CN113340626A - Method for measuring real-time interference magnitude between wheel axles and measurement early warning device - Google Patents

Method for measuring real-time interference magnitude between wheel axles and measurement early warning device Download PDF

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CN113340626A
CN113340626A CN202110571778.8A CN202110571778A CN113340626A CN 113340626 A CN113340626 A CN 113340626A CN 202110571778 A CN202110571778 A CN 202110571778A CN 113340626 A CN113340626 A CN 113340626A
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wheel
axle
predetermined point
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interference
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CN113340626B (en
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王旭
张玉茹
喻学广
刘新田
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Shanghai University of Engineering Science
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Abstract

The invention belongs to the technical field of traffic measurement, and discloses a method for measuring real-time interference between wheel axles, which can well measure the real-time interference of running wheels and axles. The invention also discloses a device for measuring and early warning the real-time interference magnitude between the wheel shafts, which can monitor the running wheel shafts in real time and early warn in time when the real-time interference magnitude does not meet the requirement.

Description

Method for measuring real-time interference magnitude between wheel axles and measurement early warning device
Technical Field
The invention belongs to the technical field of traffic measurement, and particularly relates to a method for measuring real-time interference magnitude between wheel axles and a measurement early warning device.
Background
In the design of a wheel axle of a train, the wheels are connected and matched with the axle in an interference fit mode. The size difference between the wheel hole and the axle is mainly utilized to cause the physical deformation to be generated on the combination surface of the wheel hole and the axle, and the wheel and the axle are tightly combined together through the contact stress generated by the deformation.
The interference fit can generate contact stress on the contact surface of the wheel and the shaft, if the interference is too large, the contact stress is increased, the axle is damaged, and the service life of the wheel shaft is shortened; if the interference is too small, the interference is reduced by the centrifugal force generated on the wheels and the axles when the train moves at a high speed, so that the contact stress cannot meet the tight connection of the axles, and safety accidents are caused.
At present, no perfect means is available for measuring the interference magnitude of the running wheels and axles and monitoring in real time.
Disclosure of Invention
Aiming at the defects of the prior art, through intensive research, the axle is only pressed by the inner wall of the hub of the wheel, and the inner wall of the hub of the wheel is only pressed by the axle, so that the matching problem of the wheel and the axle can be converted into a combined cylinder model, can be analyzed according to the strength problem of the thick-wall cylinder, when the maximum stress between the joint surfaces of the interference fit of the wheel and the axle is less than the minimum stress allowed by the parts without generating plastic deformation, the surface of the axle circumferential surface and the surface of the wheel hole inner circumferential surface are not subjected to plastic deformation, the connection and combination surface is in an elastic deformation state, the contact stress between the faying surfaces can be deduced by the theory of elasticity, and the forces to which the wheel and the axle are subjected in the axle direction are much smaller than those in other directions when the wheel axle is driven, so that the forces can be ignored, i.e. the wheel and the axle are equivalent to a thin disc and a thin axle, respectively.
The invention provides a method for measuring the real-time interference magnitude between wheel axles and a measurement early warning device, which can well measure the real-time interference magnitude of the wheels and axles in running and can monitor in real time.
In order to achieve the purpose, the invention provides the following technical scheme:
a method for measuring the real-time interference between wheel shafts is applied to the wheel shaft formed by assembling wheels and an axle by using initial interference, and is characterized by comprising the following steps of:
step S1, making the wheel shaft still, and obtaining the wheel shaft static contact stress on the assembly surface of the wheel and the axle based on the outer diameter of the wheel, the outer diameter of the axle and the inner diameter of the axle;
step S2, rotating the wheel shaft, setting wheel preset points on the wheel and axle preset points on the axle;
step S3, establishing an axle elastic mechanical differential equation related to the rotating centrifugal force on the wheel axle and the stress of the axle preset point in three dimensional directions, and establishing a wheel elastic mechanical differential equation related to the rotating centrifugal force on the wheel axle and the stress of the wheel preset point in three dimensional directions;
step S4: establishing an axle elastic mechanical constitutive equation and an axle elastic mechanical geometric equation related to the stress, the strain value and the displacement of the axle predetermined point in three dimensional directions, and establishing a wheel elastic mechanical constitutive equation and a wheel elastic mechanical geometric equation related to the stress, the strain value and the displacement of the wheel predetermined point in three dimensional directions;
step S5: obtaining the radial displacement of the axle and the radial displacement of the wheel based on the static contact stress of the axle, the elastic mechanical differential equation of the wheel or the axle, the elastic mechanical constitutive equation of the wheel or the axle and the elastic mechanical geometric equation of the wheel or the axle,
step S6: and obtaining real-time interference according to the initial interference, the axle radial displacement and the wheel radial displacement.
Preferably, in step S1, the wheel axles are in static contactStress pcComprises the following steps:
Figure BDA0003082974610000021
delta is the initial interference, a is the inner diameter of the axle, b is the outer diameter of the axle, c is the outer diameter of the wheel, E1Is the modulus of elasticity of the wheel, E2Is the modulus of elasticity, μ, of the axle1Is the Poisson's ratio, mu, of the wheel2Is the poisson ratio of the axle.
Preferably, the material of the wheel and the axle is the same, the wheel axle rotates at a constant preset angular speed, the radial distance of a preset point of the wheel is taken as the outer radial distance, the radial distance of a preset point of the axle is taken as the inner radial distance,
the differential equation of wheel elasticity is:
Figure BDA0003082974610000031
σorradial stress, σ, at predetermined points of the wheeloθStress in the circumferential direction at predetermined points of the wheel, σozPositive stress at predetermined points of the wheel, τozThe axial shear stress of the wheel at a predetermined point, rho is the material density of the wheel shaft, omega is a predetermined angular velocity, or is an outer radial distance,
the elastic mechanical differential equation of the axle is as follows:
Figure BDA0003082974610000032
σirradial stress, σ, for predetermined points of the axleiθCircumferential stress, σ, for predetermined points of the axleizPositive stress at predetermined point of axle, tauizThe axle axial shear stress at a predetermined point of the axle is ir the inner radial distance.
Further, the wheel elastic mechanical constitutive equation is as follows:
Figure BDA0003082974610000033
εorvalue of radial strain, epsilon, for predetermined point of wheeloθValue of circumferential strain, epsilon, for predetermined point of wheelozThe axial strain value of a wheel at a preset point is shown, mu is the Poisson's ratio of a wheel shaft,
the elastic mechanical constitutive equation of the axle is as follows:
Figure BDA0003082974610000034
εirvalue of radial strain, epsilon, for predetermined point of axleiθValue of circumferential strain, epsilon, for predetermined points of the axleizThe axial strain value of the axle at a predetermined point, E is the modulus of elasticity of the wheel axle,
the wheel elastic mechanics geometric equation is as follows:
Figure BDA0003082974610000041
uoamount of radial displacement, gamma, of predetermined point of wheelorθValue of shear strain, v, for predetermined point of wheeloA tangential displacement angle at a predetermined point of the wheel at an outer radial distance of the wheel, (or) a circumferential displacement amount at the predetermined point of the wheel at the outer radial distance of the wheel corresponding to d theta,
the elastic mechanical geometrical equation of the axle is as follows:
Figure BDA0003082974610000042
uiamount of radial displacement, gamma, of predetermined point of axleirθValue of shear strain, v, for predetermined point of axleiA tangential displacement angle of the predetermined point of the axle in the inner radial distance of the axle, (ir) d θ a circumferential displacement amount of the predetermined point of the axle in the inner radial distance of the axle corresponding to d θ,
δt＝δ-(uo+ui)
δtand delta is the initial interference amount for the real-time interference amount.
Still further, in step S5, the wheel stress boundary conditions are as follows:
Figure BDA0003082974610000043
the axle stress boundary conditions are as follows:
Figure BDA0003082974610000044
the utility model provides a measurement early warning device of real-time magnitude of interference between wheel axles which characterized in that includes:
the acquisition unit comprises a rotary encoder, and is coaxially arranged on a preset wheel shaft, and the wheel shaft is the wheel shaft;
the measurement control unit comprises a processor, a memory and a processing program which is stored on the memory and executed on the processor, and when the processor executes the processing program, the measurement early warning unit is used for implementing the measurement method of the real-time interference between the wheel shafts and sending out an early warning driving signal when the real-time interference is larger than 1.5% of the outer diameter of the wheel or smaller than 1.2% of the outer diameter of the wheel; and
and the early warning part carries out early warning when receiving the early warning driving signal.
Preferably, the early warning piece is a buzzer and/or an early warning lamp.
Compared with the prior art, the invention has the beneficial effects that:
1. the method for measuring the real-time interference between the wheel shafts firstly obtains the static contact stress of the wheel shafts by analyzing the static wheel shafts, then combines the differential equation, the constitutive equation and the geometric equation related to the stress, the strain value and the displacement of the wheels and the axles in the rotating wheel shafts, substitutes the static contact stress as a boundary condition, and finally obtains the real-time interference according to the initial interference, the radial displacement of the axles and the radial displacement of the wheels, so the method can well measure the real-time interference of the wheels and the axles in running.
2. The device for measuring and early warning the real-time interference between the wheel shafts comprises the rotary encoder coaxially arranged on the preset wheel shaft, the measurement control unit which can implement the measurement method of the real-time interference between the wheel shafts and send out the early warning driving signal, and the early warning part which carries out early warning when the early warning driving signal is received, so that the device can carry out real-time monitoring on the running wheel shafts, and can carry out early warning in time when the real-time interference does not meet the requirement.
Drawings
Fig. 1 is a schematic step diagram of a method for measuring interference between wheel axles in real time according to an embodiment of the present invention.
Detailed Description
In order to make the technical means, the original characteristics, the achieved objects and the effects of the present invention easily understood, the following embodiments are specifically described with reference to the accompanying drawings, and it is to be noted that the description of the embodiments is provided for the understanding of the present invention, but the present invention is not limited thereto.
As shown in fig. 1, the method S100 for measuring the real-time interference between the wheel axles in this embodiment is applied to a wheel axle formed by assembling the wheel and the axle with the initial interference, the material of the wheel and the axle is the same, the wheel axle rotates at a constant predetermined angular speed, the radial distance of the predetermined point of the wheel is used as the outer radial distance, and the radial distance of the predetermined point of the axle is used as the inner radial distance.
The method S100 for measuring the real-time interference magnitude between the wheel shafts comprises the following steps:
and step S1, making the wheel shaft still, and obtaining the wheel shaft static contact stress on the assembling surface of the wheel and the axle based on the outer diameter of the wheel, the outer diameter of the axle and the inner diameter of the axle.
In particular, the wheel axle static contact stress pcComprises the following steps:
Figure BDA0003082974610000061
delta is the initial interference, a is the inner diameter of the axle, b is the outer diameter of the axle, c is the outer diameter of the wheel, E1Is the modulus of elasticity of the wheel, E2Is the modulus of elasticity, μ, of the axle1Is the Poisson's ratio, mu, of the wheel2Is the poisson ratio of the axle.
Step S2, rotating the wheel shaft, setting wheel preset points on the wheel and axle preset points on the axle;
and step S3, establishing an axle elasticity differential equation related to the rotating centrifugal force on the wheel axle and the stress of the axle preset point in three dimensional directions, and establishing a wheel elasticity differential equation related to the rotating centrifugal force on the wheel axle and the stress of the wheel preset point in three dimensional directions.
Step S4: and establishing an axle elastic mechanical constitutive equation and an axle elastic mechanical geometric equation related to the stress, the strain value and the displacement in the three-dimensional directions of the axle predetermined point, and establishing a wheel elastic mechanical constitutive equation and a wheel elastic mechanical geometric equation related to the stress, the strain value and the displacement in the three-dimensional directions of the wheel predetermined point.
Step S5: and obtaining the radial displacement of the axle and the radial displacement of the wheel based on the static contact stress of the axle, the elastic mechanical differential equation of the wheel or the axle, the elastic mechanical constitutive equation of the wheel or the axle and the elastic mechanical geometric equation of the wheel or the axle.
Specifically, the wheel elastic mechanics differential equation is:
Figure BDA0003082974610000062
σorradial stress, σ, at predetermined points of the wheeloθStress in the circumferential direction at predetermined points of the wheel, σozPositive stress at predetermined points of the wheel, τozAxial shear stress of wheel at predetermined point, rho is material density of wheel shaft, omega is predetermined angular velocity, or is outer radial distance, rho omega2(or) is the centrifugal force at a predetermined point of the wheel.
In practice, since the axial force (i.e., Z-axis) of the axle is small relative to the forces in other directions, the axle can be simplified into a thin disk, and therefore, the plane stress state (Z-axis disregarded) can be expressed, and the Z-axis stress state in equation (2) is simplified to be omitted:
Figure BDA0003082974610000071
the elastic mechanical differential equation of the axle is as follows:
Figure BDA0003082974610000072
σirradial stress, σ, for predetermined points of the axleiθCircumferential stress, σ, for predetermined points of the axleizPositive stress at predetermined point of axle, tauizAxial shear stress at a predetermined point of the axle, ir is the inner radial distance, ρ ω2(ir) is the centrifugal force at a predetermined point on the axle.
The Z-axis stress state is simplified to be neglected in the formula (4):
Figure BDA0003082974610000073
the wheel elastic mechanical constitutive equation is as follows:
Figure BDA0003082974610000074
εorvalue of radial strain, epsilon, for predetermined point of wheeloθValue of circumferential strain, epsilon, for predetermined point of wheelozThe axial strain value of the wheel at a predetermined point is represented by mu, which is the poisson's ratio of the wheel shaft.
The wheel elastic mechanics geometric equation is as follows:
Figure BDA0003082974610000081
uoamount of radial displacement, gamma, of predetermined point of wheelorθValue of shear strain, v, for predetermined point of wheeloA tangential displacement angle at a predetermined point of the wheel at an outer radial distance of the wheel, (or) d θ is a circumferential displacement amount at the predetermined point of the wheel at the outer radial distance of the wheel corresponding to d θ.
Eliminating the radial displacement u of a predetermined point of the wheel from the first two equations in equation (7)oObtaining a strain coordination equation:
Figure BDA0003082974610000082
introducing an auxiliary stress function psi1(or)＝(or)σorAnd substituting the formula (3) to obtain:
Figure BDA0003082974610000083
the differential transformation is performed by combining equations (6), (8) and (9):
Figure BDA0003082974610000084
solving equation (10) yields:
Figure BDA0003082974610000085
wherein C is3、C4Is the integration constant to be solved.
By means of an auxiliary stress function psi1(or), formula (9) and formula (11) are provided:
Figure BDA0003082974610000086
Figure BDA0003082974610000087
the wheel stress boundary conditions are as follows:
Figure BDA0003082974610000088
can obtain C3、C4Mixing C with3、C4Substituting for the formulae (12) and (13) and obtaining, in conjunction with the formulae (6) and (7):
Figure BDA0003082974610000091
and delta is the initial interference.
The elastic mechanical constitutive equation of the axle is as follows:
Figure BDA0003082974610000092
εirvalue of radial strain, epsilon, for predetermined point of axleiθValue of circumferential strain, epsilon, for predetermined points of the axleizThe axial strain value of the axle at a predetermined point, and E is the modulus of elasticity of the wheel axle.
The elastic mechanical geometrical equation of the axle is as follows:
Figure BDA0003082974610000093
uiamount of radial displacement, gamma, of predetermined point of axleirθValue of shear strain, v, for predetermined point of axleiA tangential displacement angle of the predetermined point of the axle in the inner radial distance of the axle, and (ir) d θ a circumferential displacement amount of the predetermined point of the axle in the inner radial distance of the axle corresponding to d θ.
Eliminating the radial displacement u of a predetermined point of the axle from the first two equations in equation (17)iObtaining a strain coordination equation:
Figure BDA0003082974610000094
introducing an auxiliary stress function psi2(ir)＝(ir)σirAnd substituting formula (5) to obtain:
Figure BDA0003082974610000095
the differential transformation is performed by combining equations (16), (18) and (19):
Figure BDA0003082974610000096
solving equation (20) yields:
Figure BDA0003082974610000101
wherein C is1、C2Is the integration constant to be solved.
By means of an auxiliary stress function psi2(ir), formula (19), and formula (20) are provided:
Figure BDA0003082974610000102
Figure BDA0003082974610000103
the axle stress boundary conditions are as follows:
Figure BDA0003082974610000104
can obtain C1、C2Mixing C with1、C2Substituting for the formulae (22) and (23) and obtaining, in conjunction with the formulae (16) and (17):
Figure BDA0003082974610000105
step S6: and obtaining real-time interference according to the initial interference, the axle radial displacement and the wheel radial displacement.
In particular, the amount of the solvent to be used,
δt＝δ-(uo+ui) (26)
δtthe real-time interference magnitude is obtained.
The measuring and early warning device for the real-time interference magnitude between the wheel shafts in the embodiment is characterized by comprising a collecting unit, a measuring and controlling unit and an early warning piece.
The acquisition unit comprises a rotary encoder which is coaxially arranged on a preset wheel shaft, and the wheel shaft is the wheel shaft mentioned in the method S100 for measuring the interference between the wheel shafts in real time.
The measurement control unit comprises a processor, a memory and a processing program which is stored on the memory and executed on the processor, when the processor executes the processing program, the measurement early warning unit is used for implementing a measurement method S100 of the real-time interference between the wheel shafts and sending out an early warning driving signal when the real-time interference mentioned in the measurement method of the real-time interference between the wheel shafts is more than 1.5 percent of the outer diameter of the wheel or less than 1.2 percent of the outer diameter of the wheel; and
and the early warning piece carries out early warning when receiving the early warning driving signal and is a buzzer and/or an early warning lamp.
The above-described embodiments are preferred embodiments of the present invention, and are not intended to limit the scope of the present invention, and various modifications and changes can be made by those skilled in the art without inventive work within the scope of the appended claims.

Claims (7)

1. A method for measuring the real-time interference between wheel shafts is applied to the wheel shaft formed by assembling wheels and an axle by using initial interference, and is characterized by comprising the following steps of:
step S1, making the wheel shaft still, and obtaining the wheel shaft static contact stress on the assembly surface of the wheel and the axle based on the outer diameter of the wheel, the outer diameter of the axle and the inner diameter of the axle;
step S2, rotating the wheel shaft, setting wheel preset points on the wheel and axle preset points on the axle;
step S3, establishing an axle elastic mechanical differential equation related to the rotating centrifugal force on the wheel axle and the stress of the axle preset point in three dimensional directions, and establishing a wheel elastic mechanical differential equation related to the rotating centrifugal force on the wheel axle and the stress of the wheel preset point in three dimensional directions;
step S4: establishing an axle elastic mechanical constitutive equation and an axle elastic mechanical geometric equation related to the stress, the strain value and the displacement in the three-dimensional directions of the axle predetermined point, and establishing a wheel elastic mechanical constitutive equation and a wheel elastic mechanical geometric equation related to the stress, the strain value and the displacement in the three-dimensional directions of the wheel predetermined point;
step S5: obtaining the radial displacement of the axle and the radial displacement of the wheel based on the static contact stress of the wheel axle, the elastic mechanical differential equation of the wheel or the axle, the elastic mechanical constitutive equation of the wheel or the axle and the elastic mechanical geometric equation of the wheel or the axle,
step S6: and obtaining real-time interference according to the initial interference, the axle radial displacement and the wheel radial displacement.
2. The method for measuring the interference between the wheel axles in real time according to claim 1, wherein:
wherein, in step S1, the wheel axle static contact stress pcComprises the following steps:
Figure FDA0003082974600000011
delta is the initial interference, aIs the inner diameter of the axle, b is the outer diameter of the axle, c is the outer diameter of the wheel, E1Is the modulus of elasticity of the wheel, E2Is the modulus of elasticity, mu, of the axle1Is the Poisson's ratio, mu, of the wheel2Is the poisson's ratio of the axle.
3. The method for measuring the interference between the wheel axles in real time according to claim 1, wherein:
wherein the wheels and the axles are made of the same material, the wheel axles rotate at a constant predetermined angular speed, the radial distance of a predetermined point of the wheels is used as an outer radial distance, and the radial distance of a predetermined point of the axles is used as an inner radial distance,
the wheel elastic mechanics differential equation is as follows:
Figure FDA0003082974600000021
σorradial stress, σ, at a predetermined point of said wheeloθCircumferential stress at predetermined points of said wheel, σozPositive stress at predetermined point of said wheel, τozThe axial shear stress of the wheel at a predetermined point is defined, ρ is the material density of the wheel shaft, ω is the predetermined angular velocity, or is the outer radial distance,
the elastic mechanical differential equation of the axle is as follows:
Figure FDA0003082974600000022
σirradial stress, σ, for a predetermined point of the axleiθCircumferential stress, σ, for predetermined points of the axleizPositive stress at predetermined point of said axle, tauizAnd is the axle axial shear stress at the axle predetermined point, ir is the inner radial distance.
4. The method for measuring the interference between the wheel axles in real time according to claim 3, wherein:
wherein, the wheel elastic mechanics constitutive equation is as follows:
Figure FDA0003082974600000023
εora value of radial strain, ε, for a predetermined point of said wheeloθA value of circumferential strain, ε, for said wheel predetermined pointozIs the axial strain value of the wheel at a predetermined point, mu is the Poisson's ratio of the wheel axis,
the elastic mechanical constitutive equation of the axle is as follows:
Figure FDA0003082974600000031
εirvalue of radial strain, epsilon, for predetermined point of said axleiθA value of circumferential strain, ε, for said axle predetermined pointizAn axial strain value of the axle at a predetermined point, E is an elastic modulus of the wheel axle,
the wheel elastic mechanics geometric equation is as follows:
Figure FDA0003082974600000032
uois the radial displacement of a predetermined point of said wheel, gammaorθA value of shear strain, v, for a predetermined point of said wheeloA tangential displacement angle at a predetermined point of said wheel at an outer radial distance of said wheel, (or) a circumferential displacement amount at said predetermined point of said wheel at an outer radial distance of said wheel corresponding to d θ,
the elastic mechanical geometrical equation of the axle is as follows:
Figure FDA0003082974600000033
uiis the radial displacement of a predetermined point of the axle, gammairθA value of shear strain, v, for a predetermined point of said axleiA tangential displacement angle of the predetermined point of the axle at the inner radial distance of the axle, (ir) d θ is a circumferential displacement amount of the predetermined point of the axle at the inner radial distance of the axle corresponding to d θ,
δt＝δ-(uo+ui)
δtand delta is the real-time interference magnitude and the initial interference magnitude.
5. The method for measuring the interference between the wheel axles in real time according to claim 4, wherein:
in step S5, the wheel stress boundary conditions are as follows:
Figure FDA0003082974600000041
the axle stress boundary conditions are as follows:
Figure FDA0003082974600000042
6. the utility model provides a measurement early warning device of real-time magnitude of interference between wheel axles which characterized in that includes:
an acquisition unit comprising a rotary encoder coaxially mounted on a predetermined wheel axle, the wheel axle being as claimed in any one of claims 1 to 5;
a measurement control unit comprising a processor, a memory, and a processing program stored on the memory and executed on the processor, wherein when the processor executes the processing program, the measurement and early warning unit is configured to implement the method for measuring the real-time interference between the wheel axles according to any one of claims 1 to 5 and issue an early warning driving signal when the real-time interference according to any one of claims 1 to 5 is greater than 1.5% of the outer diameter of the wheel or less than 1.2% of the outer diameter of the wheel; and
and the early warning piece carries out early warning when receiving the early warning driving signal.
7. The device for measuring and warning the magnitude of interference between wheel axles according to claim 6, wherein:
wherein, the early warning piece is buzzer and/or early warning lamp.
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Citations (8)

* Cited by examiner, † Cited by third party
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