A method for calculating the impact force of a large modulus friction plate inner hub core plate

Abstract

The application discloses a method for calculating the collision force of a large modulus friction plate inner hub core plate, and specifically comprises the following steps: S1: physical parameters of a to-be-tested friction plate core plate and an experimental friction plate core plate are respectively acquired, whether the two are geometrically similar, kinetically similar and dynamically similar is judged, if yes, S2 is entered, and if not, the method is ended; S2: an angular momentum model of the to-be-tested friction plate core plate and the experimental friction plate core plate is established, and the angular velocity ratio of the to-be-tested friction plate core plate and the experimental friction plate core plate is calculated; S3: inner parameters of the to-be-tested friction plate core plate and the experimental friction plate core plate are respectively acquired, and a collision tooth root stress model of the to-be-tested friction plate core plate and the experimental friction plate core plate is established; and S4: when the tooth root stress of the to-be-tested friction plate core plate and the experimental friction plate core plate is equal, the collision force ratio of the to-be-tested friction plate core plate and the experimental friction plate core plate is calculated. Through the collision of the large modulus core plate equivalent to the small modulus core plate, the collision force of the large modulus core plate is obtained on the basis of the calculation of the collision force of the small modulus core plate.

Description

Technical Field

[0001] This invention relates to the field of mechanical transmission technology, and in particular to a method for calculating the collision force of the inner hub core plate of a large-module friction plate. Background Technology

[0002] Brakes are a crucial core component in power transmission, integrating safety, operability, and comfort for vehicles and ships. The performance of friction pads is an important part of ensuring braking safety, and they are increasingly used in engineering machinery and military vehicles. However, in actual engineering applications, the inner hub and core plate undergo elastic deformation, and the frictional force causes the contact pressure distribution between them to be extremely uneven, leading to frequent abnormal damage to the friction pad core plate.

[0003] The standard ISO and GB / T 10096—1998 both specify a maximum module size of 50mm. The formula for the module size is m=t / π, where t is the tooth pitch. That is, a module size exceeding 50mm is considered a large module, and a module size less than 50mm is considered a small module.

[0004] In the prior art, it is possible to calculate the impact force of the inner hub core plate of a small-module friction pad (refer to CN202210872253.2). However, the damage to the core plate of the friction pad is different for different modules. That is, for large-module friction pads, the prior art cannot directly derive its impact force. Summary of the Invention

[0005] To address the technical problem that existing technologies cannot accurately obtain the magnitude of the inner hub collision force of a large-module friction pad core plate, this invention proposes a method for calculating the collision force of the inner hub core plate of a large-module friction pad. By equating the collision of the large-module core plate with the collision of the small-module core plate, the collision force of the large-module core plate can be accurately obtained based on the accurate calculation of the collision force of the small-module core plate.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A method for calculating the impact force of the inner hub core plate of a large-module friction pad specifically includes the following steps:

[0008] S1: Obtain the physical parameters of the test friction plate core and the experimental friction plate core respectively, and determine whether they are geometrically similar, kinematically similar, and dynamically similar. If they are, proceed to S2; otherwise, end.

[0009] S2: Establish angular momentum models for the test friction plate core and the experimental friction plate core, and calculate the ratio of angular velocities between the test friction plate core and the experimental friction plate core;

[0010] S3: Obtain the internal parameters of the test friction plate core and the experimental friction plate core respectively, and establish the collision tooth root stress model of the test friction plate core and the experimental friction plate core.

[0011] S4: Based on the collision tooth root stress model established in S3, calculate the ratio of the collision force between the core plate of the friction plate to be tested and the core plate of the experimental friction plate, then obtain the collision force of the core plate of the experimental friction plate, and thus calculate the collision force of the core plate of the friction plate to be tested.

[0012] Preferably, in S1, the physical parameters include the core plate contact area, moment of inertia, velocity and acceleration direction, and rotational speed.

[0013] Preferably, step S1 includes the following steps:

[0014] S1-1: The method for determining geometric similarity is as follows:

[0015] Calculate the module ratio and contact area ratio of the test friction plate core plate and the experimental friction plate core plate. If the difference between the module ratio and the contact area ratio is within the preset range, they are judged to be geometrically similar. If the difference between the module ratio and the contact area ratio is not within the preset range, they are judged not to be geometrically similar.

[0016] The formula for calculating the modulus ratio is:

[0017]

[0018] In formula (1), r m This represents the module ratio between the core plate of the friction plate under test and the core plate of the experimental friction plate; m1 represents the module of the core plate of the friction plate under test; m2 represents the module of the core plate of the experimental friction plate.

[0019] The formula for calculating the contact area ratio is:

[0020]

[0021] In formula (2), r s s1 represents the contact area ratio of the friction core plate under test and the experimental friction core plate; s2 represents the contact area of ​​the friction core plate under test; s3 represents the contact area of ​​the experimental friction core plate.

[0022] S1-2: Whether the velocity or acceleration directions of the friction core plate to be tested and the experimental friction core plate are consistent. If they are consistent, it is determined that the motion is similar; if they are inconsistent, it is determined that the motion is not similar.

[0023] S1-3: Substitute the moment of inertia and contact area of ​​the test friction plate core and the experimental friction plate core into the kinematic equations, calculate the speed ratio, and if the speed ratio of the test friction plate core is a positive integer multiple of the speed ratio of the experimental friction plate core, then the dynamics are similar.

[0024] The kinematic equations are:

[0025]

[0026] In formula (3), J1 and J2 represent the moments of inertia of the friction core plate to be tested and the experimental friction core plate, respectively; ω1 and ω2 represent the angular velocities of the friction core plate to be tested and the experimental friction core plate, respectively; and s1 and s2 represent the contact areas of the friction core plate to be tested and the experimental friction core plate, respectively.

[0027] The speed ratio can be obtained according to formula (3):

[0028]

[0029] In formula (4), r s This represents the ratio of the contact area between the core plate of the friction pad under test and the core plate of the experimental friction pad; r j This represents the ratio of the inertia of the experimental friction plate core and the friction plate core under test; r v This indicates the speed ratio between the friction plate core plate under test and the experimental friction plate core plate.

[0030] Preferably, in step S2, the angular momentum models of the friction plate core plate to be tested and the experimental friction plate core plate are respectively:

[0031]

[0032] In formula (5), L1 and L2 represent the angular momentum of the friction core plate at time t1 and time t2, respectively; M1 and M2 represent the collision torque of the inner hub acting on the core plate when the friction core plate under test, the experimental friction core plate and the inner hub collide; t represents the action time from time t1 to time t2.

[0033] Preferably, in step S2, the formula for calculating the angular velocity ratio between the friction plate core plate to be tested and the experimental friction plate core plate is:

[0034] Transforming formula (5) yields:

[0035] M1Δt≈L2-L1≈Δ(J1ω1), M2Δt≈L2-L1≈Δ(J2ω2) (6)

[0036] In formula (6), Δt represents the action time; J1 and J2 represent the moments of inertia of the test friction plate core and the experimental friction plate core, respectively; ω1 and ω2 represent the angular velocities of the test friction plate core and the experimental friction plate core, respectively; M1 and M2 represent the collision torques of the inner hub on the core plate when the test friction plate core, the experimental friction plate core, and the inner hub collide; Δ represents the range of variation.

[0037] M1=F1r1cosα1,Δ(J1ω1)=J1Δω1=J1(1+P1)ω1

[0038] M2=F2r2 cosα2, Δ(J2ω2)=J2Δω2=J2(1+P2)ω2 (7)

[0039] In formula (7), F1 and F2 represent the collision forces of the inner hub on the friction core plate to be tested and the experimental friction core plate, respectively; r1 and r2 represent the pitch circle radii of the friction core plate to be tested and the experimental friction core plate, respectively; P1 and P2 represent the rebound coefficients of the friction core plate to be tested and the experimental friction core plate, respectively; ω1 and ω2 represent the angular velocities of the friction core plate to be tested and the experimental friction core plate, respectively; α1 and α2 represent the pressure angles of the friction core plate to be tested and the experimental friction core plate, respectively; Δω represents the change of the angular velocity of the friction core plate to be tested in time Δt.

[0040] According to formulas (6) and (7), for the friction core plate to be tested and the experimental friction core plate:

[0041] F1r1Δtcosα1=J1(1+P1)ω1, F2r2Δtcosα2=J2(1+P2)ω2 (8)

[0042] In formula (8), F1 and F2 represent the collision forces of the inner hub on the friction core plate under test and the experimental friction core plate, respectively; r1 and r2 represent the pitch circle radii of the inner hub on the friction core plate under test and the experimental friction core plate, respectively; α1 and α2 represent the pressure angles of the inner hub on the friction core plate under test and the experimental friction core plate, respectively; J1 and J2 represent the moments of inertia of the inner hub on the friction core plate under test and the experimental friction core plate, respectively; P1 and P2 represent the rebound coefficients of the inner hub on the friction core plate under test and the experimental friction core plate, respectively; ω1 and ω2 represent the angular velocities of the inner hub on the friction core plate under test and the experimental friction core plate, respectively.

[0043] Transforming formula (8) yields the ratio of angular velocities as follows:

[0044]

[0045] Preferably, in step S3, the internal parameters of the friction plate core plate to be tested and the experimental friction plate core plate include module, pitch circle radius, radius of curvature, tooth tip circle radius, and tooth root circle radius.

[0046] Preferably, in S3, the collision tooth root stress model of the friction core plate to be tested and the experimental friction core plate is as follows:

[0047]

[0048] In formula (9), σ1 and σ2 represent the tooth root impact stress of the test friction plate core and the experimental friction plate core, respectively; m1 and m2 represent the module of the test friction plate core and the experimental friction plate core, respectively; F1 and F2 represent the impact force of the inner hub on the test friction plate core and the experimental friction plate core, respectively; B1 and B2 represent the tooth width of the test friction plate core and the experimental friction plate core, respectively; y σ1 y σ2 α represents the tooth profile coefficient at the highest point of single-tooth meshing of the core plate of the friction plate under test and the core plate of the experimental friction plate, respectively; δα1 α δα2 These represent the tooth root stress concentration parameters of the core plate of the friction plate under test and the core plate of the experimental friction plate, respectively.

[0049] Preferably, in step S3, the formula for calculating the tooth profile coefficient at the highest point of single-tooth meshing of the friction core plate to be tested and the experimental friction core plate is as follows:

[0050]

[0051] In formula (15), y σ1 y σ2 represent the tooth profile coefficients at the highest point of single-tooth meshing of the core plate of the friction plate under test and the core plate of the experimental friction plate, respectively; where,

[0052]

[0053]

[0054] In formula (11), δ1 and δ2 represent the width S of the critical section of the friction plate core plate to be tested, respectively. F1 The ratio of the modulus m1 and the width S of the critical section of the experimental friction plate core plate F2 The ratio to the module m2; λ1 and λ2 represent the lever arm h of the friction plate core plate under test, respectively. α1 The ratio of the modulus m1 and the lever arm h of the experimental friction plate core. α2 The ratio to the modulus m2; α1 and α2 represent the pressure angles of the friction core plate under test and the experimental friction core plate, respectively; r ρ1 r ρ2 These represent the pitch circle radii of the friction plate core plate to be tested and the experimental friction plate core plate, respectively. and c1 * These are the tooth tip height coefficient and clearance coefficient of the core plate of the friction disc under test, respectively. and c2 * These are the tooth tip height coefficient and clearance coefficient of the experimental friction plate core plate, respectively;

[0055] in,

[0056]

[0057] In formula (12), S F1 S F2 These represent the widths of the critical sections.

[0058] in,

[0059]

[0060] In formula (13), r f1 r f2 R represents the tooth tip circle radius of the friction plate core plate under test and the experimental friction plate core plate, respectively; α1 r α2 These represent the root circle radii of the friction core plate under test and the experimental friction core plate, respectively.

[0061] Preferably, in step S3, the formula for calculating the stress concentration parameter at the tooth root is:

[0062]

[0063] In formula (13), α δα1 α δα2 δ1 and δ2 represent the stress concentration parameters at the tooth root of the core plate of the friction plate under test and the core plate of the experimental friction plate, respectively; δ1 and δ2 represent the width S of the critical section of the core plate of the friction plate under test, respectively. F1 The ratio of the modulus m1 and the width S of the critical section of the experimental friction plate core plate F2 The ratio to the module m2; λ1 and λ2 represent the lever arm h of the friction plate core plate under test, respectively. α1 The ratio of the modulus m1 and the lever arm h of the experimental friction plate core. α2 The ratio to the modulus m2.

[0064] Preferably, in step S4, when the root stress of the friction core plate to be tested and the experimental friction core plate are equal:

[0065]

[0066] In formula (14), F'1 and F'2 represent the impact forces experienced by the core plates of the friction plate under test and the core plates of the experimental friction plate during the collision of their gear teeth, respectively.

[0067] By transforming formula (14), the ratio of the collision forces of the friction core plate to be tested and the experimental friction core plate can be obtained:

[0068]

[0069] In formula (15), F1 and F2 represent the collision forces of the inner hub on the test friction plate core and the experimental friction plate core, respectively; B1 and B2 represent the tooth widths of the test friction plate core and the experimental friction plate core, respectively; m1 and m2 represent the modules of the test friction plate core and the experimental friction plate core, respectively; yσ1 y σ2 α represents the tooth profile coefficient at the highest point of single-tooth meshing of the core plate of the friction plate under test and the core plate of the experimental friction plate, respectively; δα1 α δα2 These represent the tooth root stress concentration parameters of the core plate of the friction plate under test and the core plate of the experimental friction plate, respectively.

[0070] In summary, by adopting the above technical solution, the present invention has at least the following beneficial effects compared with the prior art:

[0071] This invention determines the geometric, kinematic, and dynamic similarity between large-module and small-module core boards by using physical parameters, thereby constructing an angular momentum model and a collision tooth root stress model. The collision of the large-module core board is equivalent to the collision of the small-module core board. Based on the accurate calculation of the collision force of the small-module core board, the collision force of the large-module core board can be accurately obtained, thus improving the collision force detection accuracy of the large-module core board. Attached image description:

[0072] Figure 1 This is a schematic diagram of a method for calculating the collision force of the inner hub core plate of a large-module friction pad according to an exemplary embodiment of the present invention. Detailed Implementation

[0073] The present invention will be further described in detail below with reference to embodiments and specific implementation methods. However, this should not be construed as limiting the scope of the above-described subject matter of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.

[0074] In the description of this invention, it should be understood that the terms "longitudinal", "lateral", "up", "down", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0075] like Figure 1 As shown, the present invention provides a method for calculating the collision force of the inner hub core plate of a large-module friction pad, specifically including the following steps:

[0076] S1: Obtain the physical parameters of the test friction plate core and the experimental friction plate core respectively, and determine whether they are geometrically similar, kinematically similar, and dynamically similar. If so, proceed to S2; otherwise, end.

[0077] In this embodiment, the module of the experimental friction plate core is small, and the module of the friction plate core to be tested is large. Current technology can calculate the collision force of the inner hub of the small module friction plate core, so it is necessary to convert the collision of the inner hub of the large module friction plate core into an equivalent collision of the inner hub of the small module friction plate core.

[0078] In this embodiment, the physical parameters include the core plate contact area, moment of inertia, velocity and acceleration direction, rotational speed, etc.

[0079] S1-1: The method for determining geometric similarity is as follows:

[0080] Calculate the modulus ratio and contact area ratio of the test friction plate core plate and the experimental friction plate core plate. If the difference between the modulus ratio and the contact area ratio is within a preset range (e.g., 0.2), they are judged to be geometrically similar. If the difference between the modulus ratio and the contact area ratio is not within the preset range, they are judged not to be geometrically similar.

[0081] The formula for calculating the modulus ratio is:

[0082]

[0083] In formula (1), r m This represents the modulus ratio of the core plate of the friction plate under test to the core plate of the experimental friction plate; m1 represents the modulus of the core plate of the friction plate under test; m2 represents the modulus of the core plate of the experimental friction plate.

[0084] The formula for calculating the contact area ratio is:

[0085]

[0086] In formula (2), r s s1 represents the contact area ratio of the core plate of the friction plate under test and the core plate of the experimental friction plate; s2 represents the contact area of ​​the core plate of the friction plate under test; s3 represents the contact area of ​​the core plate of the experimental friction plate.

[0087] For example, when the module m1 of the friction pad core plate under test is 10 and the contact area s1 is 66.59 mm², 2 The module m2 of the experimental friction pad core plate is 3, and the contact area s2 is 21 mm. 2 When, the modulus ratio Contact area ratio The difference between the module ratio and the contact area ratio is 0.16, which is within the preset range of 0.2, and the geometric similarity is determined.

[0088] S1-2: Whether the velocity or acceleration directions of the friction core plate to be tested and the experimental friction core plate are consistent. If they are consistent, it is determined that the motion is similar; if they are inconsistent, it is determined that the motion is not similar.

[0089] S1-3: The method for determining dynamic similarity is as follows:

[0090] Substitute the moment of inertia and contact area of ​​the test friction plate core and the experimental friction plate core into the kinematic equations to calculate the speed ratio. If the speed of the test friction plate core is a positive integer multiple of the speed ratio of the experimental friction plate core, then the dynamics are considered similar.

[0091] Definition of dynamic similarity: For different models, their directions correspond to the same value, and their magnitude ratios are equal. In other words, for two dynamically similar models, the force polygons formed by the forces acting on corresponding positions on the models are geometrically similar.

[0092] The kinematic equations are:

[0093]

[0094] In formula (3), J1 and J2 represent the moments of inertia of the friction core plate to be tested and the experimental friction core plate, respectively; ω1 and ω2 represent the angular velocities of the friction core plate to be tested and the experimental friction core plate, respectively; and s1 and s2 represent the contact areas of the friction core plate to be tested and the experimental friction core plate, respectively.

[0095] The speed ratio can be obtained according to formula (3):

[0096]

[0097] In formula (4), r s This represents the ratio of the contact area between the core plate of the friction pad under test and the core plate of the experimental friction pad; r j This represents the ratio of the inertia of the experimental friction plate core and the friction plate core under test; r v This indicates the speed ratio between the friction plate core plate under test and the experimental friction plate core plate.

[0098] For example, the module m1 of the friction pad core plate under test is 10, and the contact area s1 is 66.59 mm. 2 The moment of inertia J1 is 96.71 t*mm. 2 The module m2 of the experimental friction pad core plate is 3, and the contact area s2 is 21 mm. 2 At that time, the moment of inertia J1 is 86.038t*mm. 2 ;

[0099] Then the modulus ratio Contact area ratio If the rotational speed of the friction plate core plate to be tested is 148 times that of the core plate of the experimental friction plate core plate, the two have similar dynamics.

[0100] S2: Establish angular momentum models for the test friction plate core and the experimental friction plate core, and calculate the ratio of angular velocities between the test friction plate core and the experimental friction plate core.

[0101] In this embodiment, the angular momentum model of the friction plate core is established, and its expression is:

[0102]

[0103] In formula (5), L1 and L2 represent the angular momentum of the friction core plate at time t1 and time t2, respectively; M1 and M2 represent the collision torque of the inner hub acting on the core plate when the friction core plate under test, the experimental friction core plate and the inner hub collide; t represents the action time from time t1 to time t2.

[0104] Based on the angular momentum model, the collision force and collision torque of the inner hub collision of the friction plate core plate are defined, and the equation (5) is transformed to obtain:

[0105] M1Δt≈L2-L1≈Δ(J1ω1), M2Δt≈L2-L1≈Δ(J2ω2) (6)

[0106] In formula (6), Δt = t2 - t1 represents the action time; J1 and J2 represent the moment of inertia of the test friction plate core and the experimental friction plate core, respectively; ω1 and ω2 represent the angular velocities of the test friction plate core and the experimental friction plate core, respectively; M1 and M2 represent the collision torques of the inner hub on the core plate when the test friction plate core, the experimental friction plate core, and the inner hub collide; Δ represents a range of variation.

[0107] In this embodiment, the collision torque M exerted by the inner hub on the core plate during the collision of the inner hub of the friction plate core plate is:

[0108] M1=F1r1cosα1,Δ(J1ω1)=J1Δω1=J1(1+P1)ω1

[0109] M2=F2r2 cosα2, Δ(J2ω2)=J2Δω2=J2(1+P2)ω2 (7)

[0110] In formula (7), F1 and F2 represent the collision forces of the inner hub on the friction core plate to be tested and the experimental friction core plate, respectively; r1 and r2 represent the pitch circle radii of the friction core plate to be tested and the experimental friction core plate, respectively; P1 and P2 represent the rebound coefficients of the friction core plate to be tested and the experimental friction core plate, respectively; ω1 and ω2 represent the angular velocities of the friction core plate to be tested and the experimental friction core plate, respectively; α1 and α2 represent the pressure angles of the friction core plate to be tested and the experimental friction core plate, respectively; and Δω represents the change in angular velocity of the friction core plate to be tested during the time interval Δt.

[0111] According to formulas (6) and (7), for the friction core plate to be tested and the experimental friction core plate:

[0112] F1r1Δtcosα1=J1(1+P1)ω1, F2r2Δtcosα2=J2(1+P2)ω2 (8)

[0113] In formula (8), F1 and F2 represent the collision forces of the inner hub on the friction core plate to be tested and the experimental friction core plate, respectively; r1 and r2 represent the pitch circle radii of the friction core plate to be tested and the experimental friction core plate, respectively; α1 and α2 represent the pressure angles of the friction core plate to be tested and the experimental friction core plate, respectively; J1 and J2 represent the moments of inertia of the friction core plate to be tested and the experimental friction core plate, respectively; P1 and P2 represent the rebound coefficients of the friction core plate to be tested and the experimental friction core plate, respectively; ω1 and ω2 represent the angular velocities of the friction core plate to be tested and the experimental friction core plate, respectively.

[0114] Formula (8) can be equivalent to:

[0115]

[0116] Wherein, f1 and f2 are the collision frequencies of the friction core plate to be tested and the experimental friction core plate, respectively.

[0117] S3: Obtain the internal parameters of the test friction plate core and the experimental friction plate core respectively, and establish the collision tooth root stress model of the test friction plate core and the experimental friction plate core.

[0118] In this embodiment, the collision tooth root stress model of the friction plate core plate to be tested and the experimental friction plate core plate is established according to the ISO plane section method of the International Organization for Standardization:

[0119]

[0120] In formula (9), σ1 and σ2 represent the tooth root impact stress of the test friction plate core and the experimental friction plate core, respectively; m1 and m2 represent the module of the test friction plate core and the experimental friction plate core, respectively; F1 and F2 represent the impact force of the inner hub on the test friction plate core and the experimental friction plate core, respectively; B1 and B2 represent the tooth width of the test friction plate core and the experimental friction plate core, respectively; y σ1 y σ2 α represents the tooth profile coefficient at the highest point of single-tooth meshing of the core plate of the friction plate under test and the core plate of the experimental friction plate, respectively; δα1 α δα2 These represent the tooth root stress concentration parameters of the core plate of the friction plate under test and the core plate of the experimental friction plate, respectively.

[0121] In this embodiment, the internal parameters of the friction plate core plate to be tested and the experimental friction plate core plate include the module, pitch circle radius, radius of curvature, tooth tip circle radius, tooth root circle radius, etc. These are all known parameters that can be directly obtained.

[0122] The formula for calculating the tooth form factor at the highest point of single-tooth meshing is as follows:

[0123]

[0124] In formula (10), h α1 h α2 S represents the lever arm of the friction plate core plate under test and the experimental friction plate core plate, respectively; F1 S F2 δ represents the width of the collision-prone section of the inner hub, the friction plate core plate under test, and the experimental friction plate core plate, respectively; α1 δ α2 α1 and α2 represent the load angles of the friction core plate under test and the experimental friction core plate, respectively; α1 and α2 represent the pressure angles of the friction core plate under test and the experimental friction core plate, respectively.

[0125] The formula for calculating the stress concentration parameter at the tooth root is as follows:

[0126]

[0127] In formula (11), ρ M1 ρ M2 L represents the radii of curvature of the friction plate core plate under test and the experimental friction plate core plate, respectively; α1 L α2 q represents the intermediate parameters of the friction plate core plate under test and the experimental friction plate core plate, respectively; s1 q s2 These represent the intermediate parameters of the friction core plate under test and the experimental friction core plate, respectively.

[0128] The formula for calculating the width of the critical section is as follows:

[0129]

[0130] In formula (12), r ρ1 r ρ2 These represent the pitch circle radii of the friction plate core plate to be tested and the experimental friction plate core plate, respectively.

[0131] The formula for calculating the lever arm of the friction plate core is as follows:

[0132]

[0133] In formula (13), r f1 r f2 R represents the tooth tip circle radius of the friction plate core plate under test and the experimental friction plate core plate, respectively; α1 r α2 These represent the root circle radii of the friction core plate under test and the experimental friction core plate, respectively.

[0134] In this embodiment, the lever arm and the width representing the critical section of the friction plate core are both proportional to the module, and the radius of curvature is equal to the pitch circle radius. That is, for the friction plate core to be tested and the experimental friction plate core, S F1 =δ1m1,h α1 =λ1m1,S F2 =δ2m2,h α2 =λ2m2, then combining formulas (12) and (13), we can obtain:

[0135]

[0136] In formula (14), δ1 and δ2 represent the width S of the critical section of the friction plate core plate to be tested, respectively. F1 The ratio of the modulus m1 to the critical section S of the experimental friction plate core plate F2 The ratio to the module m2; λ1 and λ2 represent the lever arm h of the friction plate core plate under test, respectively. α1 The ratio of the modulus m1 and the lever arm h of the experimental friction plate core. α2 The ratio to the modulus m2; and c1 * These are the tooth tip height coefficient and clearance coefficient of the core plate of the friction disc under test, respectively. and c2 * β1 and β2 are the tooth tip height coefficient and clearance coefficient of the experimental friction plate core plate, respectively; β1 and β2 are the undetermined coefficients for calculating the tooth thickness of the critical section in the friction plate core plate to be tested and the experimental friction plate core plate, respectively.

[0137] In this embodiment, it is assumed that the load angle δ of the friction core plate is... α The pressure angle α of the friction plate core is equal to that of the friction plate core plate, i.e., δ α1 =α1,δ α2 =α2, then according to formulas (10) and (14), we can obtain:

[0138]

[0139] In formula (15), y σ1 y σ2 These represent the tooth profile coefficients at the highest point of single-tooth meshing of the friction plate core plate under test and the experimental friction plate core plate, respectively.

[0140] In this embodiment, for q s Then, according to formulas (11) and (14), we can obtain:

[0141]

[0142] In formula (16), q s1 q s2β1 and β2 represent the intermediate parameters of the friction core plate under test and the experimental friction core plate, respectively; β1 and β2 represent the undetermined coefficients for calculating the tooth thickness of the critical section in the friction core plate under test and the experimental friction core plate, respectively; δ1 and δ2 represent the width S of the critical section of the friction core plate under test, respectively. F1 The ratio of the modulus m1 and the width S of the critical section of the experimental friction plate core plate F2 The ratio to the modulus m2.

[0143] In this embodiment, for L α Then, according to formulas (11) and (14), we can obtain:

[0144]

[0145] In formula (17), L α1 L α2 δ1 and δ2 represent the intermediate parameters of the friction plate core plate under test and the experimental friction plate core plate, respectively; δ1 and δ2 represent the width S of the critical section of the friction plate core plate under test, respectively. F1 The ratio of the modulus m1 to the critical section S of the experimental friction plate core plate F2 The ratio to the module m2; λ1 and λ2 represent the lever arm h of the friction plate core plate under test, respectively. α1 The ratio of the modulus m1 and the lever arm h of the experimental friction plate core. α2 The ratio to the modulus m2.

[0146] In this embodiment, for the tooth root stress concentration parameter α δα According to formulas (11), (16), and (17), we can obtain:

[0147]

[0148] In formula (18), α δα1 α δα2 δ1 and δ2 represent the stress concentration parameters at the tooth root of the core plate of the friction plate under test and the core plate of the experimental friction plate, respectively; δ1 and δ2 represent the width S of the critical section of the core plate of the friction plate under test, respectively. F1 The ratio of the modulus m1 and the width S of the critical section of the experimental friction plate core plate F2 The ratio to the module m2; λ1 and λ2 represent the lever arm h of the friction plate core plate under test, respectively. α1 The ratio of the modulus m1 and the lever arm h of the experimental friction plate core. α2 The ratio to the modulus m2.

[0149] S4: When the tooth root stress of the test friction plate core plate and the experimental friction plate core plate are equal, calculate the ratio of the collision forces of the test friction plate core plate and the experimental friction plate core plate.

[0150] When the tooth root stress of the friction core plate under test and the experimental friction core plate are equal:

[0151]

[0152] In formula (19), F'1 and F'2 represent the impact forces experienced by the core plates of the friction plate under test and the core plates of the experimental friction plate during the collision of their teeth.

[0153] By transforming formula (19), the ratio of the collision forces of the friction core plate to be tested and the experimental friction core plate can be obtained:

[0154]

[0155] In formula (20), F1 and F2 represent the collision forces of the inner hub on the friction core plate to be tested and the experimental friction core plate, respectively; B1 and B2 represent the tooth widths of the friction core plate to be tested and the experimental friction core plate, respectively; m1 and m2 represent the modules of the friction core plate to be tested and the experimental friction core plate, respectively; y σ1 y σ2 α represents the tooth profile coefficient at the highest point of single-tooth meshing of the core plate of the friction plate under test and the core plate of the experimental friction plate, respectively; δα1 α δα2 These represent the tooth root stress concentration parameters of the core plate of the friction plate under test and the core plate of the experimental friction plate, respectively.

[0156] In this embodiment, the meaning of formula (20) is to equate the large-module core plate to a small-module core plate, thereby accurately calculating its collision force. That is, the collision force and other parameters of the experimental friction plate core plate can be directly obtained, so the collision force of the friction plate core plate to be tested can be calculated according to formula (20).

[0157] Those skilled in the art will understand that the above embodiments are specific examples of implementing the present invention, and in practical applications, various changes in form and detail may be made without departing from the spirit and scope of the present invention.

Claims

1. A method for calculating the impact force of the inner hub core plate of a large-module friction pad, characterized in that, Specifically, the following steps are included: S1: Obtain the physical parameters of the test friction plate core and the experimental friction plate core respectively, and determine whether they are geometrically similar, kinematically similar, and dynamically similar. If they are, proceed to S2; otherwise, end. S2: Establish angular momentum models for the test friction plate core and the experimental friction plate core, and calculate the ratio of angular velocities between the test friction plate core and the experimental friction plate core; S3: Obtain the internal parameters of the test friction plate core and the experimental friction plate core respectively, and establish the collision tooth root stress model of the test friction plate core and the experimental friction plate core. S4: Based on the collision tooth root stress model established in S3, calculate the ratio of the collision force of the core plate of the friction plate to be tested and the core plate of the experimental friction plate, then obtain the collision force of the core plate of the experimental friction plate, and thus calculate the collision force of the core plate of the friction plate to be tested. In S1, the physical parameters include the core plate contact area, moment of inertia, velocity and acceleration direction, and rotational speed. S1 includes the following steps: S1-1: The method for determining geometric similarity is as follows: Calculate the module ratio and contact area ratio of the test friction plate core plate and the experimental friction plate core plate. If the difference between the module ratio and the contact area ratio is within the preset range, they are judged to be geometrically similar. If the difference between the module ratio and the contact area ratio is not within the preset range, they are judged not to be geometrically similar. The formula for calculating the modulus ratio is: In formula (1), This indicates the modulus ratio between the core plate of the friction plate under test and the core plate of the experimental friction plate; Indicates the module of the friction plate core plate under test; Indicates the module of the experimental friction plate core plate; The formula for calculating the contact area ratio is: In formula (2), This indicates the ratio of the contact area between the core plate of the friction pad under test and the core plate of the experimental friction pad; This indicates the contact area of ​​the friction pad core plate under test; This indicates the contact area of ​​the core plate of the experimental friction pad; S1-2: Whether the velocity or acceleration directions of the friction core plate to be tested and the experimental friction core plate are consistent. If they are consistent, it is determined that the motion is similar; if they are inconsistent, it is determined that the motion is not similar. S1-3: Substitute the moment of inertia and contact area of ​​the test friction plate core and the experimental friction plate core into the kinematic equations, calculate the speed ratio, and if the speed ratio of the test friction plate core is a positive integer multiple of the speed ratio of the experimental friction plate core, then the dynamics are similar. The kinematic equations are: In formula (3), , These represent the moments of inertia of the friction plate core plate under test and the experimental friction plate core plate, respectively. , These represent the angular velocities of the friction core plate under test and the experimental friction core plate, respectively. , These represent the contact areas of the friction plate core plate under test and the experimental friction plate core plate, respectively. The speed ratio can be obtained according to formula (3): In formula (4), This indicates the ratio of the contact area between the core plate of the friction pad under test and the core plate of the experimental friction pad; This represents the ratio of the inertia of the experimental friction plate core and the friction plate core under test. This indicates the speed ratio between the friction plate core plate under test and the experimental friction plate core plate.

2. The method for calculating the collision force of the inner hub core plate of a large-module friction plate as described in claim 1, characterized in that, In S2, the angular momentum models of the friction plate core to be tested and the experimental friction plate core are as follows: ， （5） In formula (5), , These represent the friction plate core plate. Time and Angular momentum at time t; , The values ​​represent the collision torques exerted by the inner hub on the core plate during the collisions of the test friction plate core plate, the experimental friction plate core plate, and the inner hub, respectively; t represents time. Time The duration of action.

3. The method for calculating the collision force of the inner hub core plate of a large-module friction plate as described in claim 1, characterized in that, In S2, the formula for calculating the angular velocity ratio between the friction core plate to be tested and the experimental friction core plate is as follows: Transforming formula (5) yields: In formula (6), Indicates the duration of action; and represent the moments of inertia of the friction plate core plate under test and the experimental friction plate core plate, respectively; , These represent the angular velocities of the friction core plate under test and the experimental friction core plate, respectively. , These represent the collision torques exerted by the inner hub on the core plate during the collisions of the test friction plate core plate, the experimental friction plate core plate, and the inner hub, respectively. Indicates the range of changes; In formula (7), , These represent the collision forces of the inner hub on the friction plate core plate under test and the experimental friction plate core plate, respectively. , The radii of the pitch circles of the friction plate cores under test and the experimental friction plate cores are respectively. , These represent the rebound coefficients of the friction core plate under test and the experimental friction core plate, respectively. , These represent the angular velocities of the friction core plate under test and the experimental friction core plate, respectively. , These represent the pressure angles of the friction plate core plate under test and the experimental friction plate core plate, respectively. Indicates that the core plate of the friction plate under test is in Change in angular velocity over time; According to formulas (6) and (7), for the friction core plate to be tested and the experimental friction core plate: In formula (8), , These represent the collision forces of the inner hub on the friction plate core plate under test and the experimental friction plate core plate, respectively. , These represent the pitch circle radii of the inner hub, namely the core plate of the friction plate under test and the core plate of the experimental friction plate. , These represent the pressure angles of the inner hub on the friction plate core plate under test and the experimental friction plate core plate, respectively. , These represent the moments of inertia of the inner hub of the friction plate core plate under test and the experimental friction plate core plate, respectively. and represent the rebound coefficients of the inner hub on the friction core plate under test and the experimental friction core plate, respectively; , These represent the angular velocities of the inner hub and the friction core plate under test and the experimental friction core plate, respectively. Transforming formula (8) yields the ratio of angular velocities as follows: 。 4. The method for calculating the collision force of the inner hub core plate of a large-module friction plate as described in claim 1, characterized in that, In S3, the internal parameters of the friction core plate to be tested and the experimental friction core plate include module, pitch circle radius, radius of curvature, tooth tip circle radius, and tooth root circle radius.

5. The method for calculating the collision force of the inner hub core plate of a large-module friction plate as described in claim 1, characterized in that, In S3, the collision tooth root stress model of the friction plate core plate to be tested and the experimental friction plate core plate is as follows: In formula (9), , These represent the tooth root impact stresses of the core plate of the friction plate under test and the core plate of the experimental friction plate, respectively. , These represent the modulus of the friction plate core plate under test and the experimental friction plate core plate, respectively. , These represent the collision forces of the inner hub on the friction plate core plate under test and the experimental friction plate core plate, respectively. , These represent the tooth widths of the friction plate core plate under test and the experimental friction plate core plate, respectively. , These represent the tooth profile coefficients at the highest point of single-tooth meshing of the friction plate core plate under test and the experimental friction plate core plate, respectively. , These represent the tooth root stress concentration parameters of the core plate of the friction plate under test and the core plate of the experimental friction plate, respectively.

6. The method for calculating the impact force of the inner hub core plate of a large-module friction plate as described in claim 5, characterized in that, In S3, the formula for calculating the tooth profile coefficient at the highest point of single-tooth meshing of the test friction plate core plate and the experimental friction plate core plate is as follows: In formula (15), , represent the tooth profile coefficients at the highest point of single-tooth meshing of the core plate of the friction plate under test and the core plate of the experimental friction plate, respectively; where, , , ； , , ， （11） In formula (11), , , respectively represent the width of the critical section of the core plate of the friction pad under test. With modulus The proportion and width of the critical section of the experimental friction plate core plate With modulus The proportion; , These represent the lever arms of the friction plate core plate under test. With modulus The ratio and the lever arm of the experimental friction plate core. With modulus The proportion; These represent the pressure angles of the friction plate core plate under test and the experimental friction plate core plate, respectively. , These represent the pitch circle radii of the friction plate core plate to be tested and the experimental friction plate core plate, respectively. and These are the tooth tip height coefficient and clearance coefficient of the core plate of the friction disc under test, respectively. and These are the tooth tip height coefficient and clearance coefficient of the experimental friction plate core plate, respectively; in, In formula (12), , These represent the widths of the critical sections; in, In formula (13), , These represent the tooth tip circle radii of the core plate of the friction plate under test and the core plate of the experimental friction plate, respectively; , These represent the root circle radii of the friction core plate under test and the experimental friction core plate, respectively.

7. The method for calculating the impact force of the inner hub core plate of a large-module friction plate as described in claim 5, characterized in that, In S3, the formula for calculating the stress concentration parameter at the tooth root is: In formula (13), , These represent the tooth root stress concentration parameters of the core plate of the friction plate under test and the core plate of the experimental friction plate, respectively. , These represent the widths of the critical cross-sections of the friction pad core plate under test. With modulus The proportion and width of the critical section of the experimental friction plate core plate With modulus The proportion; , These represent the lever arms of the friction plate core plate under test. With modulus The ratio and the lever arm of the experimental friction plate core. The ratio to the modulus.

8. The method for calculating the impact force of the inner hub core plate of a large-module friction plate as described in claim 5, characterized in that, In step S4, when the root stress of the tooth of the friction core plate to be tested and the experimental friction core plate are equal: In formula (14), , These represent the impact forces experienced by the core plates of the friction disc under test and the core plates of the experimental friction disc during the collision of their gear teeth, respectively. By transforming formula (14), the ratio of the collision forces of the friction core plate to be tested and the experimental friction core plate can be obtained: In formula (15), , These represent the collision forces of the inner hub on the friction plate core plate under test and the experimental friction plate core plate, respectively. , These represent the tooth widths of the friction plate core plate under test and the experimental friction plate core plate, respectively. , These represent the modulus of the friction plate core plate under test and the experimental friction plate core plate, respectively. , These represent the tooth profile coefficients at the highest point of single-tooth meshing of the friction plate core plate under test and the experimental friction plate core plate, respectively. , These represent the tooth root stress concentration parameters of the core plate of the friction plate under test and the core plate of the experimental friction plate, respectively.

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