Wet leveling rolling tension compensation method
By establishing a tension compensation model and calculating and setting a reasonable tension compensation coefficient, the problem of strip shape defects caused by tension changes at the head and tail of the strip during wet leveling rolling was solved, and high-precision, high-quality finished strip steel production was achieved.
Patent Information
- Application Number
- CN202510894411.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-06-30
- Publication Date
- 2025-10-31
AI Technical Summary
During wet leveling and rolling, tension changes at the head and tail of the strip lead to shape defects, affecting the quality of the finished strip. Existing technologies make it difficult to achieve reasonable tension adjustment.
By establishing a tension compensation model, calculating and setting a reasonable tension compensation coefficient, and adjusting the rolling force to stabilize, tension compensation is achieved.
It effectively solves the problem of strip shape defects at the head and tail of the strip, and realizes the production of high-precision, high-quality finished strip steel.
Smart Images

Figure CN120861601A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a method for compensating tension during wet leveling rolling, belonging to the technical field of steel rolling leveling methods. Background Technology
[0002] With the increasing use of high-quality strip steel in high-end industrial sectors, the market demands for strip products are also constantly rising, and high-precision, high-quality strip steel is receiving more and more attention. Leveling rolling, as the final rolling process for finished strip steel, is a key factor determining high-quality strip steel. Strip shape quality control, as one of the important control indicators, requires reasonable and precise rolling process parameters for adjustment. Good strip shape quality plays a significant role in the efficiency of the production line.
[0003] In wet leveling rolling, head and tail shape defects can affect the quality of the finished strip shape, primarily caused by tension variations. When the strip head enters the mill stand for rolling, unstable tension in front of the stand leads to head shape defects. Similarly, near the end of rolling, after the strip tail is ejected from the mill stand, tail shape defects can occur if there is no back tension or the back tension is unstable. Tension, as a crucial rolling process parameter during leveling, is an important means of adjusting head and tail shape defects in strip steel. Summary of the Invention
[0004] The purpose of this invention is to provide a tension compensation method for wet leveling rolling. By performing tension compensation during the rolling process of the strip head and tail, a tension compensation model is established to achieve reasonable tension settings to regulate the stability of rolling force, thereby achieving high-precision and high-quality finished strip steel, effectively solving the above-mentioned problems existing in the background technology.
[0005] The technical solution of this invention is: a method for compensating tension during wet leveling rolling, comprising the following steps:
[0006] S1. Collect key equipment characteristic parameters, rolling process parameters, and process lubrication system parameters of the leveling unit;
[0007] S2, rolling speed of each section of the computer group;
[0008] S3. Set the initial tension compensation coefficient;
[0009] S4. Calculate the additional tension value and the total tension value;
[0010] S5. Calculate the rolling pressure after compensation under wet leveling acceleration and deceleration.
[0011] S6. Determine whether the compensated rolling pressure under wet leveling speed increase or decrease is less than the set critical rolling pressure. If not, increase the tension compensation coefficient by 1 and proceed to step S3; if yes, proceed to step S7.
[0012] S7. Determine whether the back tension setting value and the front tension setting value are within the specified range when the rolling speed is set by the unit. If not, increase the tension compensation coefficient by 1 and proceed to step S3. If yes, proceed to step S8.
[0013] S8, output the optimal additional tension value.
[0014] In step S1, the key equipment characteristic parameters of the leveling unit include the work roll radius D. w The parameters include: mm, elastic modulus, GPa, and Poisson's ratio ν; rolling process parameters include strip entry thickness h0, strip width B, strip elongation ε, and strip yield strength σ. s and setting the critical rolling pressure P * The relevant parameters for the process lubrication system include the leveling fluid flow rate (l) and the leveling fluid temperature (T). l The concentration of the leveling solution is c.
[0015] In step S2, the strip speed is divided into n segments from 0 to its maximum, and v is used as the average value. ji Let the speed of the j-th frame of the double-frame wet leveling unit in the i-th segment be expressed by equation (1):
[0016]
[0017] In the formula: v jmax Let be the maximum permissible rolling speed for the j-th stand, in m / min.
[0018] In step S3
[0019] S31. Set the initial tension compensation coefficients for the first frame to k01 = 0.1 and k11 = 0.1, set the optimization step size Δr = 0.1, and the increment parameter Δk = 0.1 for each frame. Calculate the tension compensation coefficient for the first frame.
[0020] S32, Determine the first rack If the condition is true, proceed to step S33; if not, set k1 = k1 + 1 and proceed to step S31.
[0021] S33. Set the initial tension compensation coefficients for the second frame to k02 = 0.1 and k12 = 0.1, set the optimization step size Δr = 0.1, and the increment parameter Δk = 0.1 for each frame. Calculate the tension compensation coefficients for the second frame.
[0022] S34, Determine the second rack If the condition is true, proceed to step S4; if not, set k2 = k2 + 1 and proceed to step S31.
[0023] In step S4, based on the influence of tension on rolling pressure and its relationship with speed, the additional pre- and post-tension values ΔT are set. 0ji and ΔT 1ji It can be represented by equation (2);
[0024]
[0025] Simultaneously set the total tension T of the i-th segment. 0ji T 1ji It can be represented by equation (3);
[0026]
[0027] In the formula: T 0ji and T 1ji Let T be the back tension and front tension of the i-th segment of the j-th frame, in kN; 0j T 1j Here are the set values for the back tension and front tension of the j-th stand when the rolling speed is set by the unit, in kN; ΔT 0ji ΔT 1ji For the additional back tension and additional front tension of the i-th segment of the j-th frame, kN; k 1j k 2j This is the tension speed compensation coefficient; Set the rolling speed for the j-th stand, in m / min.
[0028] In step S5, the compensated rolling pressure P is calculated when the acceleration and deceleration speeds of the dual-stand wet leveling unit are increased. j The expression for the rolling pressure is shown in equation (4):
[0029] P j =f·L (4)
[0030] in:
[0031]
[0032] In the formula: L is the contact arc length between the roll and the strip in the rolling deformation zone; f is the unit rolling force; σ p σ is the equivalent deformation resistance, MPa; μ is the coefficient of friction; σ s σ is the strip deformation resistance, MPa; k1, k2 and k3 are the equivalent deformation resistance influence coefficients; a0 and a1 are the contact arc length influence coefficients in the rolling deformation range; a is the deformation resistance influence coefficient; σ1 and σ0 are the front tension and back tension, MPa.
[0033] The beneficial effects of this invention are: by performing tension compensation during the rolling process of strip steel head and tail, establishing a tension compensation model, and achieving reasonable tension setting to regulate the stability of rolling force, thereby achieving high-precision and high-quality finished strip steel. Attached Figure Description
[0034] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation
[0035] To make the purpose, technical solutions, and advantages of the invention's embodiments clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are only a small part of the embodiments of the present invention, not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the protection scope of the present invention.
[0036] A method for compensating tension during wet leveling rolling includes the following steps:
[0037] S1. Collect key equipment characteristic parameters, rolling process parameters, and process lubrication system parameters of the leveling unit;
[0038] S2, rolling speed of each section of the computer group;
[0039] S3. Set the initial tension compensation coefficient;
[0040] S4. Calculate the additional tension value and the total tension value;
[0041] S5. Calculate the rolling pressure after compensation under wet leveling acceleration and deceleration.
[0042] S6. Determine whether the compensated rolling pressure under wet leveling speed increase or decrease is less than the set critical rolling pressure. If not, increase the tension compensation coefficient by 1 and proceed to step S3; if yes, proceed to step S7.
[0043] S7. Determine whether the back tension setting value and the front tension setting value are within the specified range when the rolling speed is set by the unit. If not, increase the tension compensation coefficient by 1 and proceed to step S3. If yes, proceed to step S8.
[0044] S8, output the optimal additional tension value.
[0045] In step S1, the key equipment characteristic parameters of the leveling unit include the work roll radius D. w The parameters include: mm, elastic modulus, GPa, and Poisson's ratio ν; rolling process parameters include strip entry thickness h0, strip width B, strip elongation ε, and strip yield strength σ. s and setting the critical rolling pressure P * The relevant parameters for the process lubrication system include the leveling fluid flow rate (l) and the leveling fluid temperature (T). l The concentration of the leveling solution is c.
[0046] In step S2, the strip speed is divided into n segments from 0 to its maximum, and v is used as the average value. ji Let the speed of the j-th frame of the double-frame wet leveling unit in the i-th segment be expressed by equation (1):
[0047]
[0048] In the formula: v jmax Let be the maximum permissible rolling speed for the j-th stand, in m / min.
[0049] In step S3
[0050] S31. Set the initial tension compensation coefficients for the first frame to k01 = 0.1 and k11 = 0.1, set the optimization step size Δr = 0.1, and the increment parameter Δk = 0.1 for each frame. Calculate the tension compensation coefficient for the first frame.
[0051] S32, Determine the first rack If the condition is true, proceed to step S33; if not, set k1 = k1 + 1 and proceed to step S31.
[0052] S33. Set the initial tension compensation coefficients for the second frame to k02 = 0.1 and k12 = 0.1, set the optimization step size Δr = 0.1, and the increment parameter Δk = 0.1 for each frame. Calculate the tension compensation coefficients for the second frame.
[0053] S34, Determine the second rack If the condition is true, proceed to step S4; if not, set k2 = k2 + 1 and proceed to step S31.
[0054] In step S4, based on the influence of tension on rolling pressure and its relationship with speed, the additional pre- and post-tension values ΔT are set. 0ji and ΔT 1ji It can be represented by equation (2);
[0055]
[0056] Simultaneously set the total tension T of the i-th segment. 0ji T 1ji It can be represented by equation (3);
[0057]
[0058] In the formula: T 0ji and T 1ji Let T be the back tension and front tension of the i-th segment of the j-th frame, in kN; 0j T 1jHere are the set values for the back tension and front tension of the j-th stand when the rolling speed is set by the unit, in kN; ΔT 0ji ΔT 1ji For the additional back tension and additional front tension of the i-th segment of the j-th frame, kN; k 1j k 2j This is the tension speed compensation coefficient; Set the rolling speed for the j-th stand, in m / min.
[0059] In step S5, the compensated rolling pressure P is calculated when the acceleration and deceleration speeds of the dual-stand wet leveling unit are increased. j The expression for the rolling pressure is shown in equation (4):
[0060] P j =f·L (4)
[0061] in:
[0062]
[0063] In the formula: L is the contact arc length between the roll and the strip in the rolling deformation zone; f is the unit rolling force; σ p σ is the equivalent deformation resistance, MPa; μ is the coefficient of friction; σ s σ is the strip deformation resistance, MPa; k1, k2 and k3 are the equivalent deformation resistance influence coefficients; a0 and a1 are the contact arc length influence coefficients in the rolling deformation range; a is the deformation resistance influence coefficient; σ1 and σ0 are the front tension and back tension, MPa.
[0064] In practical applications, the present invention adopts the following technical solution:
[0065] (a) Collect key equipment characteristic parameters of the leveling unit, mainly including: work roll radius D w mm, elastic modulus, GPa, Poisson's ratio ν;
[0066] (b) Collect rolling process parameters, mainly including: strip entry thickness h0, mm, strip width B, mm, strip elongation ε, % and strip yield strength σ. s MPa, set critical rolling pressure P * , kN;
[0067] (c) Collect relevant parameters of the process lubrication regime, mainly including: l is the leveling fluid flow rate, L·min -1 ;T l is the temperature of the leveling solution, in °C; c is the concentration of the leveling solution, in %.
[0068] (d) Divide the strip speed from 0 to maximum into n segments on average, and use v jiLet the speed of the j-th frame of the double-frame wet leveling unit in the i-th segment be expressed by equation (1):
[0069]
[0070] In the formula: v jmax Let be the maximum permissible rolling speed for the j-th stand, in m / min.
[0071] (e) Set the initial tension compensation coefficients for the first frame to k01 = 0.1 and k11 = 0.1, set the optimization step size Δr = 0.1, and the increment parameter Δk = 0.1 for each frame. Calculate the tension compensation coefficients for the first frame.
[0072] (f) Determine the first rack Check if it is true. If it is true, proceed to step (g); if it is not true, let k1 = k1 + 1 and proceed to step (e).
[0073] (g) Set the initial tension compensation coefficients for the second frame to k02 = 0.1 and k12 = 0.1, set the optimization step size Δr = 0.1, and the increment parameter Δk = 0.1 for each frame. Calculate the tension compensation coefficients for the second frame.
[0074] (h) Determine the second rack If the condition is true, proceed to step (i); if not, let k2 = k2 + 1 and proceed to step (e).
[0075] (i) Based on the influence of tension on rolling pressure and its relationship with speed, set the additional pre- and post-tension values ΔT. 0ji ΔT 1ji It can be represented by equation (2);
[0076]
[0077] (j) Simultaneously set the total tension T of the i-th segment. 0ji T 1ji It can be represented by equation (3);
[0078]
[0079] In the formula: T 0ji T 1ji The back tension and front tension of the i-th segment of the j-th frame are given in kN; T 0j T 1j Here are the set values for the back tension and front tension of the j-th stand when the rolling speed is set by the unit, in kN; ΔT 0ji ΔT 1ji The additional back tension and additional front tension of the i-th segment of the j-th frame are kN; k 1jk 2j This is the tension speed compensation coefficient; Set the rolling speed for the j-th stand, in m / min.
[0080] (k) Calculate the compensated rolling pressure P when calculating the acceleration and deceleration of the dual-stand wet leveling unit. j The expression for the rolling pressure is shown in equation (4):
[0081] P j =f·L (4)
[0082] in:
[0083]
[0084] In the formula: L is the contact arc length between the roll and the strip in the rolling deformation zone; f is the unit rolling force; σ p σ is the equivalent deformation resistance, MPa; μ is the coefficient of friction; σ s denoted as strip deformation resistance, MPa; k1, k2, k3 are equivalent deformation resistance influence coefficients; a0, a1 are contact arc length influence coefficients in the rolling deformation zone; a is the deformation resistance influence coefficient; σ1, σ0 are the front tension and back tension, MPa.
[0085] (l) Judgment Is it true? If not, let k3 = k3 + 1 and proceed to step (e); if true, proceed to step (m).
[0086] (m) Judgment Is it true? If not, let k4 = k4 + 1 and go to step (e); if true, go to step (n).
[0087] (n) Output the optimal additional tension value ΔT 0ji ΔT 1ji .
[0088] Example 1:
[0089] Taking a steel grade with a specification of 0.35mm × 850mm as an example, the calculation is performed.
[0090] (a) Collect key equipment characteristic parameters of the leveling unit, mainly including: work roll radius D w =440mm, elastic modulus E=206GPa, Poisson's ratio v=0.3;
[0091] (b) Collect rolling process parameters, mainly including: strip entry thickness h0 = 0.35 mm, strip width B = 850 mm, strip elongation ε = 1.6%, and strip yield strength σ. s =251MPa, set critical rolling pressure P *=3000kN;
[0092] (c) Collect relevant parameters of the process lubrication regime, mainly including: leveling fluid flow rate l = 33 L·min -1 Leveling liquid temperature T l =31℃; leveling solution concentration c = 2.4%;
[0093] (d) Divide the strip speed from 0 to maximum into 6 average segments, and set the maximum speed v of the wet leveling unit. jmax =300m / min, the speed v of the j-th frame of the wet leveling unit under the i-th section. ji ={50, 100, 150, 200, 250, 300}m / min;
[0094] (e) Set the initial tension compensation coefficients for the first frame to k01 = 0.1 and k11 = 0.1, set the optimization step size Δr = 0.1, and the increment parameter Δk = 0.1 for each frame. Calculate the tension compensation coefficients for the first frame.
[0095] (f) Determine the first rack Check if it is true. If it is true, proceed to step (g); if it is not true, let k1 = k1 + 1 and proceed to step (e).
[0096] (g) Set the initial tension compensation coefficients for the second frame to k02 = 0.1 and k12 = 0.1, set the optimization step size Δr = 0.1, and the increment parameter Δk = 0.1 for each frame. Calculate the tension compensation coefficients for the second frame.
[0097] (h) Determine the second rack If the condition is true, proceed to step (e); if not, let k2 = k2 + 1 and proceed to step (i).
[0098] (i) Calculate the tension values ΔT before and after the addition based on the influence of tension on rolling pressure and its relationship with speed. 0ji ΔT 1ji
[0099]
[0100] (j) Calculate the total tension T of the i-th segment during the rolling process of each stand. 0ji T 1ji ;
[0101]
[0102] (k) Calculate the compensated rolling pressure P corresponding to the wet leveling acceleration and deceleration. i
[0103]
[0104] (l) Determine P ji Is -3000 < 0 true? If not, let k3 = k3 + 1, and proceed to step (e); if true, proceed to step (m).
[0105] (m) Judgment Is it true? If not, proceed to step (n); if true, let k4 = k4 + 1 and proceed to step (g).
[0106] (n) Output the optimal additional tension value ΔT 0ji ΔT 1ji .
[0107]
[0108] Example 2:
[0109] Taking a steel grade with dimensions of 0.37mm × 820mm as an example, the calculation is performed.
[0110] (a) Collect key equipment characteristic parameters of the leveling unit, mainly including: work roll radius D w =440mm, elastic modulus E=206GPa, Poisson's ratio v=0.3;
[0111] (b) Collect rolling process parameters, mainly including: strip entry thickness h0 = 0.37 mm, strip width B = 820 mm, strip elongation ε = 1.8%, and strip yield strength σ. s =238MPa, set critical rolling pressure P * =3000kN;
[0112] (c) Collect relevant parameters of the process lubrication regime, mainly including: leveling fluid flow rate l = 33 L·min -1 Leveling liquid temperature T l =31℃; leveling solution concentration c = 2.4%;
[0113] (d) Divide the strip speed from 0 to maximum into 6 average segments, and the maximum speed v of the wet leveling unit. jmax =400m / min, the speed v of the j-th frame of the wet leveling unit under the i-th section. ji ={66.7, 133.3, 200, 266.7, 333.3, 400}m / min;
[0114] (e) Set the initial tension compensation coefficients for the first frame to k01 = 0.1 and k11 = 0.1, set the optimization step size Δr = 0.1, and the increment parameter Δk = 0.1 for each frame. Calculate the tension compensation coefficients for the first frame.
[0115] (f) Determine the first rack Check if it is true. If it is true, proceed to step (g); if it is not true, let k1 = k1 + 1 and proceed to step (e).
[0116] (g) Set the initial tension compensation coefficients for the second frame to k02 = 0.1 and k12 = 0.1, set the optimization step size Δr = 0.1, and the increment parameter Δk = 0.1 for each frame. Calculate the tension compensation coefficients for the second frame.
[0117] (h) Determine the second rack Check if it is true. If it is true, proceed to step (e); if it is not true, let k2 = k2 + 1 and proceed to step (i).
[0118] (i) Calculate the tension values ΔT before and after the addition based on the influence of tension on rolling pressure and its relationship with speed. 0ji ΔT 1ji
[0119]
[0120]
[0121] (j) Calculate the total tension T of the i-th segment during the rolling process of each stand. 0ji T 1ji ;
[0122]
[0123] (k) Calculate the compensated rolling pressure P corresponding to the wet leveling acceleration and deceleration. i
[0124]
[0125] (l) Determine P ji Is -3000kN < 0 true? If not, let k3 = k3 + 1 and proceed to step (e); if true, proceed to step (m).
[0126] (m) Judgment Is it true? If not, proceed to step (n); if true, let k4 = k4 + 1 and proceed to step (g).
[0127] (n) Output the optimal additional tension value ΔT 0ji ΔT 1ji .
[0128]
[0129]
[0130] Finally, it should be noted that the above specific embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to examples, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications and substitutions should be covered within the scope of the claims of the present invention.
[0131] The preferred embodiments of the present invention have been described above. It should be noted that the present invention is not limited to the specific embodiments described above. The devices and structures not described in detail should be understood to be implemented in the ordinary way in the art. Any simple modifications, equivalent changes and modifications made by any person skilled in the art to the above embodiments based on the technical essence of the present invention without departing from the scope of the technical solution of the present invention shall still fall within the protection scope of the technical solution of the present invention.
Claims
1. A method for compensating tension during wet leveling rolling, characterized in that... Includes the following steps: S1. Collect key equipment characteristic parameters, rolling process parameters, and process lubrication system parameters of the leveling unit; S2, rolling speed of each section of the computer group; S3. Set the initial tension compensation coefficient; S4. Calculate the additional tension value and the total tension value; S5. Calculate the rolling pressure after compensation under wet leveling speed increase / decrease. S6. Determine whether the compensated rolling pressure under wet leveling speed increase or decrease is less than the set critical rolling pressure. If not, increase the tension compensation coefficient by 1 and proceed to step S3; if yes, proceed to step S7. S7. Determine whether the back tension setting value and the front tension setting value are within the specified range when the rolling speed is set by the unit. If not, increase the tension compensation coefficient by 1 and proceed to step S3. If yes, proceed to step S8. S8, output the optimal additional tension value.
2. The wet leveling rolling tension compensation method according to claim 1, characterized in that: In step S1, the key equipment characteristic parameters of the leveling unit include the work roll radius D. w The parameters include: mm, elastic modulus, GPa, and Poisson's ratio ν; rolling process parameters include strip entry thickness h0, strip width B, strip elongation ε, and strip yield strength σ. s and setting the critical rolling pressure P * The relevant parameters for the process lubrication system include the leveling fluid flow rate (l) and the leveling fluid temperature (T). l The concentration of the leveling solution is c.
3. The wet leveling rolling tension compensation method according to claim 1, characterized in that: In step S2, the strip speed from 0 to its maximum is divided into n segments on average, and v is used to... ji The speed of the j-th frame of the double-frame wet leveling unit in the i-th segment is expressed by equation (1): In the formula: v jmax Let be the maximum permissible rolling speed for the j-th stand, in m / min.
4. The wet leveling rolling tension compensation method according to claim 1, characterized in that: In step S3 S31. Set the initial tension compensation coefficients for the first frame to k01 = 0.1 and k11 = 0.1, set the optimization step size Δr = 0.1, and the increment parameter Δk = 0.1 for each frame. Calculate the tension compensation coefficient for the first frame. S32, Determine the first rack If the condition is true, proceed to step S33; if not, set k1 = k1 + 1 and proceed to step S31. S33. Set the initial tension compensation coefficients for the second frame to k02 = 0.1 and k12 = 0.1, set the optimization step size Δr = 0.1, and the increment parameter Δk = 0.1 for each frame. Calculate the tension compensation coefficients for the second frame. S34, Determine the second rack If the condition is true, proceed to step S4; if not, set k2 = k2 + 1 and proceed to step S31.
5. The wet leveling rolling tension compensation method according to claim 1, characterized in that: In step S4, based on the influence of tension on rolling pressure and its relationship with speed, the additional pre- and post-tension values ΔT are set. 0ji and ΔT 1ji It can be represented by equation (2); Simultaneously set the total tension T of the i-th segment. 0ji T 1ji It can be represented by equation (3); In the formula: T 0ji and T 1ji Let T be the back tension and front tension of the i-th segment of the j-th frame, in kN; 0j T 1j Here are the set values for the back tension and front tension of the j-th stand when the rolling speed is set by the mill, in kN; ΔT 0ji ΔT 1ji For the additional back tension and additional front tension of the i-th segment of the j-th frame, kN; k 1j k 2j This is the tension speed compensation coefficient; Set the rolling speed for the j-th stand, in m / min.
6. The wet leveling rolling tension compensation method according to claim 1, characterized in that: In step S5, the compensated rolling pressure P is calculated when the acceleration and deceleration speeds of the dual-stand wet leveling unit are increased. j The expression for the rolling pressure is shown in equation (4): P j =f·L (4) in: In the formula: L is the contact arc length between the roll and the strip in the rolling deformation zone; f is the unit rolling force; σ p σ is the equivalent deformation resistance, MPa; μ is the friction coefficient; σ s σ is the strip deformation resistance, MPa; k1, k2 and k3 are the equivalent deformation resistance influence coefficients; a0 and a1 are the contact arc length influence coefficients in the rolling deformation range; a is the deformation resistance influence coefficient; σ1 and σ0 are the front tension and back tension, MPa.