Cálculos de torque de flexão de tubos: guia detalhado

Pipe Bending Torque Calculations: Detailed Guide

The tube bending process developed with the emergence of industries such as automobiles, motorcycles, bicycles and petrochemicals.

The commonly used pipe bending methods can be divided into winding, pushing, pressing and rolling according to the bending method.

They can be divided into cold bending and hot bending depending on whether they are heated during bending. Depending on the presence of filler (or mandrel) during bending, it can be divided into core bending and coreless bending.

Figures 6-19, 6-20, 6-21 and 6-22 respectively represent the schematic diagrams of molds for rolling, pushing, pressing and rolling devices.

Figure 6-19 Bending Tube with Core on the Bending Machine

1- Pressure Block
2- Central rod
3- Fixing block
4- Bending Mold
5- Wrinkle prevention block
6- Blank tube

Figure 6-20 Cold press bent tube device in mold mode

1—Press Column
2—Guide Sleeve
3—Blank Tube
4—Bending Mold

Figure 6-21 V-shaped tube bending mold

1 – Die
2—Blank tube
3—Swinging Punch

Figure 6—22 Three-roller tube bending principle

1—Axis
2,4,6—Rollers
3—Active Axis
5—Steel Tube

I. Bending deformation of the material and minimum bending radius

When the tube material is bent, the material on the outer side of the deformation zone is stretched and lengthened by tangential tension, while the material on the inner side is compressed and shortened by tangential compression.

Since the tangential stress σ θ and strain ε θ are distributed continuously along the cross-section of the tube material, they can be thought of as similar to the bending of the plate material.

The stretch zone on the outside transitions to the compression zone on the inside, with a neutral layer at the junction.

To simplify analysis and calculation, the neutral layer is normally considered to coincide with the central layer of the tube cross-section, and its position in the cross-section can be represented by the radius of curvature (Figure 6-23).

The degree of bending deformation of the tube material depends on the relative radius of curvature R/D and the relative thickness t/D (R is the radius of curvature of the central layer of the tube cross-section, D is the outer diameter of the tube, t is the tube wall thickness).

The smaller the values ​​of R/D and t/D, the greater the degree of bending deformation (i.e., R/D and t/D are very small), the outer wall of the neutral bending layer will become excessively thin and even lead break up; the innermost wall of the tube will become thicker and even unstable and wrinkled.

At the same time, with the increase in the degree of deformation, the cross-sectional distortion (flattening) becomes more serious.

Therefore, to ensure the forming quality of tube material, the degree of deformation must be controlled within the allowable range.

The permissible degree of deformation when bending the pipe is called the bending limit. The bending forming limit of pipe material not only depends on the mechanical properties of the material and the bending method, but also considers the usage requirements of pipe fittings.

For general-purpose bent parts, the maximum elongation deformation ε max. produced at the position furthest from the neutral layer on the outside of the bending deformation area of ​​the tube material must not exceed the limit value allowed by the plasticity of the material as a condition for defining the forming limit.

That is, the limiting radius of curvature r min that can be bent on the inner side of the part under the condition that the outer surface layer on the outer side of the bending deformation area of ​​the tube part does not crack, is used as the limit of formation of the bend of the tube part.

R min is related to the mechanical properties of the material, the structural size of pipe fittings, the bending processing method and other factors.

Figure 6-23 Force and stress-strain conditions in pipe bending

a Force conditions
b Stress-strain conditions

The minimum bending radius for different bending processes can be found in Table 6-2.

Table 6-2 Minimum bending radius during pipe bending (Unit: mm)

Bending Methods Minimum bending radius
Press fold (3~5)D
Wrap Fold (2~2.5)D
Roll folding 6D
Push Fold (2.5~3)D

Note: D represents the external diameter of the tube.

For the minimum bending radius of steel and aluminum pipes, see Table 6-3.

Table 6-3 Minimum bending radius of steel and aluminum tubes (Unit: mm)

Tube External Diameter 4 6 8 10 12 14 16 18 20 22
Minimum bending radius 8 12 16 20 28 32 40 45 50 56
Tube External Diameter 24 28 30 32 35 38 40 44 48 50
Minimum bending radius 68 84 90 96 105 114 120 132 144 150

II. Distortion of the shape of the pipe cross section and its prevention

During tube bending, distortion of the cross-sectional shape is inevitable.

The material on the outside of the neutral layer undergoes tangential tensile stress, thinning the tube wall; the material on the inner side of the neutral layer undergoes tangential compressive stress, thickening the tube wall.

The material on the outer and inner sides of the bending deformation area experiences the greatest tangential stress, so the greatest changes in tube wall thickness occur there (Fig. 6-24).

In bending with fillers or center rods, the cross section is basically able to maintain a circular shape, but the wall thickness changes. In unsupported free bending, whether at the inner or outer edge, the circular cross-section of the tube becomes elliptical (Fig. 6-24a, b).

Furthermore, as the degree of bending deformation increases (i.e., the radius of curvature decreases), the inner edge becomes unstable and wrinkled. In the case of square tubes in supported bending (Fig. 6-24c, d), the cross section changes to a trapezoidal shape.

Figure 6-24: Cross-sectional shape after tube bending

Ellipticity is often used in production to measure changes in the circular cross-section of a pipe.

Ellipticity = D max. -D min /D ×100% (6-21)

In this formula, Dmax is the maximum size of the outer diameter measured in any direction of the same tube cross-section after bending, and Dmin is the minimum size of the outer diameter measured in any direction of the same tube cross-section after bending. .

Figure 6-25 is an ellipticity graph, which represents the ellipticity change corresponding to the dimensionless curvature R0/R (R0 is the outer radius of the tube, R is the radius of curvature of the central layer of the bending section) in a logarithmic coordinate, represented as a family of straight lines with the ratio t/R0 as a parameter variable.

As can be seen in the figure, the greater the degree of bending, the greater the ellipticity of the cross section.

Therefore, ellipticity is often used in production as an important index for inspecting the quality of bent tubes. Depending on the different usage performances of bent tube materials, the requirements for their ellipticity also vary.

For example, for bent pipe components used in industrial pipeline projects, the high pressure pipe does not exceed 5%; medium and low pressure pipes are 8%; aluminum tubes are 9%; and copper alloy and aluminum alloy tubes are 8%.

Figure 6-25 Ovality

Distortion of the section shape can reduce the cross-sectional area, increasing resistance to fluid flow, and can also affect the functional performance of the tube in the structure.

Therefore, in the tube bending process, measures must be taken to control distortion within the required range.

Effective methods to avoid distortion of cross-sectional shape are:

1) Support the cross section with a mandrel in the bending deformation area to avoid distortion of the cross section.

For different bending processes, different types of mandrels must be used. Rigid mandrels are often used in bending and winding, and the mandrel head is hemispherical or has other curved surface shape.

Whether a mandrel is needed during bending and what type of mandrel to use can be determined from Figure 6-26 and Figure 6-27.

Figure 6-26 Chuck Structural Shape
Figure 6-27 Chuck wireframe selection

2) Filling the bent tube mold with granular medium, fluid medium, elastic medium or low melting point alloys can also replace the central rod to avoid distortion of the section shape. This method is relatively easy to apply and is widely used, mainly for small and medium-scale production.

3) On the surface of the mold in contact with the pipe material, a groove is made to match the section shape of the pipe material, reducing the pressure on the contact surface and making the section more difficult to distort. This is a very effective measure to avoid distortions in the section format.

4) The method of using the counter-deformation method to control the change in pipe section (Figure 6-28) is often used in the coreless bending process in the pipe bender. The feature of this method is its simple structure, which is why it is widely used.

The use of counter-strain for coreless bending means that the tube blank receives a certain amount of reverse strain in advance. Then, after bending, the deformations in different directions cancel each other out, basically maintaining the gross section of the tube circular to meet the ellipticity requirements, thus ensuring the quality of the bent tube.

Figure 6-28 Schematic diagram of tube bending without mandrel

1—Bending Mold
2—Fixing block
3—Roll
4—Guide Wheel
5—Blank tube

The cross-sectional shape of the anti-deformation groove as shown in Figure 6-29, the size of the anti-deformation groove is related to the relative radius of curvature (the radius of curvature of the core layer, the outer diameter of the tube). See Table 6-4.

Table 6-4 Anti-Warp Groove Dimensions

Relative radius of curvature R/D R1 R2 R3 H
1.5~2 0.5D 0.95D 0.37D 0.56D
>2~3.5 0.5D 1.0D 0.4D 0.545D
≥3.5 0.5D 0.5D 0.5D
Figure 6-29: Anti-deformation Groove

1—Bending Mold
2—Anti-deformation roller

The change in tube thickness mainly depends on the relative bending radius R/D and the relative thickness t/D. In production, the minimum wall thickness t min in external bending and the maximum wall thickness t max. inside can generally be estimated using the following formula:

In the formula,

  • t – represents the original thickness of the tube material (mm);
  • D – represents the external diameter of the tube material (mm);
  • R- represents the radius of curvature of the central layer (mm).

Thinning of the tube material reduces the mechanical strength and usability of the connections. Therefore, in production, the wall thinning rate is often used as a technical index to measure the change in wall thickness in order to meet the usability of accessories.

Tube wall thinning rate = tt min /t×100%

In the formula:

  • t – Original thickness of the tube material (mm);
  • t min – The minimum wall thickness after the pipe material is bent (mm).

The performance of pipe materials varies, and there are different requirements for the wall thickness reduction rate.

For example, for pipe fittings used in industrial pipe engineering, the pipe high pressure does not exceed 10%; the medium and low pressure pipe does not exceed 15% and is not less than the wall thickness calculated by the project.

Measures to reduce tube thickness thinning include:

1) Reduce the numerical value of the tensile stress generated on the outside of the neutral layer. For example, using the local resistance heating method to reduce the deformation resistance of the metal material within the neutral layer, making the deformation more concentrated in the compressed part, achieving the objective of reducing the stress level of the stressed part.

2) Change the stress state of the deformation zone and increase the compressive stress component. For example, changing from bending to pushing can fundamentally overcome the defect of excessive pipe wall thinning.

III. Calculation of bending torque

The calculation of the bending torque of the tube material is the basis for determining the power parameters of the tube bender.

According to the analysis of plastic mechanics theory, the theoretical expression of the bending moment when the tube material is uniformly bent is derived as follows:

Tube material bending torque:

In the formula:

  • σ is – yield stress;
  • t – tube wall thickness;
  • r – the radius of curvature of the tube material;
  • B – the modulus of elasticity (hardening modulus);
  • ρ – the radius of curvature of the neutral layer during bending.

The actual bending moment of the tube material not only depends on the tube material properties, cross-section shape and size, bending radius and other parameters, but is also closely related to the bending method and mold structure used.

Therefore, it is currently impossible to represent all these factors with one calculation formula, and only estimates can be made in production.

The bending torque of the tube material can be estimated with the following formula:

In the equation,

  • D – represents the external diameter of the tube;
  • σ b – represents the flexural resistance of the material;
  • W – represents the sectional modulus in flexion;
  • µ – represents the coefficient that takes into account the increase in bending moment due to friction.

The coefficient µ is not the coefficient of friction; its value depends on the condition of the pipe surface, the bending method, especially whether a mandrel is used, the type and shape of the mandrel, and even several factors related to the position of the mandrel.

In general, when using a rigid chuck without lubrication, a value of 5 to 8 can be taken; when a rigid articulated chuck is used, a value of µ=3 can be obtained.

The cross-sectional shape of the anti-deformation groove is shown in Figure 6-29.

The dimensions of the anti-deformation groove are related to the relative radius of curvature (the radius of curvature of the core layer, the outer diameter of the tube).

See Table 6-4.

Table 6-4 Anti-Warp Groove Dimensions

Relative radius of curvature R/D R1 R2 R3 H
1.5~2 0.5D 0.95D 0.37D 0.56D
>2~3.5 0.5D 1.0D 0.4D 0.545D
≥3.5 0.5D 0.5D 0.5D
Figure 6-29 Anti-Deformation Groove

1—Bending Mold
2—Anti-deformation roller

The change in tube thickness mainly depends on the relative bending radius R/D and the relative thickness t/D.

In production, the minimum wall thickness t min on the outside of the bend and the maximum wall thickness t max. on the inside can generally be estimated using the following formula:

In the formula:

  • t – is the original thickness of the tube material (mm);
  • D – is the external diameter of the tube material (mm);
  • R- is the radius of curvature of the central layer (mm).

Thinning of pipe material reduces the mechanical strength and performance of pipe fittings. Therefore, the thinning rate is often used in production as a technical indicator to measure the change in wall thickness in order to meet the performance requirements of pipe fittings.

Tube wall thinning rate = (tt min )/t×100%

In the formula:

  • t – is the original thickness of the tube (mm);
  • t min – is the minimum wall thickness after bending the tube (mm).

Different pipe material performances require different grinding rates. For example, for pipe fittings used in industrial piping engineering, the high pressure pipe should not exceed 10%; medium and low pressure pipes must not exceed 15% and must not be less than the wall thickness calculated by the project.

Measures to reduce tube thickness thinning include:

1) Reduce the numerical value of the tensile stress generated on the outer side of the neutral layer, such as adopting the local resistance heating method, reducing the deformation resistance of the metal material on the inner side of the neutral layer, making the deformation more concentrated on the compressed, thus achieving the objective of reducing the tension level of the stressed part.

2) Change in the stress state of the deformation zone and increase in the compressive stress component. For example, changing from bending to pushing can fundamentally overcome the defect of excessive pipe wall thinning.

4. Calculation of bending torque

The calculation of the pipe bending torque is the basis for determining the power parameters of the pipe bender. According to the analysis of plastic mechanics theory, the theoretical expression of the uniform bending moment of the tube is derived as follows:

Tube bending torque:

In the formula:

  • σ is – Performance stress;
  • t – Tube wall thickness;
  • r – Radius of curvature of the tube;
  • B – Deformation modulus;
  • ρ – Radius of curvature of the neutral flexural layer.

The actual bending moment of the tube material not only depends on the performance of the tube material, the shape and size of the cross-section, the bending radius and other parameters, but also has a lot to do with the bending method and the structure of the mold used.

Therefore, it is currently impossible to express all factors in a calculation formula, and only estimates can be made in production.

The bending moment of the tube material can be estimated with the following formula:

In the formula:

  • D – represents the external diameter of the tube;
  • σ b – represents the flexural resistance of the material;
  • W – represents the bending section coefficient;
  • µ – represents the coefficient considering the increase in bending moment due to friction.

The coefficient is not the coefficient of friction µ, its value depends on the condition of the tube surface, the bending method and, mainly, whether a mandrel is used, the type and shape of the mandrel and even several factors related to the position of the mandrel . chuck.

In general, when a rigid chuck is used without lubrication, =5 to 8 can be considered; if a rigid articulated chuck is used, µ=3 can be considered.

V. Tube rolling forming

Pipe rolling forming is a special forming process developed from the traditional processes of stamping, flanging and throttling. It is a deformation process in which the pipe mouth edge is bent locally by applying axial pressure to the pipe part through the mold.

The use of this technology in the manufacture of parts presents a series of advantages such as simple technology, fewer processes, low cost and good quality. It can even produce parts that are difficult to achieve with other stamping methods.

This process has been widely used in various industrial fields such as automobiles and aerospace.

There are two basic forms of tube turning forming, namely outer roll and inner roll (Figure 6-30).

a, b roll out;
c, d roll in

1—Blank tube
2—Flow guide ring
3—Conical mold
4—Round edge mold

Roll out: The tube blank is turned inside out under axial pressure, increasing its circumference after forming.

Internal roll: The tube blank is rolled from the outside to the inside, reducing its circumference after forming.

The rolling process can not only effectively form various types of double-walled or multi-layer tubular parts, but also process convex bottom cups, stepped tubes, special-shaped tubes, as well as semi-double tubes, double-walled annular cylinders, hollow double wall nuts, heat exchangers, automobile mufflers, waveguide tubes in the electronics industry, etc.

At present, these parts are generally processed by multi-step stamping and welding methods, which are difficult, expensive and of poor appearance quality.

The use of the lamination process guarantees the reliability of the part, lightness and savings in raw materials.

Figure 6-31 Components formed by the profiling process
  • a) Double layer tube
  • b) Stepped pipe
  • c) Molded tube
  • d) Convex bottom cup

At present, according to data, many metal materials can be formed in the mold in various different rolling methods, such as aluminum alloy, copper and copper alloys, low carbon steel, austenitic stainless steel, etc. be rolled into double-layer tubes.

1. Roll Out

Profiling, compared with other forming processes, has a more complex deformation process, which includes widening, curling, rolling and their mutual conversion.

There are several molds to carry out this forming process, among which the simplest and most commonly used are conical molds and fillet molds.

1. Tapered Tube Rolling Mold

The structure of the tapered tube rolling mold is shown in Figure 6-32. This mold structure is simple and different specifications of tubes can be formed in one set of molds, which is difficult to achieve in other tube forming molds.

In addition, as a preforming process for precision tube roll forming, taper mold forming is widely used.

Figure 6-32 Tapered Tube Inversion Mold

a tube inverted mold structure
b Conical tube inversion process parameters

1 – Press the head
2 – Tube Bill
3 – Cone Mold

During the tube turning process, one end of the tube blank is placed in a conical die, while the other end is subjected to the axial pressure of the press slider to achieve the turning of the tube blank.

When designing this type of die, the angle α of the half-cone of the die is the most critical parameter.

The size of α not only determines the feasibility of pipe turning, but also affects the geometric dimensions of pipe turning, that is, the pipe turning coefficient K(K=D/D1, where D and D1 are the outer diameter of the tube blank and the outer diameter of the tube turning, respectively).

Obviously, there is a critical half-cone angle α0, and the turning can only be carried out normally when the half-cone angle α≥ α0.

µ, H, Golubnov derived based on the principal stress principle:

Considering the influence of material reinforcement and flared end stiffness, the above formula can be modified as follows:

In the formula:

  • L – Length of the widened straight tip;
  • D – Average diameter of the tube blank;
  • t – Wall thickness of the tube blank;
  • n – Material hardening index;
  • A – Material reinforcement coefficient;
  • σs – Resistance to flow of the material.

For a 42mm 3A21 aluminum tube, calculated by the above formula, the angle is 55° – 60°.

Empirical tests show that when the angle is α≥60° ​​(α≈68°), the tube inversion can occur smoothly. At this time, the axial pressure is the smallest.

When the angle is 55° to 60°, the end of the empty tube bends but does not enter the inversion stage. When the angle is α<55°, the end of the tube just widens in the conical die and does not curl.

During inversion of the conical die, the end of the tube slides easily, causing the inverted part of the tube to be outside the axis of the original tube blank and causing axial bending during inversion.

It is difficult to obtain a double-layer inverted tube part that meets assembly quality requirements. Consequently, a round corner rotary die was developed based on the conical die.

2. Round corner inverted matrix

The round corner rotary die uses the working part of the die, which is a circle of radius, to force the axially compressed tube end to deform along its arc to achieve tube inversion.

Figure 6-33 shows a schematic diagram of a tube blank of thickness t and mean diameter D, rolling over a round-corner die of radius r, under axial load, the end of the tube rolls upward along the arc of the die. to obtain a piece of coiled pipe with diameter D1.

Figure 6-33 Schematic diagram of round corner flange die

The most important parameter in the design of a round corner flange die is the radius r of the die corner. It determines not only the geometric dimensions of the flanged part, but also influences the magnitude of the flanging force.

For Φ41×1 type 3A21 annealed aluminum tube, both theoretical analysis and experimental results show that the critical die fillet radius (minimum fillet radius) for tube inversion instability is about 2 mm; the ideal fillet radius is approximately 3 mm; the maximum fillet radius is about 4 mm.

This indicates that the stability and inversion quality of the tube under axial load depend on the die fillet radius r. If r is less than a certain critical value, the end of the tube does not curl along the arc of the die; when r is too large, the end of the tube fractures and cannot be successfully inverted. Only when r is within an appropriate range can the tube inversion be performed.

2. Roll Inward

Similar to the external corrugation of the tube material, the internal corrugation of the tube can also be performed in the conical mold and fillet mold (Figure 6-34).

Compared to other forming processes, it is prone to instability. Because during inward curling, the diameter of the tube decreases after deformation, the tube wall becomes thicker, the inversion force of the tube increases, which makes it difficult for the corrugation to form.

According to theoretical and practical calculations, when the critical angle of the β semicone of the tube inversion cone mold is ≥120°, the corrugation process can proceed smoothly. In production, the value is generally regarded as β≥120°~125°, r p ≈4mm.

The tube winding process can only occur when the load required for winding is less than the axial instability limit. Since the dimple forming load largely depends on the geometric parameters of the mold, in terms of the fillet mold, it depends on the fillet radius r.

Therefore, a viable region for ripple formation can be determined (Figure 6-35).

Figure 6-34 Schematic diagram of tube internal turning die structure

a conical die
b Rounded Matrix

Figure 6-35 Feasibility Areas for External and Internal Lamination of Tubular Materials

In Figure 6-35, it can be seen that the internal rolling area is quite small, and the rolling load is numerically higher than that of the external rolling, reaching almost 50%.

Existing data shows that, both nationally and internationally, the optimal process parameters for external rolling have been studied theoretically and practically, and the relationship between the minimum axial compressive stress required for complete rolling and the inner diameter, outer diameter and wall thickness of tubular material was discovered.

During external rolling of tubular materials, the change in wall thickness is not significant.

However, during internal rolling, the circumferential compressive stress causes the wall thickness in the mold fillet to increase continuously until it reaches a constant value, which can be 1.5 times the original thickness. Therefore, to complete its internal lamination, a greater axial load is required.

In the above-mentioned two types of lamination (traditional lamination), there are some shortcomings:

1. The beginning of the second layer of the tube wall is not parallel to the original tube wall, but always turns towards the inner cavity of the double-wall tube;

2. There is a certain distance between the new pipe wall and the original pipe wall, which depends on the relative diameter (D/t) of the original pipe material;

3. For internal rolling, the second layer of the tube wall is considerably thicker, which in turn leads to an increase in axial pressure during rolling.

The problems that arise in the aforementioned processes are due to the forming mechanism, which limits the geometric shape of the tubes obtained, especially the poor stability and high difficulty of the internal rolling process, which needs to be improved.

Therefore, the tensile stress rolling forming method for internal rolling of tubular materials emerged.

The characteristic of the tensile rolling forming method is that it stops rolling at the first stage of internal rolling of the tubular material and gives the rolled edge a reverse curvature, directing it to the outside of the cavity.

Then, through the action of the convex mold, the tensile force acting on the reverse bending edge on the inner wall causes the tube blank to undergo internal rolling, rather than rolling by the axial pressure acting on the outer wall, thereby reducing its pressure. axial. .

This process can achieve higher inner wall height, constant wall thickness and higher product precision.

The tensile stress rolling forming method has expanded the application range of the internal rolling forming process, such as producing pipe joints, bearing seats and others (Figure 6-36).

Figure 6-36: The application of the internal bending roll forming process in the production of bearing housings.

The tensile tension roll forming method can be divided into three steps, as shown in Figure 6-37.

In the first step (Figure 6-37a), traditional internal rolling ends when the edge of the tube leaves one-quarter of the fillet matrix.

At this time, the distance between the edge of the tube and the inner wall of the die will form the radial support of the final product and should be equal to the required width.

In the second step (Figure 6-37b), the flat-bottomed convex die descends, forcing the edge of the tube to flange (similar to the plate's flanged hole). The gap between the convex die and the inner roll die is determined by the thickness of the tube wall (the thickness of the inner wall of the tube roll is slightly increased).

In the third step (Figure 6-37c, d), the convex forming die rises, causing the edge of the tube to roll inward, thus generating the second layer of the tube wall under the thrust of the convex forming die.

As can be seen in the figure, the convex forming matrix acts on the edge of the tube with tensile stress, and not with compressive stress acting on the entire tube.

There is no relative slip between the matrix and the deformed material, and a distance is maintained between the forming loads, thus reducing the axial compressive stress in the tube transmission area, thus preventing instability.

Therefore, tensile stress rolling has greater freedom in choosing the rolling radius, while the die radius is an important process parameter in traditional machining processes (Figure 6-35).

Conditions for the successful execution of this process:

F Hole ≥F Rolling (6-22)

The punching force includes three components (symbol in Figure 6-37d): the load that causes plastic deformation of the material at radius rP; the load required to overcome the friction in the corner ra between the punch and the edge of the tube; the load required to bend and unfold the edge material from radial to axial position.

In the analytical expression, σ 1 is used to represent the deformation stress of the inner wall.

Then,

(6-23)

Roll forming includes two aspects: the load required for rolling the material at different bend radius positions and the load required for bending and recovery from the beginning to the end of the deformation zone.

In the analysis, σ 0 is used to represent the deformation stress of the outer wall, and σ i represents the average plastic deformation stress in the deformation zone.

Conclusion:

The tube forming method by rolling under tensile stress has been proven through experiments.

Although two preparation steps are required before rolling begins and recrystallization annealing is required when necessary, it has the following advantages compared to the traditional rolling process:

1) The rolled edge rotates toward the center of the cavity, making it easy to coordinate with other parts such as ball bearing seats.

2) The bearing load is significantly reduced.

3) The forming limit is greatly improved and products with smaller rolling radius It can be obtained.

4) There is no friction and no need for lubrication.

5) The thickness of the inner wall is approximately equal to the thickness of the outer wall, and only the loaded edge is slightly thicker (Figure 6-38).

The experimental conditions of the part shown in Figure 6-38 are as follows:

The tube is made of low carbon steel, D out = 90 mm, t 0 = 2.4 mm, H = 150 mm.

The diameter of the concave die (Figure 6-37d) is Dd = 97mm.

The diameter of the convex die (Figure 6-37d) is D p =72mm.

6) Due to the absence of friction and the double constraint of the convex and concave dies on the part wall, the part has high dimensional accuracy (Figure 6-37d).

Figure 6-38 Product Wall Thickness Measurement

Figure 6-37 Tensile tension roll forming process (enhanced internal forming process)

Conditions for the successful implementation of this process:

F Hole ≥F Rolling (6-22)

Punching force includes three items (symbol in Figure 6-37d): the load that causes plastic deformation of the material at radius rp; the load required to overcome the friction force between the corner of the punch in ra and the edge of the tube; the load required for bending and reverse bending of the edge material from the radial position to the axial position.

In the analytical expression, σ 1 represents the deformation stress of the inner wall.

Profiling includes two aspects: the load required for the material to roll at different radius (bending) positions and the load required for bending and reverse bending from the beginning to the end of the deformation area.

In the analysis, σ 0 is used to represent the deformation stress of the outer wall, and σ i is used to represent the average plastic deformation stress in the deformation area.

Conclusion:

The method of forming tube materials by rolling under tensile stress has been proven by experiments. Although two preparation stages are required before rolling begins and recrystallization annealing is required when necessary, it has the following advantages over traditional rolling processes:

1) The rolled edge rotates toward the center of the cavity, facilitating cooperation with other parts such as ball bearing seats.

2) The rolling load is greatly reduced.

3) The forming limit is greatly improved and products with smaller rolling radii It can be obtained.

4) There is no friction and no need for lubrication.

5) The thickness of the inner wall is approximately the same as that of the outer wall, and only the loaded edges are slightly thicker (Figure 6-38).

The experimental conditions of the parts shown in Figure 6-38 are as follows:

The pipe material is low carbon steel, D outside = 90 mm, t 0 = 2.4 mm, and the radius H is 150 mm.

The diameter of the die D d (Figure 6-37d) is 97 mm.

The diameter of the punch (Figure 6-37d) is D p =72mm.

6) Due to the absence of friction and the double restrictions of the punch and the die on the part wall, the part has greater dimensional accuracy (Figure 6-37d).

Figure 6-38: Product Wall Thickness Measurement

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