Mechanical modeling and life calculation method for hub bearing unit

Abstract

The invention discloses a mechanical modeling and life calculation method for a hub bearing unit. The method comprises the following steps: S1, establishing a reference point O at the geometric center of the hub bearing unit; and S2, the bearing roller is subjected to slicing treatment. And S3, representing the relative position relationship between the roller slice and the reference point O. And S4, representing the total elastic approaching quantity between the roller slice and the bearing raceway. S5, representing the elastic approaching reduction between the roller slice and the roller path; and S6, representing the contact load between the roller slice and the raceway and the moment generated by the contact load. And S7, listing an equilibrium equation set of the hub bearing unit, solving the equation, and representing the load of the roller slice and the contact load between the roller and the outer raceway. And S8, calculating the fatigue life of the hub bearing unit. By applying the method, a mechanical analysis model comprehensively considering the convexity of the bearing roller, the convexity of the inner ring, the convexity of the outer ring and the inclination of the raceway can be established, and accurate calculation of the fatigue life of the hub bearing is realized in combination with an edge stress concentration correction function of the raceway.

Description

Technical Field

[0001] The invention relates to the technical field of bearing fatigue life prediction, in particular to a method for mechanical modeling and life calculation of a hub bearing unit. Background Art

[0002] Automobiles are important means of transportation in the modern transportation system. Wheel hub bearings are key load-bearing and transmission components of automobiles. Their reliability is closely related to the safe and smooth driving of automobiles. The development trend of high-end, intelligent and electrified automobiles has put forward increasingly stringent requirements on the performance of wheel hub bearings. Long life, low friction and light weight of wheel hub bearings are the basic requirements for high-end automobiles. During the driving process of the car, the wheel hub bearings are subjected to the combined effects of radial, axial and moment loads, and their mechanical state and failure evolution mechanism are very complex. The operating conditions of commercial vehicles are harsh, and the requirements for long life and high reliability of wheel hub bearings are very urgent.

[0003] The improvement of wheel hub bearing fatigue life and reliability is based on the mechanical analysis of the system. The existing analysis and calculation of commercial vehicle wheel hub bearings mainly uses commercial software for modeling and solving. The analysis work that can be completed depends on the functions provided by the software, and it is difficult to achieve batch calculation in the iterative optimization process of bearing parameters. The existing numerical modeling and solution algorithms for commercial vehicle wheel hub bearings fail to fully consider the impact of raceway crown, roller crown and raceway inclination on bearing life. Summary of the invention

[0004] The purpose of the present invention is to provide a mechanical modeling and life calculation method for a wheel hub bearing unit, which can establish a mechanical analysis model that comprehensively considers the bearing roller convexity, inner ring convexity, outer ring convexity and raceway inclination, and combines the edge stress concentration correction function of the raceway to achieve accurate calculation of the fatigue life of the wheel hub bearing.

[0005] In order to achieve the above object, the present invention adopts the following technical solution.

[0006] A mechanical modeling and life calculation method for a hub bearing unit comprises the following steps: S1. Establish a reference point O at the geometric center of the outer bearing and the inner bearing of the hub bearing unit; S2, slicing the bearing roller, cutting the roller into multiple slices of the same thickness along the axial direction of the roller, and indicating the position of each roller slice in the roller; S3, indicating the relative position relationship between each roller slice and the reference point O in the wheel hub bearing unit; S4, represents the total elastic approach between each roller slice and the bearing raceway; S5, represents the reduction in elasticity of each roller slice and raceway due to crowning modification; S6, represents the contact load between each roller slice and the raceway and the moment generated by the contact load; S7. List the equilibrium equations of the hub bearing unit, solve the equations and express the load of each roller slice and the contact load between each roller and the outer raceway; S8. Calculate the fatigue life of the hub bearing unit.

[0007] Further, S8 calculates the fatigue life of the hub bearing unit, including the following steps: S8.1. Express the stress concentration correction function at the edge of the bearing raceway; S8.2, the roller slice load is expressed as the equivalent dynamic load by correction of the edge stress concentration correction function; S8.3. Calculate the basic reference rated life of the bearing from the roller slice load corresponding to the rated dynamic load and the roller slice load corresponding to the equivalent dynamic load; S8.4. Correct the basic reference rated life according to the actual working condition of the bearing to obtain the corrected reference rated life of the bearing; S8.5. Calculate the modified reference rating life of the wheel hub bearing unit.

[0008] Furthermore, in S1, the radial load F borne by the bearing unit is r , axial load F a The moment load M is translated to the reference point O.

[0009] Further, in S2, when representing the position of each roller slice in the roller, the direction of the roller axis from the large end to the small end is taken as the positive direction, and the length center of the roller is taken as the origin. The position coordinates of the thickness center of each roller slice in the roller are: The meanings of the various parameter symbols are as follows: L we —— roller length; n s ——Number of roller slices; k——roller slice number.

[0010] Further, in S3, the relative position of the roller slice in the wheel hub bearing unit and the reference point O includes an axial distance between the roller slice and the reference point O and a distance between the roller slice and the reference point O along the radial direction of the bearing.

[0011] Axial distance d between the kth slice of the inner bearing roller and the reference point O h1,k for: The meanings of the various parameter symbols are as follows: d h1 ——Axial distance between the center of the inner bearing roller row and the reference point O; x 1,k ——The position coordinates of the thickness center of the inner bearing roller slice k in the roller; ——half cone angle of the inner bearing roller; α i1 ——Contact angle of the inner ring raceway of the inner bearing.

[0012] Axial distance d between the kth slice of the outer bearing roller and the reference point O h2,k for: The meanings of the various parameter symbols are as follows: d h2 ——Axial distance between the center of the outer bearing roller row and the reference point O; x 2,k ——The coordinates of the thickness center of the outer bearing roller slice k in the roller; ——half cone angle of the outer bearing roller; α i2 ——Contact angle of the inner ring raceway of the outer bearing.

[0013] The distance d between the kth slice of the inner bearing roller and the reference point O along the bearing radial direction v1,k for: Where: d m1 ——The distribution circle diameter of the inner bearing roller center.

[0014] The distance d between the kth slice of the outer bearing roller and the reference point O along the bearing radial direction v2,k for: Where: d m2 ——The distribution circle diameter of the outer bearing roller center.

[0015] Furthermore, in S4, the total elastic approach between the roller slice and the bearing raceway includes:

[0016] The total elastic approach δ between the kth slice of the jth roller of the inner bearing and the inner and outer raceways n1,j,k for: The meanings of the various parameter symbols are as follows: δ r ——External radial load Fr Radial displacement of the inner ring raceway of the bearing under the action; θ——the inclination angle displacement of the inner ring raceway of the bearing under the external moment load M; ψ 1,j ——the azimuth angle of the jth roller of the inner bearing on the bearing circumference; α e1 ——Contact angle of inner bearing outer ring raceway; δ a ——External axial load F a Axial displacement of the bearing inner ring raceway under the action; δ 01 ——Axial displacement of the inner ring raceway of the inner bearing under the action of axial preload.

[0017] The total elastic approach δ between the kth slice of the jth roller of the outer bearing and the inner and outer raceways n2,j,k for: The meanings of the various parameter symbols are as follows: ψ 2,j ——the azimuth angle of the jth roller of the outer bearing on the bearing circumference; α e2 ——Contact angle of outer ring raceway of outboard bearing; δ 02 ——Axial displacement of the inner ring raceway of the outer bearing under the action of axial preload.

[0018] Further, in S5, the reduction in elastic convergence between the roller slice and the raceway due to the crowning modification includes a reduction in the elastic convergence between the roller slice and the outer ring raceway and a reduction in the elastic convergence between the roller slice and the inner ring raceway.

[0019] The reduction in the elastic approach between the roller slice and the outer ring raceway is the sum of the crowning modification of the roller and the outer ring raceway. The reduction in the elastic approach between the roller slice and the inner ring raceway requires the crowning modification of each roller slice to be decomposed into the normal direction of the contact surface between the roller and the outer ring raceway for calculation, and then:

[0020] The reduction in the elastic approach along the normal direction of the outer ring raceway for the kth slice of the jth roller of the inner bearing c n1,j,k for: c n1,j,k =c r1,k +c e1,k +(c r1,k +c i1,k )cos(α e1 -α i1 ), (8) where the symbols of each parameter represent the following meanings: c r1,k ——Roller crown modification amount at the kth slice position of the inner bearing; c e1,k ——The crown modification amount of the outer ring raceway at the kth slice position of the inner bearing; c i1,k ——The inner ring raceway convexity modification amount at the kth slice position of the inner bearing.

[0021] The reduction in the elastic approach along the normal direction of the outer ring raceway for the kth slice of the jth roller of the outer bearing is c n2,j,k for: c n2,j,k =c r2,k +c e2,k +(c r2,k +c i2,k )cos(α e2 -α i2 ), (9) The meanings of the various parameter symbols are as follows: c r2,k ——Roller crown modification amount at the kth slice position of the outer bearing; c e2,k ——The outer ring raceway crown modification amount at the kth slice position of the outer bearing; c i2,k ——The inner ring raceway crown modification amount at the kth slice position of the outer bearing.

[0022] Further, in S6, the contact load between the roller slice and the raceway includes:

[0023] Contact load q between the kth slice of the jth roller of the inner bearing and the outer ring raceway e1,j,k for: Where: K ne1 ——The total "load-deformation" constant between the inner bearing roller and the raceway.

[0024] Contact load q between the kth slice of the jth roller of the outer bearing and the outer ring raceway e2,j,k for: Where: K ne2 ——The total "load-deformation" constant between the outer bearing roller and the raceway.

[0025] The roller slice load will generate a moment relative to the bearing unit reference point O to balance the external torque M. The moment generated by the contact load between the roller slice and the raceway includes:

[0026] For the inner bearing, the moment m generated by the contact load component in the vertical direction of the kth slice is v1,j.k for:

[0027] The moment m generated by the contact load component in the horizontal direction of the kth slice h1,j,k for,

[0028] For the outer bearing, the moment m generated by the contact load component in the vertical direction of the kth slice is v2,j,k for:

[0029] The moment m generated by the contact load component in the horizontal direction of the kth slice h2,j,k for:

[0030] Furthermore, in S7, the outer ring of the bearing unit is in equilibrium under the action of the external load and all roller loads, and the equilibrium equations are listed as:

[0031] Formulas (16) to (18) are based on δ r , δ a The nonlinear equations with unknown quantities θ and θ can be solved by iteration according to the design parameters of the hub bearing and the external load. According to the solution results, the load of each roller slice can be calculated, and the contact load between the roller and the outer raceway can be obtained by summing the loads of all slices in each roller.

[0032] Furthermore, in S8.1, the edge stress concentration correction function of the bearing raceway includes:

[0033] The edge stress concentration correction function of the inner ring raceway is: The meanings of the various parameter symbols are as follows: D wm ——average diameter of tapered rollers; p Hij,k ——Contact stress between the kth slice of roller j and the inner ring raceway; q j,k ——the load of the kth slice of roller j; γ——Auxiliary function, γ=D wm cosα / d m , α is the contact angle of the outer ring raceway.

[0034] The edge stress concentration correction function of the outer ring raceway is: Among them, p Hej,k ——Contact stress between the kth slice of roller j and the outer ring raceway.

[0035] In S8.2, after correction by the edge stress concentration correction function, the roller slice load q of the equivalent dynamic load of the rotating ring relative to the load direction is obtained. ei,k for:

[0036] Roller slice load q of the equivalent dynamic load on the stationary ring relative to the load direction ee,k for:

[0037] In S8.3, the basic reference rating life of the bearing is L 10r for: The meanings of the various parameter symbols are as follows: q ci - roller slice load corresponding to the basic dynamic load rating of the inner ring; q ce ——Roller slice load corresponding to the basic rated dynamic load of the outer ring.

[0038] In S8.4, in order to facilitate the correction calculation of bearing fatigue life, the equivalent dynamic load P of the bearing slice calculated from the roller slice load is defined as s,k for: Where: Z – number of bearing rollers.

[0039] After correcting the influence of application conditions on life, the corrected reference rated life L of the bearing is obtained. nmr for: The meanings of the various parameter symbols are as follows: a1——Reliability life correction factor; α ISO ——life correction factor; e C ——pollution coefficient; C ur —— radial load fatigue limit; K——lubricant viscosity ratio; P s,k ——Equivalent dynamic load of the kth slice.

[0040] In S8.5, the modified reference rating life L for a bearing unit consisting of two rows of bearings nmr for:

[0041] After adopting the above technical solution, the present invention has the following beneficial effects: 1. The mechanical model of the present invention comprehensively considers the roller crown, inner ring crown, outer ring crown and raceway inclination, and the calculation result of roller load distribution is more accurate and in line with reality; 2. The mechanical model includes the roller crown, inner ring crown and outer ring crown. The calculation results of this model can provide a basis for the reasonable selection of crown parameters and further optimize the design parameters; 3. The bearing life calculation takes into account the edge stress concentration of the raceway contact stress, and the life calculation result is more accurate and in line with reality; 4. By using the method of the present invention, batch calculation can be realized when bearing parameters change through programming statement settings, thereby realizing iterative optimization of bearing design. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a schematic diagram of the overall structure of the hub bearing unit in the present invention.

[0043] Figure 2 It is a structural schematic diagram of the position of the reference point O of the hub bearing unit.

[0044] Figure 3 : is the load distribution diagram of the inner bearing roller in the embodiment.

[0045] Figure 4 : is the load distribution diagram of the outer bearing roller in the embodiment.

[0046] Description of the drawings: 1. Inner bearing, 2. Outer bearing, 3. Hub shaft, 4. Hub shell, 5. Locking nut. DETAILED DESCRIPTION

[0047] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the characteristics and performance of a mechanical modeling and life calculation method of a hub bearing unit in the present invention are further described in detail below in conjunction with the accompanying drawings and embodiments.

[0048] Please refer to the attached Figures 1 to 4 , a mechanical modeling and life calculation method of a hub bearing unit, the present invention adopts the following technical solution.

[0049] The commercial vehicle wheel hub bearing unit mainly comprises an inner bearing (1), an outer bearing (2), a hub shaft (3), a hub shell (4) and a locking nut (5). Figure 1 shown.

[0050] Step 1: To facilitate the geometric description of the bearing, a reference point O is established at the geometric center of the inner bearing (1) and the outer bearing (2).

[0051] The hub bearing unit bears radial load F r , axial load F a The combined effect of the load and moment load M. According to the force translation theorem, the load action position is translated to the reference point O of the two rows of bearings, as shown in Figure 2 The inner bearing is indicated by the subscript "1" and the outer bearing is indicated by the subscript "2".

[0052] Step 2: Slice the roller.

[0053] In order to consider the influence of roller crown, inner ring crown, outer ring crown and raceway inclination on roller load distribution and raceway contact stress, the roller is sliced.

[0054] The axial position of each roller slice is defined from the large end to the small end along the roller axis. If the number of roller slices is n s , taking the center of the roller length as the origin, the position coordinates of the center of thickness of each roller slice can be expressed as: The meanings of the various parameter symbols are as follows: L we —— roller length; n s ——Number of roller slices; k——roller slice number.

[0055] Step three, indicate the position of the roller slice in the bearing.

[0056] The distance between each roller slice and the reference point O along the bearing axial direction is different. The axial distance of the kth slice of the inner bearing roller is: The meanings of the various parameter symbols are as follows: d h1 ——Axial distance between the center of the inner bearing roller row and the reference point O; x 1,k ——The position coordinates of the thickness center of the inner bearing roller slice k in the roller; ——half cone angle of the inner bearing roller; α i1 ——Contact angle of the inner ring raceway of the inner bearing.

[0057] The axial distance of the kth slice of the outer bearing roller is: The meanings of the various parameter symbols are as follows: d h2 ——Axial distance between the center of the outer bearing roller row and the reference point O; x 2,k ——The coordinates of the thickness center of the outer bearing roller slice k in the roller; ——half cone angle of the outer bearing roller; α i2 ——Contact angle of the inner ring raceway of the outer bearing.

[0058] The distance between the kth slice of the inner bearing roller and the reference point O along the bearing radial direction is: Where: d m1 ——The distribution circle diameter of the inner bearing roller center.

[0059] The distance between the kth slice of the outer bearing roller and the reference point O along the bearing radial direction is: Where: d m2 ——The distribution circle diameter of the outer bearing roller center.

[0060] Step 4: Express the elastic approach between the roller slice and the raceway.

[0061] The displacement approach between the inner ring raceway and the outer ring raceway will lead to elastic contact deformation between the raceway and the roller. The total elastic approach between the kth slice of the jth roller of the inner bearing and the inner and outer ring raceways is: The meanings of the various parameter symbols are as follows: δ r ——External radial load F r Radial displacement of the inner ring raceway of the bearing under the action; θ——the inclination angle displacement of the inner ring raceway of the bearing under the external moment load M; ψ 1,j ——the azimuth angle of the jth roller of the inner bearing on the bearing circumference; α e1 ——Contact angle of inner bearing outer ring raceway; δ a ——External axial load F a Axial displacement of the bearing inner ring raceway under the action; δ 01 ——Axial displacement of the inner ring raceway of the inner bearing under the action of axial preload.

[0062] The total elastic approach between the kth slice of the jth roller of the outer bearing and the inner and outer ring raceways is: The meanings of the various parameter symbols are as follows: ψ 2,j ——the azimuth angle of the jth roller of the outer bearing on the bearing circumference; α e2 ——Contact angle of outer ring raceway of outboard bearing; δ 02 ——Axial displacement of the inner ring raceway of the outer bearing under the action of axial preload.

[0063] Step five shows the reduction in elastic approximation caused by roller slicing and raceway crowning modification.

[0064] For tapered roller bearings, the elastic contact deformation between the roller and the raceway is analyzed along the normal direction of the outer ring raceway. Therefore, the reduction in the elastic approach between the roller slice and the outer ring raceway is the sum of the crown modification of the roller and the outer ring raceway; and for the reduction in the elastic approach between the roller slice and the inner ring raceway, the crown modification of each slice needs to be decomposed to the normal direction of the contact surface between the roller and the outer ring raceway.

[0065] For the inner bearing, the reduction in the elastic approach of the kth slice of the jth roller along the normal direction of the outer ring raceway is: c n1,j,k =c r1,k +c e1,k +(c r1,k +c i1,k )cos(α e1 -α i1 ), (8) The meanings of the various parameter symbols are as follows: c r1,k ——Roller crown modification amount at the kth slice position of the inner bearing; c e1,k ——The crown modification amount of the outer ring raceway at the kth slice position of the inner bearing; c i1,k ——The inner ring raceway convexity modification amount at the kth slice position of the inner bearing.

[0066] For the outer bearing, the reduction in the elastic approach of the kth slice of the jth roller along the normal direction of the outer ring raceway is: c n2,j,k =c r2,k +c e2,k +(c r2,k +c i2,k )cos(αe2 -α i2 ), (9) The meanings of the various parameter symbols are as follows: c r2,k ——Roller crown modification amount at the kth slice position of the outer bearing; c e2,k ——The outer ring raceway crown modification amount at the kth slice position of the outer bearing; c i2,k ——The inner ring raceway crown modification amount at the kth slice position of the outer bearing.

[0067] Step six, express the roller slice load and the torque it generates.

[0068] For the inner bearing, the contact load between the kth slice of the jth roller and the outer ring raceway is: Where: K ne1 ——The total "load-deformation" constant between the inner bearing roller and the raceway.

[0069] For the outboard bearing, the contact load between the kth slice of the jth roller and the outer ring raceway is: Where: K ne2 ——The total "load-deformation" constant between the outer bearing roller and the raceway.

[0070] The roller slice load will produce a moment action relative to the bearing unit reference point O to balance the external acting moment M.

[0071] For the inner bearing, the moment generated by the contact load component in the vertical direction of the kth slice is:

[0072] The moment generated by the contact load component of the kth slice along the horizontal direction is:

[0073] For the outboard bearing, the moment generated by the contact load component in the vertical direction of the kth slice is:

[0074] The moment generated by the contact load component of the kth slice along the horizontal direction is:

[0075] Step seven, list the equilibrium equations of the hub bearing unit.

[0076] The outer ring of the bearing unit is in equilibrium under the action of external loads and all roller loads, and the following equilibrium equations are listed:

[0077] Formulas (16) to (18) form the equations with δ r , δ a and θ are nonlinear equations with unknown quantities. When the design parameters of the hub bearing and the external load are given, the nonlinear equations can be solved by the iteration method. The load of the roller slice can be further calculated using the solution results, and the load of all slices of each roller can be summed to obtain the contact load between the roller and the outer raceway.

[0078] Step 8: Calculate the fatigue life of the hub bearing unit.

[0079] The fatigue life of the bearing depends on the rolling element load and the equivalent rolling element load corresponding to the basic dynamic load rating of the bearing. By slicing the rollers, the influence of the bearing raceway inclination displacement can be taken into account when calculating the bearing life using the roller slice load. In addition, the edge stress concentration that may occur between the roller end and the raceway surface will shorten the fatigue life of the bearing. The stress correction function is calculated based on the roller slice load and contact stress, and the influence of edge stress concentration on the bearing life is taken into account through the stress correction function.

[0080] The edge stress concentration correction function of the inner ring raceway is: The meanings of the various parameter symbols are as follows: D wm ——average diameter of tapered rollers; p Hij,k ——Contact stress between the kth slice of roller j and the inner ring raceway; q j,k ——the load of the kth slice of roller j; γ——Auxiliary function, γ=D wm cosα / d m , α is the contact angle of the outer ring raceway.

[0081] The edge stress concentration correction function of the outer ring raceway is: Among them, p Hej,k ——Contact stress between the kth slice of roller j and the outer ring raceway.

[0082] After correction by the edge stress concentration correction function, the roller slice load of the equivalent dynamic load of the rotating ring relative to the load direction is obtained as follows:

[0083] The roller slice load of the equivalent dynamic load on the stationary ring relative to the load direction is:

[0084] The basic reference rating life of the bearing is calculated from the roller slice load corresponding to the rated dynamic load and the roller slice load corresponding to the equivalent dynamic load: The meanings of the various parameter symbols are as follows: q ci - roller slice load corresponding to the basic dynamic load rating of the inner ring; q ce ——Roller slice load corresponding to the basic rated dynamic load of the outer ring.

[0085] On the basis of the basic reference rated life, it is necessary to correct the basic reference rated life according to the actual working conditions of the bearing. In order to facilitate the correction calculation of the bearing fatigue life, the equivalent dynamic load of the bearing slice calculated by the roller slice load is defined as: Where: Z——Number of bearing rollers;

[0086] After correcting the effect of the application conditions on the life, the corrected reference rated life of the bearing is obtained: The meanings of the various parameter symbols are as follows: a1——Reliability life correction factor; α ISO ——life correction factor; e C ——pollution coefficient; C ur —— radial load fatigue limit; κ——lubricant viscosity ratio; P s,k ——Equivalent dynamic load of the kth slice.

[0087] Formula (25) can be used to calculate the fatigue life of the inner bearing or the outer bearing. For a bearing unit consisting of two rows of bearings, the modified reference rated life of the bearing unit is calculated according to the following formula:

[0088] In a specific implementation, taking the left wheel hub bearing unit of a rear axle of a commercial vehicle as an example, the bearing unit comprises an inner bearing (1), an outer bearing (2), a wheel hub shaft (3), a wheel hub shell (4) and a locking nut (5), as shown in FIG. Figure 1 shown.

[0089] The main structural parameters of the bearing unit are as follows.

[0090] ①Main parameters of inner bearing:

[0091] Pitch circle diameter d m2 =117.5mm, roller diameter D wm2 =17.276mm, roller length L we2 =27.6mm, number of rollers Z2 = 20, roller semi-cone angle Inner ring raceway contact angle α i2 =11°38′32″, outer ring raceway contact angle α e2 =15°38′32″, inner ring rib contact angle α f2 =77°50′00″.

[0092] ②Main parameters of the outer bearing:

[0093] Pitch circle diameter d m2 =117.5mm, roller diameter D wm2 =17.276mm, roller length L we2 =27.6mm, number of rollers Z2 = 20, roller semi-cone angle Inner ring raceway contact angle α i2 =11°38′32″, outer ring raceway contact angle α e2 =15°38′32″, inner ring rib contact angle α f2 =77°50′00″.

[0094] The convexity equation of the roller is: The convexity equation of the outer ring raceway is: The convexity equation of the inner ring raceway is: The axial span between the centers of the two bearing rollers is d h =140mm. The bearing speed is 500r / min, and the kinematic viscosity of the gear oil 75W-90 lubricant at 40°C is 136mm 2 / s, the application environment is normal cleanliness. The axial preload of the bearing is: F a0 =34200N. The load acting on the reference point O is: F a =967N,F r =24175N, M=2543000Nmm.

[0095] The mechanical modeling and life calculation method of a commercial vehicle wheel hub bearing unit includes the following steps.

[0096] Step 1: To facilitate the geometric description of the bearing, a reference point O is established at the geometric center of the inner bearing (1) and the outer bearing (2).

[0097] The hub bearing unit bears radial load F r , axial load F a The combined effect of the load and moment load M. According to the force translation theorem, the load action position is translated to the reference point O of the two rows of bearings, as shown in Figure 2 The inner bearing is indicated by the subscript "1" and the outer bearing is indicated by the subscript "2".

[0098] Step 2: Slice the roller.

[0099] In order to consider the influence of roller crown, inner ring crown, outer ring crown and raceway inclination on roller load distribution and raceway contact stress, the roller is sliced. The axial position of each roller slice is defined from the large end to the small end along the roller axis. The number of roller slices is n s =81, with the roller length center as the origin, the position coordinates of the thickness center of each roller slice can be expressed as:

[0100] Step three, indicate the position of the roller slice in the bearing.

[0101] The distance between each roller slice and the reference point O along the bearing axial direction is different. The axial distance of the kth slice of the inner bearing roller is:

[0102] The axial distance of the kth slice of the outer bearing roller is:

[0103] The distance between the kth slice of the inner bearing roller and the reference point O along the bearing radial direction is:

[0104] The distance between the kth slice of the outer bearing roller and the reference point O along the bearing radial direction is:

[0105] Step 4: Express the elastic approach between the roller slice and the raceway.

[0106] The displacement approach between the inner ring raceway and the outer ring raceway will lead to elastic contact deformation between the raceway and the roller. The total elastic approach between the kth slice of the jth roller of the inner bearing and the inner and outer ring raceways is:

[0107] The total elastic approach between the kth slice of the jth roller of the outer bearing and the inner and outer ring raceways is:

[0108] Step five shows the reduction in elastic approximation caused by roller slicing and raceway crowning modification.

[0109] For tapered roller bearings, the elastic contact deformation between the roller and the raceway is analyzed along the normal direction of the outer ring raceway. Therefore, the reduction in the elastic approach between the roller slice and the outer ring raceway is the sum of the crown modification of the roller and the outer ring raceway; and for the reduction in the elastic approach between the roller slice and the inner ring raceway, the crown modification of each slice needs to be decomposed to the normal direction of the contact surface between the roller and the outer ring raceway.

[0110] For the inner bearing, the reduction in the elastic approach of the kth slice of the jth roller along the normal direction of the outer ring raceway is: c n1,j,k =c r1,k +c e1,k +(c r1,k +c i1,k )cos(α e1 -α i1 ).

[0111] For the outer bearing, the reduction in the elastic approach of the kth slice of the jth roller along the normal direction of the outer ring raceway is: c n2,j,k =c r2,k +c e2,k +(c r2,k +c i2,k )cos(α e2 -α i2 ).

[0112] Step six, express the roller slice load and the torque it generates.

[0113] For the inner bearing, the contact load between the kth slice of the jth roller and the outer ring raceway is:

[0114] For the outboard bearing, the contact load between the kth slice of the jth roller and the outer ring raceway is:

[0115] The roller slice load will produce a moment action relative to the bearing unit reference point O to balance the external acting moment M.

[0116] For the inner bearing, the moment generated by the contact load component in the vertical direction of the kth slice is:

[0117] The moment generated by the contact load component of the kth slice along the horizontal direction is:

[0118] For the outboard bearing, the moment generated by the contact load component in the vertical direction of the kth slice is:

[0119] The moment generated by the contact load component of the kth slice along the horizontal direction is:

[0120] Step seven, list the equilibrium equations of the hub bearing unit.

[0121] The outer ring of the bearing is in equilibrium under the action of external loads and all roller loads, and the following equilibrium equations are listed:

[0122] Input the design parameters of the hub bearing and the external load, and use the iteration method to solve the nonlinear equations to obtain the unknown variable δ r , δ a The values ​​of and θ are: 0.000879 (mm), 0.003105 (mm) and 0.004381 ​​(°). The solution results can be used to further calculate the load of the roller slices. The loads of all slices of each roller are summed to obtain the contact load between the roller and the outer raceway, as shown in the attached figure. Figure 3 and Figure 4 shown.

[0123] Step 8. The fatigue life of the bearing depends on the rolling element load and equivalent rolling element load corresponding to the basic rated dynamic load of the bearing. By slicing the rollers, the influence of the bearing raceway inclination displacement can be taken into account by calculating the bearing life using the roller slice load. In addition, the edge stress concentration that may occur between the roller end and the raceway surface will shorten the fatigue life of the bearing. The stress correction function is calculated based on the roller slice load and contact stress, and the influence of edge stress concentration on the bearing life is considered through the stress correction function.

[0124] The edge stress concentration correction function of the inner ring raceway is:

[0125] The edge stress concentration correction function of the outer ring raceway is:

[0126] After correction by the edge stress concentration correction function, the roller slice load of the equivalent dynamic load of the rotating ring relative to the load direction is obtained as follows:

[0127] The roller slice load of the equivalent dynamic load on the stationary ring relative to the load direction is:

[0128] The basic reference rating life of the bearing is calculated from the roller slice load corresponding to the rated dynamic load and the roller slice load corresponding to the equivalent dynamic load:

[0129] On the basis of the basic reference rated life, it is necessary to correct the basic reference rated life according to the actual working conditions of the bearing. In order to facilitate the correction calculation of the bearing fatigue life, the equivalent dynamic load of the bearing slice calculated by the roller slice load is defined as:

[0130] After correcting the effect of the application conditions on the life, the corrected reference rated life of the bearing is obtained:

[0131] The fatigue life of the inner bearing is calculated to be 105.76×10 4 km, the fatigue life of the outer bearing is 243.45×10 4 km.

[0132] For bearing units consisting of two rows of bearings, the modified reference rating life of the bearing unit is calculated according to the following formula:

[0133] The fatigue life of the hub bearing unit is calculated to be 78.84×10 4 km.

[0134] It should be noted that the parts not described in detail in this scheme are all prior art, and the above embodiments are only used to illustrate the present invention, but the present invention is not limited to the above embodiments. Any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention fall within the protection scope of the present invention.

Claims

1. A mechanical modeling and life calculation method for a hub bearing unit, characterized in that: The method comprises the following steps: S1, establishing a reference point O at the geometric center of the outer bearing and the inner bearing of the hub bearing unit, S2. Slice the bearing roller. When slicing, cut the roller into multiple slices of the same thickness along the axial direction of the roller, and indicate the position of each roller slice in the roller. S3, represents the relative position relationship between each roller slice and the reference point O in the hub bearing unit, S4, represents the total elastic approach between each roller slice and the bearing raceway, S5, represents the reduction in elasticity of each roller slice and raceway due to crown modification, S6, represents the contact load between each roller slice and the raceway and the torque generated by the contact load, S7. List the balance equations of the hub bearing unit, solve the equations and express the load of each roller slice and the contact load between each roller and the outer raceway. S8. Calculate the fatigue life of the wheel hub bearing unit.

2. The mechanical modeling and life calculation method of a hub bearing unit according to claim 1, characterized in that: S8 calculates the fatigue life of the hub bearing unit, The following steps are included: S8.

1. Express the correction function for the edge stress concentration of the bearing raceway. S8.

2. Express the roller slice load of the equivalent dynamic load by correction with the edge stress concentration correction function. S8.

3. Calculate the basic reference rated life of the bearing from the roller slice load corresponding to the rated dynamic load and the roller slice load of the equivalent dynamic load. S8.

4. Correct the basic reference rated life according to the actual working conditions of the bearing to obtain the corrected reference rated life of the bearing. S8.

5. Calculate the modified reference rating life of the wheel hub bearing unit.

3. The mechanical modeling and life calculation method of a hub bearing unit according to claim 2, characterized in that: In S1, the radial load F borne by the bearing unit r , axial load F a and moment load M is translated to reference point O.

4. The mechanical modeling and life calculation method of a hub bearing unit according to claim 3, characterized in that: In S2, when representing the position of each roller slice in the roller, the positive direction is from the large end to the small end of the roller axis, and the center of the roller length is the origin. The position coordinates of the center of thickness of each roller slice in the roller are: Among them, the meaning of each parameter symbol is as follows: L we - roller length, n s ——Number of roller slices, k——roller slice number.

5. The mechanical modeling and life calculation method of a hub bearing unit according to claim 4, characterized in that: In S3, the relative position of the roller slice in the hub bearing unit and the reference point O includes the axial distance between the roller slice and the reference point O and the distance between the roller slice and the reference point O along the radial direction of the bearing. Axial distance d between the kth slice of the inner bearing roller and the reference point O h1,k for, Among them, the meaning of each parameter symbol is as follows: d h1 ——The axial distance between the center of the inner bearing roller row and the reference point O, x 1,k ——The coordinates of the thickness center of the inner bearing roller slice k in the roller, ——half cone angle of the inner bearing roller, α i1 ——Contact angle of the inner ring raceway of the inner bearing; Axial distance d between the kth slice of the outer bearing roller and the reference point O h2,k for, Among them, the meaning of each parameter symbol is as follows: d h2 ——Axial distance between the center of the outer bearing roller row and the reference point O, x 2,k ——The coordinates of the thickness center of the outer bearing roller slice k in the roller, ——half cone angle of the outer bearing roller, α i2 ——Contact angle of the outer bearing inner ring raceway; The distance d between the kth slice of the inner bearing roller and the reference point O along the bearing radial direction v1,k for, Among them, d m1 ——the distribution circle diameter of the inner bearing roller center; The distance d between the kth slice of the outer bearing roller and the reference point O along the bearing radial direction v2,k for, Among them, d m2 ——The distribution circle diameter of the outer bearing roller center.

6. The mechanical modeling and life calculation method of a hub bearing unit according to claim 5, characterized in that: In S4, the total elastic approach between the roller slice and the bearing raceway includes, The total elastic approach δ between the kth slice of the jth roller of the inner bearing and the inner and outer raceways n1,j,k for, Among them, the meaning of each parameter symbol is as follows: δ r ——External radial load F r The radial displacement of the inner ring raceway of the bearing under the action of θ——The tilt angle displacement of the inner ring raceway of the bearing under the external moment load M, ψ 1,j ——the azimuth angle of the jth roller of the inner bearing on the bearing circumference, α e1 ——Contact angle of the inner bearing outer ring raceway, δ a ——External axial load F a The axial displacement of the inner ring raceway of the bearing under the action of δ 01 ——Axial displacement of the inner ring raceway of the inner bearing under the action of axial preload; The total elastic approach δ between the kth slice of the jth roller of the outer bearing and the inner and outer raceways n2,j,k for, Among them, the meaning of each parameter symbol is as follows: ψ 2,j ——the azimuth angle of the jth roller of the outer bearing on the bearing circumference, α e2 ——Contact angle of the outer ring raceway of the outer bearing, δ 02 ——Axial displacement of the inner ring raceway of the outer bearing under the action of axial preload.

7. The mechanical modeling and life calculation method of a hub bearing unit according to claim 6, characterized in that: In S5, the reduction in elastic approach between the roller slice and the raceway due to crowning modification includes the reduction in elastic approach between the roller slice and the outer ring raceway and the reduction in elastic approach between the roller slice and the inner ring raceway. The reduction in the elastic approach between the roller slice and the outer ring raceway is the sum of the crowning modification of the roller and the outer ring raceway. The reduction in the elastic approach between the roller slice and the inner ring raceway requires the crowning modification of each roller slice to be decomposed into the normal direction of the contact surface between the roller and the outer ring raceway for calculation. Then, The reduction in the elastic approach along the normal direction of the outer ring raceway for the kth slice of the jth roller of the inner bearing c n1,j,k for, c n1,j,k =c r1,k +c e1,k +(c r1,k +c i1,k )cos(α e1 -a i1 ), (8) Among them, the meaning of each parameter symbol is as follows: c r1,k ——Roller crown modification amount at the kth slice position of the inner bearing, c e1,k ——The outer ring raceway crown modification amount at the kth slice position of the inner bearing, c i1,k ——The inner ring raceway crown modification amount at the kth slice position of the inner bearing; The reduction in the elastic approach along the normal direction of the outer ring raceway for the kth slice of the jth roller of the outer bearing is c n2,j,k for, c n2,j,k =c r2,k +c e2,k +(c r2,k +c i2,k )cos(α e2 -a i2 ), (9) Among them, the meaning of each parameter symbol is as follows: c r2,k ——Roller crown modification amount at the kth slice position of the outer bearing, c e2,k ——The outer ring raceway crown modification amount at the kth slice position of the outer bearing, c i2,k ——The inner ring raceway crown modification amount at the kth slice position of the outer bearing.

8. The mechanical modeling and life calculation method of a hub bearing unit according to claim 7, characterized in that: In S6, the contact load between the roller slice and the raceway includes, Contact load q between the kth slice of the jth roller of the inner bearing and the outer ring raceway e1,j,k for, Among them, K ne1 ——The total "load-deformation" constant between the inner bearing roller and the raceway; Contact load q between the kth slice of the jth roller of the outer bearing and the outer ring raceway e2,j,k for, Among them, K ne2 ——The total "load-deformation" constant between the outer bearing roller and the raceway; The roller slice load will generate a moment relative to the bearing unit reference point O to balance the external torque M. The moment generated by the contact load between the roller slice and the raceway includes: For the inner bearing, the moment m generated by the contact load component in the vertical direction of the kth slice is v1,j.k for, The moment m generated by the contact load component in the horizontal direction of the kth slice h1,j,k for, For the outer bearing, the moment m generated by the contact load component in the vertical direction of the kth slice is v2,j,k for, The moment m generated by the contact load component in the horizontal direction of the kth slice h2,j,k for, 9. The mechanical modeling and life calculation method of a hub bearing unit according to claim 8, characterized in that: In S7, the outer ring of the bearing unit is in equilibrium under the action of external loads and all roller loads. The equilibrium equations are listed as follows: Formulas (16) to (18) are based on δ r , δ a The nonlinear equations with unknown quantities θ and θ can be solved by iteration according to the design parameters of the hub bearing and the external load. According to the solution results, the load of each roller slice can be calculated, and the contact load between the roller and the outer raceway can be obtained by summing the loads of all slices in each roller.

10. The mechanical modeling and life calculation method of a hub bearing unit according to claim 9, characterized in that: In S8.1, the correction function for the edge stress concentration of the bearing raceway includes, The edge stress concentration correction function of the inner ring raceway is: Among them, the meaning of each parameter symbol is as follows: D wm ——average diameter of tapered rollers, p Hij,k ——Contact stress between the kth slice of roller j and the inner ring raceway, q j,k ——the load of the kth slice of roller j, γ——Auxiliary function, γ=D wm cosα / d m , α is the contact angle of the outer ring raceway; The edge stress concentration correction function of the outer ring raceway is: Among them, p Hej,k ——Contact stress between the kth slice of roller j and the outer ring raceway; In S8.2, after correction by the edge stress concentration correction function, the roller slice load q of the equivalent dynamic load of the rotating ring relative to the load direction is obtained. ei,k for, Roller slice load q of the equivalent dynamic load on the stationary ring relative to the load direction ee,k for, In S8.3, the basic reference rating life of the bearing is L 10r for, Among them, the meaning of each parameter symbol is as follows: q ci - roller slice load corresponding to the basic dynamic load rating of the inner ring, q ce - roller slice load corresponding to the basic dynamic load rating of the outer ring; In S8.4, in order to facilitate the correction calculation of bearing fatigue life, the equivalent dynamic load P of the bearing slice calculated from the roller slice load is defined as s,k for, Among them, Z is the number of bearing rollers, After correcting the influence of application conditions on life, the corrected reference rated life L of the bearing is obtained. nmr for, Among them, the meaning of each parameter symbol is as follows: a1——Reliability life correction factor, α ISO ——Life correction factor, e C ——pollution coefficient, C ur —— radial load fatigue limit, κ——lubricant viscosity ratio, P s,k ——equivalent dynamic load of the kth slice; In S8.5, the modified reference rating life L for a bearing unit consisting of two rows of bearings nmr for,

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