CN104101380B - Method for measuring stress and strain of gear root of fixed center gear of planetary gear train - Google Patents

Abstract

The invention discloses a method for measuring the stress and strain of the gear root of the fixed center gear of a planetary gear train. The method of the invention comprises the following steps that: a fiber Bragg grating probe is mounted at a rounded angle of the gear root of the fixed center gear of the planetary gear train and is made to be located in a safe area, namely at a clearance where two gears are engaged with each other, and an included angle between the fiber Bragg grating probe and the axis of the gear is theta, and one end of the fiber Bragg grating probe is located at the gear root, and the other end of the fiber Bragg grating probe does not exceed the safe area, and O is a measurement point; and a fiber Bragg grating measurement system is utilized to measure the Prague wavelength lambda B of a grating when the gear is not loaded, and measures the Prague wavelength lambda' B of the fiber bragg grating after the gear is deformed, and the axial strain of the fiber bragg grating at the measurement point and the strain along the radial direction of the gear at the measurement point can be obtained according to a stress sensing model; and finally, a stress sigma at the measurement point along the radial direction of the gear can be calculated by using a basic formula of mechanics of materials sigma y=E epsilon y.

Description

The measuring method of planet circular system fixed center Gear Root Stress strain

Technical field

The present invention relates to the dynamic test of mechanical rotation device and fault diagnosis technology are and in particular to a kind of planet circular system is solid The measuring method of the transmission properties that center.

Background technology

Gear is usually according to rated load design, but in fact, bullet due to parts such as foozle, the gear teeth and axles Property deformation, vibration etc. reason, make Gear Root produce very big extra dynamic stress, this dynamic bending peak stress is if more than The fatigue limit of the gear teeth, will make tooth root produce fatigue crack, with the continuous extension of fatigue crack, ultimately cause gear teeth folding Disconnected, this is one of principal mode of gear failure.Additionally, this dynamic stress also can produce harmful vibration and noise, impact passes Dynamic precision, reduces work efficiency.In order to analyze the strength characteristics of gear, Chinese scholars propose multiple mechanical models and theory Analysis method, its analysis model is all to assume at some and set up on the basis of simplifying, though there being certain directive function, but Not very accurate.In order to make up the defect of theory analysis, more effectively condition diagnosing and prediction are carried out to gear train assembly, In transmission process, kinetic measurement is carried out to Gear Root Stress strain, significant.Because planet circular system uses material High-quality, complex structure, manufacture and installation are all relatively difficult, its stress and deformation are monitored seeming in transmission process Particularly important.

Planet circular system, as the key link in drive system, is widely used in all kinds of machineries, to planet circular system The strain of fixed center Gear Root Stress carries out on-line measurement, is conducive to accurately catching as soon as possible, detects, identifies drive system The abnormal operating condition of middle critical component or potential initial failure behavior (earlier damage), estimate the state evolution of drive system Trend and remaining life.This actually carries out failure predication to equipment, it be equipment health control primary link and Important connotation, by prediction can effectively reduce equipment using with support cost, improve change system safety, Combat readiness and Mlssion success, realizes the maintenance based on state and autonomous type guarantee, is conducive to planetary gear integrated diagnostic system to test, prison Control, diagnosis, prediction and maintenance management integration direction are developed.

At present, the measuring method of planet circular system transfer force mainly has two classes：Photoelastic method and electrical measuring method.Photoelastic method profit It is the transient state birefringence effect that elastooptic mateiral produces under load effect, during measurement, typically by elastooptic mateiral in knot After component surface directly adopts the process of light paster, measurand is placed in polarized light field, applies certain load, on model just Produce interference fringe, referred to as optical stress pattern, by analyzing and calculating the Changing Pattern that optical stress pattern just can obtain its stress.Electrical measurement Method typically pastes foil gauge in Gear Root, forms bridge, then electric bridge is accessed dynamic strain indicator, and dynamic test tooth root should Power, flexural fatigue etc..The making complicated compared to photoelastic method, mounting process and optical system, longer measure the cycle, electrical measurement Method is simpler, and technology is more ripe, thus more extensive in the fields of measurement application of Gear Root Stress at present.But when using electricity When survey method carries out multimetering, the wire harness of employing is more, it is complicated to install, and needs to take the anti-electricity of special measure strengthening system Magnetic disturbance ability, so, scene application is not very convenient.Therefore, find a kind of structure simple, electromagnetism interference, it is suitable to many The planet circular system transfer force measuring method of point measurement and scene application is significant.

Content of the invention

For the shortcomings and deficiencies of existing measuring method, it is an object of the invention to provide a kind of structure is simple, anti-electromagnetism is done Disturb, be suitable to the dynamic measurement method of the planet circular system fixed center transmission properties of multimetering.

For reaching object above, the present invention adopts the following technical scheme that and is achieved：

A kind of measuring method of planet circular system fixed center Gear Root Stress strain is it is characterised in that include following steps Suddenly：

(1) fiber grating probe is arranged at planet circular system fixed center Gear Root fillet, and is at safety Region, i.e. the gap location of two gear engagements, fiber grating probe is θ with the angle of Gear axis, and its one end is located at tooth root, separately One end is less than safety zone, and O is measuring point；

(2) utilize fiber grating measuring system, during the non-stand under load of prototype gear, the bragg wavelengths of grating_B, prototype gear The bragg wavelengths ' of fiber grating after deformation_B, can be obtained according to stress sensing model：

Wherein, P_eFor the valid elastic-optic constants of grating, choose a rectangular area OAPB in measuring point O neighborhood, represent not State during loading, after loading, this rectangular area is changed into rectangle OA₁B₁P₁Region, defining OA direction is gear axial direction x, OB side To for gear radial direction y, then the axial strain of the fiber grating of measuring point is represented by：

If l_OA=s, after loading, the strain in y direction is ε_y, then it is easy to get l by geometrical relationship and material mechanics principle_OB=s Tan θ,υ is Poisson's ratio, so the axial strain of fiber grating is represented by：

Can obtain after abbreviation：

Formula (6) is carried out with deformation and can obtain measuring point along the strain of gear radial direction：

(3) utilize fundamental formular σ of the mechanics of materials_y=E ε_yCalculate measuring point along gear radial direction stress σ_y；Wherein；E is tooth The elastic modelling quantity of wheel material.

In said method, one end of described fiber grating probe is pasted onto the intersection point H of tooth root HG and gear teeth radial boundary HE Place, the other end is pasted onto at the intersection point JC of safety zone coboundary IJ and gear teeth radial boundary FG, so that fiber grating is popped one's head in and tooth The angle theta of wheel axis reaches maximum, is obtained in that the maximum axial deformation of fiber grating.

On fiber grating probe, arrange multistage fibre core effective refractive index n_effIdentical grating, chooses different grating grid Away from being designated as Λ respectively₁,Λ₂,Λ₃..., then expression formula λ according to bragg wavelength_B=2n_effΛ understands, each section during non-stand under load The bragg wavelengths of grating_B1,λ_B2,λ_B3... difference, the bragg wavelengths ' after measuring multistage grating stand under load_B1,λ′_B2, λ′_B3..., obtain multi-measuring point along gear radial direction stress σ_yi, i=1,2,3 ... selection σ_yiIn maximum, as measurement knot Really, thus realizing the multimetering of fixed center Gear Root Stress strain.

This have the advantage that, it is possible to achieve in planet circular system transmission process, fixed center gear ess-strain On-line dynamic measurement, compared with prior art, this test system structure is simple, easy for installation, is suitable to multimetering and engineering should With, and can effectively prevent electromagnetic interference.

Brief description

Below in conjunction with the drawings and the specific embodiments, the present invention is described in further detail.

Fig. 1 is measuring system schematic diagram of the present invention.

Fig. 2 is the mounting means schematic diagram of fibre-optical probe in Fig. 1.Wherein：A figure is basic mounting means；B figure is optimum peace Dress mode.

Fig. 3 is that the fiber grating axial strain of Fig. 2 calculates schematic diagram.

Fig. 4 is three test point embodiments of Fig. 2 fiber grating.

The specific algorithm flow chart that Fig. 5 strains for root stress of the present invention.

Specific embodiment

Fiber grating measures the ultimate principle of stress

Fiber grating is made up of fibre core and covering, and when broadband light incides in fiber grating, centre wavelength meets certain The incident light wave of condition can reflect, and this wavelength is referred to as bragg wavelength.The expression formula of bragg wavelength is：

λ_B=2n_effΛ (1)

Wherein n_effFor the effective refractive index of fiber core, Λ is the pitch of fiber grating.

When optical fiber is subject to axial stress, grating causes pitch and refractive index to change due to flexible and elasto-optical effect, And then causing optical fiber Bragg wavelength shift, the side-play amount of wavelength is：

Δλ_B=(1-P_e)ελ_B(2)

Formula (2) is the stress sensing model of fiber grating, P in formula_eFor valid elastic-optic constants, can be asked by optical fiber parameter , ε is the axial strain of fiber grating.As long as can be seen that by this model recording fiber grating reflection before and after stress Variation delta λ of wavelength_B, you can try to achieve the strain value ε of fiber grating, and then the stress value at measuring point can be obtained.

Referring to Fig. 1, the present invention measures the strain of planet circular system fixed center Gear Root Stress based on fiber grating principle Method：

The measuring system of the present invention is as shown in figure 1, the incident illumination 3 that wideband light source sends passes sequentially through optoisolator 1, optocoupler Clutch 2 reaches the fiber grating probe 6 being arranged on central gear tooth root, and centre wavelength is that the light of bragg wavelength occurs instead Penetrate, reflected light 4 enters adjustable F-P wave filter 5 by photo-coupler, the structure of this wave filter is parallel to each other and phase by two Constitute away from the high reflection mirror for H, one of reflecting mirror is fixed, another reflecting mirror may move and piezoelectric ceramics is posted at the back side, Apply scanning voltage (being sawtooth voltage in the system) to piezoelectric ceramics, piezoelectric ceramics just produces flexible, thus changing F-P cavity Chamber long, make to change through the optical wavelength of F-P cavity, that is, the transmitted light wavelength of scanning voltage value and F-P cavity is to correspond 's.The transmitted light 7 of F-P cavity, through photo-detector opto-electronic conversion, after filter and amplification etc. is processed, is adopted by data with scanning voltage simultaneously Truck collects computer, and computer catches scanning voltage value when F-P cavity transmitted light intensity maximum, just can obtain grating fibers Echo long value.When the gear teeth are not deformed, if the bragg wavelength of fiber grating 9 is λ_B, after fiber grating determines, this wavelength It is definite value, this wavelength value is stored in the memorizer of computer；After gear tooth deformation, fiber grating also deforms therewith, if this When fiber grating bragg wavelength be λ '_B, this wavelength value wavelength value that as measuring system measures.According to stress sensing model Can obtain：

In formula, ε is the axial strain value of fiber grating at measuring point.

Therefore, using Fig. 1 measuring system, the bragg wavelength after prototype gear stand under load is it is possible to utilize computer Obtain the axial strain value of fiber grating at measuring point, then just can try to achieve the footpath of the gear teeth at measuring point (tooth root) using the algorithm of Fig. 5 To strain and stress.

The effect of computer is the process of measurement running planet circular system fixed center Gear Root Stress, and this journey includes monitoring Program, the root stress algorithm of the present invention, mapping program, fault diagnostic program and early warning program.Passage 1 gathers FBG (optical fiber light Grid) signal after F-P cavity, photo-detector, filtering and amplifying circuit for the reflected light, passage 2 acquisition scans voltage signal.Monitoring journey The effect of sequence is the magnitude of voltage of capture channel 2 when passage 1 produces instantaneous crest, and calculates FBG reflection wavelength accordingly；Tooth Root stress algorithm calculates tooth root at measuring point along the strain of gear radial direction and stress according to FBG reflection wavelength；Mapping program according to The stress value calculating draws stress changing curve；Fault diagnostic program passes through at a series of signal according to the stress value calculating Adjustment method diagnoses planet circular system fault；Early warning program carries out early warning according to the result of fault diagnostic program.

With reference to Fig. 2, make multistage Bragg grating on fiber grating probe in Fig. 1, the fibre core of each section of grating effectively reflects Rate is identical, and grating pitch is different, understands that by formula (1) the original bragg wavelength of each section of grating is different, should make each section of light during making The bragg wavelength of grid keeps appropriately distance, prevents from occurring signal aliasing during measurement.

The mounting means of fiber grating probe mainly considers that three aspects require：Probe should be made near root fillet first as far as possible Place, to obtain maximum stress；Secondly, in gear drive stress measurement, for avoiding the damage of fiber grating, fibre-optical probe is necessary It is arranged on safety zone 12, that is, the gap location of two gears engagement；Finally, due to stress measurement is the axle by fiber grating To reflect to strain, so in order to improve resolution, optical fiber axial direction strain should be made as far as possible maximum.

The basic mounting means of fibre-optical probe as shown in Figure 2 a, in this mounting means, fibre-optical probe and Gear axis Angle is θ, and its one end is located at tooth root, and the other end is less than safety zone, and O is measuring point.On this mounting means can meet Require of both before stating, the requirement of last one side need to be met by selecting angle theta, optimum angle theta_optSelection course As follows：

Calculate the axial strain of fiber grating at measuring point O using Fig. 3, in the figure, choose a square in measuring point O neighborhood Shape region OAPB, represents state when not loading, after loading, this rectangular area is changed into rectangle OA₁B₁P₁Region, defines OA direction For gear axial direction x, OB direction is gear radial direction y, then the axial strain of fiber grating 9 is represented by：

If l_OA=s, after loading, the strain in y direction is ε_y, then it is easy to get l by geometrical relationship and material mechanics principle_OB=s Tan θ,(υ is Poisson's ratio), so the axial strain of fiber grating 9 is represented by：

Can obtain after abbreviation：

Obviously, whenWhen, ε is the monotonic increasing function with regard to θ, and that is, ε increases with the increase of θ.Based on above point Analysis, in this measuring system, as shown in Figure 2 b, one end of wherein fibre-optical probe is pasted onto tooth root to the optimal mounting means of fibre-optical probe At the intersection point H of HG and gear teeth radial boundary HE, the other end is pasted onto the friendship of safety zone coboundary IJ and gear teeth radial boundary FG At point JC, using this mounting means, θ can be made to reach maximum, therefore fiber grating is obtained in that the axial deformation of maximum.

After the mounting means of fibre-optical probe the determines it is thus necessary to determine that position of measuring point.According to the theory of the mechanics of materials, measuring point should It is selected at tooth root dangerouse cross-section." Lewis " method (i.e. pressure method in parabola) and 30 ° of tangential methods are typically adopted to determine involute at present The dangerouse cross-section position of gear, also has scholar to adopt Finite element arithmetic by two-dimensional stress and determine using plane photoelastic experiment double The dangerous spot of wildhaber-novikov gear tooth root.These methods make every effort to more accurately find the maximum moving stress position of tooth root, implement Complex, it is unfavorable for engineer applied.The present invention considers requirement of engineering, makes and multiple have different cloth on a fibre-optical probe The grating of glug wavelength, the stress value of measurement multiple spot, final maximum stress of choosing is as measurement result.In order to improve the essence of measurement Really property, needs to increase the quantity of grating, but grating quantity is excessive, it will make each bragg wavelength recording aliasing occur, to rear Continuous Stress calculation interferes it is contemplated that the space of safety zone is less, so the result recording after reducing the quantity of grating Do not have larger gap with legitimate reading, engineering demand can be met.Based on considerations above, a kind of typical distributed measurement Method is as shown in figure 4, three sections of gratings are located at the two ends popped one's head in and central authorities respectively.When the facewidth is larger, can suitably increase grating Quantity, now, two end points of probe are appointed so as measuring point, and remaining measuring point is uniformly distributed between the two endpoints.

The mounting means according to fibre-optical probe for the present invention and the requirement of multimetering, design fixed center Gear Root Stress The computational methods of strain.

Formula (6) is carried out deforming and can obtain：

The fibre core effective refractive index n of three sections of gratings on fibre-optical probe_effIdentical, choose different grating pitches, be designated as respectively Λ₁,Λ₂,Λ₃, then understood according to formula (1), the bragg wavelengths of three sections of gratings during non-stand under load_B1,λ_B2,λ_B3Difference, by measurement Bragg wavelengths ' after three sections of grating stands under load_B1,λ′_B2,λ′_B3, just can realize the many of fixed center Gear Root Stress strain Point measurement.

With reference to Fig. 5, the algorithm of Gear Root Stress strain

The calculation flow chart of algorithm is as shown in figure 5, the step of this algorithm is：

1) when measuring non-stand under load, the bragg wavelengths of three sections of gratings_Bi(i=1,2,3 ...)；

2) calculate the valid elastic-optic constants P of three sections of gratings_e；

3) after measurement loads, the bragg wavelengths ' of three sections of gratings_Bi(i=1,2,3)；

4) formula (3) is utilized to calculate the axial strain ε of optical fiber_i(i=1,2,3)；

5) formula (7) is utilized to calculate measuring point along the strain stress of gear radial direction_yi(i=1,2,3)；

6) utilize fundamental formular σ of the mechanics of materials_yi=E ε_yi(i=1,2,3, E are the elastic modelling quantity of gear material) calculates Measuring point is along the stress σ of gear radial direction_yi；

7) choose σ_yiIn maximum, as measurement result.

Claims (3)

1. a kind of measuring method of planet circular system fixed center Gear Root Stress strain is it is characterised in that comprise the steps：

(1) fiber grating probe is arranged at planet circular system fixed center Gear Root fillet, and is at safety zone, The i.e. gap location of two gear engagements, fiber grating probe is θ with the angle of Gear axis, and its one end is located at tooth root, the other end Less than safety zone, O is measuring point；

(2) utilize fiber grating measuring system, during the non-stand under load of prototype gear, the bragg wavelengths of grating_B, after prototype gear deformation The bragg wavelengths ' of fiber grating_B, can be obtained according to stress sensing model：

$\mathrm{\ϵ}=\frac{{\mathrm{\λ}}_B^{\′}-{\mathrm{\λ}}_B}{(1-P_e){\mathrm{\λ}}_B}---\left(3\right)$

Wherein, ε is the axial strain of fiber grating, P_eFor the valid elastic-optic constants of grating, choose a square in measuring point O neighborhood Shape region OAPB, represents state when not loading, after loading, this rectangular area is changed into rectangle OA₁B₁P₁Region, defines OA direction For gear axial direction x, OB direction is gear radial direction y, then the axial strain of the fiber grating of measuring point is represented by：

$\mathrm{\ϵ}=\frac{l_{{\mathrm{OP}}_1}-l_{OP}}{l_{OP}}---\left(4\right)$

If l_OA=s, after loading, the strain in y direction is ε_y, then it is easy to get by geometrical relationship and material mechanics principleυ is Poisson's ratio, so the axial strain of fiber grating is represented by：

$\mathrm{\ϵ}=\frac{\sqrt{{(stan\mathrm{\θ}+{\mathrm{\ϵ}}_{y}stan\mathrm{\θ})}^2+{(s-{\mathrm{\υ\ϵ}}_{y}s)}^2}-\sqrt{{\left(stan\mathrm{\θ}\right)}^2+s^2}}{\sqrt{{\left(stan\mathrm{\θ}\right)}^2+s^2}}---\left(5\right)$

Can obtain after abbreviation：

$\mathrm{\ϵ}=\sqrt{{(1+{\mathrm{\ϵ}}_y)}^2-\frac{{(1+{\mathrm{\ϵ}}_y)}^2-{(1-{\mathrm{\υ\ϵ}}_y)}^2}{1+{\tan }^2\mathrm{\θ}}}-1---\left(6\right)$

Formula (6) is carried out with deformation and can obtain measuring point along the strain of gear radial direction：

${\mathrm{\ϵ}}_y=\frac{2\mathrm{\υ}-2{\tan }^2\mathrm{\θ}+\sqrt{4{({\tan }^2\mathrm{\θ}-\mathrm{\υ})}^2-4({\tan }^2\mathrm{\θ}+{\mathrm{\υ}}^2)\[2(1+{\tan }^2\mathrm{\θ}){(1+\mathrm{\ϵ})}^2\]}}{2{\tan }^2\mathrm{\θ}+2{\mathrm{\υ}}^2}---\left(7\right)$

(3) utilize fundamental formular σ of the mechanics of materials_y=E ε_yCalculate measuring point along gear radial direction stress σ_y；Wherein；E is gear material The elastic modelling quantity of material.

2. planet circular system fixed center Gear Root Stress as claimed in claim 1 strain measuring method it is characterised in that One end of described fiber grating probe is pasted onto at the intersection point H of tooth root HG and gear teeth radial boundary HE, and the other end is pasted onto safety At the intersection point J of region coboundary IJ and gear teeth radial boundary FG, so that fiber grating is popped one's head in and the angle theta of Gear axis reaches maximum Value, is obtained in that the maximum axial deformation of fiber grating.

3. planet circular system fixed center Gear Root Stress as claimed in claim 2 strain measuring method it is characterised in that On fiber grating probe, arrange multistage fibre core effective refractive index n_effIdentical grating, chooses different grating pitches, respectively It is designated as Λ₁,Λ₂,Λ₃..., then expression formula λ according to bragg wavelength_B=2n_effΛ understands, wherein, Λ is fiber grating Pitch, the bragg wavelengths of each section of grating during non-stand under load_B1,λ_B2,λ_B3... difference, the cloth after measuring multistage grating stand under load Glug wavelength X '_B1,λ′_B2,λ′_B3..., obtain multi-measuring point along gear radial direction stress σ_yi, i=1,2,3 ... selection σ_yiIn Maximum, as measurement result, thus realize the multimetering of fixed center Gear Root Stress strain.