CN105678106A - Method for selecting planetary transmission schemes - Google Patents

Abstract

The invention relates to a method for selecting planetary transmission schemes. The method comprises the following steps that firstly, a multi-target optimization model for transmission errors is established; secondly, transmission performance is analyzed; thirdly, the structure geometric contradiction is analyzed; fourthly, a planetary transmission scheme is determined. By means of the selecting method, the preset requirements for performance indexes such as the planet wheel relative rotating speed, the manipulation moment and the transmission efficiency are met, no interference is caused on the structure, the optimal planetary transmission designing scheme of a designer is met, and multiple gears, high power, high rotation speed and high power density of a transmission system are achieved.

Description

The system of selection of a kind of Gear Planet Transmission scheme

Technical field

The present invention relates to the system of selection of a kind of scheme, specifically relate to the system of selection of a kind of Gear Planet Transmission scheme.

Background technology

Along with modern vehicle is gradually to the development in many grades of changes, rotating speed high-power, high and high power density direction, drive technology is had higher requirement, in this case, epicyclic variable-speed gear high-power, the gearshift of compact construction, high rotating speed power can be realized to be widely used in transmission system. In planet kinetics design process, known transmission scheme, it need to be carried out absolute rotating speed, the definitely performance analysis such as torque and transmission efficiency, analyze whether this transmission scheme meets predetermined every performance index (satellite gear relative rotation speed, operating torque, transmission efficiency etc.) by calculation result. Consider meet to the transmission scheme quantity of stable drive ratio continuous request more, if rely on manually they are carried out performance analysis one by one, its counting yield is low and is easy to make mistakes. And it is not often unique for being met in every predetermined performance index and structure the scheme not interfered, need planner, from all respects, scheme is carried out balance to analyze, realize best transmission scheme to select, conventional scheme decision-making relies on experimental knowledge and the Thinking Characteristics of planner completely, lacks appraisement system and the method for science.

Summary of the invention

In order to solve above-mentioned deficiency existing in prior art, the present invention provides the system of selection of a kind of Gear Planet Transmission scheme.

Technical scheme provided by the invention is: the system of selection of a kind of Gear Planet Transmission scheme, described method comprises the steps:

Described method comprises the steps:

I, the Model for Multi-Objective Optimization setting up transmission error;

II, analysis transmission performance;

III, analytical structure geometry contradiction;

IV, determine Gear Planet Transmission scheme.

Preferably, the Model for Multi-Objective Optimization that described step I sets up transmission error comprises:

(1) Optimum Matching of structural parameter and gear number is determined;

(2) Model for Multi-Objective Optimization is set up.

Preferably, described step (1) described structural parameter comprise number of degrees of freedom, planet row, stopper number and clutch coupling number;

The objective function of the Optimum Matching of structural parameter and gear number is determined with following formula:

$\min f\left(x\right)=\frac{n+p+Z+L}{d_g}---\left(1\right)$

The constraint condition of described objective function is shown below:

$\left\{\begin{array}{c}p\≤Z+2\\ Z+L\≥n\\ p-n+1\≥0\\ 1\≤p\≤5\\ 1\≤Z\≤5\\ 1\≤L\≤5\end{array}\right.---\left(2\right)$

Wherein, n represents number of degrees of freedom, and p represents planet row, and Z represents stopper number, and L represents clutch coupling number, d_gRepresent gear number.

Preferably, described step (1) Model for Multi-Objective Optimization is shown below:

$\left\{\begin{array}{c}\min n_{x\max }(i_1,i_2,...,i_p)\\ \min M_{\mathrm{\φ}max}(i_1,i_2,...,i_p)\\ {\mathrm{max\η}}_{\min }(i_1,i_2,...,i_p)\end{array}\right.---\left(4\right)$

The oriented limit e2 on the oriented limit e1 on input link and frame summit and output link and frame summit, when the conceptual design of reality, each independent gear transmitting ratio size is difficult to accurately provide its concrete numerical value, usually with certain limit of error, is shown below:

$\left\{\begin{array}{c}{e}_1=1\\ \frac{1}{i_{j\max }}\≤e_2\≤\frac{1}{i_{j\min }}\end{array}\right.,(j=1,2,...,d_g)---\left(3\right)$

Wherein, n_xmax: the maximum relative rotation speed of each planet seniority among brothers and sisters star-wheel in all available non-immediate gears;M_φmaxRepresent the maximum operating torque of each operating element in all available non-immediate gears; η_min: minimum transmission efficiency in all available non-immediate gears; i₁、i₂、…、i_pRepresent p respectively and independently keep off transmitting ratio, i_jmax: the maximum value that jth gear transmitting ratio allows; i_jmin: the minimum value that jth gear transmitting ratio allows;

The constraint condition of described Model for Multi-Objective Optimization is shown below:

$\left|\frac{i_j-i_j^{\′}(i_1,i_2,...,i_p)}{i_j}\right|\≤R_j,(j=1,2,...,d_g)---\left(5\right)$

k_min≤k_j(i₁,i₂,…,i_p)≤k_max, (j=1,2 ..., p) (6)

In formula, k_min、k_maxRepresent the lower value that planet row's characteristic parameter allows and higher limit respectively; k_jRepresent planet row's characteristic parameter; i_jThe non-gear of expression scheme jth needs the transmitting ratio accurately realized; I'_jThe transmitting ratio that expression scheme reality can realize; R_jRepresent the relative error that jth gear transmitting ratio allows; J=1,2 ..., p represents p independent gear.

Preferably, described Step II is analyzed transmission performance and is comprised: adopting graph theory modeling method, basic movement parts each in transmission scheme is mapped as the summit of figure, between them, connecting relation is mapped as the limit of figure, sets up the system diagram model being used for transmission performance and analyzing.

Preferably, described system diagram model carries out the model that topological transformation obtains comprise: performance analysis graph theory model, kinematics analyze graph theory model, dynamic analysis graph theory model and Gear Planet Transmission loss efficiency calculation formula.

Preferably, described performance analysis graph theory model comprises: leave out the limit associated by summit, clutch coupling active and passive limit on system diagram G basis, and dotted line limit only makes two summits being associated, obtain Components Analysis figure model G1, system diagram G model basis is deleted remaining and does not engage the thin solid line limit corresponding to operating element, then obtain corresponding working condition chart G2 model;

Wherein, the number connected component Q (G) of basic scantling numeral J Components Analysis figure G1, represents with following formula:

J=Q (G) (7);

Described kinematics is analyzed graph theory model and is comprised: is deleted from working condition chart G2 on the dotted line limit of correspondence, is transformed to corresponding rotating speed analysis chart G3 model;

Each planet arranges the rotation speed relation formula of three basic movement parts:

n_ti+k_i×n_qi-(1+k_i)×n_ji=0 (i=1,2 ..., p) (8)

In formula, n_ti、n_qi、n_jiRepresent sun gear, gear ring and planet carrier rotating speed that i-th planet is arranged respectively; k_iRepresent the characteristic parameter of i-th planet row;

The equal relational expression of rotating speed that two summits being associated on every bar limit are set up automatically is shown below:

n_ai-n_bi=0 (i=1,2 ..., E (G3)) and (9)

In formula, n_ai、n_biRepresenting two summit (ai, bi) rotating speeds that in rotating speed analysis chart G3, i-th limit is associated, E (G3) is the limit number of figure G3;

Satellite gear relative rotation speed n_xiIt is shown below:

$n_{xi}=\frac{-2}{k_i-1}(n_{ti}-n_{ji})=\frac{2k_i}{k_i-1}(n_{qi}-n_{ji})=\frac{2k_i}{1-k_i^2}(n_{ti}-n_{qi})---\left(10\right)$

The transmitting ratio i of operating mode is shown below:

$i=\frac{n_o}{n_b}---\left(11\right)$

Wherein n₀Represent input speed, n_bRepresent output speed, satellite gear relative rotation speed n_xiIn i=1,2 ..., p;

Described dynamic analysis graph theory model comprises the torque relationship formula that each planet arranges three basic movement parts, engaged the active and passive limit of clutch coupling (L1, L2) torque relationship formula and in conjunction with the torque relationship formula on the active and passive limit of clutch coupling (L3, L4);

Represent that each planet described arranges the torque relationship of three basic movement parts with following formula:

M_ti:M_qi:M_ji=1:k_i:-(1+k_i) (i=1,2 ..., p) (12)

In formula, M_ti、M_qi、M_jiRepresent the torque that i-th planet row's sun gear, gear ring and planet carrier bear, k respectively_iRepresent the characteristic parameter of i-th planet row;

The torque relationship on the active and passive limit of clutch coupling (L1, L2) has been engaged with following formula described in representing:

M_L1+M_L2=0 (13)

The active and passive limit of clutch coupling (L3, L4) torque relationship is not engaged with following formula described in representing:

$\left\{\begin{array}{c}{M}_{L3}=0\\ M_{L4}=0\end{array}\right.---\left(14\right);$

Described Gear Planet Transmission loss efficiency eta is calculated with following formula:

$\mathrm{\η}=\frac{P_o-(P_{s1}+P_{s2}+...)}{P_o}=1-\[(1-{\mathrm{\η}}_{x1}){\mathrm{\β}}_1+(1-{\mathrm{\η}}_{x2}){\mathrm{\β}}_2+...\]---\left(15\right)$

In formula, P_oRepresent input link power, P_s1、P_s2Represent each planet row's power loss respectively, η_x1、η_x2Represent the relative movement efficiency that each planet is arranged, β respectively₁、β₂Represent the relative power efficiencies that each planet is arranged, M_L1、M_L2、M_L3、M_L4Represent limit L respectively₁、L₂、L₃、L₄Torque.

Preferably, described Step II I analytical structure geometry contradiction graph theory comprises planarity figure model carrying out simplify processes and using D.M.P algorithm detection figure;

The simplify processes that figure model carries out is comprised the steps:

(1) if figure is not connected graph, then each connection branch to it is needed to detect;

(2) if figure can divide figure, each being connected block and detects respectively, and if only if, and its each connection block is orthographic plan, then figure is planarity;

(3) all of figure are deleted from ring;

(4) between each opposite vertexes, except retaining a limit, remaining parallel limit is deleted;

(5) two adjacent edges associated with two summits replace with a limit.

Preferably, described step IV determines that Gear Planet Transmission scheme comprises: the determination of index weight and the calculating of comprehensive evaluation value.

Preferably, the determination of described index weight comprises:

(1) represent, with following formula, the matrix A that 1～9 grade of scale judges:

$\left\{\begin{array}{c}{a}_{ii}=\frac{{\mathrm{\ω}}_i}{{\mathrm{\ω}}_j}=1\\ a_{ji}=\frac{{\mathrm{\ω}}_j}{{\mathrm{\ω}}_i}=\frac{1}{a_{ij}}\\ a_{ij}\·a_{jk}=\frac{{\mathrm{\ω}}_i}{{\mathrm{\ω}}_j}\·\frac{{\mathrm{\ω}}_j}{{\mathrm{\ω}}_k}=a_{ik}\end{array}\right.---\left(16\right)$

In formula, element a_ijRepresent that the factor Bi that obtains from judgment matrix A angle is to the relative importance of factor Bj, element a_jiRepresent that the factor Bj that obtains from judgment matrix A angle is to the relative importance of factor Bi, element a_jkRepresent that the factor Bj that obtains from judgment matrix A angle is to the relative importance of factor Bk, element a_iiRepresenting that the factor Bi obtained from judgment matrix A angle is to the importance of self, factor Bi, Bj, Bk represent one of as main rule layer 7 indexs respectively, ω_i、ω_j、ω_kIt is respectively the weighted value of factor i, j and k;

Coincident indicator C.I is calculated with following formula:

$C.I=\frac{{\mathrm{\λ}}_{max}-n}{n-1}---\left(17\right)$

In formula, λ_maxFor the maximum eigenwert of judgment matrix A, n=1～9;

Consistence ratio C.R is represented with following formula:

$C.R=\frac{C.I}{R.I}---\left(18\right)$

In formula, R.I represents Aver-age Random Consistency Index, during using C.R < 0.10 as the consistence judging criterion of matrix, by the weight of proper vector corresponding to its maximum eigenwert as each key element, otherwise do to be suitable for this matrix and revise, obtain decision-making stdn matrix Y=(y_i,j)_m×n', then be normalized;

It is normalized with following formula:

$p_{i,j}=\frac{y_{i,j}}{\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{y}_{i,j}},(i=1,2,...,m;j=1,2,...,n^{\&prime;})---\left(19\right)$

The entropy e of jth index is calculated with following formula_j:

$e_j=-\frac{1}{\ln m}\&CenterDot;\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{p}_{i,j}\ln p_{i,j},(j=1,2,...,n^{\&prime;})---\left(20\right)$

The discrimination factor g of jth index is calculated with following formula_j:

g_j=1-e_j(j=1,2 ..., n') and (21)

The weights omega of jth index is determined with following formula_j:

${\mathrm{\&omega;}}_j=\frac{g_j}{\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{g}_j},(j=1,2,...,n^{\&prime;})---\left(22\right)$

Each each factor B of main criterion is calculated with following formula_iRelative weighting to general objective A:

${\mathrm{\&omega;}}_{(A-B)}={({\mathrm{\&omega;}}_1^{\left(0\right)},{\mathrm{\&omega;}}_2^{\left(0\right)},...,{\mathrm{\&omega;}}_7^{\left(0\right)})}^T---\left(23\right)$

M in formula, n' all represent integer,Represent each main rule layer weight respectively;

C is calculated with following formula_ijTo sub-goal B_iRelative weighting:

${\mathrm{\&omega;}}_{(B-C)}^{\left(i\right)}={({\mathrm{\&omega;}}_1^{\left(i\right)},{\mathrm{\&omega;}}_2^{\left(i\right)},...,{\mathrm{\&omega;}}_{n^{\&prime;}}^{\left(i\right)})}^T---\left(24\right)$

Wherein, the value one_to_one corresponding of n' and i, i=1,2 ..., 7, then corresponding n' is respectively I-1,5,3I-1,2I, I-1,2,2, and wherein I represents the number of the further refinement of every index;

Each index C is represented with following formula_ijRelative weighting to general objective A:

$\mathrm{\&omega;}={({\mathrm{\&omega;}}_{12},{\mathrm{\&omega;}}_{22},...,{\mathrm{\&omega;}}_{72})}^T=({\mathrm{\&omega;}}_1^{\left(0\right)}\&CenterDot;{\mathrm{\&omega;}}_1^{\left(1\right)},{\mathrm{\&omega;}}_1^{\left(0\right)}\&CenterDot;{\mathrm{\&omega;}}_2^{\left(1\right)},...{\mathrm{\&omega;}}_7^{\left(0\right)}\&CenterDot;{\mathrm{\&omega;}}_2^{\left(1\right)})---\left(25\right)$

Described comprehensive evaluation value z is calculated with following formula_i:

$z_i=\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_j\&CenterDot;y_{i,j},(i=1,2,...,m;j=1,2,...,7I+6)---\left(26\right)$

Wherein, 7I+6 represents that suitability, reasonable structure, kinematics performance, dynamic performance, economy, steering quality, manufacturability 7 indexs are as main rule layer, and by the indicator layer that further for every index refinement obtains, I represents the number of the further refinement of every index;

Gear Planet Transmission scheme is by { z_iThe size of value determines.

Compared with prior art, the present invention has following useful effect:

The present invention obtains the requirement meeting every performance index such as predetermined satellite gear relative rotation speed, operating torque, transmission efficiency by this system of selection, and structurally do not interfere, meet the Gear Planet Transmission design of the optimum of planner's intention, it is achieved many grades of changes of transmission system, rotating speed high-power, high and high power density.

Accompanying drawing explanation

Fig. 1 is the system of selection schema of the Gear Planet Transmission scheme of the present invention;

Fig. 2 is planet speed-change case transmission sketch and system diagram model G schematic diagram thereof;

Fig. 3 is poower flow visable representation;

Fig. 4 is the selection of the Gear Planet Transmission scheme of the present invention;

Embodiment

In order to understand the present invention better, below in conjunction with Figure of description and example, the content of the present invention is described further.

Shown in the system of selection schema of the Gear Planet Transmission scheme of composition graphs 1 the present invention, the system of selection of described Gear Planet Transmission scheme comprises the steps:

I, the Model for Multi-Objective Optimization setting up transmission error;

II, analysis transmission performance;

III, analytical structure geometry contradiction;

IV, determine Gear Planet Transmission scheme.

The Model for Multi-Objective Optimization that described step I sets up transmission error comprises:

(1) Optimum Matching of structural parameter and gear number is determined;

(2) Model for Multi-Objective Optimization is set up.

Described step (1) described structural parameter comprise number of degrees of freedom, planet row, stopper number and clutch coupling number;

The objective function of the Optimum Matching of structural parameter and gear number is determined with following formula:

$\min f\left(x\right)=\frac{n+p+Z+L}{d_g}---\left(1\right)$

The constraint condition of described objective function is shown below:

$\left\{\begin{array}{c}p\&le;Z+2\\ Z+L\&GreaterEqual;n\\ p-n+1\&GreaterEqual;0\\ 1\&le;p\&le;5\\ 1\&le;Z\&le;5\\ 1\&le;L\&le;5\end{array}\right.---\left(2\right)$

Wherein, n represents number of degrees of freedom, and p represents planet row, and Z represents stopper number, and L represents clutch coupling number, d_gRepresent gear number.

Described step (1) Model for Multi-Objective Optimization is shown below:

$\left\{\begin{array}{c}\min n_{x\max }(i_1,i_2,...,i_p)\\ \min M_{\mathrm{\&phi;}max}(i_1,i_2,...,i_p)\\ {\mathrm{max\&eta;}}_{\min }(i_1,i_2,...,i_p)\end{array}\right.---\left(4\right)$

The oriented limit e2 on the oriented limit e1 on input link and frame summit and output link and frame summit, when the conceptual design of reality, each independent gear transmitting ratio size is difficult to accurately provide its concrete numerical value, usually with certain limit of error, is shown below:

$\left\{\begin{array}{c}{e}_1=1\\ \frac{1}{i_{j\max }}\&le;e_2\&le;\frac{1}{i_{j\min }}\end{array}\right.,(j=1,2,...,d_g)---\left(3\right)$

Wherein, n_xmax: the maximum relative rotation speed of each planet seniority among brothers and sisters star-wheel in all available non-immediate gears; M_φmaxRepresent the maximum operating torque of each operating element in all available non-immediate gears; η_min: minimum transmission efficiency in all available non-immediate gears; i₁、i₂、…、i_pRepresent p respectively and independently keep off transmitting ratio, i_jmax: the maximum value that jth gear transmitting ratio allows; i_jmin: the minimum value that jth gear transmitting ratio allows;

The constraint condition of described Model for Multi-Objective Optimization is shown below:

$\left|\frac{i_j-i_j^{\&prime;}(i_1,i_2,...,i_p)}{i_j}\right|\&le;R_j,(j=1,2,...,d_g)---\left(5\right)$

k_min≤k_j(i₁,i₂,…,i_p)≤k_max, (j=1,2 ..., p) (6)

In formula, k_min、k_maxRepresent the lower value that planet row's characteristic parameter allows and higher limit respectively; k_jRepresent planet row's characteristic parameter; i_jThe non-gear of expression scheme jth needs the transmitting ratio accurately realized; I'_jThe transmitting ratio that expression scheme reality can realize; R_jRepresent the relative error that jth gear transmitting ratio allows; J=1,2 ..., p represents p independent gear.

Described Step II is analyzed transmission performance and is comprised: adopting graph theory modeling method, basic movement parts each in transmission scheme is mapped as the summit of figure, between them, connecting relation is mapped as the limit of figure, sets up the system diagram model being used for transmission performance and analyzing.

Described system diagram model carries out the model that topological transformation obtains comprise: performance analysis graph theory model, kinematics analyze graph theory model, dynamic analysis graph theory model and Gear Planet Transmission loss efficiency calculation formula.

Described performance analysis graph theory model comprises: leave out the limit associated by summit, clutch coupling active and passive limit on system diagram G basis, and dotted line limit only makes two summits being associated, obtain Components Analysis figure model G1, system diagram G model basis is deleted remaining and does not engage the thin solid line limit corresponding to operating element, then obtain corresponding working condition chart G2 model;

Wherein, the number connected component Q (G) of basic scantling numeral J Components Analysis figure G1, represents with following formula:

J=Q (G) (7);

Described kinematics is analyzed graph theory model and is comprised: is deleted from working condition chart G2 on the dotted line limit of correspondence, is transformed to corresponding rotating speed analysis chart G3 model;

Each planet arranges the rotation speed relation formula of three basic movement parts:

n_ti+k_i×n_qi-(1+k_i)×n_ji=0 (i=1,2 ..., p) (8)

In formula, n_ti、n_qi、n_jiRepresent sun gear, gear ring and planet carrier rotating speed that i-th planet is arranged respectively; k_iRepresent the characteristic parameter of i-th planet row;

The equal relational expression of rotating speed that two summits being associated on every bar limit are set up automatically is shown below:

n_ai-n_bi=0 (i=1,2 ..., E (G3)) and (9)

In formula, n_ai、n_biRepresenting two summit (ai, bi) rotating speeds that in rotating speed analysis chart G3, i-th limit is associated, E (G3) is the limit number of figure G3;

Satellite gear relative rotation speed n_xiIt is shown below:

$n_{xi}=\frac{-2}{k_i-1}(n_{ti}-n_{ji})=\frac{2k_i}{k_i-1}(n_{qi}-n_{ji})=\frac{2k_i}{1-k_i^2}(n_{ti}-n_{qi})---\left(10\right)$

The transmitting ratio i of operating mode is shown below:

$i=\frac{n_o}{n_b}---\left(11\right)$

Wherein n₀Represent input speed, n_bRepresent output speed, satellite gear relative rotation speed n_xiIn i=1,2 ..., p;

Described dynamic analysis graph theory model comprises the torque relationship formula that each planet arranges three basic movement parts, engaged the active and passive limit of clutch coupling (L1, L2) torque relationship formula and in conjunction with the torque relationship formula on the active and passive limit of clutch coupling (L3, L4);

Represent that each planet described arranges the torque relationship of three basic movement parts with following formula:

M_ti:M_qi:M_ji=1:k_i:-(1+k_i) (i=1,2 ..., p) (12)

In formula, M_ti、M_qi、M_jiRepresent the torque that i-th planet row's sun gear, gear ring and planet carrier bear, k respectively_iRepresent the characteristic parameter of i-th planet row;

The torque relationship on the active and passive limit of clutch coupling (L1, L2) has been engaged with following formula described in representing:

M_L1+M_L2=0 (13)

The active and passive limit of clutch coupling (L3, L4) torque relationship is not engaged with following formula described in representing:

$\left\{\begin{array}{c}{M}_{L3}=0\\ M_{L4}=0\end{array}\right.---\left(14\right);$

Described Gear Planet Transmission loss efficiency eta is calculated with following formula:

$\mathrm{\&eta;}=\frac{P_o-(P_{s1}+P_{s2}+...)}{P_o}=1-\&lsqb;(1-{\mathrm{\&eta;}}_{x1}){\mathrm{\&beta;}}_1+(1-{\mathrm{\&eta;}}_{x2}){\mathrm{\&beta;}}_2+...\&rsqb;---\left(15\right)$

In formula, P_oRepresent input link power, P_s1、P_s2Represent each planet row's power loss respectively, η_x1、η_x2Represent the relative movement efficiency that each planet is arranged, β respectively₁、β₂Represent the relative power efficiencies that each planet is arranged, M_L1、M_L2、M_L3、M_L4Represent limit L respectively₁、L₂、L₃、L₄Torque.

Described Step II I analytical structure geometry contradiction graph theory comprises planarity figure model carrying out simplify processes and using D.M.P algorithm detection figure;

The simplify processes that figure model carries out is comprised the steps:

(1) if figure is not connected graph, then each connection branch to it is needed to detect;

(2) if figure can divide figure, each being connected block and detects respectively, and if only if, and its each connection block is orthographic plan, then figure is planarity;

(3) all of figure are deleted from ring;

(4) between each opposite vertexes, except retaining a limit, remaining parallel limit is deleted;

(5) two adjacent edges associated with two summits replace with a limit.

Described step IV determines that Gear Planet Transmission scheme comprises: the determination of index weight and the calculating of comprehensive evaluation value.

The determination of described index weight comprises:

(1) represent, with following formula, the matrix A that 1～9 grade of scale judges:

$\left\{\begin{array}{c}{a}_{ii}=\frac{{\mathrm{\&omega;}}_i}{{\mathrm{\&omega;}}_j}=1\\ a_{ji}=\frac{{\mathrm{\&omega;}}_j}{{\mathrm{\&omega;}}_i}=\frac{1}{a_{ij}}\\ a_{ij}\&CenterDot;a_{jk}=\frac{{\mathrm{\&omega;}}_i}{{\mathrm{\&omega;}}_j}\&CenterDot;\frac{{\mathrm{\&omega;}}_j}{{\mathrm{\&omega;}}_k}=a_{ik}\end{array}\right.---\left(16\right)$

In formula, element a_ijRepresent that the factor Bi that obtains from judgment matrix A angle is to the relative importance of factor Bj, element a_jiRepresent that the factor Bj that obtains from judgment matrix A angle is to the relative importance of factor Bi, element a_jkRepresent that the factor Bj that obtains from judgment matrix A angle is to the relative importance of factor Bk, element a_iiRepresenting that the factor Bi obtained from judgment matrix A angle is to the importance of self, factor Bi, Bj, Bk represent one of as main rule layer 7 indexs respectively, ω_i、ω_j、ω_kIt is respectively the weighted value of factor i, j and k;

Coincident indicator C.I is calculated with following formula:

$C.I=\frac{{\mathrm{\&lambda;}}_{max}-n}{n-1}---\left(17\right)$

In formula, λ_maxFor the maximum eigenwert of judgment matrix A, n=1～9;

Consistence ratio C.R is represented with following formula:

$C.R=\frac{C.I}{R.I}---\left(18\right)$

In formula, R.I represents Aver-age Random Consistency Index, during using C.R < 0.10 as the consistence judging criterion of matrix, by the weight of proper vector corresponding to its maximum eigenwert as each key element, otherwise do to be suitable for this matrix and revise, obtain decision-making stdn matrix Y=(y_i,j)_m×n', then be normalized;

It is normalized with following formula:

$p_{i,j}=\frac{y_{i,j}}{\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{y}_{i,j}},(i=1,2,...,m;j=1,2,...,n^{\&prime;})---\left(19\right)$

The entropy e of jth index is calculated with following formula_j:

$e_j=-\frac{1}{\ln m}\&CenterDot;\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{p}_{i,j}\ln p_{i,j},(j=1,2,...,n^{\&prime;})---\left(20\right)$

The discrimination factor g of jth index is calculated with following formula_j:

g_j=1-e_j(j=1,2 ..., n') and (21)

The weights omega of jth index is determined with following formula_j:

${\mathrm{\&omega;}}_j=\frac{g_j}{\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{g}_j},(j=1,2,...,n^{\&prime;})---\left(22\right)$

Each each factor B of main criterion is calculated with following formula_iRelative weighting to general objective A:

${\mathrm{\&omega;}}_{(A-B)}={({\mathrm{\&omega;}}_1^{\left(0\right)},{\mathrm{\&omega;}}_2^{\left(0\right)},...,{\mathrm{\&omega;}}_7^{\left(0\right)})}^T---\left(23\right)$

M in formula, n' all represent integer,Represent each main rule layer weight respectively;

C is calculated with following formula_ijTo sub-goal B_iRelative weighting:

${\mathrm{\&omega;}}_{(B-C)}^{\left(i\right)}={({\mathrm{\&omega;}}_1^{\left(i\right)},{\mathrm{\&omega;}}_2^{\left(i\right)},...,{\mathrm{\&omega;}}_{n^{\&prime;}}^{\left(i\right)})}^T---\left(24\right)$

Wherein, the value one_to_one corresponding of n' and i, i=1,2 ..., 7, then corresponding n' is respectively I-1,5,3I-1,2I, I-1,2,2, and wherein I represents the number of the further refinement of every index;

Each index C is represented with following formula_ijRelative weighting to general objective A:

$\mathrm{\&omega;}={({\mathrm{\&omega;}}_{12},{\mathrm{\&omega;}}_{22},...,{\mathrm{\&omega;}}_{72})}^T=({\mathrm{\&omega;}}_1^{\left(0\right)}\&CenterDot;{\mathrm{\&omega;}}_1^{\left(1\right)},{\mathrm{\&omega;}}_1^{\left(0\right)}\&CenterDot;{\mathrm{\&omega;}}_2^{\left(1\right)},...{\mathrm{\&omega;}}_7^{\left(0\right)}\&CenterDot;{\mathrm{\&omega;}}_2^{\left(1\right)})---\left(25\right)$

Described comprehensive evaluation value z is calculated with following formula_i:

$z_i=\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_j\&CenterDot;y_{i,j},(i=1,2,...,m;j=1,2,...,7I+6)---\left(26\right)$

Wherein, 7I+6 represents that suitability, reasonable structure, kinematics performance, dynamic performance, economy, steering quality, manufacturability 7 indexs are as main rule layer, and by the indicator layer that further for every index refinement obtains, I represents the number of the further refinement of every index;

Gear Planet Transmission scheme is by { z_iThe size of value determines.

In Fig. 2, a figure is planet speed-change case transmission sketch, b figure is the schematic diagram of the system diagram model G of the present invention, the form of figure a schematic circuit illustrates planet speed-change case transmission sketch, scheme the system diagram model G that b then represents Gear Planet Transmission scheme in the way of line, both contrasts, the system diagram model of the Gear Planet Transmission scheme drawing the present invention that can be undoubted is more visual and understandable.

Fig. 3 is poower flow visable representation, can analyze the whole transmission scheme poower flow of a certain operating mode by the present invention, and realizes it is carried out quantificational expression with oriented line segment.

Fig. 4 is the selection of the Gear Planet Transmission scheme of the present invention, lists 7 main criterions and indicator layer that each main criterion refinement obtains, by main criterion and indicator layer, the present invention does further scheme preferred.

These are only embodiments of the invention, be not limited to the present invention, within the spirit and principles in the present invention all, any amendment of making, equivalent replacements, improvement etc., be all included in and apply within the right of the present invention that awaits the reply.

Claims (10)

1. the system of selection of a Gear Planet Transmission scheme, it is characterised in that, described method comprises the steps:

I, the Model for Multi-Objective Optimization setting up transmission error;

II, analysis transmission performance;

III, analytical structure geometry contradiction;

IV, determine Gear Planet Transmission scheme.

2. optimization method as claimed in claim 1, it is characterised in that, the Model for Multi-Objective Optimization that described step I sets up transmission error comprises:

(1) Optimum Matching of structural parameter and gear number is determined;

(2) Model for Multi-Objective Optimization is set up.

3. optimization method as claimed in claim 2, it is characterised in that, described step (1) structural parameter comprise number of degrees of freedom, planet row, stopper number and clutch coupling number;

The objective function of the Optimum Matching of structural parameter and gear number is determined with following formula:

$\min f\left(x\right)=\frac{n+p+Z+L}{d_g}---\left(1\right)$

The constraint condition of described objective function is shown below:

$\left\{\begin{array}{c}p\&le;Z+2\\ Z+L\&GreaterEqual;n\\ p-n+1\&GreaterEqual;0\\ 1\&le;p\&le;5\\ 1\&le;Z\&le;5\\ 1\&le;L\&le;5\end{array}\right.---\left(2\right)$

Wherein, n represents number of degrees of freedom, and p represents planet row, and Z represents stopper number, and L represents clutch coupling number, d_gRepresent gear number.

4. optimization method as claimed in claim 2, it is characterised in that, described step (2) Model for Multi-Objective Optimization is shown below:

$\left\{\begin{array}{c}\min n_{xmax}(i_1,i_2,...,i_p)\\ \min M_{\mathrm{\&phi;}max}(i_1,i_2,...,i_p)\\ {\mathrm{max\&eta;}}_{\min }(i_1,i_2,...,i_p)\end{array}\right.---\left(4\right)$

The oriented limit e2 on the oriented limit e1 on input link and frame summit and output link and frame summit, when the conceptual design of reality, each independent gear transmitting ratio size is difficult to accurately provide its concrete numerical value, usually with certain limit of error, is shown below:

$\left\{\begin{array}{c}{e}_1=1\\ \frac{1}{i_{jmax}}\&le;e_2\&le;\frac{1}{i_{j\min }}\end{array}\right.,(j=1,2,...,d_g)---\left(3\right)$

Wherein, n_xmax: the maximum relative rotation speed of each planet seniority among brothers and sisters star-wheel in all available non-immediate gears; M_φmaxRepresent the maximum operating torque of each operating element in all available non-immediate gears; η_min: minimum transmission efficiency in all available non-immediate gears; i₁、i₂、…、i_pRepresent p respectively and independently keep off transmitting ratio, i_jmax: the maximum value that jth gear transmitting ratio allows; i_jmin: the minimum value that jth gear transmitting ratio allows;

The constraint condition of described Model for Multi-Objective Optimization is shown below:

$\left|\frac{i_j-i_j^{\&prime;}(i_1,i_2,...,i_p)}{i_j}\right|\&le;R_j,(j=1,2,...,d_g)---\left(5\right)$

k_min≤k_j(i₁,i₂,…,i_p)≤k_max, (j=1,2 ..., p) (6)

In formula, k_min、k_maxRepresent the lower value that planet row's characteristic parameter allows and higher limit respectively; k_jRepresent planet row's characteristic parameter; i_jThe non-gear of expression scheme jth needs the transmitting ratio accurately realized; I'_jThe transmitting ratio that expression scheme reality can realize; R_jRepresent the relative error that jth gear transmitting ratio allows; J=1,2 ..., p represents p independent gear.

5. optimization method as claimed in claim 1, it is characterized in that, described Step II is analyzed transmission performance and is comprised: adopt graph theory modeling method, basic movement parts each in transmission scheme is mapped as the summit of figure, between them, connecting relation is mapped as the limit of figure, sets up the system diagram model being used for transmission performance and analyzing.

6. optimization method as claimed in claim 5, it is characterized in that, described system diagram model is carried out the model that topological transformation obtains and comprises: performance analysis graph theory model, kinematics analyze graph theory model, dynamic analysis graph theory model and Gear Planet Transmission loss efficiency calculation formula.

7. optimization method as claimed in claim 6, it is characterized in that, described performance analysis graph theory model comprises: leave out the limit associated by summit, clutch coupling active and passive limit on system diagram G basis, and dotted line limit only makes two summits being associated, obtain Components Analysis figure model G1, system diagram G model basis is deleted remaining and does not engage the thin solid line limit corresponding to operating element, then obtain corresponding working condition chart G2 model;

Wherein, the number connected component Q (G) of basic scantling numeral J Components Analysis figure G1, represents with following formula:

J=Q (G) (7);

Described kinematics is analyzed graph theory model and is comprised: is deleted from working condition chart G2 on the dotted line limit of correspondence, is transformed to corresponding rotating speed analysis chart G3 model;

Each planet arranges the rotation speed relation formula of three basic movement parts:

n_ti+k_i×n_qi-(1+k_i)×n_ji=0 (i=1,2 ..., p) (8)

In formula, n_ti、n_qi、n_jiRepresent sun gear, gear ring and planet carrier rotating speed that i-th planet is arranged respectively; k_iRepresent the characteristic parameter of i-th planet row;

The equal relational expression of rotating speed that two summits being associated on every bar limit are set up automatically is shown below:

n_ai-n_bi=0 (i=1,2 ..., E (G3)) and (9)

In formula, n_ai、n_biRepresenting two summit (ai, bi) rotating speeds that in rotating speed analysis chart G3, i-th limit is associated, E (G3) is the limit number of figure G3;

Satellite gear relative rotation speed n_xiIt is shown below:

$n_{xi}=\frac{-2}{k_i-1}(n_{ti}-n_{ji})=\frac{2k_i}{k_i-1}(n_{qi}-n_{ji})=\frac{2k_i}{1-k_i^2}(n_{ti}-n_{qi})---\left(10\right)$

The transmitting ratio i of operating mode is shown below:

$i=\frac{n_o}{n_b}---\left(11\right)$

Wherein n₀Represent input speed, n_bRepresent output speed, satellite gear relative rotation speed n_xiIn i=1,2 ..., p;

Described dynamic analysis graph theory model comprises the torque relationship formula that each planet arranges three basic movement parts, engaged the active and passive limit of clutch coupling (L1, L2) torque relationship formula and in conjunction with the torque relationship formula on the active and passive limit of clutch coupling (L3, L4);

Represent that each planet described arranges the torque relationship of three basic movement parts with following formula:

M_ti:M_qi:M_ji=1:k_i:-(1+k_i) (i=1,2 ..., p) in (12) formula, M_ti、M_qi、M_jiRepresent the torque that i-th planet row's sun gear, gear ring and planet carrier bear, k respectively_iRepresent the characteristic parameter of i-th planet row;

The torque relationship on the active and passive limit of clutch coupling (L1, L2) has been engaged with following formula described in representing:

M_L1+M_L2=0 (13) represent with following formula described in do not engage the active and passive limit of clutch coupling (L3, L4) torque relationship:

$\left\{\begin{array}{c}{M}_{L3}=0\\ M_{L4}=0\end{array}\right.---\left(14\right);$

Described Gear Planet Transmission loss efficiency eta is calculated with following formula:

$\mathrm{\&eta;}=\frac{P_o-(P_{s1}+P_{s2}+...)}{P_o}=1-\&lsqb;(1-{\mathrm{\&eta;}}_{x1}){\mathrm{\&beta;}}_1+(1-{\mathrm{\&eta;}}_{x2}){\mathrm{\&beta;}}_2+...\&rsqb;---\left(15\right)$

In formula, P_oRepresent input link power, P_s1、P_s2Represent each planet row's power loss respectively, η_x1、η_x2Represent the relative movement efficiency that each planet is arranged, β respectively₁、β₂Represent the relative power efficiencies that each planet is arranged, M_L1、M_L2、M_L3、M_L4Represent limit L respectively₁、L₂、L₃、L₄Torque.

8. optimization method as claimed in claim 1, it is characterised in that, described Step II I analytical structure geometry contradiction graph theory comprises planarity figure model carrying out simplify processes and using D.M.P algorithm detection figure;

The simplify processes that figure model carries out is comprised the steps:

(1) if figure is not connected graph, then each connection branch to it is needed to detect;

(2) if figure can divide figure, each being connected block and detects respectively, and if only if, and its each connection block is orthographic plan, then figure is planarity;

(3) all of figure are deleted from ring;

(4) between each opposite vertexes, except retaining a limit, remaining parallel limit is deleted;

(5) two adjacent edges associated with two summits replace with a limit.

9. optimization method as claimed in claim 1, it is characterised in that, described step IV determines that Gear Planet Transmission scheme comprises: the determination of index weight and the calculating of comprehensive evaluation value.

10. optimization method as claimed in claim 9, it is characterised in that, the determination of described index weight comprises:

(1) represent, with following formula, the matrix A that 1～9 grade of scale judges:

$\left\{\begin{array}{c}{a}_{ii}=\frac{{\mathrm{\&omega;}}_i}{{\mathrm{\&omega;}}_j}=1\\ a_{ji}=\frac{{\mathrm{\&omega;}}_j}{{\mathrm{\&omega;}}_i}=\frac{1}{a_{ij}}\\ a_{ij}\&CenterDot;a_{jk}=\frac{{\mathrm{\&omega;}}_i}{{\mathrm{\&omega;}}_j}\&CenterDot;\frac{{\mathrm{\&omega;}}_j}{{\mathrm{\&omega;}}_k}=a_{ik}\end{array}\right.---\left(16\right)$

In formula, element a_ijRepresent that the factor Bi that obtains from judgment matrix A angle is to the relative importance of factor Bj, element a_jiRepresent that the factor Bj that obtains from judgment matrix A angle is to the relative importance of factor Bi, element a_jkRepresent that the factor Bj that obtains from judgment matrix A angle is to the relative importance of factor Bk, element a_iiRepresenting that the factor Bi obtained from judgment matrix A angle is to the importance of self, factor Bi, Bj, Bk represent one of as main rule layer 7 indexs respectively, ω_i、ω_j、ω_kIt is respectively the weighted value of factor i, j and k;

Coincident indicator C.I is calculated with following formula:

$C.I=\frac{{\mathrm{\&lambda;}}_{max}-n}{n-1}---\left(17\right)$

In formula, λ_maxFor the maximum eigenwert of judgment matrix A, n=1～9;

Consistence ratio C.R is represented with following formula:

$C.R=\frac{C.I}{R.I}---\left(18\right)$

In formula, R.I represents Aver-age Random Consistency Index, during using C.R < 0.10 as the consistence judging criterion of matrix, by the weight of proper vector corresponding to its maximum eigenwert as each key element, otherwise do to be suitable for this matrix and revise, obtain decision-making stdn matrix Y=(y_i,j)_m×n', then be normalized;

It is normalized with following formula:

$p_{i,j}=\frac{y_{i,j}}{\underset{i=1}{\overset{m}{\&Sigma;}}{y}_{i,j}},(i=1,2,...,m;j=1,2,...,n^{\&prime;})---\left(19\right)$

The entropy e of jth index is calculated with following formula_j:

$e_j=-\frac{1}{\ln m}\&CenterDot;\underset{i=1}{\overset{m}{\&Sigma;}}{p}_{i,j}\ln p_{i,j},(j=1,2,...,n^{\&prime;})---\left(20\right)$

The discrimination factor g of jth index is calculated with following formula_j:

g_j=1-e_j(j=1,2 ..., n') and (21)

The weights omega of jth index is determined with following formula_j:

${\mathrm{\&omega;}}_j=\frac{g_j}{\underset{j=1}{\overset{n}{\&Sigma;}}{g}_j},(j=1,2,...,n^{\&prime;})---\left(22\right)$

Each each factor B of main criterion is calculated with following formula_iRelative weighting to general objective A:

${\mathrm{\&omega;}}_{(A-B)}={({\mathrm{\&omega;}}_1^{\left(0\right)},{\mathrm{\&omega;}}_2^{\left(0\right)},...,{\mathrm{\&omega;}}_7^{\left(0\right)})}^T---\left(23\right)$

M in formula, n' all represent integer,Represent each main rule layer weight respectively;

C is calculated with following formula_ijTo sub-goal B_iRelative weighting:

${\mathrm{\&omega;}}_{(B-C)}^{\left(i\right)}={({\mathrm{\&omega;}}_1^{\left(i\right)},{\mathrm{\&omega;}}_2^{\left(i\right)},...,{\mathrm{\&omega;}}_{n^{\&prime;}}^{\left(i\right)})}^T---\left(24\right)$

Wherein, the value one_to_one corresponding of n' and i, i=1,2 ..., 7, then corresponding n' is respectively I-1,5,3I-1,2I, I-1,2,2, and wherein I represents the number of the further refinement of every index;

Each index C is represented with following formula_ijRelative weighting to general objective A:

$\mathrm{\&omega;}={({\mathrm{\&omega;}}_{12},{\mathrm{\&omega;}}_{22},...,{\mathrm{\&omega;}}_{72})}^T=({\mathrm{\&omega;}}_1^{\left(0\right)}\&CenterDot;{\mathrm{\&omega;}}_1^{\left(1\right)},{\mathrm{\&omega;}}_1^{\left(0\right)}\&CenterDot;{\mathrm{\&omega;}}_2^{\left(1\right)},...{\mathrm{\&omega;}}_7^{\left(0\right)}\&CenterDot;{\mathrm{\&omega;}}_2^{\left(1\right)})---\left(25\right)$

Described comprehensive evaluation value z is calculated with following formula_i:

$z_i=\underset{j=1}{\overset{n}{\&Sigma;}}{\mathrm{\&omega;}}_j\&CenterDot;y_{i,j}---\left(26\right)$

Wherein, i=1,2 ..., m; J=1,2 ... 7I+6,7I+6 represents that suitability, reasonable structure, kinematics performance, dynamic performance, economy, steering quality, manufacturability 7 indexs are as main rule layer, and by the indicator layer that further for every index refinement obtains, I represents the number of the further refinement of every index;

Gear Planet Transmission scheme is by { z_iThe size of value determines.