CN111475896B - Method for determining neutral position of bar straightening stress - Google Patents
Method for determining neutral position of bar straightening stress Download PDFInfo
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- CN111475896B CN111475896B CN202010289642.3A CN202010289642A CN111475896B CN 111475896 B CN111475896 B CN 111475896B CN 202010289642 A CN202010289642 A CN 202010289642A CN 111475896 B CN111475896 B CN 111475896B
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Abstract
The invention belongs to the technical field of neutral layer position determination, and particularly relates to a method for determining a neutral layer position of a bar straightening stress, which comprises the following steps: intercepting a bar in unit length in a contact area of the convex straightening roller and the bar; dividing a bar in unit length into n sheet units along the tangential direction theta of the arc surface xy; establishing a differential balance equation of the sheet unit j in the tangential direction theta; establishing a differential balance equation of the sheet unit j in the radial direction r; adding the equal sign two sides of the differential balance equation of each sheet unit; obtaining a stress neutral position determination formula when the bar and the concave straightening roller are in a full contact state; and (5) obtaining a stress neutral layer offset value. According to the invention, the stress neutral layer position when the bar is straightened and stressed is determined, so that the rebound prediction precision after the bar is straightened and the bar straightening quality are improved, the accuracy of process parameter setting is improved, and the dependence on experience of operators is overcome. The method can also be used for determining the straightening neutral layer position of the wide and thick plate.
Description
Technical Field
The invention belongs to the technical field of neutral layer position determination, and particularly relates to a method for determining a neutral layer position of a bar straightening stress.
Background
During rolling, cooling, heat treatment and transportation, the bar is affected by uneven pressing, cooling, collision and other factors, so that quality defects such as bending, twisting, non-circular cross section and the like are often generated to different degrees. The two-roller straightener has the advantages of high straightening precision, good quality after straightening, simple equipment and the like, and becomes an important equipment for improving the product quality in the bar production process.
The straightening of both the plate and the pipe and bar is realized by using rebound, and the rebound has influence on the setting of the roll shape and the technological parameters of the straightening roll. Therefore, to obtain a stable high-precision sheet or pipe, it is necessary to predict the springback of the metal material with high accuracy. However, the influence of the stress neutral layer deflection on the rebound is not considered in rebound prediction of many plates or bars at present, so that the accuracy of a rebound prediction model is not high. The low-precision rebound prediction can influence the design of the roll shape of the straightening roll and the setting of technological parameters, and the high-precision straightening target of the plate or the bar is difficult to realize.
Disclosure of Invention
Aiming at the technical problem that the accuracy of the rebound prediction model is not high, the invention provides a method for determining the neutral position of the straightening stress of a bar with high prediction accuracy and high efficiency.
In order to solve the technical problems, the invention adopts the following technical scheme:
a method for determining the neutral position of the straightening stress of a bar comprises the following steps:
s1, defining a tangent line of an axis of a bar in the horizontal direction as an x-axis, defining a line which is perpendicular to a horizontal plane and passes through a tangent point of the x-axis and the axis of the bar as a z-axis, and establishing an xyz coordinate system according to a right-hand rule;
s2, intercepting a unit length bar in a contact area of the convex straightening roller and the bar, wherein the unit length bar is symmetrical about a yz plane;
s3, uniformly dividing the bar in unit length into n sheet units along the tangential direction theta of the arc surface xy;
s4, carrying out stress analysis on each sheet unit, and establishing a differential balance equation of the sheet unit j in the tangential direction theta;
s5, assuming that the stress neutral layer is positioned between the sheet unit i and the sheet unit i+1 during straightening, and establishing a differential equilibrium equation of the sheet unit j in the radial direction r;
s6, adding the equal sign two sides of the differential balance equation of each sheet unit in the S5;
s7, obtaining a stress neutral position determination formula when the bar and the concave straightening roller are in a full contact state;
s8, substituting tangential stress distribution functions of the straightening, bending, stretching and compressing sides of the bar into the formula in S7, and obtaining the offset value of the stress neutral layer.
The differential equilibrium equation of the lamellar unit j in the tangential direction θ in S4 is:
the sigma θ Is the stress of the lamellar unit j in the tangential direction theta,
the stress variation of the sheet unit j in the tangential direction theta is represented by r, which is the radius of the bar per unit length, and z is the position of the sheet unit j in the z axis.
The differential equilibrium equation of the sheet unit j in the radial direction r in S5 is:
the stretching side sheet unit takes "+", the compression side sheet unit takes "-", the
Is the central angle of the thin sheet unit where the neutral layer is positioned.
The method for adding the equal sign two sides of the differential equilibrium equation of each sheet unit in the S6 is as follows: due to
Smaller, can be approximately regarded as->
Obtaining:
the e is the offset of the stress neutral layer, the
The sigma is the central angle of the thin sheet unit where the neutral layer is positioned r0 Contact stress of the bar per unit length at the center of the gravure roll, b 1 The width of the contact area of the bar per unit length at the center of the concave straightening roller, the sigma rn Contact stress of the bar per unit length at the center of the straightening roll, b 2 The width of the contact area of the bar per unit length at the center of the convex straightening roller, the sigma θy Tangential stress of the sheet unit on the pressed side, the sigma θl Is the tangential stress of the sheet element on the stretching side.
The method for obtaining the stress neutral layer position determination formula in the S7 comprises the following steps: will be
i＝[1/2+e/(2r)]n is substituted into the formula in the S6, and the stress neutral position determination formula when the bar and the concave straightening roller are in a full contact state is as follows:
said ρ w Radius of recurve of bar per unit length, said sigma t Being the yield strength of the bar, said r t Is the elastic core radius of the rod per unit length.
And in the step S8, tangential stress distribution functions of the straightening, bending, stretching and compressing sides of the bar are as follows:
and lambda is the hardening coefficient of the bar and is obtained by room temperature stretching experimental equipment.
When the bar material is in partial contact with the concave straightening roller, sigma in the formula of S7 r0 =0, the bar straightening stress neutral layer position determination formula is:
sigma in the formula of S7 r0 ＝0，r＝H/2，b 1 ＝b 2 ＝(r 2 -z 2 ) 1/2 When=b, the determination formula for obtaining the straightening stress neutral layer position of the wide and thick plate is:
the H is the thickness of a plate with unit length, and t the thickness of the elastic area of the plate in unit length is shown, and the B is the width of the plate in unit length.
Compared with the prior art, the invention has the beneficial effects that:
according to the invention, the stress neutral layer position is determined when the bar is subjected to straightening stress, so that the rebound prediction precision after the bar is straightened and the bar straightening quality are improved, the accuracy of process parameter setting is improved, the dependence on experience of operators is overcome, the number of bars used for process parameter debugging is reduced, and the working efficiency and economic benefit are improved.
Drawings
FIG. 1 is a schematic diagram of the full contact of a bar material and a straightening roller according to the invention;
FIG. 2 is a schematic view of the partial contact of the bar material with the straightening roll according to the invention;
FIG. 3 is a schematic view of the stress of the sheet unit during bar straightening according to the present invention;
FIG. 4 is a schematic view of the contacting of a wide and thick sheet material with a straightening roll according to the present invention;
FIG. 5 is an enlarged view of the contact area G between the wide and thick plates and the straightening roll according to the invention;
wherein: 1 is a concave straightening roller, 2 is a bar, 3 is a convex straightening roller, 4 is a unit length bar, 5 is a flat straightening roller, 6 is a wide and thick plate, and 7 is a unit length plate.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
As shown in fig. 1, when the bar 2 is in full contact with the concave straightening roller 1, the bar straightening stress neutral layer position determining method comprises the following steps: firstly, cutting a unit length bar 4 at the contact area of the convex straightening roller 3 and the bar 2, wherein the unit length bar 4 is symmetrical about a yz plane; then, uniformly dividing the bar 4 in unit length into n sheet units along the tangential direction theta of the arc surface xy; finally, stress analysis was performed for each sheet unit, as shown in fig. 3.
During the straightening process, the side of the bar 4 of unit length in contact with the male straightening roller 3 is subjected to compressive stress sigma in the radial direction rn The sheet unit is compressively deformed in the tangential direction θ with a compressive stress σ rn The pressure sensor or finite element software is used for simulation; the other side is also subjected to compressive stress sigma in radial direction r0 But the sheet element is deformed in tension in the tangential direction θ, also simulated by a pressure sensor or finite element software. The differential equilibrium equation of the lamellar unit j in tangential direction θ is:
in sigma θ Is the stress of the lamellar unit j in the tangential direction theta,
the stress variation of the sheet unit j in the tangential direction theta is that r is the radius of the bar 4 in unit length and is measured by a vernier caliper; z is the position of the sheet unit j in the z-axis, mm.
Simplifying the formula to obtain:
i.e. tangential stress sigma θ Is a constant value.
Assuming that the stress neutral layer is located between the sheet unit i and the sheet unit i+1 at the time of straightening, the differential equilibrium equation of the sheet unit j in the radial direction r is:
in the formula, the stretching side sheet unit is "+", and the compression side sheet unit is "-".
The differential balance equation equal sign of each sheet element in the radial direction r is added on both sides, due to
Smaller, can be approximately regarded as->
Obtaining:
wherein e is the offset of the stress neutral layer, and mm;
the central angle and rad of the thin sheet unit where the neutral layer is positioned; sigma (sigma) r0 The contact stress of the bar 4 in unit length at the center of the concave straightening roller 1 is obtained by simulation of a pressure sensor or finite element software, and is MPa; b 1 The width of the contact area of the bar 4 in unit length at the center of the concave straightening roller 1 is measured by a metal bending device and a vernier caliper, and is mm; sigma (sigma) rn The contact stress of the bar 4 in unit length at the center of the convex straightening roller 3 is obtained by simulation of a pressure sensor or finite element software, and is MPa; b 2 The width of the contact area of the bar 4 in unit length at the center of the convex straightening roller 3 is measured by a metal bending device and a vernier caliper, and is mm; sigma (sigma) θy Tangential stress of the sheet unit on the pressed side is obtained by room temperature stretching experimental equipment and is MPa; sigma (sigma) θl Tangential stress of the sheet unit on the stretching side is obtained by room temperature stretching and compression experimental equipment and is MPa.
Will be
i＝[1/2+e/2r]n is substituted into the above formula to obtain a bar straightening stress neutral layer position determination formula when the bar 2 and the concave straightening roller 1 are in a full contact state:
wherein ρ is w The radius of the reverse bending is mm and is obtained by a metal bending device; sigma (sigma) t The yield strength of the bar 2 is obtained by room temperature tensile experimental equipment and is MPa; r is (r) t The elastic core radius of the bar 4 in unit length is obtained by room temperature stretching experimental equipment and is mm.
Substituting tangential stress distribution functions of the straightening, bending and stretching sides and the compression sides of the bar into the above formula to obtain a stress neutral layer offset value, wherein the stress distribution functions are as follows:
wherein lambda is the hardening coefficient of the bar 2, and is obtained by room temperature tensile test equipment.
As shown in FIG. 2, σ is when the bar 2 is in partial contact with the concave straightening roll 1 r0 =0, the bar straightening stress neutral layer position determination formula is:
in sigma rn The contact stress of the bar 4 in unit length at the center of the convex straightening roller 3 is obtained by simulation of a pressure sensor or finite element software, and is MPa; b 2 The width of the contact area of the bar 4 in unit length at the center of the convex straightening roller 3 is measured by a metal bending device and a vernier caliper, and is mm; ρ w The reverse bending radius of the bar 4 in unit length is obtained by a metal bending device and is mm; r is the radius of the bar 4 in unit length, measured by a vernier caliper, mm; r is (r) t The elastic core radius of the unit length bar 4 is obtained by room temperature stretching experimental equipment and is mm; e is the offset of the stress neutral layer, mm; sigma (sigma) t The yield strength of the bar 2 material is obtained by room temperature tensile experimental equipment and is MPa; sigma (sigma) θl Tangential stress of the sheet unit at the stretching side is obtained by room temperature stretching experimental equipment and is MPa; sigma (sigma) θy The tangential stress of the sheet unit on the pressed side is obtained by room temperature tensile compression experimental equipment and is MPa.
As shown in fig. 4 and 5, a method for determining the position of the stress neutral layer of the straightened bar material, i.e. sigma, can also be used for determining the position of the stress neutral layer of the straightened wide and thick plate material 6 r0 ＝0，r＝H/2，0 1 ＝b 2 ＝(r 2 -z 2 ) 1/2 When=b, the stress neutral layer position determination formula of the sheet material 6 is:
in the method, in the process of the invention,h is the thickness of the plate 7 in unit length, measured by a vernier caliper, and mm; h t The thickness of the elastic area of the material of the plate 7 in unit length is obtained by room temperature stretching experimental equipment and is mm; b is the width of the plate per unit length, measured by a length tool, mm.
The preferred embodiments of the present invention have been described in detail, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the spirit of the present invention, and the various changes are included in the scope of the present invention.
Claims (1)
1. A method for determining the neutral position of the straightening stress of a bar is characterized by comprising the following steps: comprises the following steps:
s1, defining a tangent line of an axis of a bar in the horizontal direction as an x-axis, defining a line which is perpendicular to a horizontal plane and passes through a tangent point of the x-axis and the axis of the bar as a z-axis, and establishing an xyz coordinate system according to a right-hand rule;
s2, intercepting a unit length bar in a contact area of the convex straightening roller and the bar, wherein the unit length bar is symmetrical about a yz plane;
s3, uniformly dividing the bar in unit length into n sheet units along the tangential direction theta of the arc surface xy;
s4, carrying out stress analysis on each sheet unit, and establishing a differential balance equation of the sheet unit j in the tangential direction theta; the differential equilibrium equation of the lamellar unit j in the tangential direction θ in S4 is:
the sigma θ Is the stress of the lamellar unit j in the tangential direction theta,
the stress variation of the sheet unit j in the tangential direction theta is represented by r, the radius of the bar in unit length, and z is the position of the sheet unit j in the z axis;
s5, assuming that the stress neutral layer is positioned between the sheet unit i and the sheet unit i+1 during straightening, and establishing a differential equilibrium equation of the sheet unit j in the radial direction r;
the differential equilibrium equation of the sheet unit j in the radial direction r in S5 is:
the stretching side sheet unit takes "+", the compression side sheet unit takes "-", said
The central angle is the central angle of the thin sheet unit where the neutral layer is positioned;
s6, adding the equal sign two sides of the differential balance equation of each sheet unit in the S5;
the method for adding the equal sign two sides of the differential equilibrium equation of each sheet unit in the S6 is as follows: due to
Smaller, can be approximately regarded as->
Obtaining:
the e is the offset of the stress neutral layer, the
The sigma is the central angle of the thin sheet unit where the neutral layer is positioned r0 Contact stress of the bar per unit length at the center of the gravure roll, b 1 The width of the contact area of the bar per unit length at the center of the concave straightening roller, the sigma rn Contact stress of the bar per unit length at the center of the straightening roll, b 2 The width of the contact area of the bar per unit length at the center of the convex straightening roller, the sigma θy On the pressed side of the sheet unitTangential stress, S θl Tangential stress on the stretching side of the sheet unit;
s7, obtaining a stress neutral position determination formula when the bar and the concave straightening roller are in a full contact state; the method for obtaining the stress neutral layer position determination formula in the S7 comprises the following steps: will be
i＝[1/2+e/(2r)]n is substituted into the formula in the S6, and the stress neutral position determination formula when the bar and the concave straightening roller are in a full contact state is as follows: />
Said ρ w Radius of recurve of bar per unit length, said sigma t Being the yield strength of the bar, said r t The elastic core radius of the bar is the unit length;
when the bar material is in partial contact with the concave straightening roller, sigma in the formula of S7 r0 =0, the bar straightening stress neutral layer position determination formula is:
sigma in the formula of S7 r0 ＝0，r＝H/2，b 1 ＝b 2 ＝(r 2 -z 2 ) 1/2 When=b, the determination formula for obtaining the straightening stress neutral layer position of the wide and thick plate is:
the H is the thickness of a plate with unit length, and t the thickness of the elastic area of the plate in unit length is set as B, and the width of the plate in unit length is set as B;
s8, substituting tangential stress distribution functions of the straightening, bending, stretching and compressing sides of the bar into the formula in the S7, and obtaining a stress neutral layer offset value; and in the step S8, tangential stress distribution functions of the straightening, bending, stretching and compressing sides of the bar are as follows:
and lambda is the hardening coefficient of the bar and is obtained by room temperature stretching experimental equipment.
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