Active determination method and precision machining method of dynamic pressure oil film worm gear pair

Abstract

The present invention discloses an active determination method and precision machining method of a dynamic pressure oil film worm gear pair, which relates to the field of worm gear pair design and machining. The method includes establishing an accurate three-dimensional digital model of the modified tooth surface of the worm gear pair considering the rough morphology; proposing a cross-scale meshing contact analysis method of the worm gear pair, establishing a three-dimensional contact thermal elastic hydrodynamic lubrication model of the worm gear pair considering the macroscopic morphology of the modified tooth surface, the roughness and the waviness of the tooth surface, and solving the model; taking the friction coefficient, oil film thickness, oil film pressure and friction force as the target, based on the improved non-dominated sorting genetic algorithm and the principal component analysis method, determining the optimal worm gear modification curve, worm tooth thickness distribution, pressure angle, helix lead angle, tooth surface roughness and waviness; and machining the worm gear tooth surface using a determined double-lead variable tooth thickness hob. The present invention can accurately design the worm gear pair, realize the precise control of the modification trajectory and the precision machining of the worm gear pair.

Description

Technical Field

[0001] The invention relates to the field of worm and worm gear pair design and processing, and in particular to an active determination method and a precision processing method for a dynamic pressure oil film worm and worm gear pair. Background Art

[0002] The worm gear pair is a key basic component for transmitting motion and power. It has the advantages of large transmission ratio and self-locking. It is widely used in major equipment such as high-end CNC machine tools and large astronomical telescopes, and directly determines the service performance of the equipment. Since the tooth surface of the worm gear pair is a relative sliding motion form, the friction resistance is large; at the same time, in order to reduce the bonding of the tooth surface, the material of the worm wheel is copper alloy, which has poor wear resistance; resulting in low transmission efficiency, poor load-bearing capacity, severe vibration, high noise, and poor precision retention of the worm gear pair. The existing method mainly improves the meshing performance of the worm gear pair by simply modifying the worm and worm wheel to increase the contact area and avoid unbalanced loads, but it cannot fundamentally improve the meshing performance.

[0003] In addition, the tooth surface design method will lead to complex modified surfaces of the worm and worm gear pair, which is extremely difficult to process. Because the worm gear material is copper alloy, which is soft and cannot be ground, it can only be cut by hobbing. Hobbing is an expansion process, so the cutting trace is fixed in the worm gear expansion and enveloping process. The existing enveloping process can only achieve the purpose of removing more material near the two end faces of the worm gear by moving the hob a small amount along the axial direction of the worm gear. Therefore, it can only achieve the qualitative removal of more tooth surface material, and it is difficult to achieve precise control of the modification trajectory, and it is impossible to ensure the accurate creation of the designed open shape and surface macro and micro parameters, which cannot meet actual needs. Summary of the invention

[0004] The purpose of the present invention is to provide a method for actively determining and precisely machining a dynamic pressure oil film worm and gear pair, which can accurately design the worm and gear pair, achieve precise control of the shaping trajectory and precise machining of the worm and gear pair.

[0005] To achieve the above object, the present invention provides the following solutions:

[0006] A method for actively determining a dynamic pressure oil film worm gear pair, comprising:

[0007] Establish an accurate three-dimensional digital model of the modified tooth surface of the worm and worm gear pair taking into account the rough morphology;

[0008] A cross-scale meshing contact analysis method for worm and worm gear pairs is proposed;

[0009] A three-dimensional contact thermal elastic hydrodynamic lubrication model of the worm and worm gear pair is established considering the macroscopic morphology of the modified tooth surface, the tooth surface roughness and the waviness, and the friction coefficient, oil film thickness, oil film pressure and friction force are obtained by solving the model.

[0010] Taking the friction coefficient, oil film thickness, oil film pressure and friction force as the targets, the optimal worm and worm wheel modification curve, worm tooth thickness distribution, pressure angle, helix lead angle, tooth surface roughness and waviness that can form a dynamic pressure oil film are determined based on the improved non-dominated sorting genetic algorithm NSGA-II and principal component analysis method PCA.

[0011] The dynamic pressure oil film worm and worm gear pair is determined according to the optimal worm and worm wheel modification curve, worm tooth thickness distribution, pressure angle, helix lead angle, tooth surface roughness and corrugation.

[0012] Optionally, the establishing of an accurate three-dimensional digital model of the modified tooth surface of the worm and worm gear pair taking into account the rough morphology specifically includes:

[0013] Based on the principle of spatial meshing of conjugate surfaces, the spatial coordinate system of the worm and worm gear pair envelope process is established, the worm tooth surface equation is derived using kinematics and coordinate transformation, and the worm wheel tooth surface profile is derived using the point vector envelope method, and then the worm and worm wheel tooth surface equation is obtained;

[0014] The rough surface is regarded as a random process, and the probability density function is determined by using the exponential autocorrelation function. Then, according to the probability density function, the amplitude and phase angle components are used to characterize the rough surface of the worm and worm wheel, and the rough surface equation is obtained.

[0015] According to the tooth surface equation of the worm and worm wheel, the tooth profile modification and tooth direction modification are adopted to obtain the tooth surface equation of the worm and worm wheel after modification;

[0016] According to the tooth surface equations of the worm and worm wheel after modification and the rough surface equations, a three-dimensional digital model of the worm and worm wheel pair is obtained.

[0017] Optionally, the tooth profile modification and tooth guide modification are used according to the tooth surface equation of the worm and worm wheel to obtain the modified tooth surface equation of the worm and worm wheel, which specifically includes:

[0018] Using the formula Determine the maximum modification amount; where δ Parabolic Represents a parabolic shaping curve; Δ max represents the maximum modification amount; L represents the total length of the double-tooth meshing area; x represents the distance from any point in the double-tooth meshing area to the alternating point of single and double teeth on the meshing line;

[0019] Using the formula Determine the inward offset of the tooth surface point after tooth modification compared to before modification; where e M is the inward offset before shaping, r c is the drum radius of the drum gear, z M is the coordinate of the discrete point along the Z axis; Δe is the deviation between the midpoint of the bulging circle and the center point of the gear; B is the tooth width; C maxis the maximum drum volume;

[0020] Using the formula Determine the tooth surface equation of the worm and worm wheel after modification; where, represents the tooth surface equation after modification; x k c ,y k c and z k c Respectively represent the x, y, and z coordinates of the tooth surface after modification; k ,y k and z k Respectively represent the x, y, and z coordinates of the tooth surface before modification; u k represents the axial parameters of the tooth surface, Indicates the involute parameter during machining rotation, e Mp is the offset, is the expansion angle of the tooth surface point.

[0021] Optionally, obtaining a three-dimensional digital model of the worm and worm gear pair according to the modified worm and worm wheel tooth surface equation and the rough surface equation specifically includes:

[0022] The modified worm and worm wheel tooth surface equations and the rough surface equations are coupled, and a program is written using MATLAB software to solve the worm and worm wheel tooth surface profile considering the rough morphology and modification, and the discrete point set of the worm and worm wheel tooth surface profile is obtained;

[0023] Solidworks is used to create a blank and the coordinate points of the discrete point set are inserted to obtain the tooth surface curve; based on the tooth surface curve, a three-dimensional digital model of the worm and worm gear pair considering the rough morphology and modification is obtained.

[0024] Optionally, the proposed cross-scale worm and worm gear pair meshing contact analysis method specifically includes:

[0025] The contact point and the tooth surface clearance are derived based on the tooth surface equation, and the inter-tooth load distribution is calculated to obtain the tooth surface contact mechanical properties; the tooth surface equation includes: the tooth surface equation after modification.

[0026] Optionally, the three-dimensional contact thermal elastohydrodynamic lubrication model of the worm and worm gear pair is established considering the macroscopic morphology of the modified tooth surface, the roughness and the waviness of the tooth surface, and the friction coefficient, oil film thickness, oil film pressure and friction force are obtained by solving the model, specifically including:

[0027] Average Reynolds equation:

[0028] In the formula, represents the average oil film pressure, μ is the viscosity of the lubricating oil, h is the thickness of the oil film, u is the entrainment velocity, represents the pressure flow factor in the x direction, represents the pressure flow factor in the y direction, represents the contact factor, represents the shear flow factor;

[0029] Oil film thickness equation h(x,y):

[0030] In the formula, R x ,R y is the equivalent radius of curvature, E' is the equivalent elastic modulus, h0 is a constant including the film thickness at the center of the rigid body and an undetermined constant C, δ(x, y) is the equivalent roughness of the two surfaces, and v(x, y) is the elastic deformation;

[0031] Lubricating oil viscosity equation μ:

[0032] μ=η0exp{(lnη0+9.67)[(1+5.1×10 -9 p) z -1]}; where η0 is the viscosity at atmospheric pressure, z is a constant, α is the viscosity-pressure coefficient;

[0033] Lubricating oil density equation ρ:

[0034] Where ρ0 is the density at atmospheric pressure and temperature T0;

[0035] Load balance equation W:

[0036] W = ∫∫ Ω [p(x,y)+p c (x,y))]dxdy; where p(x,y) is the load per unit area of ​​the lubricating film, p c (x, y) is the load per unit area of ​​the surface asperity, Ω is the integration area;

[0037] Suction speed v:

[0038] In the formula, v 1n is the component of the worm meshing point velocity along the normal direction of the contact line, v 2n is the component of the worm gear meshing point velocity along the normal direction of the contact line;

[0039] Thermal correction coefficient of oil film thickness c T :

[0040] Where k is the thermal conductivity of the lubricating oil and β is the viscosity-temperature coefficient.

[0041] A method for precision machining of a dynamic pressure oil film worm gear pair, based on the active determination method of a dynamic pressure oil film worm gear pair, uses a double-lead variable tooth thickness hob to perform precision machining of the worm gear tooth surface, specifically comprising:

[0042] A double-lead variable tooth thickness hob is determined; the double-lead variable tooth thickness hob includes a reference blade helix angle γ1 and a variable blade helix angle γ2, and different hob blade thicknesses are achieved by changing the helix angle;

[0043] Use the standard blade thickness position of the double-lead variable tooth thickness hob on the gear hobbing machine for processing: Use the standard tooth thickness position to cut the worm and worm gear pair according to the standard gear hobbing processing method until the gear hobbing allowance of the tooth surface of the worm and worm gear pair is only the processing allowance of the last cut, and then stop processing;

[0044] Perform double-lead variable tooth thickness hob shifting processing at the current radial feed position: shift the double-lead variable tooth thickness hob along the axial direction of the tool, and use the double-lead variable tooth thickness hob blade with a larger tooth thickness for cutting. The axial shifting amount of the double-lead variable tooth thickness hob is equal to the set value L;

[0045] The double-lead variable tooth thickness hob moves in the opposite direction and returns to the standard cutting thickness position.

[0046] The double-lead variable tooth thickness hob is fed radially to complete the cutting of the last cut.

[0047] Optionally, the set value L is determined according to the single-side exposure D.

[0048] Optionally, the use formula Determine the set value L;

[0049] Where q is the hob pitch circle diameter coefficient, m n is the normal modulus, l is the minimum unit tool displacement, z is the number of hob heads and k is the number of hob grooves.

[0050] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0051] The present invention provides an active determination method and precision machining method for a dynamic oil film worm and worm gear pair, establishes a three-dimensional digital model of the worm and worm gear pair taking into account rough morphology and modification, and provides an accurate model basis for subsequent lubrication simulation and optimization based on the three-dimensional digital model; develops a multi-objective optimization method for meshing performance such as friction coefficient, oil film thickness, oil film pressure and friction force, forms a worm and worm gear pair with dynamic oil film meshing, and improves the meshing performance in principle; when designing the modification of the worm and worm wheel tooth surface, the present invention actively modifies the tooth surface of the worm and worm wheel pair to achieve an open shape (wedge angle) at the meshing end and the meshing end, so as to facilitate the entry of lubricating oil into the meshing area and form a dynamic oil film; optimizes the surface micro-morphology, controls the rough peak height of the rough contact surface of the worm and worm wheel, promotes the increase of the dynamic oil film thickness to achieve complete lubrication, and achieves a fundamental improvement in the meshing performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0053] Figure 1 A schematic diagram of an active determination method for a dynamic pressure oil film worm gear pair provided by the present invention;

[0054] Figure 2 It is a schematic diagram of the spatial coordinate system;

[0055] Figure 3 Schematic diagram of tooth profile modification;

[0056] Figure 4 It is a schematic diagram of tooth modification;

[0057] Figure 5 Schematic diagram of the improved NSGA-II process for the local differential search method based on differential evolution;

[0058] Figure 6 The principal component analysis flow chart;

[0059] Figure 7 This is a schematic diagram of the worm gear pair processing. DETAILED DESCRIPTION

[0060] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0061] The purpose of the present invention is to provide a method for actively determining and precisely machining a dynamic pressure oil film worm and gear pair, which can accurately design the worm and gear pair, achieve precise control of the shaping trajectory and precise machining of the worm and gear pair.

[0062] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0063] like Figure 1 As shown, a method for determining a worm gear pair provided by the present invention comprises:

[0064] S101, establish an accurate three-dimensional digital model of the modified tooth surface of the worm and worm gear pair considering the rough morphology;

[0065] S101 specifically includes:

[0066] S110, based on the principle of spatial meshing of conjugate surfaces, establish the spatial coordinate system of the worm gear pair enveloping process, use kinematics and coordinate transformation to derive the worm gear tooth surface equation, and use the point vector enveloping method to derive the worm gear tooth surface profile, and then obtain the worm gear tooth surface equation;

[0067] The spatial coordinate system is Figure 2 As shown, the worm tooth surface equation is as follows:

[0068]

[0069] Among them, r b is the base circle radius of the worm gear, u is the length from Q0 to Q1, Q0 is the intersection of the i'0 axis of the moving coordinate system σ'0 and the base circle, a is the distance between the i0 axis and the i1 axis, i.e. the center distance, is the rotation angle of the moving coordinate system σ'0 (O'0; X'0, Y'0, Z'0) along the k0 axis, is the angle of rotation of the moving coordinate system σ'1 (O'1; X'1, Y'1, Z'1) along the i1 axis. The tooth surface equation of the other side of the worm can be obtained by coordinate transformation of the tooth surface equation of the worm on one side through the angle of the envelope generatrix on both sides at the initial moment;

[0070] The use of the point vector envelope method to derive the worm gear tooth surface profile can refer to the patent point vector secondary envelope method for determining the profile of the processed spiral surface by the generating tool;

[0071] S111, the rough surface is regarded as a random process, and the probability density function is determined by using the exponential form of the autocorrelation function; then, according to the probability density function, the amplitude and phase angle components are used to characterize the rough surface of the worm and worm wheel, and the rough surface equation is obtained;

[0072] The rough surface equation is established, including treating the rough surface as a random process and taking the autocorrelation function of exponential form:

[0073] (x, y) = σ 2 exp[2.3(x 2 / β x 2 +y 2 / β y 2 ) 1 / 2 ];

[0074] Where σ is the standard deviation of the rough surface height distribution; β x and β y are the autocorrelation lengths along the x and y directions, respectively.

[0075] Using the autocorrelation function to solve the probability density function P k,l :

[0076]

[0077] Among them, M and N are the number of generated points in the x and y directions respectively, i is an imaginary number, and exp is an exponential function with e as the base.

[0078] The rough surface equation is obtained by using the amplitude and phase angle components to characterize the rough surface of the worm gear:

[0079]

[0080] Among them, p, q, k, and l are all numbers ranging from 0 to M-1; P k,l is the probability density function; is the phase angle component of the rough surface;

[0081] S112, according to the tooth surface equation of the worm and worm wheel, the tooth profile modification and tooth direction modification are used to obtain the tooth surface equation of the worm and worm wheel after modification; the tooth profile modification and tooth direction modification are respectively as follows: Figure 3 and Figure 4 shown.

[0082] The tooth profile modification adopts tooth top modification. The modification parameters of tooth top modification include: maximum modification amount, modification length and modification curve; the maximum modification amount is calculated according to the maximum elastic deformation of the tooth profile after being loaded; the modification length is divided into long modification and short modification; the modification curve is parabolic modification;

[0083] Using the formula Determine the maximum modification amount; where δ Parabolic Represents a parabolic shaping curve; Δ max represents the maximum modification amount; L represents the total length of the double-tooth meshing area; x represents the distance from any point in the double-tooth meshing area to the alternating point of single and double teeth on the meshing line;

[0084] Using the formula Determine the inward offset of the tooth surface point after tooth modification compared to before modification; where e M is the inward offset before shaping, r c is the drum radius of the drum gear, z M is the coordinate of the discrete point along the Z axis; Δe is the deviation between the midpoint of the bulging circle and the center point of the gear; B is the tooth width; C max is the maximum drum volume;

[0085] According to the tooth surface forming principle, the offset e Mp The direction is the involute tangent to the base circle through a point on the tooth surface, and the angle of this point is Then at this time e Mp In the gear coordinate system, it can be expressed as:

[0086]

[0087]

[0088] In the formula, e xp and e yp are the offset e Mp Components in the X and Y directions;

[0089] Using the formula Determine the tooth surface equation of the worm and worm wheel after modification; where, represents the tooth surface equation after modification; x k c ,y k c and z k c Respectively represent the x, y, and z coordinates of the tooth surface after modification; k ,y k and z k Respectively represent the x, y, and z coordinates of the tooth surface before modification; u k represents the axial parameters of the tooth surface, Indicates the involute parameter during machining rotation, e Mp is the offset, is the expansion angle of the tooth surface point.

[0090] S113, obtaining a three-dimensional digital model of the worm and worm wheel pair according to the modified worm and worm wheel tooth surface equation and the rough surface equation.

[0091] The modified worm and worm wheel tooth surface equations and the rough surface equations are coupled, and a program is written using MATLAB software to solve the worm and worm wheel tooth surface profile considering the rough morphology and modification, and the discrete point set of the worm and worm wheel tooth surface profile is obtained;

[0092] Solidworks is used to create a blank and the coordinate points of the discrete point set are inserted to obtain the tooth surface curve; based on the tooth surface curve, a three-dimensional digital model of the worm and worm gear pair considering the rough morphology and modification is obtained.

[0093] S102, propose a cross-scale meshing contact analysis method for worm and worm gear pairs;

[0094] The contact point and the tooth surface clearance are derived based on the tooth surface equation, and the inter-tooth load distribution is calculated to obtain the tooth surface contact mechanical properties; the tooth surface equation includes: the tooth surface equation after modification.

[0095] When a certain instantaneous contact position is engaged, let the contact point P s The coordinates in the meshing coordinate system are (x s ,y s ,z s ), the normal vector of this point is Assume that along P s There is a point P0(x0,y0,z0) in the tangent direction. Parallel lines Wire It intersects with the two tooth surfaces at points P1 and P2 respectively; Parallel to Then we have:

[0096]

[0097]

[0098] in, and Respectively represent point P s The unit normal vector Components in the X, Y and Z directions; (x s ,y s ,z s ) represents point P s Coordinates in the gear meshing coordinate system; (x0, y0, z0) represents the coordinates of point P0 in the gear meshing coordinate system;

[0099] The coordinates of point P1 are:

[0100] The coordinates of point P2 are divided into:

[0101] Find the length of point P1 and point P2 Get the contact point P s Tooth surface clearance at each discrete point in the tangential direction.

[0102] In this way, the tooth surface clearance of each discrete point in the tangent direction of the contact point can be calculated in turn.

[0103] Under the action of external load FN, the elastic potential energy of each discrete point is mainly composed of bending energy, shear energy, radial compression energy and contact energy. The Weber energy method is used to solve the stiffness of any point P of the tooth profile:

[0104]

[0105]

[0106]

[0107]

[0108] In the formula, k b represents bending stiffness; k n represents radial compression stiffness; k s represents shear stiffness; k H represents the contact stiffness; point P is the point of action of the normal load FN; yp is the distance between the intersection of the center line of the tooth profile and the load action line and the center of the gear; y is the distance between the center of the gear and any point of the tooth profile along the center line of the tooth profile; yr is the distance between the center of the gear and the root circle; rb is the base circle radius; rp is the radius of the action point; rd is the pitch circle radius; α p is the angle between point P and the center line of the tooth profile; e(y) is the tooth thickness at any point of the tooth profile; E is the elastic modulus of the material; ν is the Poisson's ratio; B is the tooth width; G is the shear elastic modulus; Cs is the shear stress correction factor;

[0109] The total stiffness of any meshing position point P is:

[0110]

[0111] In the formula, k P Represents the stiffness of any meshing position point P; k bp , k sp and k np They represent the bending stiffness, shear stiffness and radial compression stiffness of the driving wheel respectively; k bg , k sg and k ngThey represent the bending stiffness, shear stiffness, and radial compression stiffness of the driven wheel respectively;

[0112] By introducing the tooth profile position parameter ε, the total stiffness of any meshing position point P is expressed as:

[0113] k P =k P (ε i );

[0114] In the formula, ε i Indicates that at different driving wheel rotation angles θ i Tooth profile position parameters of each contact line.

[0115] The definition of tooth profile position parameter ε can refer to the overlap ε α Specifically, the overlap degree ε α The definition is: the ratio of the actual meshing line (AD) length to the base circle pitch Pb:

[0116]

[0117] In this way, we can get i Tooth profile position parameter ε of each contact line i for:

[0118]

[0119] In the formula, subscript A represents point A, which is the actual engagement point position; X A and Y A are the X-axis and Y-axis coordinates of point A respectively; P is the rotation angle θ i The contact point below; X Pi and Y Pi are the X-axis and Y-axis coordinates of point P respectively; p b is the base circle pitch;

[0120] The load on each pair of gear teeth and the total applied load should satisfy the relationship:

[0121]

[0122] In the formula, R(ε i ) is the inter-tooth load distribution coefficient; k represents a certain gear tooth involved in the meshing; Fk is the load on the contact line of the pair of gear teeth, kPk is the total stiffness of the pair of gear teeth, FN is the total normal load, and z represents the number of gear tooth pairs involved in the meshing at the same time.

[0123] In the load-bearing contact analysis, any contacting tooth surface is divided into i×j discrete points. The curvature radius of each discrete point on the tooth surface is extracted along the contact line direction, and a simplified cylinder model is established to transform the tooth surface contact into two pairs of loaded contacts of elastic cylinders with different curvature radii. According to the specific distribution of the tooth surface load, each pair of cylinders is loaded to obtain the load distribution of each discrete point.

[0124] From differential geometry, we know that at a certain meshing point on the tooth surface, the unit normal vector When it is determined, the principal curvature ρ1 of each point on the driving gear tooth surface is obtained by the following formula:

[0125]

[0126] In the formula, E, F, G are the first basic quantities of the tooth surface; L, M, N are the second basic quantities of the tooth surface;

[0127] in, They are the first and second derivatives of the tooth surface equation with respect to parameters u and v respectively.

[0128] The curvatures of the two conjugate tooth surfaces in the meshing coordinate system satisfy the relationship:

[0129]

[0130] Where r is the distance between M and P; r1 and r2 are the pitch circle radii of the driving wheel and the driven wheel respectively; α is the pressure angle; ρ1 and ρ2 are the curvature radii of point M on the tooth profile of the driving wheel and the driven wheel respectively.

[0131] According to the specific distribution of the tooth surface load, each pair of cylinders is loaded. The ratio of the contact area length to the base circle radius is the rotation angle θ of the driving wheel. Taking the contact of the gear in the first double-tooth meshing area as an example, its simplified model is two pairs of elastic cylinders with different curvature radii that are loaded and contacted separately. Specifically, the load on each discrete point is:

[0132] f nij =F nj *R(ε ni )*P(n=a,b);

[0133]

[0134] Where P represents the total load; n = a, b, respectively represent two contact points; i represents the driving wheel rotation angle θ i The i-th contact line under the contact line; j represents the j-th discrete point along the contact line direction; f nij represents the load at the jth discrete point on the ith contact line; F nj Represents the tooth load distribution coefficient; R(ε ni ) represents the inter-tooth load distribution coefficient.

[0135] Based on the rough surface characterization and according to the contact pressure theory of Greenwood and Tripp, the contact pressure equation of the surface micro-convex body is:

[0136]

[0137] Among them, η is the roughness peak density, β is the peak element curvature radius, E′ is the comprehensive elastic modulus, and H is the film thickness ratio. According to the experiments of Greenwood and Tripp, the value of ηβσ is a constant between 0.03-0.05. is a statistical formula and can be determined by the following fitting formula:

[0138]

[0139] S103, for the determined service conditions such as lubricating oil viscosity and relative motion speed, a three-dimensional contact thermal elastic hydrodynamic lubrication model of the worm and worm gear pair is established considering the macroscopic morphology of the modified tooth surface, the tooth surface roughness and the waviness, and the model is solved to obtain the friction coefficient, oil film thickness, oil film pressure and friction force.

[0140] A three-dimensional contact thermal elastohydrodynamic lubrication model of the worm and worm gear pair considering the macroscopic morphology of the modified tooth surface, the roughness and the waviness of the tooth surface is established. The specific method is as follows: Based on the elastohydrodynamic lubrication theory and the Hertz contact theory, a three-dimensional thermal elastohydrodynamic lubrication model of the worm and worm gear pair considering the above factors is established and a thermal elastohydrodynamic lubrication analysis is performed. The relevant formulas of the thermal elastohydrodynamic lubrication model are as follows:

[0141] Average Reynolds equation:

[0142] In the formula, represents the average oil film pressure, μ is the viscosity of the lubricating oil, h is the thickness of the oil film, u is the entrainment velocity, represents the pressure flow factor in the x direction, represents the pressure flow factor in the y direction, represents the contact factor, represents the shear flow factor;

[0143] Oil film thickness equation h(x,y):

[0144] In the formula, R x ,R y is the equivalent radius of curvature, E' is the equivalent elastic modulus, h0 is a constant including the film thickness at the center of the rigid body and an undetermined constant C, δ(x, y) is the equivalent roughness of the two surfaces, and v(x, y) is the elastic deformation;

[0145] Lubricating oil viscosity equation μ:

[0146] μ=η0exp{(lnη0+9.67)[(1+5.1×10 -9 p) z -1]}; where η0 is the viscosity at atmospheric pressure, z is a constant, α is the viscosity-pressure coefficient;

[0147] Lubricating oil density equation ρ:

[0148] Where ρ0 is the density at atmospheric pressure and temperature T0;

[0149] Load balance equation W:

[0150] W = ∫∫ Ω [p(x,y)+p c (x,y))]dxdy; where p(x,y) is the load per unit area of ​​the lubricating film, p c (x, y) is the load per unit area of ​​the surface asperity, Ω is the integration area;

[0151] Suction speed v:

[0152] In the formula, v 1n is the component of the worm meshing point velocity along the normal direction of the contact line, v 2n is the component of the worm gear meshing point velocity along the normal direction of the contact line;

[0153] Thermal correction coefficient of oil film thickness c T :

[0154] Where k is the thermal conductivity of the lubricating oil and β is the viscosity-temperature coefficient.

[0155] The above thermoelastic-hydrodynamic lubrication model is solved based on the coupled differential deflection method and the multi-grid method to obtain the friction coefficient, oil film thickness, oil film pressure, friction force, etc.

[0156] S104, taking friction coefficient, oil film thickness, oil film pressure and friction force as targets, a multi-objective optimization method based on uniform non-dominated sorting genetic algorithm is proposed. Based on the improved non-dominated sorting genetic algorithm NSGA-II and principal component analysis method PCA, the optimal worm and worm wheel modification curve, worm tooth thickness distribution, pressure angle, helix lead angle, tooth surface roughness and waviness parameters that can form a dynamic pressure oil film are determined.

[0157] In order to better improve the lubrication performance of the hydrodynamic oil film, it is necessary to perform multi-objective optimization to improve the friction coefficient, oil film thickness, oil film pressure, friction force, etc. When the optimization target is not less than 3 (the present invention needs to optimize 4), the existing multi-objective optimization method (NSGA-II) is prone to uneven distribution of non-dominated solution sets. The present invention proposes to use a local differential search method based on differential evolution to improve the search performance of NSGA-II and improve the distribution uniformity of the Pareto frontier during multi-objective (not less than 3) optimization. The specific process is as follows: Figure 5 shown.

[0158] After obtaining the Pareto front containing multiple non-dominated solutions, the principal component analysis method (PCA) is used to automatically determine the optimal parameter combination, thereby replacing the manual decision-making of experienced engineers. When using PCA for parameter decision-making, the target weights of each solution in the Pareto front are determined based on the maximum variance criterion of the solution distribution in the Pareto front, that is, the candidate solutions in the Pareto front are well dispersed. This criterion enables PCA to reasonably and objectively automatically determine the weight of each target. The specific steps are as follows Figure 6 When using the principal component analysis method to determine the target value weight, the original target value is first standardized using the following formula.

[0159] x i (t) = (x i (t)-x min ) / (x min -x max ),i=1,2,...,N;

[0160] In the formula, x max and x min are the maximum and minimum values ​​of the target respectively; x i (t) takes values ​​between 0 and 1; N is the number of solutions in the Pareto front.

[0161] When using principal component analysis to weight the target, it essentially converts q original target vectors into q ind linearly independent target vectors, which are linear combinations of the original target vectors. Then, the coefficient matrix of each target is calculated to obtain the unit target vector and the corresponding eigenvalue λ i , which are the coefficient vector and weight of the i-th principal component respectively. i Arrange in descending order and select the first K components as the principal components. The variance contribution rate (α i ). i The larger the value of , the stronger the ability of the principal component to integrate the original target.

[0162]

[0163] The cumulative contribution rate of the first K principal components is calculated by the following formula.

[0164]

[0165] Where K≤q ind ; When the cumulative contribution rate η reaches a certain value (usually set to 90%), it is considered that the first K principal components can reflect all the information of the original target value.

[0166] Based on the variance contribution rate and target value vector of each principal component, the final score of each solution is calculated using the following formula. The solution with the highest score in the Pareto frontier is determined as the optimal tooth surface parameter combination, and the tooth surface optimization design of the worm gear pair is completed. The optimized wedge angle of the worm gear opening can ensure the formation of the dynamic pressure oil film.

[0167]

[0168] In the formula, S i is the total score of the ith solution; Y i is the normalized target value vector.

[0169] S105 determines the dynamic pressure oil film worm and worm gear pair based on the optimal worm and worm wheel modification curve, worm tooth thickness distribution, pressure angle, helix lead angle, tooth surface roughness and waviness.

[0170] like Figure 7 As shown, the present invention also provides a precision machining method for the worm and worm gear pair as described above, comprising:

[0171] A double-lead variable tooth thickness hob is determined; the double-lead variable tooth thickness hob includes a reference blade helix angle γ1 and a variable blade helix angle γ2, and different hob blade thicknesses are achieved by changing the helix angle;

[0172] Use the standard blade thickness position of the double-lead variable tooth thickness hob on the gear hobbing machine for processing: Use the standard tooth thickness position to cut the worm and worm gear pair according to the standard gear hobbing processing method until the gear hobbing allowance of the tooth surface of the worm and worm gear pair is only the processing allowance of the last cut, and then stop processing;

[0173] Perform double-lead variable tooth thickness hob shifting processing at the current radial feed position: shift the double-lead variable tooth thickness hob along the axial direction of the tool, and use the double-lead variable tooth thickness hob blade with a larger tooth thickness for cutting. The axial shifting amount of the double-lead variable tooth thickness hob is equal to the set value L;

[0174] The double-lead variable tooth thickness hob moves in the opposite direction and returns to the standard cutting thickness position.

[0175] The double-lead variable tooth thickness hob is fed radially to complete the cutting of the last cut.

[0176] The set value L is determined according to the single-side exposure amount D.

[0177] Using the formula Determine the set value L;

[0178] Where q is the hob pitch circle diameter coefficient, m n is the normal modulus, l is the minimum unit tool displacement, z is the number of hob heads and k is the number of hob grooves.

[0179] The open worm gear tooth surface processing method based on a variable tooth thickness hob of the present invention can realize hobbing processing with variable tooth thickness and blade by changing the cutting position of the hob, ensure the controllable processing of the open shape of the worm gear tooth surface, and effectively improve the tooth surface meshing performance of the worm and worm gear pair.

[0180] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0181] The principles and implementation methods of the present invention are described in this article using specific examples. The description of the above embodiments is only used to help understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A method for actively determining a dynamic pressure oil film worm gear pair, characterized in that: include: Establish an accurate three-dimensional digital model of the modified tooth surface of the worm and worm gear pair taking into account the rough morphology; A cross-scale meshing contact analysis method for worm and worm gear pairs is proposed; A three-dimensional contact thermal elastic hydrodynamic lubrication model of the worm and worm gear pair is established considering the macroscopic morphology of the modified tooth surface, the tooth surface roughness and the waviness, and the friction coefficient, oil film thickness, oil film pressure and friction force are obtained by solving the model. Taking the friction coefficient, oil film thickness, oil film pressure and friction force as the targets, the optimal worm and worm wheel modification curve, worm tooth thickness distribution, pressure angle, helix lead angle, tooth surface roughness and waviness that can form a dynamic pressure oil film are determined based on the improved non-dominated sorting genetic algorithm NSGA-II and principal component analysis method PCA. Determine the dynamic pressure oil film worm and worm gear pair according to the best worm and worm wheel modification curve, worm tooth thickness distribution, pressure angle, helix lead angle, tooth surface roughness and waviness; The proposed cross-scale worm and worm gear meshing contact analysis method specifically includes: Based on the tooth surface equation, the contact point and the tooth surface clearance are derived, and the inter-tooth load distribution is calculated to obtain the tooth surface contact mechanical properties; the tooth surface equation includes: the tooth surface equation after modification; The establishment of an accurate three-dimensional digital model of the modified tooth surface of the worm and worm gear pair taking into account the rough morphology specifically includes: Based on the principle of spatial meshing of conjugate surfaces, the spatial coordinate system of the worm and worm gear pair envelope process is established, the worm tooth surface equation is derived using kinematics and coordinate transformation, and the worm wheel tooth surface profile is derived using the point vector envelope method, and then the worm and worm wheel tooth surface equation is obtained; The rough surface is regarded as a random process, and the probability density function is determined by using the exponential autocorrelation function. Then, according to the probability density function, the amplitude and phase angle components are used to characterize the rough surface of the worm and worm wheel, and the rough surface equation is obtained. According to the tooth surface equation of the worm and worm wheel, the tooth profile modification and tooth direction modification are adopted to obtain the tooth surface equation of the worm and worm wheel after modification; According to the modified worm and worm wheel tooth surface equation and rough surface equation, a three-dimensional digital model of the worm and worm wheel pair is obtained; The tooth profile modification and tooth guide modification are used according to the tooth surface equation of the worm and worm wheel to obtain the modified tooth surface equation of the worm and worm wheel, which specifically includes: Using the formula Determine the maximum modification amount; where δ Parabolic Represents a parabolic shaping curve; Δ max represents the maximum modification amount; L represents the total length of the double-tooth meshing area; x represents the distance from any point in the double-tooth meshing area to the alternating point of single and double teeth on the meshing line; Using the formula Determine the inward offset of the tooth surface point after tooth modification compared to before modification; where e M is the inward offset before shaping, r c is the drum radius of the drum gear, z M is the coordinate of the discrete point along the Z axis; Δe is the deviation between the midpoint of the bulging circle and the center point of the gear; B is the tooth width; C max is the maximum drum volume; Using the formula Determine the tooth surface equation of the worm and worm wheel after modification; where, represents the tooth surface equation after modification; x k c ,y k c and z k c Respectively represent the x, y, and z coordinates of the tooth surface after modification; k ,y k and z k Respectively represent the x, y, and z coordinates of the tooth surface before modification; u k represents the axial parameters of the tooth surface, Indicates the involute parameter during machining rotation, e Mp is the offset, is the expansion angle of the tooth surface point.

2. The method for actively determining a dynamic pressure oil film worm gear pair according to claim 1, characterized in that: The three-dimensional digital model of the worm and worm gear pair is obtained according to the modified worm and worm wheel tooth surface equation and the rough surface equation, which specifically includes: The modified worm and worm wheel tooth surface equations and the rough surface equations are coupled, and a program is written using MATLAB software to solve the worm and worm wheel tooth surface profile considering the rough morphology and modification, and the discrete point set of the worm and worm wheel tooth surface profile is obtained; Solidworks is used to create a blank and the coordinate points of the discrete point set are inserted to obtain the tooth surface curve; based on the tooth surface curve, a three-dimensional digital model of the worm and worm gear pair considering the rough morphology and modification is obtained.

3. The method for actively determining a dynamic pressure oil film worm gear pair according to claim 1, characterized in that: The three-dimensional contact thermal elastic hydrodynamic lubrication model of the worm and worm gear pair considering the macroscopic morphology of the modified tooth surface, the roughness and the waviness of the tooth surface is established and the friction coefficient, the oil film thickness, the oil film pressure and the friction force are obtained by solving the model, specifically including: Average Reynolds equation: In the formula, represents the average oil film pressure, μ is the viscosity of the lubricating oil, h is the thickness of the oil film, u is the entrainment velocity, represents the pressure flow factor in the x direction, represents the pressure flow factor in the y direction, represents the contact factor, represents the shear flow factor, σ is the standard deviation of the rough surface height distribution; Oil film thickness equation h(x,y): In the formula, R x ,R y is the equivalent radius of curvature, h0 is a constant, including the film thickness at the center of the rigid body and an undetermined constant C, δ(x, y) is the equivalent roughness of the two surfaces, and v(x, y) is the elastic deformation; Lubricating oil viscosity equation μ: μ=η0exp{(lnη0+9.67)[(1+5.1×10 -9 p) z -1]}; where η0 is the viscosity at atmospheric pressure, z is a constant, α is the viscosity-pressure coefficient, and p is a number from 0 to M-1; Lubricating oil density equation ρ: Where ρ0 is the density at atmospheric pressure and temperature T0; Load balance equation W: W = ∫∫ Ω [p(x,y)+p c (x,y))]dxdy; where p(x,y) is the load per unit area of ​​the lubricating film, p c (x, y) is the load per unit area of ​​the surface asperity, Ω is the integration area; Suction speed v: In the formula, v 1n is the component of the worm meshing point velocity along the normal direction of the contact line, v 2n is the component of the worm gear meshing point velocity along the normal direction of the contact line; Thermal correction coefficient of oil film thickness C T : Where k is the thermal conductivity of the lubricating oil and β is the viscosity-temperature coefficient.

4. A precision machining method for a dynamic pressure oil film worm gear pair, based on a dynamic pressure oil film worm gear pair active determination method according to any one of claims 1 to 3, characterized in that: The double-lead variable tooth thickness hob is used for precision machining of the worm gear tooth surface, including: A double-lead variable tooth thickness hob is determined; the double-lead variable tooth thickness hob includes a reference blade helix angle γ1 and a variable blade helix angle γ2, and different hob blade thicknesses are achieved by changing the helix angle; Use the standard blade thickness position of the double-lead variable tooth thickness hob on the gear hobbing machine for processing: Use the standard tooth thickness position to cut the worm and worm gear pair according to the standard gear hobbing processing method until the gear hobbing allowance of the tooth surface of the worm and worm gear pair is only the processing allowance of the last cut, and then stop processing; Perform double-lead variable tooth thickness hob shifting processing at the current radial feed position: shift the double-lead variable tooth thickness hob along the axial direction of the tool, and use the double-lead variable tooth thickness hob blade with a larger tooth thickness for cutting. The axial shifting amount of the double-lead variable tooth thickness hob is equal to the set value L; The double-lead variable tooth thickness hob moves in the opposite direction and returns to the standard cutting thickness position; The double-lead variable tooth thickness hob is fed radially to complete the cutting of the last cut.

5. The precision machining method of a dynamic pressure oil film worm gear pair according to claim 4, characterized in that: The set value L is determined according to the single-side exposure amount D.

6. The precision machining method of a dynamic pressure oil film worm gear pair according to claim 5, characterized in that: Using the formula Determine the set value L; Where q is the hob pitch circle diameter coefficient, m n is the normal modulus, l is the minimum unit tool displacement, z is the number of hob heads and k is the number of hob grooves.

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