CN105893710A - Method for calculating geometric return difference of NGWN planetary gear train - Google Patents

Abstract

The invention firstly provides a method for calculating the geometric return difference of an NGWN planetary gear train. According to the method, based on geometric return difference calculation of an NGW planetary gear train, the backlash among gear pairs can be determined by acquiring the teeth number, pressure angle and actual engagement angle of gears, upper and lower deviation of a common normal line and radial run-out tolerance of each gear, the center distance tolerance among gear pairs and other parameters, and the value of the geometric return difference can be acquired by utilizing the transmission ratio. By adopting the method, the problem that people cannot determine the structure accuracy in the designing phase can be solved to a great extent by combining the calculation of NGW gear train geometric return difference and calculation of return difference of each gear, and accordance is provided to accurate design of the gear train. According to the return difference calculation method, the mode is simple, the required parameter can be easily obtained, and the result approaches the reality, so that time, energy and cost can be saved for designing staff, and the system reliability can be improved, and the service life of the system can be prolonged.

Description

NGWN epicyclic train geometric lost motion computational methods

Technical field

The present invention relates to STRUCTURAL SENSITIVITY ANALYSIS INDESIGN computing technique field, be the computational methods of a kind of train return difference, be specially A kind of NGWN epicyclic train geometric lost motion computational methods, can be applicable to all application NGWN row such as Aero-Space The occasion of star gear train.

Background technology

At present, NGWN train (N-inside engaged gear；W-external gear pump；In the middle of two gear Meshing Pair of G- Composite gear) big by its gear ratio, the advantage such as compact conformation, in the every field of machinery industry, especially aviation boat The application of it field is the most extensive.Along with the development of China's aeronautical and space technology, for the high lift device of aircraft, such as wing flap The drive mechanism of slat is had higher requirement.We not only require the normal transmission of train therein, more require that it has There is good sensitivity to guarantee synchronicity and the stability of each mechanism kinematic, and then improve its transmission accuracy.As A part for whole drive mechanism, NGWN train geometric lost motion calculates the breach solving these problems exactly.Just because of So, each developed country all starts the research of these train geometric lost motion computational methods.In China's research in recent years, Research to geometric lost motion computational methods is much, but only stays in single gear pair and NGW epicyclic train In the Calculation and Study of (structure is as shown in Figure 2).NGWN gear train is higher than the stationarity of NGW gear train, Overall structure rigidity is more preferable, ought to be favored and pay attention in terms of geometric lost motion computational methods.In order to preferably analyze Research and the precision of raising wheel train structure, the exploitation of the geometric lost motion computational methods of NGWN train becomes particularly important.

Summary of the invention

In order to preferably study the stationarity of drive mechanism, improving the precision of structure, the present invention provides a kind of NGWN The geometric lost motion computational methods of planet circular system, the method considers several factor that geometric lost motion produces main impact, Ignoring the secondary cause that impact is less, the computational methods obtained are the most understandable, and the results contrast obtained is accurate, energy Enough instruct real work.

The technical solution adopted in the present invention:

By the sideshake size of each gear being meshed carry out train geometric lost motion calculate, it is considered to several Major influence factors is respectively 1) gear backlash that causes of common normal average length deviation；2) gear run-out error draws The gear backlash risen；3) gear backlash that between gear pair, limit deviation of centre distance causes.

The NGWN gear train geometric lost motion computational methods set up herein are built upon existing NGW gear train return difference meter On the basis of calculation, accompanying drawing 1 is NGWN wheel train structure form, and composite gear N2 with N5 is coaxial, does not consider N5 During the geometric lost motion self produced, the geometric lost motion of N5 Yu N2 is identical, namely NGW train outfan Return difference.The N1N2N3 being made up of sun gear N1, composite gear N2 and internal gear N3 wheel is tied up to composite gear N2 The return difference that outfan and output gear N4 produce all is folded on composite gear N5 calculate, the most again with gear ratio i₄₅ Convert into back output gear N4 outfan, just obtained the core of the present invention: the return difference computing formula of NGWN train, In this formula, the calculating of return difference is relevant with the parameter value of gear.In practical implementation or design, Ke Yitong Cross and table look-up or measure base tangent length deviation, gear run-out error, between gear pair limit deviation of centre distance these Parameter, determines the backlash values between gear, and then obtains geometric lost motion result.

Described a kind of NGWN epicyclic train geometric lost motion computational methods, it is characterised in that:

One, according to formula

$\stackrel{\‾}{{\mathrm{\φ}}_4}=\frac{\stackrel{\‾}{{\mathrm{\φ}}_{5start}}+\stackrel{\‾}{{\mathrm{\φ}}_{5self}}+\stackrel{\‾}{{\mathrm{\φ}}_{4self}}\×i_{54}}{i_{54}}$

Calculate the geometric lost motion average of the output gear N4 of NGWN epicyclic train

Wherein:

For composite gear N5 input geometric lost motion average in NGWN epicyclic train；

For the geometric lost motion average of composite gear N2 outfan in NGWN epicyclic train；

$\stackrel{\‾}{{\mathrm{\φ}}_2}=\frac{6875.5}{{\mathrm{mz}}_2}({\mathrm{\Σj}}_{w,N1N2}+{\mathrm{\Σj}}_{w,N2N3})$

M is modulus, z₂The number of teeth for composite gear N2；

∑j_w,N1N2=j_w1,N1N2+j_w2,N1N2+j_w3,N1N2

j_w1,N1N2=j_w1dan,N1+j_w1dan,N2

j_w2,N1N2=j_w2dan,N1+j_w2dan,N2

∑j_w,N2N3=j_w1,N2N3+j_w2,N2N3+j_w3,N2N3

j_w1,N2N3=j_w1dan,N2+j_w1dan,N3

j_w2,N2N3=j_w2dan,N2+j_w2dan,N3

j_w1dan,N1、j_w1dan,N2、j_w1dan,N3It is respectively in NGWN epicyclic train sun gear N1, composite gear N2 and interior The gear N3 gear backlash that on business normal average length variation causes, j_w2dan,N1、j_w2dan,N2、j_w2dan,N3It is respectively too The gear backlash that sun wheel N1, composite gear N2 and internal gear N3 causes because of gear run-out error, j_w3,N1N2With j_w3,N2N3Be respectively limit deviation of centre distance causes between gear pair N1N2 gear backlash and gear pair N2N3 it Between the gear backlash that causes of limit deviation of centre distance；

The geometric lost motion average produced for composite gear N5 self:

$\stackrel{\‾}{{\mathrm{\φ}}_{5self}}=\frac{6875.5}{{\mathrm{mz}}_5}(j_{w1dan,N5}+j_{w2dan,N5})$

z₅The number of teeth for composite gear N5；j_w1dan,N5For the composite gear N5 gear side that on business normal average length variation causes Gap, j_w2dan,N5The gear backlash caused because of gear run-out error for composite gear N5；

The geometric lost motion average produced for output gear N4 self:

$\stackrel{\‾}{{\mathrm{\φ}}_{4self}}=\frac{6875.5}{{\mathrm{mz}}_4}(j_{w1dan,N4}+j_{w2dan,N4})$

z₄The number of teeth for output gear N4；j_w1dan,N4For the output gear N4 gear side that on business normal average length variation causes Gap, j_w2dan,N4The gear backlash caused because of gear run-out error for output gear N4；

i₅₄For composite gear N5 and the gear ratio of output gear N4；

Two, according to formula

${\mathrm{T\Δ\φ}}_4=\frac{{\mathrm{T\Δ\φ}}_{5start}+{\mathrm{T\Δ\φ}}_{5self}+{\mathrm{T\Δ\φ}}_{4self}\×i_{54}}{i_{54}}$

Calculate the geometric lost motion tolerance T Δ φ of the output gear N4 of NGWN epicyclic train₄；

Wherein:

TΔφ_5startFor composite gear N5 input geometric lost motion tolerance in NGWN epicyclic train；

TΔφ_5start=T Δ φ₂, T Δ φ₂For the geometric lost motion tolerance of composite gear N2 outfan in NGWN epicyclic train；

${\mathrm{T\Δ\φ}}_2=\frac{6875.5}{{\mathrm{mz}}_2}\left(\mathrm{\Σ}T\right(j_{w,N1N2})+\mathrm{\Σ}T(j_{w,N2N3}\left)\right)$

$\mathrm{\Σ}T\left(j_{w,N1N2}\right)=6\×\sqrt{\mathrm{\Σ}D\left(j_{w,N1N2}\right)}$

$\mathrm{\Σ}T\left(j_{w,N2N3}\right)=6\×\sqrt{\mathrm{\Σ}D\left(j_{w,N2N3}\right)}$

∑D(j_w,N1N2)=D (j_w1,N1N2)+D(j_w2,N1N2)+D(j_w3,N1N2)

D(j_w1,N1N2)=D (j_w1dan,N1)+D(j_w1dan,N2)

D(j_w2,N1N2)=D (j_w2dan,N1)+D(j_w2dan,N2)

∑D(j_w,N2N3)=D (j_w1,N2N3)+D(j_w2,N2N3)+D(j_w3,N2N3)

D(j_w1,N2N3)=D (j_w1dan,N2)+D(j_w1dan,N3)

D(j_w2,N2N3)=D (j_w2dan,N2)+D(j_w2dan,N3)

D(j_w1dan,N1)、D(j_w1dan,N2)、D(j_w1dan,N3) it is respectively sun gear N1, composite gear in NGWN epicyclic train N2 and the internal gear N3 gear backlash variance that on business normal average length variation causes, D (j_w2dan,N1)、D(j_w2dan,N2)、 D(j_w2dan,N3) it is respectively the tooth that sun gear N1, composite gear N2 and internal gear N3 cause because of gear run-out error Wheel sideshake variance, D (j_w3,N1N2) and D (j_w3,N2N3) it is respectively what limit deviation of centre distance between gear pair N1N2 caused The gear backlash variance that between gear backlash variance and gear pair N2N3, limit deviation of centre distance causes；

TΔφ_5selfThe geometric lost motion variance produced for composite gear N5 self:

${\mathrm{T\Δ\φ}}_{5self}=\frac{6875.5}{{\mathrm{mz}}_5}\left(D\right(j_{w1dan,N5})+D(j_{w2dan,N5}\left)\right)$

D(j_w1dan,N5) it is the composite gear N5 gear backlash tolerance that on business normal average length variation causes, D (j_w2dan,N5) it is The gear backlash tolerance that composite gear N5 causes because of gear run-out error；

TΔφ_4selfThe geometric lost motion variance produced for output gear N4 self:

${\mathrm{T\Δ\φ}}_{4self}=\frac{6875.5}{{\mathrm{mz}}_4}\left(D\right(j_{w1dan,N4})+D(j_{w2dan,N4}\left)\right)$

D(j_w1dan,N4) it is the output gear N4 gear backlash tolerance that on business normal average length variation causes, D (j_w2dan,N4) it is The gear backlash tolerance that output gear N4 causes because of gear run-out error；

Three, according to formula

${\mathrm{\φ}}_{4max}=\stackrel{\‾}{{\mathrm{\φ}}_4}+{\mathrm{T\Δ\φ}}_4$

${\mathrm{\φ}}_{4min}=\stackrel{\‾}{{\mathrm{\φ}}_4}-{\mathrm{T\Δ\φ}}_4$

Obtain the output gear N4 geometric lost motion maximum φ of NGWN epicyclic train_4maxWith minima φ_4min。

Further preferred version, described a kind of NGWN epicyclic train geometric lost motion computational methods, its feature exists In:

A certain gear N gear backlash j that on business normal average length variation causes_w1dan,NAccording to formula

$j_{w1dan,N}=-\frac{w_{Es,N}+w_{Ei,N}}{2cos\mathrm{\α}}$

Obtain；Wherein, α is pressure angle, w_Es,NFor the gear N common normal upper deviation, w_Ei,NFor gear N common normal Lower deviation；

The a certain gear N gear backlash variance D (j that on business normal average length variation causes_w1dan,N) according to formula

$D\left(j_{w1dan,N}\right)={\left(\frac{w_{Es,N}-w_{Ei,N}}{6cos\mathrm{\α}}\right)}^2$

Obtain；

The gear backlash tolerance D (j that a certain gear N causes because of gear run-out error_w2dan,N) according to formula

$D\left(j_{w2dan,N}\right)={\left(\frac{F_{r,N}\×K_{\mathrm{\α}}\×tan\mathrm{\α}}{3}\right)}^2$

Obtain；Wherein, F_r,NFor gear N run-out error,α ' is the gear angle of engagement；

The gear backlash variance D (j that a certain gear pair NN ' causes because of limit deviation of centre distance_w3,NN′) according to formula

$D\left(j_{w3,{\mathrm{NN}}^{\′}}\right)={\left(\frac{F_{a,{\mathrm{NN}}^{\′}}\×K_{\mathrm{\α}}\×tan\mathrm{\α}}{3}\right)}^2$

Obtain；Wherein, F_a,NN′For gear pair NN ' limit deviation of centre distance.

Beneficial effect

The invention has the beneficial effects as follows:

Present invention firstly provides the geometric lost motion computational methods of a kind of NGWN epicyclic train.The method is to pass through Calculating and the combination of single gear return difference calculating of NGW train geometric lost motion, largely solves people long-term Cannot determine the puzzlement of structure precision in the design phase, the careful design for train provides foundation.This return difference calculates Method form is simple, and required parameter is readily available, and result, close to reality, saves time, energy for designer And cost, and improve reliability and the life-span of system.

The additional aspect of the present invention and advantage will part be given in the following description, and part will become from the following description Obtain substantially, or recognized by the practice of the present invention.

Accompanying drawing explanation

Fig. 1: NGWN planet circular system schematic diagram；

Fig. 2: NGW train schematic diagram.

Detailed description of the invention

Embodiments of the invention are described below in detail, and the embodiment of description is exemplary, it is intended to be used for explaining the present invention, And be not considered as limiting the invention.

In order to preferably study the stationarity of drive mechanism, improve the precision of structure, provided below a kind of NGWN The geometric lost motion computational methods of planet circular system, the method considers several factor that geometric lost motion produces main impact, Ignoring the secondary cause that impact is less, the computational methods obtained are the most understandable, and the results contrast obtained is accurate, energy Enough instruct real work.

By the sideshake size of each gear being meshed carry out train geometric lost motion calculate, it is considered to several Major influence factors is respectively 1) gear backlash that causes of common normal average length deviation；2) gear run-out error draws The gear backlash risen；3) gear backlash that between gear pair, limit deviation of centre distance causes.

The NGWN gear train geometric lost motion computational methods set up herein are built upon existing NGW gear train return difference meter On the basis of calculation, accompanying drawing 1 is NGWN wheel train structure form, and composite gear N2 with N5 is coaxial, does not consider N5 During the geometric lost motion self produced, the geometric lost motion of N5 Yu N2 is identical, namely NGW train outfan Return difference.The N1N2N3 being made up of sun gear N1, composite gear N2 and internal gear N3 wheel is tied up to composite gear N2 The return difference that outfan and output gear N4 produce all is folded on composite gear N5 calculate, the most again with gear ratio i₄₅ Convert into back output gear N4 outfan, just obtained the core of the present invention: the return difference computing formula of NGWN train, In this formula, the calculating of return difference is relevant with the parameter value of gear.In practical implementation or design, Ke Yitong Cross and table look-up or measure base tangent length deviation, gear run-out error, between gear pair limit deviation of centre distance these Parameter, determines the backlash values between gear, and then obtains geometric lost motion result.

Method particularly includes:

One, according to formula

$\stackrel{\‾}{{\mathrm{\φ}}_4}=\frac{\stackrel{\‾}{{\mathrm{\φ}}_{5start}}+\stackrel{\‾}{{\mathrm{\φ}}_{5self}}+\stackrel{\‾}{{\mathrm{\φ}}_{4self}}\×i_{54}}{i_{54}}$

Calculate the geometric lost motion average of the output gear N4 of NGWN epicyclic train

Wherein:

For composite gear N5 input geometric lost motion average in NGWN epicyclic train；

For the geometric lost motion average of composite gear N2 outfan in NGWN epicyclic train；

$\stackrel{\‾}{{\mathrm{\φ}}_2}=\frac{6875.5}{{\mathrm{mz}}_2}({\mathrm{\Σj}}_{w,N1N2}+{\mathrm{\Σj}}_{w,N2N3})$

M is modulus, z₂The number of teeth for composite gear N2；

Σj_w,N1N2=j_w1,N1N2+j_w2,N1N2+j_w3,N1N2

j_w1,N1N2=j_w1dan,N1+j_w1dan,N2

j_w2,N1N2=j_w2dan,N1+j_w2dan,N2

Σj_w,N2N3=j_w1,N2N3+j_w2,N2N3+j_w3,N2N3

j_w1,N2N3=j_w1dan,N2+j_w1dan,N3

j_w2,N2N3=j_w2dan,N2+j_w2dan,N3

j_w1dan,N1、j_w1dan,N2、j_w1dan,N3It is respectively in NGWN epicyclic train sun gear N1, composite gear N2 and interior The gear N3 gear backlash that on business normal average length variation causes, j_w2dan,N1、j_w2dan,N2、j_w2dan,N3It is respectively too The gear backlash that sun wheel N1, composite gear N2 and internal gear N3 causes because of gear run-out error, j_w3,N1N2With j_w3,N2N3Be respectively limit deviation of centre distance causes between gear pair N1N2 gear backlash and gear pair N2N3 it Between the gear backlash that causes of limit deviation of centre distance；

The geometric lost motion average produced for composite gear N5 self:

$\stackrel{\‾}{{\mathrm{\φ}}_{5self}}=\frac{6875.5}{{\mathrm{mz}}_5}(j_{w1dan,N5}+j_{w2dan,N5})$

z₅The number of teeth for composite gear N5；j_w1dan,N5For the composite gear N5 gear side that on business normal average length variation causes Gap, j_w2dan,N5The gear backlash caused because of gear run-out error for composite gear N5；

The geometric lost motion average produced for output gear N4 self:

$\stackrel{\‾}{{\mathrm{\φ}}_{4self}}=\frac{6875.5}{{\mathrm{mz}}_4}(j_{w1dan,N4}+j_{w2dan,N4})$

z₄The number of teeth for output gear N4；j_w1dan,N4For the output gear N4 gear side that on business normal average length variation causes Gap, j_w2dan,N4The gear backlash caused because of gear run-out error for output gear N4；

i₅₄For composite gear N5 and the gear ratio of output gear N4.

For a certain gear N, its gear backlash j that on business normal average length variation causes_w1dan,NAccording to formula

$j_{w1dan,N}=-\frac{w_{Es,N}+w_{Ei,N}}{2cos\mathrm{\α}}$

Obtain；Wherein, α is pressure angle, w_Es,NFor the gear N common normal upper deviation, w_Ei,NFor gear N common normal Lower deviation.

And in the design phase, for a certain gear N, the gear backlash that its gear run-out error causes can take 0, For a certain gear pair NN ', its gear backlash caused because of limit deviation of centre distance can take 0.

Two, according to formula

${\mathrm{T\Δ\φ}}_4=\frac{{\mathrm{T\Δ\φ}}_{5start}+{\mathrm{T\Δ\φ}}_{5self}+{\mathrm{T\Δ\φ}}_{4self}\×i_{54}}{i_{54}}$

Calculate the geometric lost motion tolerance T Δ φ of the output gear N4 of NGWN epicyclic train₄；

Wherein:

TΔφ_5startFor composite gear N5 input geometric lost motion tolerance in NGWN epicyclic train；

TΔφ_5start=T Δ φ₂, T Δ φ₂For the geometric lost motion tolerance of composite gear N2 outfan in NGWN epicyclic train；

${\mathrm{T\Δ\φ}}_2=\frac{6875.5}{{\mathrm{mz}}_2}\left(\mathrm{\Σ}T\right(j_{w,N1N2})+\mathrm{\Σ}T(j_{w,N2N3}\left)\right)$

$\mathrm{\Σ}T\left(j_{w,N1N2}\right)=6\×\sqrt{\mathrm{\Σ}D\left(j_{w,N1N2}\right)}$

$\mathrm{\Σ}T\left(j_{w,N2N3}\right)=6\×\sqrt{\mathrm{\Σ}D\left(j_{w,N2N3}\right)}$

ΣD(j_w,N1N2)=D (j_w1,N1N2)+D(j_w2,N1N2)+D(j_w3,N1N2)

D(j_w1,N1N2)=D (j_w1dan,N1)+D(j_w1dan,N2)

D(j_w2,N1N2)=D (j_w2dan,N1)+D(j_w2dan,N2)

ΣD(j_w,N2N3)=D (j_w1,N2N3)+D(j_w2,N2N3)+D(j_w3,N2N3)

D(j_w1,N2N3)=D (j_w1dan,N2)+D(j_w1dan,N3)

D(j_w2,N2N3)=D (j_w2dan,N2)+D(j_w2dan,N3)

D(j_w1dan,N1)、D(j_w1dan,N2)、D(j_w1dan,N3) it is respectively sun gear N1, composite gear in NGWN epicyclic train N2 and the internal gear N3 gear backlash variance that on business normal average length variation causes, D (j_w2dan,N1)、D(j_w2dan,N2)、 D(j_w2dan,N3) it is respectively the tooth that sun gear N1, composite gear N2 and internal gear N3 cause because of gear run-out error Wheel sideshake variance, D (j_w3,N1N2) and D (j_w3,N2N3) it is respectively what limit deviation of centre distance between gear pair N1N2 caused The gear backlash variance that between gear backlash variance and gear pair N2N3, limit deviation of centre distance causes；

TΔφ_5selfThe geometric lost motion variance produced for composite gear N5 self:

${\mathrm{T\Δ\φ}}_{5self}=\frac{6875.5}{{\mathrm{mz}}_5}\left(D\right(j_{w1dan,N5})+D(j_{w2dan,N5}\left)\right)$

D(j_w1dan,N5) it is the composite gear N5 gear backlash tolerance that on business normal average length variation causes, D (j_w2dan,N5) it is The gear backlash tolerance that composite gear N5 causes because of gear run-out error；

TΔφ_4selfThe geometric lost motion variance produced for output gear N4 self:

${\mathrm{T\Δ\φ}}_{4self}=\frac{6875.5}{{\mathrm{mz}}_4}\left(D\right(j_{w1dan,N4})+D(j_{w2dan,N4}\left)\right)$

D(j_w1dan,N4) it is the output gear N4 gear backlash tolerance that on business normal average length variation causes, D (j_w2dan,N4) it is The gear backlash tolerance that output gear N4 causes because of gear run-out error；

Three, according to formula

${\mathrm{\φ}}_{4max}=\stackrel{\‾}{{\mathrm{\φ}}_4}+{\mathrm{T\Δ\φ}}_4$

${\mathrm{\φ}}_{4min}=\stackrel{\‾}{{\mathrm{\φ}}_4}-{\mathrm{T\Δ\φ}}_4$

Obtain the output gear N4 geometric lost motion maximum φ of NGWN epicyclic train_4maxWith minima φ_4min。

For a certain gear N, its gear backlash j that on business normal average length variation causes_w1dan,NAccording to formula

$j_{w1dan,N}=-\frac{w_{Es,N}+w_{Ei,N}}{2cos\mathrm{\α}}$

Obtain；Wherein, α is pressure angle, w_Es,NFor the gear N common normal upper deviation, w_Ei,NFor gear N common normal Lower deviation；

The a certain gear N gear backlash variance D (j that on business normal average length variation causes_w1dan,N) according to formula

$D\left(j_{w1dan,N}\right)={\left(\frac{w_{Es,N}-w_{Ei,N}}{6cos\mathrm{\α}}\right)}^2$

Obtain；

The gear backlash tolerance D (j that a certain gear N causes because of gear run-out error_w2dan,N) according to formula

$D\left(j_{w2dan,N}\right)={\left(\frac{F_{r,N}\×K_{\mathrm{\α}}\×tan\mathrm{\α}}{3}\right)}^2$

Obtain；Wherein, F_r,NFor gear N run-out error,α ' is the gear angle of engagement；

The gear backlash variance D (j that a certain gear pair NN ' causes because of limit deviation of centre distance_w3,NN′) according to formula

$D\left(j_{w3,{\mathrm{NN}}^{\′}}\right)={\left(\frac{F_{a,{\mathrm{NN}}^{\′}}\×K_{\mathrm{\α}}\×tan\mathrm{\α}}{3}\right)}^2$

Obtain；Wherein, F_a,NN′For gear pair NN ' limit deviation of centre distance.

After obtaining above method, according to the different phase used, such as design phase and maintenance or maintenance stage, pass through Different modes (table look-up or measure) relevant parameter, calculates, and obtains outfan geometric lost motion, and and national standard Compare, can be used for determining or prioritization scheme in the design phase, can be used for considering it in maintenance or maintenance stage His parts, system stability and the impact of sensitivity, preferably instruct and safeguard and maintenance, and then increase train reliability With the life-span.

Although above it has been shown and described that embodiments of the invention, it is to be understood that above-described embodiment is example Property, it is impossible to be interpreted as limitation of the present invention, those of ordinary skill in the art without departing from the present invention principle and Above-described embodiment can be changed within the scope of the invention in the case of objective, revise, replace and modification.

Claims (2)

1. NGWN epicyclic train geometric lost motion computational methods, it is characterised in that:

One, according to formula

$\stackrel{\‾}{{\mathrm{\φ}}_4}=\frac{\stackrel{\‾}{{\mathrm{\φ}}_{5start}}+\stackrel{\‾}{{\mathrm{\φ}}_{5self}}+\stackrel{\‾}{{\mathrm{\φ}}_{4self}}\×i_{54}}{i_{54}}$

Calculate the geometric lost motion average of the output gear N4 of NGWN epicyclic train

Wherein:

For composite gear N5 input geometric lost motion average in NGWN epicyclic train；

For the geometric lost motion average of composite gear N2 outfan in NGWN epicyclic train；

$\stackrel{\‾}{{\mathrm{\φ}}_2}=\frac{6875.5}{{\mathrm{mz}}_2}({\mathrm{\Σj}}_{w,N1N2}+{\mathrm{\Σj}}_{w,N2N3})$

M is modulus, z₂The number of teeth for composite gear N2；

∑j_w,N1N2=j_w1,N1N2+j_w2,N1N2+j_w3,N1N2

j_w1,N1N2=j_w1dan,N1+j_w1dan,N2

j_w2,N1N2=j_w2dan,N1+j_w2dan,N2

∑j_w,N2N3=j_w1,N2N3+j_w2,N2N3+j_w3,N2N3

j_w1,N2N3=j_w1dan,N2+j_w1dan,N3

j_w2,N2N3=j_w2dan,N2+j_w2dan,N3

j_w1dan,N1、j_w1dan,N2、j_w1dan,N3It is respectively in NGWN epicyclic train sun gear N1, composite gear N2 and interior The gear N3 gear backlash that on business normal average length variation causes, j_w2dan,N1、j_w2dan,N2、j_w2dan,N3It is respectively too The gear backlash that sun wheel N1, composite gear N2 and internal gear N3 causes because of gear run-out error, j_w3,N1N2With j_w3,N2N3Be respectively limit deviation of centre distance causes between gear pair N1N2 gear backlash and gear pair N2N3 it Between the gear backlash that causes of limit deviation of centre distance；

The geometric lost motion average produced for composite gear N5 self:

$\stackrel{\‾}{{\mathrm{\φ}}_{5self}}=\frac{6875.5}{{\mathrm{mz}}_5}(j_{w1dan,N5}+j_{w2dan,N5})$

z₅The number of teeth for composite gear N5；j_w1dan,N5For the composite gear N5 gear side that on business normal average length variation causes Gap, j_w2dan,N5The gear backlash caused because of gear run-out error for composite gear N5；

The geometric lost motion average produced for output gear N4 self:

$\stackrel{\‾}{{\mathrm{\φ}}_{4self}}=\frac{6875.5}{{\mathrm{mz}}_4}(j_{w1dan,N4}+j_{w2dan,N4})$

z₄The number of teeth for output gear N4；j_w1dan,N4For the output gear N4 gear side that on business normal average length variation causes Gap, j_w2dan,N4The gear backlash caused because of gear run-out error for output gear N4；

i₅₄For composite gear N5 and the gear ratio of output gear N4；

Two, according to formula

${\mathrm{T\Δ\φ}}_4=\frac{{\mathrm{T\Δ\φ}}_{5start}+{\mathrm{T\Δ\φ}}_{5self}+{\mathrm{T\Δ\φ}}_{4self}\×i_{54}}{i_{54}}$

Calculate the geometric lost motion tolerance T Δ φ of the output gear N4 of NGWN epicyclic train₄；

Wherein:

TΔφ_5startFor composite gear N5 input geometric lost motion tolerance in NGWN epicyclic train；

TΔφ_5start=T Δ φ₂, T Δ φ₂For the geometric lost motion tolerance of composite gear N2 outfan in NGWN epicyclic train；

${\mathrm{T\Δ\φ}}_2=\frac{6875.5}{{\mathrm{mz}}_2}\left(\mathrm{\Σ}T\right(j_{w,N1N2})+\mathrm{\Σ}T(j_{w,N2N3}\left)\right)$

$\mathrm{\Σ}T\left(j_{w,N1N2}\right)=6\×\sqrt{\mathrm{\Σ}D\left(j_{w,N1N2}\right)}$

$\mathrm{\Σ}T\left(j_{w,N2N3}\right)=6\×\sqrt{\mathrm{\Σ}D\left(j_{w,N2N3}\right)}$

ΣD(j_w,N1N2)=D (j_w1,N1N2)+D(j_w2,N1N2)+D(j_w3,N1N2)

D(j_w1,N1N2)=D (j_w1dan,N1)+D(j_w1dan,N2)

D(j_w2,N1N2)=D (j_w2dan,N1)+D(j_w2dan,N2)

ΣD(j_w,N2N3)=D (j_w1,N2N3)+D(j_w2,N2N3)+D(j_w3,N2N3)

D(j_w1,N2N3)=D (j_w1dan,N2)+D(j_w1dan,N3)

D(j_w2,N2N3)=D (j_w2dan,N2)+D(j_w2dan,N3)

D(j_w1dan,N1)、D(j_w1dan,N2)、D(j_w1dan,N3) it is respectively sun gear N1, composite gear in NGWN epicyclic train N2 and the internal gear N3 gear backlash variance that on business normal average length variation causes, D (j_w2dan,N1)、D(j_w2dan,N2)、 D(j_w2dan,N3) it is respectively the tooth that sun gear N1, composite gear N2 and internal gear N3 cause because of gear run-out error Wheel sideshake variance, D (j_w3,N1N2) and D (j_w3,N2N3) it is respectively what limit deviation of centre distance between gear pair N1N2 caused The gear backlash variance that between gear backlash variance and gear pair N2N3, limit deviation of centre distance causes；

TΔφ_5selfThe geometric lost motion variance produced for composite gear N5 self:

${\mathrm{T\Δ\φ}}_{5self}=\frac{6875.5}{{\mathrm{mz}}_5}\left(D\right(j_{w1dan,N5})+D(j_{w2dan,N5}\left)\right)$

D(j_w1dan,N5) it is the composite gear N5 gear backlash tolerance that on business normal average length variation causes, D (j_w2dan,N5) it is The gear backlash tolerance that composite gear N5 causes because of gear run-out error；

TΔφ_4selfThe geometric lost motion variance produced for output gear N4 self:

${\mathrm{T\Δ\φ}}_{4self}=\frac{6875.5}{{\mathrm{mz}}_4}\left(D\right(j_{w1dan,N4})+D(j_{w2dan,N4}\left)\right)$

D(j_w1dan,N4) it is the output gear N4 gear backlash tolerance that on business normal average length variation causes, D (j_w2dan,N4) it is The gear backlash tolerance that output gear N4 causes because of gear run-out error；

Three, according to formula

${\mathrm{\φ}}_{4max}=\stackrel{\‾}{{\mathrm{\φ}}_4}+{\mathrm{T\Δ\φ}}_4$

${\mathrm{\φ}}_{4\min }=\stackrel{\‾}{{\mathrm{\φ}}_4}-{\mathrm{T\Δ\φ}}_4$

Obtain the output gear N4 geometric lost motion maximum φ of NGWN epicyclic train_4maxWith minima φ_4min。

A kind of NGWN epicyclic train geometric lost motion computational methods, it is characterised in that:

A certain gear N gear backlash j that on business normal average length variation causes_w1dan,NAccording to formula

$j_{w1dan,N}=-\frac{w_{Es,N}+w_{Ei,N}}{2cos\mathrm{\α}}$

Obtain；Wherein, α is pressure angle, w_Es,NFor the gear N common normal upper deviation, w_Ei,NFor gear N common normal Lower deviation；

The a certain gear N gear backlash variance D (j that on business normal average length variation causes_w1dan,N) according to formula

$D\left(j_{w1dan,N}\right)={\left(\frac{w_{Es,N}-w_{Ei,N}}{6cos\mathrm{\α}}\right)}^2$

Obtain；

The gear backlash tolerance D (j that a certain gear N causes because of gear run-out error_w2dan,N) according to formula

$D\left(j_{w2dan,N}\right)={\left(\frac{F_{r,N}\×K_{\mathrm{\α}}\×tan\mathrm{\α}}{3}\right)}^2$

Obtain；Wherein, F_r,NFor gear N run-out error,α ' is the gear angle of engagement；

The gear backlash variance D (j that a certain gear pair NN ' causes because of limit deviation of centre distance_w3,NN′) according to formula

$D\left(j_{w3,{\mathrm{NN}}^{\′}}\right)={\left(\frac{F_{a,{\mathrm{NN}}^{\′}}\×K_{\mathrm{\α}}\×tan\mathrm{\α}}{3}\right)}^2$

Obtain；Wherein, F_a,NN′For gear pair NN ' limit deviation of centre distance.