A thermal behavior control method for ultrasonic gear honing based on mechanical-thermal analysis

Abstract

The present invention relates to the technical field of ultrasonic honing thermal processing, and specifically to a method for controlling the thermal behavior of ultrasonic honing based on force-thermal analysis. The method comprises the following steps: constructing a three-dimensional resonant frequency characteristic equation of an ultrasonic horn with an indeterminate coupling boundary condition; studying the motion trajectory, wear rate, and material removal rate of a single abrasive grain on the honing wheel to obtain the cutting force of the single abrasive grain, calculating the number of abrasive grains participating in honing in the processing area, and establishing a dynamic grinding force model of the ultrasonic honing processing area. Based on this, a three-dimensional transient temperature field distribution model of the ultrasonic honing processing area is constructed in combination with a high-order function curve and a moving heat source theory, thereby providing a thermal control strategy for ultrasonic honing; finally, a thermal-structural coupling dynamic equilibrium equation of ultrasonic honing is established, revealing the thermal deformation law of the horn, realizing dynamic compensation for the thermal deformation of the horn during the processing process, and improving the surface integrity and processing accuracy of hardened gears after ultrasonic honing.

Description

Technical Field

[0001] The present invention relates to the technical field of ultrasonic gear honing thermal processing, and in particular to a method for controlling thermal behavior of ultrasonic gear honing based on force-heat analysis. Background Art

[0002] Hardened gears with low noise and high load-bearing capacity play a decisive role in transmitting motion and power systems, and are widely used in high-end equipment fields such as high-speed transportation, aerospace, and new energy. Because they serve in harsh environments such as high speeds, heavy / alternating / impact loads for a long time, they are prone to fatigue failure behaviors such as tooth root bending fatigue, tooth surface contact fatigue, corrosion and wear, and the life and reliability requirements of hardened gears are more stringent. Studies have shown that the surface integrity and machining accuracy of hardened gears are key factors affecting their life and reliability. Therefore, how to improve the surface integrity and machining accuracy of hardened gears and manufacture high-performance hardened gears that meet the above service requirements has become an important challenge facing mechanical equipment innovation and high-end equipment manufacturing.

[0003] Ultrasonic honing is commonly used for the finishing of hardened gears. It offers higher processing efficiency and lower equipment costs. The residual stress from machining is compressive, which helps improve the surface integrity of hardened gears. The resulting tooth surface texture reduces transmission noise and improves the reliability of hardened gears. It can also effectively reduce honing wheel blockage, lower honing forces, and improve the micromorphology of the tooth surface. However, during ultrasonic honing, friction between the honing wheel and the hardened gear generates a significant amount of heat in the machining area, causing the surface temperature of the hardened gear to rise sharply, leading to thermal damage. This reduces the surface integrity of the hardened gear and shortens its service life. Furthermore, a significant amount of heat diffuses into the amplitude regulator, causing thermal deformation of the amplitude regulator. This changes the relative position between the honing wheel and the hardened gear being machined, exacerbating tooth profile and pitch errors, reducing machining accuracy, and generating transmission noise. Summary of the Invention

[0004] In order to solve the technical defects in the existing ultrasonic honing process, the friction between the honing wheel and the hard-toothed gear will generate a large amount of heat in the processing area, resulting in a decrease in the surface integrity of the hard-toothed gear, causing thermal deformation of the amplitude rod, reducing the processing accuracy, and generating transmission noise. The present invention provides an ultrasonic honing thermal behavior control method based on force-thermal analysis, which explores a new path to improve the surface integrity and processing accuracy of ultrasonic honing, and is of great significance to extending the service life of hard-toothed gears and reducing transmission noise.

[0005] The present invention provides a method for controlling thermal behavior of ultrasonic gear honing based on force-heat analysis, comprising the following steps:

[0006] Step 1: Establish a three-dimensional resonant frequency characteristic equation of the ultrasonic horn with indefinite coupling boundary conditions to accurately solve the resonant frequency of the ultrasonic horn;

[0007] Step 2: Based on the resonant frequency of the ultrasonic horn obtained in step 1, a dynamic grinding force model of ultrasonic gear honing is established;

[0008] Step 3: Based on the dynamic grinding force model of the ultrasonic honing processing area established in step 2, a three-dimensional transient temperature field distribution model of ultrasonic honing is established;

[0009] Step 4: Based on the three-dimensional transient temperature field distribution model of the ultrasonic honing processing area established in step 3, an ultrasonic honing thermal-structural coupling analysis model is established. The thermal deformation law of the horn is analyzed by the ultrasonic honing thermal-structural coupling analysis model to achieve dynamic compensation for the thermal deformation of the horn during the processing process.

[0010] Preferably, the sub-steps of step 1 are:

[0011] Step 1.1: Construction In the cylindrical coordinate system, the ultrasonic horn composed of the horn and the simplified ring disk of the hard tooth surface gear is divided into The integral regions are as follows: the amplitude rod is referred to as the rod, and the simplified ring disk of the hardened gear is referred to as the disk; based on the penalty function, the penalty factor is introduced to construct the integral regions of the rod and disk in the cylindrical coordinate system under the non-coupling condition. Essential boundary condition admissible function in the direction 、 、 ,in ;

[0012] When the rod and disc are in interference fit, each integral region is in the cylindrical coordinate system Essential boundary condition admissible function in the direction 、 、 for:

[0013] (1-1),

[0014] When the rod and disk are in clearance fit, each integral region is in the cylindrical coordinate system. Essential boundary condition admissible function in the direction 、 、 for:

[0015] (1-2),

[0016] In formulas (1-1) and (1-2), The integration area of ​​the ultrasonic horn is The dimensionless coordinates in the direction, The integration area of ​​the ultrasonic horn is The dimensionless coordinates in the direction, The integration area of ​​the ultrasonic horn is , 、 and exist Take values ​​between For time, 、 、 They are The penalty factor in the direction, The amplitude transformer is Boundary condition function in direction; 、 、 All are undetermined coefficients; is an orthogonal function, where ,in for ; , ω is the angular velocity; are natural numbers greater than 0 respectively;

[0017] Step 1.2: Potential energy function of each integral region of ultrasonic horn and kinetic energy function Both 、 、 Functional, according to the matching form of the rod and disk in the ultrasonic horn, if the rod and disk are interference fit, then substitute formula (1-1) into and ; If the rod and disc are clearance fit, substitute formula (1-2) into and , and then find the integral regions under different coordination conditions. The potential energy function and kinetic energy function Then, the potential energy function and kinetic energy function of each integral region are added to obtain the overall ultrasonic horn The total potential energy function and the total potential energy function ;

[0018] Step 1.3: Build an experimental platform and use a washer-type pressure sensor to measure the threaded connection preload between the rod and the disc. The effect of the threaded connection preload on the vibration characteristics of the ultrasonic horn is considered to be the effect of elastic constraint on the ultrasonic horn. The elastic potential energy function generated by the threaded connection preload is expressed as V e ;

[0019] Step 1.4: Establish the energy equation of the ultrasonic horn for:

[0020] (1-3),

[0021] Step 1.5: For the energy equations in formula (1-3) Solve about 、 、 The derivative of is used to obtain the three-dimensional resonant frequency characteristic equation that does not reflect the coupling relationship of the ultrasonic horn:

[0022] (1-4),

[0023] In formula (1-4), Represents the stiffness matrix generated by the ultrasonic horn's own material and geometric parameters, It represents the stiffness matrix generated by the pre-tightening force of the threaded connection between the ultrasonic horn rod and the disc, is the mass matrix; for , is a zero matrix;

[0024] Step 1.6: Due to the coupling relationship between the rod and the disk in the ultrasonic horn, assuming that the displacements of the rod and the disk at the coupling point are continuous, the displacements at the coupling point of the rod and the disk are equal. Therefore, the matrix [X] in formula (1-4) is expressed as:

[0025] (1-5),

[0026] In formula (1-5), the matrix is the matrix obtained based on the equal displacement of the rod and disk coupling; is obtained based on the displacement continuity condition and contains 、 、 Matrix of

[0027] Step 1.7: Substitute formula (1-5) into formula (1-4) to obtain the three-dimensional resonant frequency characteristic equation with indefinite coupling boundary conditions:

[0028] (1-6),

[0029] In formula (1-6), for The inversion of , ; is the characteristic frequency of the ultrasonic horn, and the characteristic frequency of the ultrasonic horn is solved according to formula (1-6) ,because is the resonant frequency of the ultrasonic horn function, on this basis the resonant frequency of the ultrasonic amplifier is obtained ;

[0030] Preferably, the sub-steps of step 2 are:

[0031] Step 2.1, establish In the rectangular coordinate system, the kinematic analysis of a single abrasive grain on the honing wheel during ultrasonic honing is carried out to obtain the time dependence of the single abrasive grain. exist Velocity equation in direction :

[0032] (2-1),

[0033] In formula (2-1), is the feed rate of the hardened gear, is the linear speed of the honing wheel, is the rotation speed of the honing wheel, is the amplitude of the ultrasonic horn, is the resonant frequency of the ultrasonic horn;

[0034] Step 2.2: Assume that the volume of a single abrasive grain before ultrasonic honing is The time required to complete a honing process is , the volume of a single abrasive grain after one honing process becomes , based on the volume change function of a single abrasive particle under the influence of ultrasonic vibration :

[0035] (2-2);

[0036] In the same way, the single abrasive grain on the honing wheel is established. Material removal rate function for removing material from hardened gears in time for:

[0037] (2-3),

[0038] In formula (2-3), is the volume of the hardened gear before machining, The volume of the hardened gear after a single honing process of a single abrasive grain is calculated, and the cutting force of a single abrasive grain is analyzed to establish the relationship between the single abrasive grain and the hardened gear. and Normal friction Tangential friction for:

[0039] (2-4),

[0040] And the normal force caused by the deformation of a single abrasive particle due to cutting Function of tangential force The function is:

[0041] (2-5),

[0042] In formulas (2-4) and (2-5), is a constant, assuming that the single abrasive particle is spherical, is the central angle of the circle corresponding to the part processed by a single abrasive grain, is the radius of a single abrasive particle, is the feed rate of the hardened gear, is the linear speed of the honing wheel, is the cutting arc length of the honing wheel;

[0043] Step 2.3: Determine the interference length and number of interferences between two abrasive grain tracks within one vibration cycle, and calculate the number of abrasive grains involved in honing in the ultrasonic honing area based on the ultrasonic honing processing parameters and abrasive grain distribution. for:

[0044] (2-6);

[0045] In formula (2-6), The time it takes to complete a honing process is: is the number of abrasive grains per unit area on the honing wheel;

[0046] is the honing wheel speed, , is the resonant frequency of the ultrasonic horn, is the feed rate of the hardened gear; based on the number of abrasive particles involved in honing in the ultrasonic honing processing area As well as formula (2-4) and formula (2-5), the dynamic grinding force model of the ultrasonic honing processing area is established:

[0047] (2-7),

[0048] In formula (2-7), is the macro normal force in the ultrasonic honing processing area, is the macroscopic tangential force in the ultrasonic honing processing area;

[0049] Preferably, the sub-steps of step 3 are:

[0050] Step 3.1: Based on the dynamic grinding force model of the ultrasonic honing processing area established in step 2, calculate the total heat of the processing area :

[0051] (3-1),

[0052] In formula (3-1), is the honing width, is the cutting arc length of the honing wheel, is the linear speed of the honing wheel, is the macroscopic tangential force in the ultrasonic honing processing area;

[0053] At the same time, the heat entering the surface of the hardened gear is obtained , for:

[0054] (3-2),

[0055] In formula (3-2), ,in 、 represent the heat transfer coefficients of cutting fluid and hardened gear respectively; , ,in is the contact radius between a single abrasive grain and the hardened gear surface in the ultrasonic honing area, is the linear speed of the honing wheel, is the density of the hardened gear, is the specific heat capacity of the hardened gear, is the thickness of the chip;

[0056] Step 3.2: Assuming that a single abrasive particle is spherical, when a single abrasive particle cuts a hardened gear, the single abrasive particle intersects with the plane where the hardened gear surface is located before machining. The cross-sectional shape of the single abrasive particle at the intersection plane is circular. The radius of the circle is the contact radius between the single abrasive particle and the hardened gear surface in the ultrasonic honing area. ,Establish About the cutting depth of a single abrasive grain function; Assuming that there are multiple abrasive grains in the ultrasonic honing area, the cutting depth of each abrasive grain is The distribution of is consistent with the Rayleigh distribution, then the probability density function of the cutting depth h of each abrasive grain in the ultrasonic honing area can be obtained. , for:

[0057] (3-3),

[0058] In formula (3-3), is the standard deviation, and the contact radius between the abrasive and the hardened gear at any position in the ultrasonic honing area is obtained. about 、 and function, for:

[0059] (3-4),

[0060] In formula (3-4), is the radius probability density function of multiple abrasive particles in the processing area, is the area of ​​ultrasonic honing processing area, is the radius of a single abrasive particle;

[0061] Step 3.3, based on the moving heat source theory, use the superposition method of heat source temperature field to calculate the surface temperature of the hardened gear; the heat generated by the honing process between the honing wheel and the hardened gear can be simplified to a surface heat source, which can be regarded as a combination of countless linear heat sources, and the linear heat source is regarded as a combination of multiple point heat sources; it is assumed that the point heat source is located at the coordinate origin of the heat conductor At the initial surface temperature of the hardened gear is T = 0 ° C, the heat q entering the hardened gear surface is w Simplified as a point heat source; based on the heat conduction theory, the three-dimensional heat conduction differential equation is Fourier transformed to obtain the coordinate position point M of the hardened gear surface in the ultrasonic honing processing area at any time. Temperature , Expressed as:

[0062] (3-5),

[0063] In formula (3-5), is the density of the hardened gear, is the specific heat capacity of the hardened gear, is the thermal diffusivity of the hardened gear, is the distance from any point in the hardened gear to the heat source, , ,in, is the base circle radius of the hardened gear; is the roll angle of the hardened gear; is the feed rate of the hardened gear; Any time during the ultrasonic gear honing process;

[0064] Step 3.4: Based on the high-order function curve, on the basis of formula (3-5), combined with the single abrasive velocity equation established by formula (2-1) and the function shown in formula (3-4) , establish a three-dimensional transient temperature field distribution model for ultrasonic honing processing area , for:

[0065] (3-6),

[0066] In formula (3-6), is the ultrasonic honing processing time, is the maximum rolling angle of each point on the surface of the hardened gear, for about function;

[0067] Preferably, the sub-steps of step 4 are:

[0068] Step 4.1: Based on the three-dimensional transient temperature field distribution model of ultrasonic gear honing established in step 3, the temperature field distribution of the horn is discretized and analyzed. The horn is divided into several units along the axial direction to obtain the axial force load on each unit of the horn. and the thermal bending moment loads it is subjected to , considering the deformation of each unit of the horn as a linear problem and applying the superposition principle, we can get the following equation for each unit of the horn:

[0069] (4-1);

[0070] Step 4.2, establish In a rectangular coordinate system, a two-node horn element is used to define the nodal generalized displacement of the two-node horn element. for:

[0071] (4-2),

[0072] In formula (4-2), (i=1,2) represents the node displacement, (i=1,2) represents the corner vector, In the rectangular coordinate system, the generalized force vector acting on the unit node is , the unit node thermal load is And the node prestress is , establish the force balance equation of each unit of the horn:

[0073] (4-3),

[0074] In formula (4-3), is the stiffness matrix of each unit of the horn, is the generalized displacement of each unit of the horn;

[0075] Step 4.3: The radius vector of any point P on each unit of the horn before deformation is , then after any unit on the horn is deformed, the radius vector of any point P on each unit of the horn satisfies the following relationship:

[0076] (4-4),

[0077] In formula (4-4), the initial position vector of point P is exist In rectangular coordinate system, it is expressed as ; Generalized displacement of each unit of the horn exist In rectangular coordinate system, it is expressed as , from which we can infer exist The expression in the rectangular coordinate system, and the point P in Linear velocity in rectangular coordinates , acceleration ;

[0078] Step 4.4: Analyze each unit of the horn according to the Euler-Bernoulli beam, and obtain the Kinetic energy of a unit and potential energy , assuming that the amplitude rod is divided into units, the kinetic energy of the entire horn is and potential energy Expressed as:

[0079] (4-5),

[0080] The kinetic energy of the entire horn and potential energy Substituting into the Lagrange equation, the thermodynamic equilibrium equation is derived as follows:

[0081] (4-6),

[0082] In formula (4-6), is the mass matrix of the overall structure of the horn, is the overall damping matrix of the horn, for the reason The overall stiffness matrix of the horn is determined by is the load matrix, from which the overall deformation displacement of the horn is obtained ,in for The first derivative of for The second-order derivative of the horn is the overall deformation displacement of the horn , the deformation displacement value of the amplitude variable rod at any time and any position during the ultrasonic gear honing process is clarified. Therefore, the thermal deformation law of the amplitude variable rod can be analyzed through the deformation displacement value to achieve dynamic compensation for the thermal deformation of the amplitude variable rod during the processing process.

[0083] Compared with the prior art, the technical solution provided by the present invention has the following technical effects:

[0084] First, the three-dimensional coupling boundary conditions at the contact point between the horn and the hardened gear were studied, the three-dimensional coupling resonance analysis model of the ultrasonic horn was improved, and the characteristic equation of the three-dimensional resonant frequency of the ultrasonic horn with indefinite coupling boundary conditions was constructed. This laid the foundation for the study of the three-dimensional transient temperature field distribution and thermal-structural coupling in the ultrasonic honing area.

[0085] Second, the motion trajectory, wear rate, and material removal rate of a single abrasive particle on the honing wheel are studied to obtain the cutting force of a single abrasive particle. The trajectory interference between different abrasive particles is also taken into account to determine the number of abrasive particles involved in the honing process. A dynamic grinding force model for the ultrasonic honing process is established. On this basis, the characteristic parameters of the abrasive particles and the contact relationship between the abrasive particles and the workpiece are considered. Combining high-order function curves with the theory of moving heat sources, a three-dimensional transient temperature field distribution model for the ultrasonic honing process is constructed to provide a thermal control strategy for ultrasonic honing.

[0086] Third, based on the finite element method, three-dimensional transient temperature field distribution, and Lagrange equation, the thermal load and thermal bending moment functions of the horn are obtained, and the thermal-structural coupling dynamic equilibrium equation of ultrasonic honing is established. The thermal deformation law of the horn is revealed, and the thermal deformation of the horn during machining can be dynamically compensated based on the thermal deformation law of the horn, providing theoretical support for the dynamic compensation technology of ultrasonic honing.

[0087] Fourth, the present invention can improve the surface integrity and processing accuracy of hardened gears after ultrasonic honing, reduce transmission noise, and explore a new way to manufacture long-life, high-reliability hardened gears. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention.

[0089] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0090] Figure 1This is a flowchart of an overall process corresponding to a method for controlling thermal behavior of ultrasonic gear honing based on force-heat analysis according to an embodiment of the present invention;

[0091] Figure 2 Schematic diagram of cutting of a single abrasive particle according to an embodiment of the present invention;

[0092] Figure 3 Schematic diagram of the xyz rectangular coordinate system established in step 4 of the ultrasonic gear honing thermal behavior control method according to an embodiment of the present invention. DETAILED DESCRIPTION

[0093] In order to more clearly understand the above-mentioned objectives, features and advantages of the present invention, the scheme of the present invention will be further described below. It should be noted that, in the absence of conflict, the embodiments of the present invention and the features therein can be combined with each other.

[0094] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein; it is obvious that the embodiments in the specification are only part of the embodiments of the present invention, rather than all the embodiments.

[0095] The specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0096] In one embodiment, Figure 1 As shown, a method for controlling thermal behavior of ultrasonic gear honing based on force-thermal analysis is disclosed, comprising the following steps:

[0097] Step 1: Establish a three-dimensional resonant frequency characteristic equation of the ultrasonic horn with indefinite coupling boundary conditions to accurately solve the resonant frequency of the ultrasonic horn. The sub-steps are:

[0098] Step 1.1: Construction In the cylindrical coordinate system, the ultrasonic horn composed of the horn and the simplified ring disk of the hard tooth surface gear is divided into The integral regions are as follows: the amplitude rod is referred to as the rod, and the simplified ring disk of the hardened gear is referred to as the disk; based on the penalty function, the penalty factor is introduced to construct the integral regions of the rod and disk in the cylindrical coordinate system under the non-coupling condition. Essential boundary condition admissible function in the direction 、 、 ,in ;

[0099] When the rod and disc are in interference fit, each integral region is in the cylindrical coordinate system. Essential boundary condition admissible function in the direction 、 、 for:

[0100] (1-1),

[0101] When the rod and disk are in clearance fit, each integral region is in the cylindrical coordinate system. Essential boundary condition admissible function in the direction 、 、 for:

[0102] (1-2),

[0103] In formulas (1-1) and (1-2), The integration area of ​​the ultrasonic horn is The dimensionless coordinates in the direction, The integration area of ​​the ultrasonic horn is The dimensionless coordinates in the direction, The integration area of ​​the ultrasonic horn is , 、 and exist Take values ​​between For time, 、 、 They are The penalty factor in the direction, The amplitude transformer is Boundary condition function in direction; 、 、 All are undetermined coefficients; is an orthogonal function, where ,in for ; , ω is the angular velocity; are natural numbers greater than 0 respectively;

[0104] Step 1.2: Potential energy function of each integral region of ultrasonic horn and kinetic energy function Both 、 、 Functional, according to the matching form of the rod and disk in the ultrasonic horn, if the rod and disk are interference fit, then substitute formula (1-1) into and ; If the rod and disc are clearance fit, substitute formula (1-2) into and , and then find the integral regions under different coordination conditions. The potential energy function and kinetic energy function Then, the potential energy function and kinetic energy function of each integral region are added to obtain the overall ultrasonic horn The total potential energy function and the total potential energy function ;

[0105] Step 1.3: Build an experimental platform and use a washer-type pressure sensor to measure the threaded connection preload between the rod and the disc. The effect of the threaded connection preload on the vibration characteristics of the ultrasonic horn is considered to be the effect of elastic constraint on the ultrasonic horn. The elastic potential energy function generated by the threaded connection preload is expressed as V e ;

[0106] Step 1.4: Establish the energy equation of the ultrasonic horn for:

[0107] (1-3),

[0108] Step 1.5: For the energy equations in formula (1-3) Solve about 、 、 The derivative of is used to obtain the three-dimensional resonant frequency characteristic equation that does not reflect the coupling relationship of the ultrasonic horn:

[0109] (1-4),

[0110] In formula (1-4), Represents the stiffness matrix generated by the ultrasonic horn's own material and geometric parameters, It represents the stiffness matrix generated by the pre-tightening force of the threaded connection between the ultrasonic horn rod and the disc, is the mass matrix; for , is a zero matrix;

[0111] Step 1.6: Due to the coupling relationship between the rod and the disk in the ultrasonic horn, assuming that the displacements of the rod and the disk at the coupling point are continuous, the displacements at the coupling point of the rod and the disk are equal. Therefore, the matrix [X] in formula (1-4) is expressed as:

[0112] (1-5),

[0113] In formula (1-5), the matrix is the matrix obtained based on the equal displacement of the rod and disk coupling; is obtained based on the displacement continuity condition and contains 、 、 Matrix of

[0114] Step 1.7: Substitute formula (1-5) into formula (1-4) to obtain the three-dimensional resonant frequency characteristic equation with indefinite coupling boundary conditions:

[0115] (1-6),

[0116] In formula (1-6), for The inversion of , ; is the characteristic frequency of the ultrasonic horn, and the characteristic frequency of the ultrasonic horn is solved according to formula (1-6) ,because is the resonant frequency of the ultrasonic horn function, on this basis the resonant frequency of the ultrasonic amplifier is obtained ;

[0117] Step 2: Based on the resonant frequency of the ultrasonic horn obtained in step 1, a dynamic grinding force model of ultrasonic gear honing is established, and its sub-steps are:

[0118] Step 2.1, establish In the rectangular coordinate system, the kinematic analysis of a single abrasive grain on the honing wheel during ultrasonic honing is carried out to obtain the time dependence of the single abrasive grain. exist Velocity equation in direction :

[0119] (2-1),

[0120] In formula (2-1), is the feed rate of the hardened gear, is the linear speed of the honing wheel, is the rotation speed of the honing wheel, is the amplitude of the ultrasonic horn, is the resonant frequency of the ultrasonic horn;

[0121] Step 2.2: Assume that the volume of a single abrasive grain before ultrasonic honing is The time required to complete a honing process is , the volume of a single abrasive grain after one honing process becomes , based on the volume change function of a single abrasive particle under the influence of ultrasonic vibration :

[0122] (2-2);

[0123] In the same way, the single abrasive grain on the honing wheel is established. Material removal rate function for removing material from hardened gears in time for:

[0124] (2-3),

[0125] In formula (2-3), is the volume of the hardened gear before machining, The volume of the hardened gear after a single honing process of a single abrasive grain is calculated, and the cutting force of a single abrasive grain is analyzed to establish the relationship between the single abrasive grain and the hardened gear. and Normal friction Tangential friction for:

[0126] (2-4),

[0127] And the normal force caused by the deformation of a single abrasive particle due to cutting Function of tangential force The function is:

[0128] (2-5),

[0129] In formulas (2-4) and (2-5), is a constant, assuming that the single abrasive particle is spherical, is the central angle of the circle corresponding to the part processed by a single abrasive grain, is the radius of a single abrasive particle, is the feed rate of the hardened gear, is the linear speed of the honing wheel, is the cutting arc length of the honing wheel;

[0130] Step 2.3: Determine the interference length and number of interferences between two abrasive grain tracks within one vibration cycle, and calculate the number of abrasive grains involved in honing in the ultrasonic honing area based on the ultrasonic honing processing parameters and abrasive grain distribution. for:

[0131] (2-6);

[0132] In formula (2-6), The time it takes to complete a honing process is: is the number of abrasive grains per unit area on the honing wheel;

[0133] is the honing wheel speed, , is the resonant frequency of the ultrasonic horn, is the feed rate of the hardened gear; based on the number of abrasive particles involved in honing in the ultrasonic honing processing area As well as formula (2-4) and formula (2-5), the dynamic grinding force model of the ultrasonic honing processing area is established:

[0134] (2-7),

[0135] In formula (2-7), is the macro normal force in the ultrasonic honing processing area, is the macroscopic tangential force in the ultrasonic honing processing area;

[0136] Step 3: Based on the dynamic grinding force model of the ultrasonic honing processing area established in step 2, a three-dimensional transient temperature field distribution model of ultrasonic honing is established, and its sub-steps are:

[0137] Step 3.1: Based on the dynamic grinding force model of the ultrasonic honing processing area established in step 2, calculate the total heat of the processing area :

[0138] (3-1),

[0139] In formula (3-1), is the honing width, is the cutting arc length of the honing wheel, is the linear speed of the honing wheel, is the macroscopic tangential force in the ultrasonic honing processing area;

[0140] At the same time, the heat entering the surface of the hardened gear is obtained , for:

[0141] (3-2),

[0142] In formula (3-2), ,in 、 represent the heat transfer coefficients of cutting fluid and hardened gear respectively; , ,in is the contact radius between a single abrasive grain and the hardened gear surface in the ultrasonic honing area, is the linear speed of the honing wheel, is the density of the hardened gear, is the specific heat capacity of the hardened gear, is the thickness of the chip;

[0143] Step 3.2: Assuming that a single abrasive particle is spherical, when a single abrasive particle cuts a hardened gear, the single abrasive particle intersects with the plane where the hardened gear surface is located before machining. The cross-sectional shape of the single abrasive particle at the intersection plane is circular. The radius of the circle is the contact radius between the single abrasive particle and the hardened gear surface in the ultrasonic honing area. ,Establish About the cutting depth of a single abrasive grain function; Assuming that there are multiple abrasive grains in the ultrasonic honing area, the cutting depth of each abrasive grain is The distribution of is consistent with the Rayleigh distribution, then the probability density function of the cutting depth h of each abrasive grain in the ultrasonic honing area can be obtained. , for:

[0144] (3-3),

[0145] In formula (3-3), is the standard deviation, and the contact radius between the abrasive and the hardened gear at any position in the ultrasonic honing area is obtained. about 、 and function, for:

[0146] (3-4),

[0147] In formula (3-4), is the radius probability density function of multiple abrasive particles in the processing area, is the area of ​​ultrasonic honing processing area, is the radius of a single abrasive particle;

[0148] Step 3.3, based on the moving heat source theory, use the superposition method of heat source temperature field to calculate the surface temperature of the hardened gear; the heat generated by the honing process between the honing wheel and the hardened gear can be simplified to a surface heat source, which can be regarded as a combination of countless linear heat sources, and the linear heat source is regarded as a combination of multiple point heat sources; it is assumed that the point heat source is located at the coordinate origin of the heat conductor At the initial surface temperature of the hardened gear is T = 0 ° C, the heat q entering the hardened gear surface is w Simplified as a point heat source; based on the heat conduction theory, the three-dimensional heat conduction differential equation is Fourier transformed to obtain the coordinate position point M of the hardened gear surface in the ultrasonic honing processing area at any time. Temperature , Expressed as:

[0149] (3-5),

[0150] In formula (3-5), is the density of the hardened gear, is the specific heat capacity of the hardened gear, is the thermal diffusivity of the hardened gear, is the distance from any point in the hardened gear to the heat source, , ,in, is the base circle radius of the hardened gear; is the roll angle of the hardened gear; is the feed rate of the hardened gear; Any time during the ultrasonic gear honing process;

[0151] Step 3.4: Based on the high-order function curve, on the basis of formula (3-5), combined with the single abrasive velocity equation established by formula (2-1) and the function shown in formula (3-4) , establish a three-dimensional transient temperature field distribution model for ultrasonic honing processing area , for:

[0152] (3-6),

[0153] In formula (3-6), is the ultrasonic honing processing time, is the maximum rolling angle of each point on the surface of the hardened gear, for about function;

[0154] Step 4: Based on the three-dimensional transient temperature field distribution model of the ultrasonic honing processing area established in step 3, an ultrasonic honing thermal-structural coupling analysis model is established. The thermal deformation law of the horn is analyzed by the ultrasonic honing thermal-structural coupling analysis model to achieve dynamic compensation for the thermal deformation of the horn during the processing process. The sub-steps are:

[0155] Step 4.1: Based on the three-dimensional transient temperature field distribution model of ultrasonic gear honing established in step 3, the temperature field distribution of the horn is discretized and analyzed. The horn is divided into several units along the axial direction to obtain the axial force load on each unit of the horn. and the thermal bending moment loads it is subjected to , considering the deformation of each unit of the horn as a linear problem and applying the superposition principle, we can get the following equation for each unit of the horn:

[0156] (4-1);

[0157] Step 4.2, establish In a rectangular coordinate system, a two-node horn element is used to define the nodal generalized displacement of the two-node horn element. for:

[0158] (4-2),

[0159] In formula (4-2), (i=1,2) represents the node displacement, (i=1,2) represents the corner vector, In the rectangular coordinate system, the generalized force vector acting on the unit node is , the unit node thermal load is And the node prestress is , establish the force balance equation of each unit of the horn:

[0160] (4-3),

[0161] In formula (4-3), is the stiffness matrix of each unit of the horn, is the generalized displacement of each unit of the horn;

[0162] Step 4.3: The radius vector of any point P on each unit of the horn before deformation is , then after any unit on the horn is deformed, the radius vector of any point P on each unit of the horn satisfies the following relationship:

[0163] (4-4),

[0164] In formula (4-4), the initial position vector of point P is exist In rectangular coordinate system, it is expressed as ; Generalized displacement of each unit of the horn exist In rectangular coordinate system, it is expressed as , from which we can infer exist The expression in the rectangular coordinate system, and the point P in Linear velocity in rectangular coordinates , acceleration ;

[0165] Step 4.4: Analyze each unit of the horn according to the Euler-Bernoulli beam, and obtain the Kinetic energy of a unit and potential energy , assuming that the amplitude rod is divided into units, the kinetic energy of the entire horn is and potential energy Expressed as:

[0166] (4-5),

[0167] The kinetic energy of the entire horn and potential energy Substituting into the Lagrange equation, the thermodynamic equilibrium equation is derived as follows:

[0168] (4-6),

[0169] In formula (4-6), is the mass matrix of the overall structure of the horn, is the overall damping matrix of the horn, for the reason The overall stiffness matrix of the horn is determined by is the load matrix, from which the overall deformation displacement of the horn is obtained ,in for The first derivative of for The second-order derivative of the horn is the overall deformation displacement of the horn , the deformation displacement value of the amplitude variable rod at any time and any position during the ultrasonic gear honing process is clarified. Therefore, the thermal deformation law of the amplitude variable rod can be analyzed through the deformation displacement value to achieve dynamic compensation for the thermal deformation of the amplitude variable rod during the processing process.

[0170] The above description is merely a specific embodiment of the present invention, which enables those skilled in the art to understand or implement the present invention. Although detailed descriptions have been made with reference to the aforementioned embodiments, those skilled in the art should understand that they may still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents; and such modifications or replacements do not deviate from the essence of the corresponding technical solutions within the scope of the technical solutions of the embodiments, and they should all be included in the scope of protection of the claims.

Claims

1. A method for controlling thermal behavior of ultrasonic gear honing based on force-heat analysis, characterized in that: The following steps are involved: Step 1: Establish a three-dimensional resonant frequency characteristic equation of the ultrasonic horn with indefinite coupling boundary conditions to accurately solve the resonant frequency of the ultrasonic horn; Step 2: Based on the resonant frequency of the ultrasonic horn obtained in step 1, a dynamic grinding force model of ultrasonic gear honing is established; Step 3: Based on the dynamic grinding force model of the ultrasonic honing processing area established in step 2, a three-dimensional transient temperature field distribution model of ultrasonic honing is established; Step 4: Based on the three-dimensional transient temperature field distribution model of the ultrasonic honing processing area established in step 3, an ultrasonic honing thermal-structural coupling analysis model is established. The thermal deformation law of the horn is analyzed by the ultrasonic honing thermal-structural coupling analysis model to achieve dynamic compensation for the thermal deformation of the horn during the processing process. The sub-steps of step 4 are: Step 4.1: Based on the three-dimensional transient temperature field distribution model of ultrasonic gear honing established in step 3, the temperature field distribution of the horn is discretized and analyzed. The horn is divided into several units along the axial direction to obtain the axial force load on each unit of the horn. and the thermal bending moment loads it is subjected to , considering the deformation of each unit of the horn as a linear problem and applying the superposition principle, we can get the following equation for each unit of the horn: （4-1）； Step 4.2, establish In a rectangular coordinate system, a two-node horn element is used to define the nodal generalized displacement of the two-node horn element. for: （4-2）， In formula (4-2), (i=1,2) represents the node displacement, (i=1,2) represents the corner vector, In the rectangular coordinate system, the generalized force vector acting on the unit node is , the unit node thermal load is And the node prestress is , establish the force balance equation of each unit of the horn: （4-3）， In formula (4-3), is the stiffness matrix of each unit of the horn, is the generalized displacement of each unit of the horn; Step 4.3: The radius vector of any point P on each unit of the horn before deformation is , then after any unit on the horn is deformed, the radius vector of any point P on each unit of the horn satisfies the following relationship: （4-4）， In formula (4-4), the initial position vector of point P is exist In rectangular coordinate system, it is expressed as ; Generalized displacement of each unit of the horn exist In rectangular coordinate system, it is expressed as , from which we can infer exist The expression in the rectangular coordinate system, and the point P in Linear velocity in rectangular coordinates , acceleration ; Step 4.4: Analyze each unit of the horn according to the Euler-Bernoulli beam, and obtain the Kinetic energy of a unit and potential energy , assuming that the amplitude rod is divided into units, the kinetic energy of the entire horn is and potential energy Expressed as: （4-5）， The kinetic energy of the entire horn and potential energy Substituting into the Lagrange equation, the thermodynamic equilibrium equation is derived as follows: （4-6）， In formula (4-6), is the mass matrix of the overall structure of the horn, is the overall damping matrix of the horn, for the reason The overall stiffness matrix of the horn is determined by is the load matrix, from which the overall deformation displacement of the horn is obtained ,in for The first derivative of for The second-order derivative of the horn is the overall deformation displacement of the horn , the deformation displacement value of the amplitude variable rod at any time and any position during the ultrasonic gear honing process is clarified. Therefore, the thermal deformation law of the amplitude variable rod can be analyzed through the deformation displacement value to achieve dynamic compensation for the thermal deformation of the amplitude variable rod during the processing process.

2. The method for controlling thermal behavior of ultrasonic gear honing based on mechanical-thermal analysis according to claim 1, characterized in that: The sub-steps of step 1 are: Step 1.1: Construction In the cylindrical coordinate system, the ultrasonic horn composed of the horn and the simplified ring disk of the hard tooth surface gear is divided into The integral regions are as follows: the amplitude rod is referred to as the rod, and the simplified ring disk of the hardened gear is referred to as the disk; based on the penalty function, the penalty factor is introduced to construct the integral regions of the rod and disk in the cylindrical coordinate system under the non-coupling condition. Essential boundary condition admissible function in the direction 、 、 ,in ; When the rod and disc are in interference fit, each integral region is in the cylindrical coordinate system. Essential boundary condition admissible function in the direction 、 、 for: （1-1）， When the rod and disk are in clearance fit, each integral region is in the cylindrical coordinate system. Essential boundary condition admissible function in the direction 、 、 for: （1-2）， In formulas (1-1) and (1-2), The integration area of ​​the ultrasonic horn is The dimensionless coordinates in the direction, The integration area of ​​the ultrasonic horn is The dimensionless coordinates in the direction, The integration area of ​​the ultrasonic horn is , 、 and exist Take values ​​between For time, 、 、 They are The penalty factor in the direction, The amplitude transformer is Boundary condition function in direction; 、 、 All are undetermined coefficients; is an orthogonal function, where ,in for ; , ω is the angular velocity; are natural numbers greater than 0 respectively; Step 1.2: Potential energy function of each integral region of ultrasonic horn and kinetic energy function Both 、 、 Functional, according to the matching form of the rod and disk in the ultrasonic horn, if the rod and disk are interference fit, then substitute formula (1-1) into and ; If the rod and disc are clearance fit, substitute formula (1-2) into and , and then find the integral regions under different coordination conditions. The potential energy function and kinetic energy function Then, the potential energy function and kinetic energy function of each integral region are added to obtain the overall ultrasonic horn The total potential energy function and the total potential energy function ; Step 1.3: Build an experimental platform and use a washer-type pressure sensor to measure the threaded connection preload between the rod and the disc. The effect of the threaded connection preload on the vibration characteristics of the ultrasonic horn is considered to be the effect of elastic constraint on the ultrasonic horn. The elastic potential energy function generated by the threaded connection preload is expressed as V e ; Step 1.4: Establish the energy equation of the ultrasonic horn for: （1-3）， Step 1.5: For the energy equations in formula (1-3) Solve about 、 、 The derivative of is used to obtain the three-dimensional resonant frequency characteristic equation that does not reflect the coupling relationship of the ultrasonic horn: （1-4）， In formula (1-4), Represents the stiffness matrix generated by the ultrasonic horn's own material and geometric parameters, It represents the stiffness matrix generated by the pre-tightening force of the threaded connection between the ultrasonic horn rod and the disc, is the mass matrix; for , is a zero matrix; Step 1.6: Due to the coupling relationship between the rod and the disk in the ultrasonic horn, assuming that the displacements of the rod and the disk at the coupling point are continuous, the displacements at the coupling point of the rod and the disk are equal. Therefore, the matrix [X] in formula (1-4) is expressed as: （1-5）， In formula (1-5), the matrix is the matrix obtained based on the equal displacement of the rod and disk coupling; is obtained based on the displacement continuity condition and contains 、 、 Matrix of Step 1.7: Substitute formula (1-5) into formula (1-4) to obtain the three-dimensional resonant frequency characteristic equation with indefinite coupling boundary conditions: （1-6）， In formula (1-6), for The inversion of , ; is the characteristic frequency of the ultrasonic horn, and the characteristic frequency of the ultrasonic horn is solved according to formula (1-6) ,because is the resonant frequency of the ultrasonic horn function, on this basis the resonant frequency of the ultrasonic amplifier is obtained .

3. The method for controlling thermal behavior of ultrasonic gear honing based on mechanical-thermal analysis according to claim 1, characterized in that: The sub-steps of step 2 are: Step 2.1, establish In the rectangular coordinate system, the kinematic analysis of a single abrasive grain on the honing wheel during ultrasonic honing is carried out to obtain the time dependence of the single abrasive grain. exist Velocity equation in direction : （2-1）， In formula (2-1), is the feed rate of the hardened gear, is the linear speed of the honing wheel, is the rotation speed of the honing wheel, is the amplitude of the ultrasonic horn, is the resonant frequency of the ultrasonic horn; Step 2.2: Assume that the volume of a single abrasive grain before ultrasonic honing is The time required to complete a honing process is , the volume of a single abrasive grain after one honing process becomes , based on the volume change function of a single abrasive particle under the influence of ultrasonic vibration : （2-2）； In the same way, the single abrasive grain on the honing wheel is established. Material removal rate function for removing material from hardened gears in time for: （2-3）， In formula (2-3), is the volume of the hardened gear before machining, The volume of the hardened gear after a single honing process of a single abrasive grain is calculated, and the cutting force of a single abrasive grain is analyzed to establish the relationship between the single abrasive grain and the hardened gear. and Normal friction Tangential friction for: （2-4）， And the normal force caused by the deformation of a single abrasive particle due to cutting Function of tangential force The function is: （2-5）， In formulas (2-4) and (2-5), is a constant, assuming that the single abrasive particle is spherical, is the central angle of the circle corresponding to the part processed by a single abrasive grain, is the radius of a single abrasive particle, is the feed rate of the hardened gear, is the linear speed of the honing wheel, is the cutting arc length of the honing wheel; Step 2.3: Determine the interference length and number of interferences between two abrasive grain tracks within one vibration cycle, and calculate the number of abrasive grains involved in honing in the ultrasonic honing area based on the ultrasonic honing processing parameters and abrasive grain distribution. for: （2-6）； In formula (2-6), The time it takes to complete a honing process is: is the number of abrasive grains per unit area on the honing wheel; is the honing wheel speed, , is the resonant frequency of the ultrasonic horn, is the feed rate of the hardened gear; based on the number of abrasive particles involved in honing in the ultrasonic honing processing area As well as formula (2-4) and formula (2-5), the dynamic grinding force model of the ultrasonic honing processing area is established: （2-7）， In formula (2-7), is the macro normal force in the ultrasonic honing processing area, is the macroscopic tangential force in the ultrasonic honing processing area.

4. The method for controlling thermal behavior of ultrasonic gear honing based on mechanical-thermal analysis according to claim 1, characterized in that: The sub-steps of step 3 are: Step 3.1: Based on the dynamic grinding force model of the ultrasonic honing processing area established in step 2, calculate the total heat of the processing area : （3-1）， In formula (3-1), is the honing width, is the cutting arc length of the honing wheel, is the linear speed of the honing wheel, is the macroscopic tangential force in the ultrasonic honing processing area; At the same time, the heat entering the surface of the hardened gear is obtained , for: （3-2）, In formula (3-2), ,in 、 represent the heat transfer coefficients of cutting fluid and hardened gear respectively; , ,in is the contact radius between a single abrasive grain and the hardened gear surface in the ultrasonic honing area, is the linear speed of the honing wheel, is the density of the hardened gear, is the specific heat capacity of the hardened gear, is the thickness of the chip; Step 3.2: Assuming that a single abrasive particle is spherical, when a single abrasive particle is cutting a hardened gear, the single abrasive particle intersects with the plane of the unprocessed surface of the hardened gear. The cross-sectional shape of the single abrasive particle at the intersection plane is circular. The radius of this circle is the contact radius between the single abrasive particle and the hardened gear in the ultrasonic honing area. ,Establish About the cutting depth of a single abrasive grain function; Assuming that there are multiple abrasive grains in the ultrasonic honing area, the cutting depth of each abrasive grain is The distribution of is consistent with the Rayleigh distribution, then the probability density function of the cutting depth h of each abrasive grain in the ultrasonic honing area can be obtained. , for: （3-3）, In formula (3-3), is the standard deviation, and the contact radius between the abrasive and the hardened gear at any position in the ultrasonic honing area is obtained. about 、 and function, for: （3-4）, In formula (3-4), is the radius probability density function of multiple abrasive particles in the processing area, is the area of ​​ultrasonic honing processing area, is the radius of a single abrasive particle; Step 3.3, based on the moving heat source theory, use the superposition method of heat source temperature field to calculate the surface temperature of the hardened gear; the heat generated by the honing process between the honing wheel and the hardened gear can be simplified to a surface heat source, which can be regarded as a combination of countless linear heat sources, and the linear heat source is regarded as a combination of multiple point heat sources; it is assumed that the point heat source is located at the coordinate origin of the heat conductor At the initial surface temperature of the hardened gear is T = 0 ° C, the heat q entering the hardened gear surface is w Simplified as a point heat source; based on the heat conduction theory, the three-dimensional heat conduction differential equation is Fourier transformed to obtain the coordinate position point M of the hardened gear surface in the ultrasonic honing processing area at any time. Temperature , Expressed as: （3-5）， In formula (3-5), is the density of the hardened gear, is the specific heat capacity of the hardened gear, is the thermal diffusivity of the hardened gear, is the distance from any point in the hardened gear to the heat source, , ,in, is the base circle radius of the hardened gear; is the roll angle of the hardened gear; is the feed rate of the hardened gear; Any time during the ultrasonic gear honing process; Step 3.4: Based on the high-order function curve, on the basis of formula (3-5), combined with the single abrasive velocity equation established by formula (2-1) and the function shown in formula (3-4) , establish a three-dimensional transient temperature field distribution model for ultrasonic honing processing area , for: （3-6）， In formula (3-6), is the ultrasonic honing processing time, is the maximum rolling angle of each point on the surface of the hardened gear, for about function.

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