tension roller, the tension difference between the inlet and outlet of the kth tension roller can be calculated. The specific calculation method is as follows: , where is expressed as the tension change of the kth tension roller, is expressed as the ultimate tension reduction coefficient, is expressed as the ultimate tension amplification coefficient, is expressed as the reference tension and the common scale factor.

[0018] Step A4: Calculate the required transmission power and torque of each tension roller according to the tension difference borne by each tension roller, and check according to the power and torque of the drive motor; In the said step A4, the required transmission power of the kth tension roller consists of three parts, namely the power required for tension amplification , the friction loss of the transmission shaft , and the bending loss of the strip steel ; Then the specific calculation method of the power required for tension amplification is as follows: , where is expressed as the power required for tension amplification, is expressed as the tension change of the kth tension roller, is expressed as the running speed of the strip steel, is expressed as the mechanical transmission efficiency; The specific calculation method of the friction loss of the transmission shaft is as follows: , where is expressed as the friction loss of the transmission shaft, is expressed as the friction coefficient at the bearing of the tension roller, is expressed as the sum of the inlet and outlet tensions of the tension roller, is expressed as the running speed of the strip steel, is expressed as the mechanical transmission efficiency; The calculation method of the strip bending loss is specifically as follows: , where, denotes the strip bending loss, denotes the yield strength, denotes the strip width, denotes the strip thickness, denotes the strip running speed, denotes the radius, denotes the mechanical transmission efficiency; Then the driving power required for the k-th tension roll is: , where, denotes the driving power required for the k-th tension roll, denotes the power required for tension amplification, denotes the frictional loss of the transmission shaft, denotes the strip bending loss; The torque required for the k-th tension roll also consists of three parts, namely the torque required to overcome the tension difference between the inlet and outlet , the torque required to overcome the friction of the transmission shaft , and the torque required to overcome the bending deformation of the strip ; The calculation method of the torque required to overcome the tension difference between the inlet and outlet is specifically as follows: , where, denotes the torque required to overcome the tension difference between the inlet and outlet, denotes the tension change of the k-th tension roll, and R denotes the radius; The calculation method of the torque required to overcome the friction of the transmission shaft is specifically as follows: , where, denotes the torque required to overcome the friction of the transmission shaft, denotes the friction coefficient at the tension roll bearing, denotes the sum of the inlet and outlet tensions of the tension roll, denotes the radius; The calculation method of the torque required to overcome the bending deformation of the strip is specifically as follows: , where, denotes the torque required to overcome the bending deformation of the strip, denotes the yield strength, denotes the strip width, and h denotes the strip thickness; Then the maximum working torque required for the normal operation of the k-th tension roll is: , where, It is denoted as the maximum working torque required for the normal operation of the k-th tension roll. It is denoted as the torque required to overcome the tension difference between the inlet and outlet, and is denoted as the torque required to overcome the friction of the transmission shaft. It is denoted as the torque required to overcome the bending deformation of the strip steel. According to the tension conditions at the inlet and outlet of each tension roll calculated by the tension load distribution, substitute them into the calculation of the power and torque required for each tension roll, and compare them with the power and torque of the corresponding drive motor. When the power and torque required for the tension roll are both less than the power and torque of the corresponding drive motor, this load distribution can be completed.

[0019] Step A5: If the power or torque of a tension roll exceeds the capacity of the drive motor, adjust the tension amplification ratio of the upstream and downstream tension rolls until the power and torque of all tension rolls meet the requirements.

[0020] In the above-mentioned step A5, when the power or torque required by more than one tension roll exceeds the power or torque of the corresponding drive motor, it is necessary to adjust the tension values at the inlet and outlet of this tension roll according to the exceeding ratio of this tension roll, the surplus of the tension amplification capacity of the upstream and downstream tension rolls, and the surplus of the power and torque of the drive motor, so as to give full play to the capacity of the tension roll group as much as possible and meet the production requirements. When the torque required by the k-th tension roll exceeds the maximum torque provided by the drive motor, according to the calculation formula of the torque required by the tension roll, the main way to reduce the torque required by the current roll is to reduce the tension difference between the inlet and outlet of the current roll; at this time, it is necessary to adjust the outlet tension of the (k - 1)-th tension roll and the inlet tension of the (k + 1)-th tension roll; respectively set the of the (k - 1)-th tension roll and the of the (k + 1)-th tension roll to 1, recalculate the power and torque required for each tension roll, and conduct a check. If the torque required by the k-th tension roll still exceeds the maximum torque provided by the drive motor, continue to adjust the amplification ratio of the upstream and downstream tension rolls until the power and torque required by all tension rolls meet the requirements; if all upstream and downstream tension rolls have been adjusted, but the torque still does not meet the requirements, it is determined that the set tension values at the inlet and outlet of the tension roll group exceed the adjustment capacity of the current equipment, and the process personnel adjust the inlet / outlet tension values according to the actual requirements of the upstream and downstream processes.

[0021] Finally: The above is only the preferred embodiment of the present invention and is not used to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A dynamic load distribution method for a tension roll group based on the slip mechanism, characterized in that Including: Step A1: Calculate the tension loss and the actual tension values at the inlet and outlet of the tension roller. Step A2: Divide the wrapping angle of the strip on the tension roller into multiple micro-arc segments, perform a force analysis on each micro-arc segment, and calculate the tension change under the critical sliding state. Step A3: According to the limit tension amplification coefficient of each tension roller, evenly distribute the tension ratio that the tension roller group needs to increase or decrease to each tension roller. Step A4: Calculate the required transmission power and torque of each tension roller according to the tension difference borne by each tension roller, and check according to the power and torque of the drive motor. Step A5: If the power or torque of a tension roller exceeds the capacity of the drive motor, adjust the tension amplification ratio of the upstream and downstream tension rollers until the power and torque of all tension rollers meet the requirements.

2. The dynamic load distribution method of a tension roll group based on a slipping mechanism according to claim 1, wherein: In the said Step A1, when the strip is wrapped around the tension roller, elastic deformation and plastic deformation will occur inside it, resulting in tension loss. The calculation method of the tension loss caused by the elastic bending of the strip at the inlet and outlet of the tension roller is specifically as follows: , where represents the tension loss caused by the elastic bending of the strip at the inlet and outlet represents the yield strength of the strip, h represents the thickness of the strip, b represents the width of the strip, and R represents the bending radius of the strip, which is about 1.1 - 1.2 times the radius of the tension roll.

3. A dynamic load distribution method for a tension roll group based on a slip mechanism according to claim 2, characterized in that: After considering the tension loss, the actual inlet tension of the strip on the tension roller is: , where represents the actual inlet tension of the strip on the tension roll after considering the tension loss, represents the nominal inlet tension of the strip on the tension roll, represents the tension loss caused by the elastic bending of the strip at the inlet and outlet; Similarly, for the actual outlet tension of the strip on the tension roller after considering the tension loss is: , where represents the actual inlet tension of the strip on the tension roll after considering the tension loss, represents the nominal inlet tension of the strip on the tension roll, represents the tension loss caused by the elastic bending of the strip at the inlet and outlet.

4. A dynamic load distribution method for a tension roller set based on a slipping mechanism according to claim 1, characterized in that: In the said Step A2, for the strip wrapped around the tension roller, its normal force needs to satisfy the centripetal force balance condition; the strip within the actual wrap angle is evenly divided into n micro-arc segments. For the i-th micro-arc segment, the normal force equation of the strip is: , where represents the inlet tension of the i-th micro-arc segment; represents the central angle corresponding to the i-th micro-arc segment, represents the difference between the outlet tension and the inlet tension on the i-th micro-arc segment, represents the normal pressure of the i-th micro-arc segment on the surface of the tension roll, represents the angle between the i-th micro-arc segment and the perpendicular bisector, represents the mass of the i-th micro-arc segment, g represents the acceleration due to gravity, represents the moving speed of the strip steel, R represents the radius of the tension roll; For the inclined installation of the tension roller or the vertical movement component of the strip, the gravity changes the contact force between the strip and the tension roller, affecting the friction force. Then the tangential force equation is: , where represents the inlet tension of the i-th micro-arc segment; represents the central angle corresponding to the i-th micro-arc segment, represents the difference between the outlet tension and the inlet tension on the i-th micro-arc segment, represents the frictional force between the i-th micro-arc segment and the surface of the tension roll, represents the angle between the i-th micro-arc segment and the perpendicular bisector, represents the mass of the i-th micro-arc segment, g represents the acceleration due to gravity, represents the moving speed of the strip, R represents the radius of the tension roll, and a represents the acceleration of the strip; When the strip of this micro-arc segment is in the critical sliding state with the tension roller, according to the sliding friction law, the following relationship is satisfied: , where is expressed as the frictional force, is expressed as the normal pressure of the i-th micro-arc segment on the surface of the tension roller, and μ is expressed as the sliding friction coefficient.

5. A dynamic load distribution method for a tension roll group based on a slip mechanism according to claim 4, characterized in that: When the strip of this micro-arc segment is in the critical sliding state with the tension roller, the combined force of this micro-arc segment is: ； , where μ represents the sliding friction coefficient, represents the central angle corresponding to the i-th micro-arc segment, represents the inlet tension of the i-th micro-arc segment, represents the difference between the outlet tension and the inlet tension on the i-th micro-arc segment, represents the mass of the i-th micro-arc segment, represents the moving speed of the strip steel, R represents the radius of the tension roll, and g represents the acceleration due to gravity, represents the angle between the i-th micro-arc segment and the vertical line, and a represents the acceleration of the strip steel; The outlet tension of the i-th micro-arc segment is equal to the inlet tension of the (i + 1)-th micro-arc segment Specifically, the calculation method is as follows: , where is expressed as the inlet tension of the (i + 1)-th micro-arc segment; is expressed as the inlet tension of the i-th micro-arc segment; is expressed as the difference between the outlet tension and the inlet tension on the i-th micro-arc segment; The included angle between the i-th micro-arc segment and the perpendicular bisector and the included angle between the (i + 1)-th micro-arc segment and the perpendicular bisector has the following relationship: , where is represented as the angle between the (i + 1)-th micro-arc segment and the perpendicular bisector; is represented as the angle between the i-th micro-arc segment and the perpendicular bisector; is represented as the angle between the i-th micro-arc segment and the perpendicular bisector; is represented as the angle between the (i + 1)-th micro-arc segment and the perpendicular bisector.

6. A dynamic load distribution method for a tension roll group based on a slip mechanism according to claim 5, characterized in that: Combine the combined force equations of the n micro-arc segments of the strip wrapped around the tension roller to obtain a finite difference calculation model of the limit tension amplification coefficient of the tension roller considering elastic-plastic loss, centripetal force, gravity, and acceleration and deceleration conditions: , where is represented as the coefficient matrix of the difference equation system, is represented as the unknown term array of the difference equation system, is represented as the constant term array of the difference equation system; , where represents the coefficient of the inlet tension in the equation of the i-th micro-arc segment, ; , where represents the inlet tension of the i-th micro-arc segment; represents the difference between the outlet tension and the inlet tension on the i-th micro-arc segment; , where is expressed as the constant term in the equation of the i-th micro-arc segment, ; is expressed as the coefficient of the inlet tension in the equation of the first micro-arc segment, ; is expressed as the inlet tension of the first micro-arc segment.

7. A dynamic load distribution method for a tension roll group based on a slip mechanism according to claim 6, characterized in that: The coefficient matrix of the established finite difference equations is invertible, and the solution of the established difference equations can be expressed as: , where is represented as an array of unknown terms of the difference equation system, is represented as the inverse matrix of the coefficient matrix of the difference equation system, is represented as an array of constant terms of the difference equation system; Solution of the difference equations The last term is the outlet tension of the last micro-arc segment, that is, the actual outlet tension of the strip on the tension roll after considering the tension loss .

8. A dynamic load distribution method for a tension roll group based on a slip mechanism according to claim 1, characterized in that: In the step A3, the tension roll group consists of N tension rolls. According to the geometric position of the strip steel winding at each tension roll, the cross-sectional dimension of the strip steel, the speed of the unit, the acceleration and deceleration conditions, and combined with the friction coefficient at each tension roll, the ultimate tension amplification coefficient of each roll under the current working condition is obtained. ; The specific calculation method of the limit tension amplification coefficient is: , where is expressed as the limit tension amplification coefficient, is expressed as the actual outlet tension of the strip on the tension roll after considering the tension loss, is expressed as the actual inlet tension of the strip on the tension roll after considering the tension loss, is expressed as the tension loss caused by the elastic bending of the strip at the inlet and outlet; Distribute the tension ratio that the tension roller group needs to increase or decrease evenly to each tension roller according to the actual tension amplification capacity of each roller; assume that the ratio of the actual tension amplification ratio of each tension roller to the corresponding limit tension amplification coefficient is equal during the initial calculation; that is: , where , , ……, , ……, represent the proportionality factors of the 1st, 2nd, …… k …… Nth tension rollers, represents the common proportionality factor.

9. A dynamic load distribution method for a tension roll group based on a slipping mechanism according to claim 1, characterized in that: In the step A4, the driving power required for the k-th tension roll consists of three parts, namely the power required for tension amplification , the frictional loss of the transmission shaft , and the bending loss of the strip steel ; Then the specific calculation method of the power required for tension amplification is: , where represents the power required for tension amplification, represents the change in tension of the k-th tension roll, represents the running speed of the strip steel, represents the mechanical transmission efficiency; The specific calculation method of the friction loss of the transmission shaft is: , where represents the frictional loss of the transmission shaft, represents the friction coefficient at the tension roll bearing, represents the sum of the tensions at the inlet and outlet of the tension roll, represents the running speed of the strip steel, represents the mechanical transmission efficiency; The specific calculation method of the bending loss of the strip is: , where represents the strip bending loss, represents the yield strength, represents the strip width, represents the strip thickness, represents the strip running speed, represents the radius, represents the mechanical transmission efficiency; The specific calculation method of the torque required to overcome the inlet and outlet tension difference is: , where represents the torque required to overcome the tension difference between the inlet and outlet, represents the change in tension of the k-th tension roller, and R represents the radius; According to the tension conditions at the inlet and outlet of each tension roller calculated by the tension load distribution, substitute them to calculate the power and torque required for each tension roller, and compare them with the power and torque of the corresponding drive motor; when the power and torque required for the tension roller are both less than the power and torque of the corresponding drive motor, this load distribution can be completed.

10. A dynamic load distribution method for a tension roll group based on a slipping mechanism according to claim 1, characterized in that: In the said Step A5, when the power or torque required by more than one tension roller exceeds the power or torque of the corresponding drive motor, it is necessary to adjust the tension values at the inlet and outlet of this tension roller according to the exceeding ratio of this tension roller, the surplus of the tension amplification ability of the upstream and downstream tension rollers, and the surplus of the power and torque of the drive motor; The torque required by the k-th tension roller exceeds the maximum torque provided by the drive motor. According to the calculation formula of the torque required by the tension roller, the main way to reduce the torque required by the current roller is to reduce the tension difference at the inlet and outlet of the current roller. At this time, it is necessary to adjust the outlet tension of the (k - 1)-th tension roller and the inlet tension of the (k + 1)-th tension roller; respectively set the of the (k - 1)-th tension roller and the of the (k + 1)-th tension roller to 1, recalculate the power and torque required for each tension roller, and conduct a check.

Images