Accurate prediction method for metal hydraulic extrusion force

Abstract

The invention provides an accurate prediction method for metal hydraulic extrusion force. According to the method, on the theoretical basis of a Reynolds equation and a Trichos yield criterion, the fluid power lubrication effect is focused, theoretical analysis of the metal hydraulic extrusion force is carried out, and finally an expression of the metal hydraulic extrusion force is obtained. Based on the Newtonian fluid hypothesis, the dynamic change of the viscosity of the pressure transmission medium along with the pressure and the nonlinear characteristic of the fluid shear force are considered, a hydraulic extrusion force theoretical model closer to the actual physical process is established, and the simplified hypothesis of a traditional model for a fixed friction coefficient is broken through; the effectiveness of the method is verified by tests of tungsten alloy, W6Mo5Cr4V2 high-speed steel and the like.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of special equipment; in particular, it relates to a precise prediction method of metal hydrodynamic extrusion force. BACKGROUND

[0002] Hydrodynamic extrusion is also known as dieless extrusion or hydrodynamic extrusion, which uses high-pressure liquid as a pressure transmission medium to extrude metal blanks into the required shape. Its greatest advantage is that the deformation amount is large (up to 60% of cold deformation), which can greatly improve the strength and toughness of metal materials, and has the characteristics of fast forming speed, good surface quality, high production efficiency, etc. It is an advanced difficult deformation metal forming method and is widely used in the forming and modification of difficult deformation materials such as tungsten alloy and high-speed steel.

[0003] The hydrodynamic extrusion force is the highest pressure of the pressure transmission medium required in the metal hydrodynamic extrusion process, that is, the pressure of the pressure transmission medium required when the extrusion breaks through. The hydrodynamic extrusion force is a key process parameter for metal hydrodynamic extrusion forming, and is the basic basis for selecting hydrodynamic extrusion equipment, extrusion dies, extrusion ratio and pressure transmission medium. At the same time, the size of the hydrodynamic extrusion force has a decisive influence on the design of ultra-high pressure seals, seal life, pressure transmission medium selection, pre-stressed extrusion cylinder design, die design, pre-stressed frame design, manufacturing cost, safety protection requirements, etc. Therefore, predicting the hydrodynamic extrusion force is a key problem in the research and development of the technology.

[0004] The monograph "Hydrodynamic Extrusion Technology" (Author: Wang Fuchi, Zhang Chaohui) gives the expression of the hydrodynamic extrusion force based on the viscoelastic force balance equation as follows:

[0005]

[0006] The foreign monograph "Hydrodynamic Extrusion Technology" (Author: Masao Nishihara) also gives the expression of the hydrodynamic extrusion force through experimental research and theoretical analysis based on force balance.

[0007] p = (aHV + b) ln R

[0008] In engineering practice, it is found that the calculation results of the above two expressions are greatly different from the true extrusion force, which is difficult to effectively guide engineering practice. Therefore, a more accurate prediction method of hydrodynamic extrusion force is urgently needed. SUMMARY

[0009] The purpose of the present application is to provide a precise prediction method of metal hydrodynamic extrusion force.

[0010] The present application is realized by the following technical solutions:

[0011] The present application relates to a kind of accurate prediction method of metal hydraulic extrusion pressure, with Reynolds equation and Lurie's yield criterion as theoretical basis, focusing on fluid dynamic lubrication, carry out the theoretical analysis of metal hydraulic extrusion pressure, finally obtain the expression of metal hydraulic extrusion pressure is:

[0012]

[0013] In the formula, p A The pressure of transmission medium in extrusion cylinder,

[0014] R is extrusion ratio,

[0015] γ is the pressure coefficient of dynamic viscosity under different pressure;

[0016] σ is the yield stress of bar material;

[0017] G=γσ.

[0018] Preferably, the expression of the metal hydraulic extrusion pressure is suitable for accurate prediction of the hydraulic extrusion pressure of tungsten alloy, high-speed steel metal material, and has accuracy and universality.

[0019] Preferably, the transmission medium of the metal hydraulic extrusion pressure is Newtonian fluid.

[0020] Preferably, the billet is rigid plastic body in high pressure environment and the deformation resistance remains constant during the whole extrusion process.

[0021] Preferably, the transmission medium does not slide relative to the surface of the billet, that is, the fluid velocity adhering to the surface of the billet is the same as the surface speed of the billet.

[0022] Preferably, the tool is a rigid body, and temperature change is not considered.

[0023] The present application has the following advantages:

[0024] (1) The present application is based on Newtonian fluid assumption, considers the dynamic change of transmission medium viscosity with pressure and the nonlinear characteristics of fluid shear force, establishes a more realistic physical process of hydraulic extrusion pressure theoretical model, breaks through the simplification assumption of fixed friction coefficient in traditional model, and its effectiveness is verified by tungsten alloy and W6Mo5Cr4V2 high speed steel test.

[0025] (2) The present application derives the calculation formula of hydraulic extrusion pressure, so as to realize the accurate prediction of hydraulic extrusion pressure, solves the problem of inaccurate calculation of hydraulic extrusion pressure for a long time, or needs to rely on test to determine the hydraulic extrusion pressure. BRIEF DESCRIPTION OF DRAWINGS

[0026] Figure 1It is a precise prediction method process demonstration diagram of metal hydraulic extrusion force; wherein: 1, pressure transmission medium; 2, blank; 3, extrusion die, and the hydraulic extrusion process is divided into two regions of a deformation zone and a deformation zone. DETAILED DESCRIPTION

[0027] The application will be described in detail below with specific examples. It should be noted that the following examples are only further illustrations of the application, and the protection scope of the application is not limited to the following examples.

[0028] Example 1

[0029] This example relates to a precise prediction method of metal hydraulic extrusion force, the detailed process is as follows:

[0030] As shown in Figure 1 , in which 1 is a pressure transmission medium; 2 is a blank; 3 is an extrusion die, and the method makes the following basic assumptions: Figure 1

[0031] (1) The hydraulic extrusion pressure transmission medium is a Newtonian fluid, that is, the shear stress of the fluid is linearly related to the shear rate.

[0032] (2) The hydraulic extrusion pressure transmission medium does not slide relative to the surface of the blank, that is, the fluid flow rate adhering to the surface of the blank is the same as the surface speed of the blank.

[0033] (3) The blank is a rigid plastic body in a high pressure environment and the deformation resistance remains constant during the entire extrusion process.

[0034] (4) The die is a rigid body.

[0035] (5) Temperature changes are not considered.

[0036] In the deformation zone, during the deformation of the blank, there is an oil film between the die and the blank. According to the above basic assumptions and the basic definition of the Reynolds equation, the relationship between the velocity of the hydraulic extrusion pressure transmission medium fluid and the pressure is expressed as:

[0037]

[0038] v is the velocity of the liquid at (x, y), and η is the viscosity of the liquid, which changes with the change of pressure.

[0039] After first and second integrations of the first expression of formula (1) are performed, the following formula is obtained:

[0040]

[0041] Further operation of the second expression in formula (2) gives the following expression:

[0042] ​

[0043] Let Equation (3) is expressed as:

[0044]

[0045] In equation (4), Q is a fluid constant. According to the basic characteristics of Newtonian fluid, the expression of the change of liquid viscosity with pressure is:

[0046] η = η0e γp (5)

[0047] p and In the whole process, is a continuous function, according to Figure 1 They satisfy the following boundary conditions:

[0048] When y = 0, v = 0, then C2 = 0.

[0049] In the area to be deformed, the speed of the blank υ = u1 is a constant.

[0050] In the deformation zone, according to the geometric characteristics of the hydraulic extrusion shown in Figure 1 According to the principle of invariable volume, the relationship between the speed of deformation zone and the blank u1 and x is obtained:

[0051]

[0052] After the extrusion deformation is completed, Since u1, x1, and x2 are constants, v = u2 at this time is also a constant.

[0053] When y = h, substitute the above speed boundary conditions and C2 = 0 into the second expression of equation (2) to solve:

[0054]

[0055] Substitute equation (7) into equation (2) to obtain the following equation:

[0056]

[0057] Combine equation (8) and equation (4) to get:

[0058]

[0059] Rearrange equation (9) to get:

[0060]

[0061] On the other hand, according to the basic assumption that the transmission medium of hydraulic extrusion is Newtonian fluid, the transmission medium satisfies the Newtonian fluid flow equation:

[0062]

[0063] Substitute it into the first expression of formula (2), we get:

[0064]

[0065] According to the force balance and Lurie yield criterion, the balance equation of the blank in the hydrodynamic extrusion process is expressed by Hoffman equation, as follows:

[0066]

[0067] Substitute formula (11) into formula (12), we get:

[0068]

[0069] Because the value of the oil film thickness h on the surface of the deformation zone bar is small, compared with x, it can be ignored, so formula (13) becomes:

[0070]

[0071] According to the geometric characteristics of the hydrodynamic extrusion as shown in Figure 1 , we can know that

[0072]

[0073] Substitute formula (15) into formula (14) and arrange it, we get:

[0074]

[0075] Let G = γσ, B = e -γp , and substitute it into formula (16) and arrange it, we get:

[0076]

[0077] Solve formula (17), we get:

[0078]

[0079] where,

[0080]

[0081] C is the integral constant, which is determined by the boundary condition.

[0082] When , p = p1 = p A + σ

[0083] Then Substitute equation (18) into equation (17) to get

[0084]

[0085] When , p = p2= σ, Substitute equation (22) into equation (21) to get

[0086]

[0087] On the other hand, for equation (14), when x = x1, we have

[0088]

[0089] Substitute equation (22) into equation (9) to get

[0090]

[0091] For the convenience of subsequent operation, let

[0092] Then, in the area to be deformed, i.e. x = x1, we have from equations (23) and (10)

[0093]

[0094] According to the geometric characteristics of hydraulic extrusion, as shown in Figure 1 , we have

[0095]

[0096] Differentiate equation (25) above, since dD = 0, we can get the relationship between dh and dx as follows:

[0097] dh = dx * tan α (26)

[0098] Substitute equation (26) into equation (24) to get

[0099]

[0100] Integrate equation (27) to get

[0101]

[0102] For the area to be deformed, p = p A , we can consider that h = ∞ in the Reynolds formula, so

[0103]

[0104] When x = x1, p = p1, h = h1, substituting into equation (28) gives:

[0105]

[0106] Substituting the expression of C3 into equation (30) gives:

[0107]

[0108] In equation (31), h1 and are small enough in comparison, so the term h1 can be neglected, and equation (31) is converted to:

[0109]

[0110] Substituting equation (32) gives the expression of h1 as follows:

[0111]

[0112] Substituting equation (33) into equation (19) gives:

[0113]

[0114] Substituting equation (34) into equation (21) gives:

[0115]

[0116] The above equation is rearranged to give:

[0117]

[0118] Taking the logarithm of both sides of equation (36) gives:

[0119]

[0120] In the above equation, since u1 and γ are small in comparison with x1 tan 2 α, the term can be neglected, and equation (37) can be written as:

[0121]

[0122] Thus, the expression of the hydraulic extrusion force is obtained.

[0123] In the above equation, the meanings of the letters involved are as follows:

[0124] σ k The average deformation resistance of the extruded billet;

[0125] d The diameter of the extruded product;

[0126] l d The length of the sizing belt of the die;

[0127] m z Friction factor on the taper of the die, m z = 0.05-0.1;

[0128] m d Friction factor on the sizing zone of the die, m d = 0.1-0.15;

[0129] HV Vickers hardness

[0130] a, b are experimental constants, where a = 3.85, b = 36

[0131] A, B are experimental constants

[0132] p1, p, p2 are the film pressure of the transmission medium of the liquid at the zone to be deformed, the deformation zone and the sizing zone;

[0133] p A is the pressure of the transmission medium in the extrusion cylinder;

[0134] h1, h, h2 are the film thickness of the liquid on the surface of the bar at the zone to be deformed, the deformation zone and the sizing zone;

[0135] D1, D, D2 are the diameters of the bar at the zone to be deformed, the deformation zone and the sizing zone;

[0136] R is the extrusion ratio,

[0137] u1, u, u2 are the speeds of the bar at the zone to be deformed, the deformation zone and the sizing zone;

[0138] x1, x, x2 are the distances from the intersection of the extension line of the forming surface of the die with the center line to the bar at the critical point of the zone to be deformed, the deformation zone and the sizing zone;

[0139] α is half the included angle of the forming surface of the die;

[0140] η, η0 are the dynamic viscosity of the transmission medium at different pressures and the static viscosity at atmospheric pressure, respectively;

[0141] γ is the pressure coefficient of the dynamic viscosity at different pressures;

[0142] σ is the yield stress of the bar;

[0143] τ is the shear stress on the bar in the deformation zone;

[0144] λ is the film thickness ratio. G = γσ, B = e -γp .

[0145] Experimental verification

[0146] In order to further verify the accuracy of the metal hydraulic extrusion force precise prediction method, the tungsten alloy hydraulic extrusion test verification is carried out, and the specific steps are as follows:

[0147] Step 1: Obtain the physical parameters of the tungsten alloy blank and the pressure transmission medium, as shown in the following table 1.

[0148] Table 1

[0149]

[0150] Step 2: Substitute the parameters in table 1 into formula (38) to obtain the prediction result of 854 MPa;

[0151] Step 3: Develop relevant test verification, and the extrusion force measured by the hydraulic extrusion test equipment is 872 MPa. The error between the prediction result of the application and the test result is only 2.1%.

[0152] In order to further verify the accuracy of the metal hydraulic extrusion force precise prediction method, the tungsten alloy hydraulic extrusion test verification is carried out, and the specific steps are as follows:

[0153] Table 2

[0154] Parameter Value Pressure coefficient γ of dynamic viscosity of pressure transmission medium 0.01153 Yield stress σ of bar 700 MPa Blank outer diameter D1 22.36, 23.90, 25.82, 26.97 mm ​ 20 mm

[0155] Table 3 gives the comparison table of the calculation results according to formula (38) and the test results in the literature.

[0156] Table 3

[0157] Serial number Deformation amount (%) Calculated value (MPa) Test value (MPa) 1 20 725 700 2 30 896 910 3 40 1093 1120 4 45 1202 1260

[0158] The results in table 3 show that the average error is only 1.2%. The above results prove the accuracy and universality of the application.

[0159] The application is based on the assumption of Newtonian fluid, considers the dynamic change of the viscosity of the pressure transmission medium with pressure and the nonlinear characteristics of fluid shear force, establishes a hydraulic extrusion force theoretical model closer to the actual physical process, breaks through the simplification assumption of fixed friction coefficient in the traditional model, and the effectiveness is verified by the tests of tungsten alloy and W6Mo5Cr4V2 high speed steel.

[0160] The specific embodiments of the present application are described above. It needs to be understood that the present application is not limited to the specific embodiments described above, and various modifications or changes can be made by those skilled in the art within the scope of the claims, which do not affect the essence of the present application.

Claims

1. A method for accurately predicting the hydraulic extrusion force of metal, characterized in that, Based on the Reynolds equation and the Tresga yield criterion, this study focuses on the effects of hydrodynamic lubrication and conducts a theoretical analysis of the hydraulic extrusion force of metal. The final expression for the hydraulic extrusion force of metal is: In the formula, p A The pressure of the pressure-transmitting medium inside the extrusion cylinder. R is the extrusion ratio. γ is the pressure coefficient of dynamic viscosity under different pressures; σ is the yield stress of the bar stock; G = γσ.

2. The method for accurately predicting the hydraulic extrusion pressure of metal as described in claim 1, characterized in that, The expression for the hydraulic extrusion force of metal is applicable to the accurate prediction of the hydraulic extrusion force of tungsten alloys and high-speed steel materials.

3. The method for accurately predicting the hydraulic extrusion pressure of metal as described in claim 1, characterized in that, The pressure transmission medium for the metal hydraulic extrusion is a Newtonian fluid.

4. The method for accurately predicting the hydraulic extrusion pressure of metal as described in claim 1, characterized in that, The basic assumptions of this method are: (1) The pressure transmission medium of hydraulic extrusion is a Newtonian fluid, that is, there is a linear relationship between the shear stress and the shear rate of the fluid; (2) The hydraulic extrusion pressure transmission medium does not slide relative to the billet surface, that is, the fluid velocity on the billet surface is the same as the velocity on the billet surface. (3) The billet is a rigid-plastic body under high pressure and the deformation resistance remains constant throughout the extrusion process; (4) The mold is a rigid body; (5) Temperature changes are not considered.

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