A method for calculating meshing impact vibration coefficient when a straight gear tooth root crack fault occurs

Abstract

The application provides a meshing impact vibration coefficient calculation method for a straight gear root crack fault, comprising a driving wheel and a driven wheel, wherein the driving wheel and the driven wheel are straight gears, a tooth root of the driving wheel has a crack fault, and the meshing impact vibration coefficient is calculated through the following steps: step 1) calculating a corresponding reverse angle θ of a driving wheel meshing point position change c ; step 2) calculating a meshing impact force F generated by the driving wheel tooth root crack fault z ; step 3) calculating a theoretical meshing force F of the driving wheel without a fault; and step 4) calculating an impact vibration coefficient V of the gear meshing when the driving wheel tooth root has a crack fault z . The method considers the influence of the tooth root crack fault on the actual meshing point position, calculates the meshing impact force in the tooth root crack fault state, and obtains the impact vibration coefficient of the straight gear with the tooth root crack fault, thereby providing a theoretical basis for the establishment of a gear vibration signal model using an impact function, and being more in line with the actual situation.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of dynamic modeling of gear transmission system, in particular, relates to a kind of meshing impact vibration coefficient calculation method when straight tooth gear root crack fault. BACKGROUND

[0002] Gear vibration signal phenomenological modeling is an effective modeling method in dynamic modeling and fault diagnosis of gear transmission system. By modeling the vibration signal of gear transmission system, the frequency spectrum structure under different health conditions of the system can be obtained, thereby providing a theoretical basis for gear fault diagnosis. For example, in the invention patent with application number CN201410365909.7 and the invention name of a normal single-stage epicyclic gear train phenomenological modeling method considering meshing phase difference, a vibration signal simulation model is established to provide a basis for fault diagnosis of single-stage epicyclic gear train.

[0003] However, meshing impact will occur during gear meshing. In the modeling process, in order to accurately simulate the impact vibration characteristics of the gear, an impact function is usually used to simulate the meshing impact phenomenon when the gear is meshing. In the impact function, the size of the impact vibration coefficient will have a great influence on the time domain waveform and frequency spectrum structure of the vibration signal phenomenological model.

[0004] In the existing impact function, the impact vibration coefficient is usually valued according to experience. Although this method can roughly describe the characteristics of the impact vibration when the gear enters the meshing, it lacks theoretical basis, is not rigorous enough, and cannot comprehensively consider many factors that affect the meshing impact force in the actual meshing process.

[0005] Especially when the gear has a root crack fault, the stiffness of the gear will change, and the meshing point position of the gear will shift slightly, which will have a great influence on the impact force. The impact function is closely related to these parameters, which will cause great changes in the impact vibration coefficient.

[0006] The above factors cause the existing impact vibration coefficient description method to be unable to accurately reflect the vibration characteristics of the gear system when the gear has a root crack fault, which makes the fault diagnosis of the gear system more difficult.

[0007] In the above problems, the meshing stiffness of the gear is described in detail in the invention patent with application number CN201510634304.8 and the name of a method for modeling the meshing of a spalling gear based on meshing stiffness, but it is not associated with the study of the impact vibration coefficient.

[0008] In order to solve the above problems, people have been seeking an ideal technical solution. SUMMARY

[0009] The present application aims at the deficiencies of the prior art, and provides a meshing impact vibration coefficient calculation method for a straight gear with a tooth root crack fault, which considers the influence of the tooth root crack fault on the actual meshing point position, calculates the meshing impact force in the tooth root crack fault state, and provides a theoretical basis for the establishment of a gear vibration signal model using an impact function, and is more in line with the actual situation.

[0010] In order to achieve the above-mentioned purpose, the technical scheme adopted by the present application is as follows: a meshing impact vibration coefficient calculation method for a straight gear with a tooth root crack fault, comprising a driving wheel and a driven wheel, wherein the driving wheel and the driven wheel are straight gears, and the tooth root of the driving wheel has a crack fault, and the calculation of the meshing impact vibration coefficient is carried out through the following steps:

[0011] Step 1) calculating the corresponding reverse angle θ of the driving wheel meshing point position change c

[0012] Step 2) calculating the meshing impact force F generated by the meshing of the driving wheel with a tooth root crack fault z

[0013] Step 3) calculating the theoretical meshing force F of the driving wheel without a fault

[0014] Step 4) calculating the impact vibration coefficient V of the gear meshing when the tooth root of the driving wheel has a crack fault z

[0015] The present application has outstanding substantial features and significant progress compared with the prior art. Specifically, the present application starts from the principle of gear meshing transmission, considers the influence of the tooth root crack fault on the meshing point position when the driving wheel is a straight gear, calculates the size of the gear meshing impact force when the driving wheel has a tooth root crack fault, and then calculates the size of the theoretical meshing force of the driving wheel without a fault, so as to reflect the impact vibration coefficient of the driving wheel with a tooth root crack fault when the driving wheel is a straight gear through the ratio of the two forces.

[0016] The present method has the advantages over the traditional assignment method in that it establishes a meshing impact vibration coefficient calculation method for a straight gear with a tooth root crack fault, changes the previous method of assigning the impact vibration coefficient through experience, and has a theoretical basis; and overcomes the inaccuracy of the traditional assignment method in the tooth root crack fault state, and provides a theoretical basis for the establishment of a gear vibration signal model using an impact function, so that the phenomenological modeling method can be used to model and analyze the gear with a tooth root crack fault. BRIEF DESCRIPTION OF DRAWINGS

[0017] Fig. 1 ​​​is a flow chart of a meshing impact vibration coefficient calculation method in a straight gear root crack fault in the present application.

[0018] Fig. 2 is a principle diagram of a straight gear crack fault and a reverse angle calculation principle diagram in step 1) in the present application.

[0019] Fig. 3 is a meshing impact principle diagram in a driving wheel fault in the present application. DETAILED DESCRIPTION

[0020] The technical solutions of the present application are described in further detail below through a specific embodiment.

[0021] As shown in Figs. 1-3 , a meshing impact vibration coefficient calculation method in a straight gear root crack fault, the physical structure basis of the present calculation method includes a driving wheel and a driven wheel, the driving wheel and the driven wheel are straight gears, and the driving wheel has a root crack fault.

[0022] The calculation of the meshing impact vibration coefficient is carried out through the following steps:

[0023] Step 1) as shown in Fig. 2 , the reverse angle θ c ′ corresponding to the change of the driving wheel meshing point position is calculated. c ′ is calculated through the following formula:

[0024]

[0025] Wherein, a1 is the arc length turned by the actual meshing point position change caused by the root crack fault;

[0026] r ac is the addendum circle radius of the driven wheel.

[0027] Step 2) the meshing impact force F z generated by the meshing of the driving wheel root crack fault is calculated.

[0028]

[0029]

[0030]

[0031]

[0032] Wherein,

[0033] Δv n_z represents the relative speed difference between the driving wheel and the driven wheel when the driving wheel has a root crack fault.

[0034] b represents the tooth width of the driving wheel;

[0035] k z the meshing stiffness of the gear tooth when there is a root crack fault in the driving wheel, which is calculated according to the potential energy method: the gear tooth is simplified as a cantilever beam on the root circle, the Hertz contact energy, the bending potential energy, the axial compression potential energy and the shear potential energy generated due to deformation of the gear tooth under load are calculated; correspondingly, the gear meshing stiffness can be obtained by superimposing the Hertz contact stiffness, the bending stiffness, the axial compression stiffness and the shear stiffness corresponding to the above four parts of energy, so the technology of calculating the gear meshing stiffness by using the potential energy method is relatively mature, and will not be expanded here;

[0036] J z the moment of inertia of the driving wheel;

[0037] J c_z the moment of inertia of the driven wheel;

[0038] r bc_z the instantaneous base circle radius of the driven wheel;

[0039] r bz the base circle radius of the driving wheel;

[0040] r hz the inner hole radius of the gear hub of the driving wheel;

[0041] r hc the inner hole radius of the gear hub of the driven wheel;

[0042] In this step, the meshing impact force F z There are several necessary parameters that need to be further calculated, and the general process is as follows:

[0043] First, the distance from the center of the driving wheel to the meshing point A is calculated

[0044] l OzA = [r ac 2 + (r z + r c ) 2 - 2r ac (r z + r c )cosη c ] 1 / 2 (6)

[0045] wherein,

[0046] r ac the addendum circle radius of the driven wheel;

[0047] rz and r c These are the pitch circle radii of the driving and driven wheels, respectively.

[0048] Center O of the driven wheel c The distance to the engagement point A;

[0049] η c for The angle between the center lines of the driving wheel and the driven wheel.

[0050] Secondly, calculation The angle η between the center lines of the driving wheel and the driven wheel c :

[0051] η c =γ c +θ c +θ c (7)

[0052] in,

[0053] γ c for The angle between the center lines of the driving wheel and the driven wheel, A1′ is the angle θ through which the initial engagement point A rotates. c +θ c The corresponding meshing point after '.

[0054] θ c for arrive The included angle between them, A′ is the theoretical engagement point when the driving wheel is in good condition;

[0055] θ c 'The reverse angle is caused by a crack in the root of the drive gear tooth.'

[0056] Secondly, when the driving gear has a tooth root crack fault, calculate the relative speed difference Δv between the driving gear and the driven gear. n_z It is calculated using the following formula:

[0057] Δv n_z =v Az cosβ z -v Ac cosβ c (8)

[0058]

[0059] v Ac =r ac ω c (10)

[0060] in:

[0061] v Az is the instantaneous speed of the driving wheel;

[0062] v Ac is the instantaneous speed of the driven wheel;

[0063] is the center of the driving wheel O z to the distance from the meshing point A;

[0064] r ac is the tip circle radius of the driven wheel;

[0065] is the instantaneous common normal line of the two tooth profiles;

[0066] β z is the angle between v Az and ;

[0067] β c is the angle between v Ac and ;

[0068] ω z , ω c are the angular velocities of the driving wheel and the driven wheel, respectively.

[0069] At this point, the meshing impact force F z generated by the meshing of the driving wheel with a cracked tooth root fault in step 2) can be calculated.

[0070] Step 3) Calculate the theoretical meshing force F of the driving wheel without fault:

[0071]

[0072] wherein,

[0073] T is the torque when the gear is in transmission;

[0074] d z is the pitch diameter of the driving wheel.

[0075] Step 4) Calculate the impact vibration coefficient V z of the gear meshing when the driving wheel has a cracked tooth root fault.

[0076]

[0077] This calculation method considers the impact of the tooth root crack fault of the gear on the meshing point position according to the meshing transmission mechanism of the gear, and calculates the impact vibration coefficient when the tooth root crack fault occurs according to the obtained reverse angle.

[0078] The method has the advantages that, unlike the previous experience-based assignment of the impact vibration coefficient, the impact vibration coefficient under the gear root crack fault is obtained from the gear meshing vibration mechanism, the influence of the gear root crack fault on the meshing impact force is considered, and the theoretical meshing impact force when the gear is fault-free is combined, which can provide an effective theoretical basis for the establishment of a gear vibration signal model.

[0079] The method overcomes the inaccuracy of the traditional assignment method when the gear root crack fault occurs, provides a theoretical basis for the establishment of a gear vibration signal model using an impact function, and further enables the use of a phenomenological modeling method to model and analyze the gear with the gear root crack fault.

[0080] Finally, it should be noted that: the above examples are only used to illustrate the technical solutions of the present application, but not to limit it; although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the specific embodiments of the present application can be modified or some technical features can be replaced by equivalent ones; without departing from the spirit of the technical solutions of the present application, they should be covered in the technical solution range of the present application claimed.

Claims

1. A method of calculating a meshing impact vibration coefficient at the time of a gear root crack failure of a spur gear, characterized by: Including driving wheel and driven wheel, the driving wheel and driven wheel are all straight gears, the tooth root of the driving wheel is cracked, the calculation of the meshing impact vibration coefficient is carried out through the following steps: Step 1) calculating the inverse angle θ corresponding to the change in position of the engagement point of the driving wheel c '; Step 2) Calculate the meshing impact force F generated by the meshing when the tooth root of the driving wheel is cracked z ; The meshing impact force F z The calculation formula is as follows: Wherein, Δv n_z the relative speed difference between the driving wheel and the driven wheel when the driving wheel has a root crack fault; B represents the tooth width of the driving wheel; k z Meshing stiffness of the gear tooth when there is a root crack failure for the driving wheel; J z Ia is the moment of inertia for the driven wheel; J c_z moment of inertia of the driven wheel; r bc_z the instantaneous base circle radius of the driven wheel; r bz R is the base circle radius of the driving wheel; Step 3) calculate the theoretical meshing force F of the driving wheel without fault; Step 4) Calculate the impact vibration coefficient V of the gear meshing when the tooth root of the driving wheel is cracked z , 2. The method of claim 1, wherein the method is characterized by: In step 2), when the driving wheel has a root crack fault, the relative speed difference Δv between the driving wheel and the driven wheel n_z is calculated by the following formula: Δv n_z = v Az cos β z - v Ac cos β c v Ac = r ac ω c Wherein: v Az V is the instantaneous speed of the driving wheel; v Ac instantaneous speed of the driven wheel; For the driving wheel center O z Distance to the point of engagement A; r ac addendum circle radius of the driven wheel; is the instantaneous common normal to both profiles; beta z for v Az with the angle between beta c for v Ac with the angle between ω z , ω c are the angular velocities of the driving and driven wheels, respectively.

3. The method of claim 2, wherein the meshing impact vibration coefficient is calculated when a crack in a tooth root of the spur gear occurs. In step 2), the center O of the driving wheel z Distance to the point of engagement A is obtained by the following equation: Wherein, r ac addendum circle radius of the driven wheel; r z and r c are the pitch radii of the driving and driven wheels, respectively; For the center of the driven wheel O c Distance to the point of engagement A; η c For to the angle between the center lines of the driving and driven wheels.

4. The method of claim 3, wherein the meshing impact vibration coefficient is calculated when a crack in a tooth root of the spur gear occurs. In step 2), the angle η between the center lines of the driving wheel and the driven wheel c is calculated by the following formula: η c = γ c + θ c + θ c ' Wherein, gamma c for to the angle between the center lines of the driving and driven wheels, A1' is the initial point of engagement A rotated through an angle θ c + theta c the corresponding point of engagement after θ c For To the angle between A' is the theoretical meshing point of the driving wheel in good condition; θ c The angle of reversal due to the root crack of the driving wheel.

5. The method of claim 4, wherein the meshing impact vibration coefficient is calculated when a crack in a tooth root of the spur gear occurs. In step 1), the angle of reversal θ caused by the root crack of the driving gear tooth c is calculated by the following equation: Wherein, a1 is the arc length turned by the change of the actual meshing point position caused by the tooth root crack fault; r ac addendum circle radius of the driven wheel.

6. The method of claim 5, wherein the meshing impact vibration coefficient is calculated when a crack in a tooth root of the spur gear occurs. The theoretical meshing force F of the driving wheel without fault is calculated by the following formula: Wherein, T is the torque when the gear is driven; d z Diameter of pitch circle of driving wheel.

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