Method for determining the friction coefficient in multi-degree-of-freedom envelope forming

Abstract

The present application relates to a kind of multi-degree-of-freedom envelope forming friction coefficient determination method, comprising the following steps: S1, establish multi-degree-of-freedom envelope forming mathematical physics model, deduce the mathematical relationship between multi-degree-of-freedom envelope forming friction coefficient and friction force, and establish multi-degree-of-freedom envelope forming equipment mechanical model;Relationship between multi-degree-of-freedom envelope forming friction model and multi-degree-of-freedom envelope forming equipment mechanical model is constructed;S2, multi-degree-of-freedom envelope forming force data is collected by multi-degree-of-freedom envelope forming experiment, to determine the friction coefficient of multi-degree-of-freedom envelope forming.The multi-degree-of-freedom envelope forming friction coefficient determination method of the present application can determine the friction coefficient in the contact area of envelope forming process, and reveal the dynamic change mechanism of friction coefficient in envelope forming process.

Description

Technical Field

[0001] This invention relates to the field of friction behavior at metal forming contact interfaces, and more specifically, to a method for determining the friction coefficient of multi-degree-of-freedom envelope forming. Background Technology

[0002] The main purpose of friction coefficient testing is to determine the interaction between friction force and friction contact interface, and then use friction model to study the friction behavior of the contact area. At present, the methods for determining friction coefficient in plastic forming process are mainly divided into two categories: direct testing method and simulation test method: (1) The direct testing method is based on Coulomb's law and uses a sensor installed on the mold to directly measure the friction force and normal pressure on the contact surface of the blank during forming, and then obtains the friction coefficient; (2) The simulation test method is to design similar simulation test devices according to different forming methods, such as the ring upsetting method. This method involves placing a ring of a specific size on a flat felt for upsetting, and then using the change in the inner diameter of the ring as an indicator to indirectly determine the friction coefficient through a calibration curve.

[0003] Multi-degree-of-freedom (DOF) envelope forming is a new precision plastic forming technology involving continuous localized loading. During forming, the envelope mold makes localized contact with the workpiece surface. The small contact area allows for easy metal flow, significantly reducing forming force and improving the forming limits and performance of the product. It represents an important development direction for advanced manufacturing technology of thin-walled complex components. However, in multi-degree-of-freedom envelope forming, the formed part undergoes plastic deformation under the envelope motion of the mold in different directions. The contact surface between the mold and the formed part is complex, and the friction behavior is dynamically changing, making the measurement of the friction coefficient extremely complex. The aforementioned direct testing methods and simulation experiments cannot be used to determine the friction coefficient of multi-degree-of-freedom envelope forming. Currently, there are no reports on methods for determining the friction coefficient of multi-degree-of-freedom envelope forming. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a method for determining the friction coefficient of multi-degree-of-freedom envelope forming, which can realize the determination of the friction coefficient of the contact surface in multi-degree-of-freedom envelope forming, and provides a more accurate research method for the influence of friction behavior on material flow characteristics in multi-degree-of-freedom envelope forming process.

[0005] The technical solution adopted by this invention to solve its technical problem is: to construct a method for determining the friction coefficient of multi-degree-of-freedom envelope forming, including the following steps:

[0006] S1. Establish a mathematical and physical model for multi-degree-of-freedom envelope forming, derive the mathematical relationship between the friction coefficient and friction force in multi-degree-of-freedom envelope forming, and establish a mechanical model for multi-degree-of-freedom envelope forming equipment; construct the relationship between the friction model and the mechanical model of multi-degree-of-freedom envelope forming equipment.

[0007] S2. Collect multi-degree-of-freedom envelope forming force data through multi-degree-of-freedom envelope forming experiments to determine the multi-degree-of-freedom envelope forming friction coefficient.

[0008] According to the above scheme, step S1 includes the following steps:

[0009] S11. Establish a three-dimensional geometric model of the disk part envelope forming. Take the center of the contact surface between the envelope mold and the disk part as the origin of the coordinate system O, and establish a cylindrical coordinate system rθz. Assume that the envelope forming force is uniformly distributed on the surface of the contact area, and the resultant force acts on the edge part of the half-circular central angle θ of the contact deformation area of ​​the disk part, i.e., point X.

[0010] S12. Based on the deformation characteristics of the enveloping forming contact surface, at the point of application of the resultant force X in the contact area, the contact surface of the disk part undergoes plastic deformation under the combined action of the enveloping forming force P, the radial friction force τ1, and the tangential friction force τ2. Among them, the enveloping forming force P forms an angle γ with the central axis of the disk part, and the tangential friction force is distributed circumferentially along the contact surface, with the direction opposite to the direction of metal flow.

[0011] S13. Based on the material flow characteristics of the disk-shaped enveloping forming material, establish the z' axis by drawing a perpendicular line from the inlet end R to the contact surface. Connect the outlet end C and the point where it intersects the z' axis as the origin o'. The radial direction makes an angle of θ / 2 with the r-axis, denoted as the r' axis, and the tangential direction as the θ' axis. Establish the coordinate system r'θ'z'. Decompose the enveloping forming force P into P1 and P2 along the r' axis and z' axis respectively. Assuming the contact interface friction coefficient is μ, then according to Coulomb's law of friction, the mechanical relationship between the enveloping forming force, radial friction force, and tangential friction force satisfies:

[0012]

[0013] S14. On the θ'o'z' plane, let the central angle of the arc at the inlet and outlet ends of the interface between the envelope mold and the billet be α at any time t. Decompose the envelope force P2 into tangential directions P. 1’ and axial direction P 2’ The tangential frictional force is decomposed into tangential τ 2’ and axial τ n The relationship between the component forces satisfies:

[0014]

[0015] S15. Based on the above force component relationships, calculate the radial resultant force F at the force center point X. r’ Tangential resultant force F θ’ and axial resultant force F z’ The resultant force relationship at the center of force X during deformation is obtained:

[0016]

[0017] S16. During the enveloping forming process, assume the lower die feed speed is v, the enveloping die rotation speed is n, the feed per revolution is S, the initial radius of the disk part is R0, the thickness is T0, and the thickness of the formed part at any time t is t. t The radius r of the disk component is determined based on the principle of constant volume. t change:

[0018]

[0019]

[0020] S17. According to the characteristics of the envelope forming process, at any time t on the θ'o'z' plane, the central arc angle α at the inlet and outlet ends of the interface between the envelope mold and the blank is:

[0021]

[0022] S18. Combine the formulas from the above steps to determine the formula for calculating the friction coefficient during the envelope forming process:

[0023]

[0024] According to the above scheme, step S2 includes the following steps:

[0025] S21. Place the disc blank on the envelope forming equipment, adjust the position of the blank so that the center of the envelope mold coincides with the center of the disc, start the equipment, and form the disc. According to the working principle of the envelope forming equipment, measure the radial resultant force Fr', tangential resultant force Fθ', and axial resultant force Fz' at the center of the resultant force on the contact surface X point, and determine the values ​​of Fr', Fθ', and Fz' at the center of the resultant force X in the contact area during the envelope forming process of the disc.

[0026] S22. Based on the working principle of the envelope forming equipment, the rotational speed n of the envelope mold can be extracted. The feed speed of the disc part envelope forming can be determined based on the relationship between the feed speed v, the rotational speed n and the feed per revolution S.

[0027] v=n*S (8)

[0028] S23. The values ​​of Fr', Fθ' and Fz' at the center of the resultant force X determined in step S21 as a function of time, the feed rate determined in step S22, and the initial radius R0 and initial thickness T0 of the forming blank can be substituted into the friction coefficient calculation formula in the envelope forming process to determine the dynamic change value of the friction coefficient in the contact area during the envelope forming process.

[0029] According to the above scheme, step S21 includes the following steps:

[0030] S211. During the enveloping forming process of the disc part, the force of the six links on the drive platform of the enveloping forming equipment is measured by the force measuring device of the enveloping forming equipment. The force is then moved to the center of the enveloping mold through the force system translation. The values ​​of the component forces Fx, Fy, and Fz in the x, y, and z directions as a function of time are obtained respectively, and the data is output through the data acquisition device of the enveloping forming equipment.

[0031] S212. Based on the positional relationship between the mechanical model of the center of the envelope mold and the mechanical model of the center of the resultant force at point X during the envelope forming of the disk part, determine the calculation equations for the radial, tangential, and axial resultant forces at the center of the resultant force at point X:

[0032]

[0033] in,

[0034] S213. Using the data of Fx, Fy, and Fz output by the computer in step S211 as a function of time t, determine the values ​​of Fr', Fθ', and Fz' at the center of the resultant force in the contact area during the envelope forming process of the disc part as a function of time.

[0035] The method for determining the friction coefficient of multi-degree-of-freedom envelope forming according to the present invention has the following beneficial effects:

[0036] (1) The method for determining the friction coefficient of multi-degree-of-freedom envelope forming in this invention can determine the friction coefficient of the contact area during the envelope forming process and reveal the dynamic change mechanism of the friction coefficient during the envelope forming process.

[0037] (2) The present invention designs and calculates the friction coefficient based on the deformation characteristics of the envelope forming material, providing a more accurate value for determining the envelope forming process parameters, and can more accurately predict the influence of the contact interface friction behavior on material flow, forming accuracy and forming quality during the envelope forming process. Attached Figure Description

[0038] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings:

[0039] Figure 1 This is a schematic diagram of the force analysis during the enveloping forming process of a disc component;

[0040] Figure 2 A schematic diagram showing the components of the enveloping forming force, radial friction force, and tangential friction force during the enveloping forming process of a disc part;

[0041] Figure 3 This is a schematic diagram of force decomposition in the θ'o'z' plane;

[0042] Figure 4 This is a schematic diagram of an envelope forming device;

[0043] Figure 5 This is a schematic diagram of the force system decomposition of the envelope forming equipment;

[0044] Figure 6 A schematic diagram showing the change of axial force over time in the six links of the drive platform of the envelope forming equipment.

[0045] Figure 7 A schematic diagram showing the changes of Fx, Fy, and Fz at the center of the envelope module over time;

[0046] Figure 8 This is a schematic diagram showing the changes of Fr', Fθ', and Fz' at the center of the resultant force X in the contact area during the envelope formation process over time.

[0047] Figure 9 This is a schematic diagram showing the results of friction coefficient measurement during the envelope forming process. Detailed Implementation

[0048] To provide a clearer understanding of the technical features, objectives, and effects of this invention, specific embodiments are now described in detail with reference to the accompanying drawings. This example focuses on an enveloping forming process experiment conducted on a disc-shaped component with an initial radius R0 of 15 mm and an initial thickness T0 of 6 mm to determine the coefficient of friction during deformation.

[0049] The process of determining this instance includes the following steps:

[0050] S1. Establish a three-dimensional geometric model for the envelope forming of the disk part, such as... Figure 1 As shown, a cylindrical coordinate system rθz is established with the center of the contact surface between the enveloping mold and the disc as the origin O. It is assumed that the enveloping forming force is uniformly distributed on the surface of the contact area, and the resultant force acts on the edge part of the half-circular central angle θ of the contact deformation area of ​​the disc, i.e., point X.

[0051] S2. Based on the deformation characteristics of the enveloping forming contact surface, at the point of application of the resultant force X in the contact area, the contact surface of the disk part undergoes plastic deformation under the combined action of the enveloping forming force P, the radial friction force τ1, and the tangential friction force τ2. Among them, the enveloping forming force P is at an angle of 1.5° to the central axis of the disk part, and the tangential friction force is distributed circumferentially along the contact surface, with the direction opposite to the direction of metal flow;

[0052] S3. Based on the flow characteristics of the material enveloping the disc component, such as... Figure 2 As shown, a z' axis is established by drawing a perpendicular line from the inlet end R to the contact surface. The point where the outlet end C intersects the z' axis is the origin o'. The radial direction makes an angle of θ / 2 with the r axis, denoted as the r' axis, and the tangential direction is denoted as the θ' axis. A coordinate system r'θ'z' is established. The envelope forming force P is decomposed into P1 and P2 along the r' axis and z' axis, respectively. Assuming the contact interface friction coefficient is μ, then according to Coulomb's law of friction, the mechanical relationship between the envelope forming force, radial friction force, and tangential friction force satisfies:

[0053]

[0054] S4, such as Figure 3 As shown, on the θ'o'z' plane, let the central angle of the arc at the inlet and outlet ends of the interface between the envelope mold and the billet at any time t be α. Decompose the envelope force P2 into tangential directions P 1’ and axial direction P 2’ The tangential frictional force is decomposed into τ2 and tangential τ. 2’ and axial τ n The relationship between the component forces satisfies:

[0055]

[0056] S5. Based on the force component relationships in S1, calculate the radial resultant force F at the force center point X. r’ Tangential resultant force F θ’ and axial resultant force F z’ The resultant force relationship at the center of force X during deformation is obtained:

[0057]

[0058] S6. During the enveloping deformation process, assume the lower die feed speed is v, the enveloping die rotation speed is n, the feed per revolution is S, the initial radius of the disk part is R0, the thickness is T0, and the thickness of the formed part is t at any deformation time t. t The radius r of the disk component is determined based on the principle of constant volume. t The changes are as follows: the initial radius R0 is 15 mm, the thickness T0 is 6 mm, and the feed rate S per revolution is 0.15 mm / r;

[0059]

[0060]

[0061] S7. According to the characteristics of the envelope forming process, at any time t on the θ'o'z' plane, the central arc angle α at the inlet and outlet ends of the interface between the envelope mold and the blank is:

[0062]

[0063] S8. Combine the formulas from the above steps to determine the formula for calculating the friction coefficient during the envelope forming process:

[0064]

[0065] S9, such as Figure 4The disk blank is placed on the envelope forming equipment. The blank position is adjusted so that the center of the envelope mold coincides with the center of the disk. The equipment is then started to form the disk. Based on the working principle of the envelope forming equipment, the radial resultant force Fr', tangential resultant force Fθ', and axial resultant force Fz' at the center of the resultant force on the contact surface X are measured respectively.

[0066] S91. In the above scheme, during the enveloping forming process of the disc part, the force of the six links on the drive platform of the enveloping forming equipment is measured by the force measuring device of the enveloping forming equipment, such as... Figure 5 As shown, the force is moved to the center of the envelope swinging mold by the force system translation, and the values ​​of the component forces Fx, Fy, and Fz in the x, y, and z directions as a function of time are obtained respectively, and the data is output through the data acquisition device of the envelope forming equipment. Figure 6 The figure shows the computer output of the axial force of the six links as a function of time when the disk component is deformed by 50%. Figure 7 The figure shows the computer output of the force components Fx, Fy, and Fz in the x, y, and z directions as a function of time.

[0067] S92. Based on the positional relationship between the mechanical model of the center of the envelope mold and the mechanical model of the center of the resultant force at point X during the envelope forming of the disk part, the calculation equations for the radial, tangential, and axial resultant forces at the center point X can be determined:

[0068]

[0069] in,

[0070] S93. The data on the changes of Fx, Fy, and Fz with time t output by the computer from equation (8) and S91 can be used to determine the values ​​of Fr', Fθ', and Fz' at the center of the resultant force in the contact area during the envelope forming process of the disk part, as follows: Figure 8 As shown.

[0071] S10. Based on the working principle of the envelope forming equipment, the rotational speed n of the envelope mold can be extracted as 0.25 r / s. Based on the relationship between the feed speed v, the rotational speed n, and the feed per revolution S, the feed speed for the envelope forming of the disc part can be determined to be 0.0375 mm / s.

[0072] Substituting the data output by computer S93 and the feed rate of 0.0375 mm / s determined by S10, and the enveloping die rotation speed n = 0.25 r / s into equation (7), the curve of the friction coefficient of the contact area changing with time during the enveloping forming process can be determined, such as... Figure 9 As shown.

[0073] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A method for determining the friction coefficient of multi-degree-of-freedom envelope forming, characterized in that, Includes the following steps: S1. Establish a mathematical and physical model of multi-degree-of-freedom envelope forming, derive the mathematical relationship between the friction coefficient and friction force of multi-degree-of-freedom envelope forming, and establish a mechanical model of multi-degree-of-freedom envelope forming equipment. To establish the relationship between the multi-degree-of-freedom envelope forming friction model and the multi-degree-of-freedom envelope forming equipment mechanical model; S2. Collect multi-degree-of-freedom envelope forming force data through multi-degree-of-freedom envelope forming experiments to determine the multi-degree-of-freedom envelope forming friction coefficient; Step S1 includes the following steps: S11. Establish a three-dimensional geometric model of the disk part envelope forming. Take the center of the contact surface between the envelope mold and the disk part as the origin of the coordinate system O, and establish a cylindrical coordinate system rθz. Assume that the envelope forming force is uniformly distributed on the surface of the contact area, and the resultant force acts on the edge part of the half-circular central angle θ of the contact deformation area of ​​the disk part, i.e., point X. S12. Based on the deformation characteristics of the envelope forming contact surface, at the point X where the resultant force acts in the contact area, the contact surface of the disk part is under the envelope forming force. P radial friction τ 1 and tangential friction τ Plastic deformation occurs under the combined action of 2; among which the enveloping forming force P The tangential frictional force is distributed circumferentially along the contact surface at an angle γ to the central axis of the disc component, and its direction is opposite to the direction of metal flow. S13. Based on the material flow characteristics of the disk-shaped enveloping forming material, establish the z' axis by drawing a perpendicular line from the inlet end R to the contact surface. Connect the outlet end C and the point where it intersects the z' axis as the origin o'. The radial direction makes an angle θ / 2 with the r' axis, denoted as the r' axis, and the tangential direction is denoted as the θ' axis. Establish the coordinate system r' θ'z'. The enveloping forming force... P Decompose along the r' axis and z' axis respectively P 1 and P 2. Let the coefficient of friction at the contact interface be μ. According to Coulomb's law of friction, the mechanical relationship between the envelope forming force, radial friction force, and tangential friction force satisfies: (1) S14, in θ' o'z' Let the surface be any time. t The central arc angles at the inlet and outlet ends of the interface between the enveloping mold and the blank are: α , to divide the envelope force P 2 is decomposed into tangential direction P 1’ and axial direction P 2’ Tangential friction is decomposed into tangential... τ 2’ and axial τ n The relationship between the component forces satisfies: (2) S15. Based on the above force component relationships, calculate the radial resultant force at the force center point X. F r’ Tangential resultant force F θ’ axial resultant force F z’ The resultant force relationship at the center of force X during deformation is obtained: (3) S16. During the envelope forming process, assume the lower die feed speed is... v The envelope mode rotation speed is n The feed per revolution is S, the initial radius of the disk part is R0, the thickness is T0, and the thickness of the formed part at any time t is... t t The radius of the disk component is determined based on the principle of constant volume. r t change: (4) (5) S17. Based on the characteristics of the envelope forming process, θ' o'z' Surface, at any time t The central arc angle at the inlet and outlet ends of the interface between the enveloping mold and the blank α for: (6) S18. Combine the formulas from the above steps to determine the formula for calculating the friction coefficient during the envelope forming process: (7)。 2. The method for determining the friction coefficient of multi-degree-of-freedom envelope forming according to claim 1, characterized in that, Step S2 includes the following steps: S21. Place the disc blank on the envelope forming equipment, adjust the position of the blank so that the center of the envelope mold coincides with the center of the disc, start the equipment, and form the disc; according to the working principle of the envelope forming equipment, measure the radial resultant force Fr', tangential resultant force Fθ', and axial resultant force Fz' at the center of the resultant force X on the contact surface, and determine the values ​​of Fr', Fθ', and Fz' at the center of the resultant force X in the contact area during the envelope forming process of the disc; S22. Based on the working principle of the envelope forming equipment, the rotational speed of the envelope mold can be extracted. n According to the feed rate v With rotational speed n The relationship between the feed rate S per revolution and the feed rate S can determine the feed rate for the envelope forming of the disc part; (8) S23. The values ​​of Fr', Fθ' and Fz' at the center of the resultant force X determined in step S21 as a function of time, the feed rate determined in step S22, and the initial radius R0 and initial thickness T0 of the forming blank can be substituted into the friction coefficient calculation formula in the envelope forming process to determine the dynamic change value of the friction coefficient in the contact area during the envelope forming process.

3. The method for determining the friction coefficient of multi-degree-of-freedom envelope forming according to claim 2, characterized in that, Step S21 includes the following steps: S211. During the enveloping forming process of the disc part, the force of the six links on the drive platform of the enveloping forming equipment is measured by the force measuring device of the enveloping forming equipment. The force is then translated to the center of the enveloping mold through force system translation, and the results are obtained respectively. x , y , z Components of force in three directions Fx , Fy , Fz The value changes over time and is output as data through the data acquisition device of the envelope forming equipment; S212. Based on the positional relationship between the mechanical model of the center of the envelope mold and the mechanical model of the center of the resultant force at point X during the envelope forming of the disk part, determine the calculation equations for the radial, tangential, and axial resultant forces at the center of the resultant force at point X: (9) in, (10) S213, The computer output from equation (9) and step S211. Fx , Fy , Fz Using data that varies with time t, determine the values ​​of Fr', Fθ', and Fz' at the center of the resultant force in the contact area X during the envelope forming process of the disc part.

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