A method for coupling optimization design of scale and layout of multi-stage cylindrical gear transmission system

Abstract

The purpose of the present invention is to provide a method for optimizing the scale and layout coupling of a multi-stage cylindrical gear transmission system, comprising the following steps: establishing a layout space model of a cylindrical gear pair, a transmission shaft, and a housing, and defining a global coordinate system; determining the scale and layout design requirements of a multi-stage cylindrical gear transmission system; establishing a combined scale and layout coupling optimization model of a multi-stage cylindrical gear transmission system; substituting the above-established optimization model into a sorting-based particle swarm algorithm RPSO to solve the optimization problem, and outputting the optimization result. The present invention can simultaneously realize the optimization design of scale parameters and layout parameters with coupling relationships in a multi-stage cylindrical gear transmission system through a single optimization operation, thereby obtaining a multi-stage cylindrical transmission system with lighter weight and more compact structure. The present invention is applicable to the scale and layout coupling optimization problem of a cylindrical gear transmission system with any number of transmission stages, avoiding repeated modeling when changing the number of transmission stages, and greatly improving work efficiency.

Description

Technical Field

[0001] The invention relates to a gear design method, in particular to a cylindrical gear transmission system design method. Background Art

[0002] The cylindrical gear transmission system is a gear transmission system used to transmit power and motion between parallel axes. In recent years, with the increasing demand for high reduction ratio gear transmission systems, the design demand for multi-stage cylindrical gear transmission systems has increased day by day. The traditional design method has the disadvantages of complex design process and high time cost when designing multi-stage cylindrical gear transmission systems, and it is often impossible to obtain an optimal design solution. Therefore, optimization design, as a systematic and automated design method, is increasingly used in the design of multi-stage cylindrical gear transmission systems.

[0003] In the existing optimization design of multi-stage cylindrical gear transmission system, the optimization design is mainly based on the optimization goal of minimizing the weight of the gear transmission system, and optimizing the scale parameters of the cylindrical gear and shaft, that is, the number of teeth of the master / driven gear, normal module, tooth width or tooth width coefficient, shaft diameter, etc. This type of optimization design ignores the influence of the layout of the cylindrical gear and shaft on the weight of the gear transmission system, that is, a reasonable layout can make the transmission system more compact, thereby making the box smaller and lighter. Although there are some studies on the layout optimization design of multi-stage cylindrical gear transmission system, such studies are based on the determination of the scale parameters of the cylindrical gear and shaft, and only optimize the layout parameters, ignoring the mutual coupling relationship between the scale parameters and layout parameters of the cylindrical gear and shaft, that is, the scale parameters of the cylindrical gear and shaft affect the value of the layout parameters by determining their respective geometric dimensions, while the layout parameters of the cylindrical gear and shaft affect the value of the scale parameters through conditions such as non-interference constraints. Summary of the invention

[0004] The purpose of the present invention is to provide a multi-stage cylindrical gear transmission system scale and layout coupling optimization design method that can solve the problem of scale and layout coupling optimization of a cylindrical gear transmission system with any number of transmission stages, thereby obtaining a cylindrical gear transmission system with lighter weight and more compact structure.

[0005] The object of the present invention is achieved in that:

[0006] The present invention provides a method for optimizing the design of the coupling of scale and layout of a multi-stage cylindrical gear transmission system, which is characterized by:

[0007] (1) Establish the layout space model of the cylindrical gear pair, transmission shaft, and housing, and define the global coordinate system;

[0008] (2) Determine the size and layout design requirements of the multi-stage cylindrical gear transmission system;

[0009] (3) Establish a combined scale and layout coupling optimization model for a multi-stage cylindrical gear transmission system;

[0010] (4) Substitute the optimization model established above into the sorting-based particle swarm algorithm RPSO to solve the optimization problem and output the optimization results.

[0011] The present invention may also include:

[0012] 1. Step (1) is specifically as follows: the establishment of the layout space model of the cylindrical gear pair, the transmission shaft and the housing includes the definition of the layout space shape, the layout space scale and the positioning point. The layout space shape of the cylindrical gear pair is defined as the combination of the outer envelope cylinders of the master and driven wheels, and the layout space scale is defined as the sum of the volumes of the outer envelope cylinders of the master and driven wheels V gp The layout space positioning point is defined as the geometric center P of the outer envelope cylinder of the master and driven wheels. op \P ow The transmission axis is simplified to the optical axis, and its layout space shape is defined as the outer envelope cylinder of the optical axis. The layout space scale is defined as the volume V of the cylinder. sh , the layout space positioning point is defined as the geometric center P of the optical axis os ; The box layout space shape is defined as a cuboid, and the layout space scale is defined as the length L of the cuboid box , Width W box , high H box The layout space positioning point is defined as the intersection point P of the input axis of the box and the front face of the rectangular layout space in , the intersection point P of the output axis of the box and the rear end surface of the rectangular layout space out , and the upper left vertex V of the rear end face of the box cuboid layout space lt and the lower right vertex V of the front face rb ; Global coordinate system O g -X g Y g Z g Use a right-handed Cartesian coordinate system and make Z g The axis direction is parallel to the input / output axis direction of the box, and the coordinate origin is O g Located at the lower right vertex of the rear end face of the box cuboid layout space, so in this coordinate system:

[0013]

[0014] Where: and P in X g Coordinate value and Y g Coordinate values, and Then they are P out X g Coordinate value and Y g Coordinate value.

[0015] 2. Layout of cylindrical gear space positioning point P op and P ow And the transmission shaft layout spatial positioning point P os The calculation method is:

[0016]

[0017]

[0018]

[0019] Where: and Respectively represent the i(j)th cylindrical gear pair P op,i (P op,j ) g Coordinate value and Y g Coordinate values, and Respectively represent the i(j)th cylindrical gear pair P ow,i (P ow,j ) g Coordinate value and Y g Coordinate value; L sh,j represents the length of the j-th transmission shaft. The lengths of all transmission shafts are numerically equal to the width of the box rectangular layout space. sh,j =W box .

[0020] 3. Determination of the size and layout design requirements of the multi-stage cylindrical gear transmission system includes: Transmission stage number N s Determination of the value, the prime mover input power P and speed n r Determination of the value, the total transmission ratio U tol Determination of the value, the length L of the box rectangular layout space box , Width W box , high H box as well as Determination of value.

[0021] 4. Step (3) is specifically as follows: the establishment of the combined scale and layout coupling optimization model of the multi-stage cylindrical gear transmission system includes the definition of the combined design variables, the definition of the combined objective function and the definition of the combined design constraints. The combined design variable X is defined as the sequential arrangement and combination of the local variables of the cylindrical gear pair and the local variables of the transmission shaft, as shown below:

[0022]

[0023] Where: x gp,i It represents the local variable of the i-th cylindrical gear pair, which consists of the scale variable and layout variable of the i-th cylindrical gear pair. The scale variable includes the number of teeth on the driving gear z p,i 、Number of teeth on the driven gear z w,i , normal modulus m n,i , tooth width coefficient ψ i , the layout variables include the driving wheel geometric center P op,i Z g Coordinate p o z p,i and the rotation angle θ of the cylindrical gear around the axis of the driving wheel i Composition, x sh,i Represents the local variable of the j-th transmission shaft, which is determined by the minimum shaft diameter d of the transmission shaft scale variable sh,j composition;

[0024] The combined objective function F(X) is defined as the minimum sum of the volume of the layout space of each level of cylindrical gears, the volume of the layout space of each transmission shaft, and the volume of the outer envelope bounding box of all cylindrical gears, as shown below:

[0025]

[0026] Where: V gp,i is the volume of the layout space of the i-th cylindrical gear pair, V sh,j is the volume of the j-th transmission shaft layout space, V bd The outer envelope bounding box volume of all cylindrical gears in the transmission system;

[0027] The combined design constraints are defined as the combination of the local constraints of the cylindrical gear pairs at each level, the local constraints of each transmission shaft, and the global constraints of the transmission system, as shown below:

[0028]

[0029] Where: represents the mth local constraint of the i-th cylindrical gear pair, N cgp Indicates the number of local constraints of the cylindrical gear pair; represents the nth local constraint of the jth transmission shaft, N csh Indicates the number of local constraints of the transmission shaft; represents the kth global constraint of the transmission system, N csys Represents the number of global constraints of the transmission system.

[0030] 5. Step (4) The algorithm flow of the sorting-based particle swarm algorithm RPSO is as follows:

[0031] (4.1) Map the design variables to the position variables of the particles in RPSO;

[0032] (4.2) Set the parameter values ​​of RPSO, including the maximum number of iterations, particle swarm size, acceleration factor, and inertia weight;

[0033] (4.3) Randomly initialize the velocity and position variable values ​​of each particle in the particle swarm;

[0034] (4.4) Calculate the fitness of each particle: calculate the objective function value, constraint violation degree value, and number of constraint violations of each particle; sort the objective function value, constraint violation degree value, and number of constraint violations of each particle; calculate the fitness value of each particle according to the sorting result;

[0035] (4.5) Update the speed and position of each particle according to the fitness value;

[0036] (4.6) Determine whether the maximum number of iterations has been reached. If so, output the position of the optimal particle, which is also the optimal solution. Otherwise, jump to step (4.4) to continue iterating and optimizing.

[0037] 6. V in the combined objective function F(X) gp,i 、V sh,j and V bd The calculation method is:

[0038]

[0039]

[0040] V bd =L net W net H net

[0041] Where: B i is the tooth width of the i-th cylindrical gear; d pa,i L is the diameter of the tooth top circle of the i-th cylindrical gear pair of the driving wheel; net , W net , H net are the length, width and height of the outer envelope bounding box of all cylindrical gears in the transmission system, and:

[0042]

[0043] Where: max({*}) means taking the maximum value in the set {*}, min({*}) means taking the minimum value in the set {*}; x max,i With x min,i Respectively represent the points X on the outer envelope cylinder of the i-th cylindrical gear to the master and driven wheels g The maximum and minimum values ​​of the coordinates; ymax,i With y min,i Respectively represent the points Y on the outer envelope cylinder of the i-th cylindrical gear to the master and driven wheels g The maximum and minimum values ​​of the coordinates; z max,i With z min,i Respectively represent the points Z on the outer envelope cylinder of the i-th cylindrical gear to the master and driven wheels g The maximum and minimum values ​​of the coordinates, and:

[0044]

[0045] Where: d wa,i is the top circle diameter of the driven gear of the i-th cylindrical gear; max(* 1 ,* 2 ) means to take * 1 and* 2 The maximum value among them, while min(* 1 ,* 2 ) means taking * 1 and* 2 The minimum value in

[0046] 7. In the combined design constraints, the local constraints of the cylindrical gear pair include x gp,i The upper and lower limit constraints, the non-root cutting constraint of the number of teeth of the driving wheel, the transmission ratio range constraint of the cylindrical gear pair, the contact fatigue strength of the tooth surface of the cylindrical gear pair and the bending fatigue strength constraint of the tooth root; the local constraints of the transmission shaft include x sh,i The upper and lower limit constraints and the torsional strength constraint of the transmission shaft; the global constraints of the transmission system include the total transmission ratio constraint, the non-interference constraint between gear pairs, the non-interference constraint between gear pairs and the transmission shaft, the non-interference constraint between gear pairs and the box rectangular layout space, and the box output axis position constraint.

[0047] 8. The calculation method of the particle constraint violation degree value, constraint violation number and fitness value in the RPSO algorithm process step (4.4) is:

[0048]

[0049]

[0050] Φ(X)=R fx +R cval +R cnum

[0051] Where: C val (X) and C num(X) represents the constraint violation degree and number of constraint violations of the particle respectively; <*> means when *≤0, <*>=0, otherwise <*>=|*|; [*] means when *≤0, [*]=0, otherwise [*]=1; Φ(X) represents the fitness value of the particle; R fx , R cval and R cnum They represent particles Φ(X), C val (X) and C num (X) values ​​are sorted from small to large.

[0052] The advantages of the present invention are:

[0053] (1) The optimization design method proposed in the present invention can simultaneously realize the optimization design of the dimensional parameters and layout parameters with coupling relationship in the multi-stage cylindrical gear transmission system through a single optimization operation, thereby obtaining a multi-stage cylindrical transmission system with lighter weight and more compact structure.

[0054] (2) The combined scale and layout coupling optimization model constructed in the present invention is applicable to the scale and layout coupling optimization problem of a cylindrical gear transmission system with any number of transmission stages, avoiding repeated modeling when changing the number of transmission stages and greatly improving work efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 It is a schematic diagram of the process of the present invention;

[0056] Figure 2 It is a schematic diagram of the layout space model of the cylindrical gear pair;

[0057] Figure 3 It is a schematic diagram of the spatial model of the transmission shaft layout;

[0058] Figure 4 This is a schematic diagram of the box layout space model;

[0059] Figure 5a , Figure 5b The schematic diagram of the design scheme for the coupling optimization of the scale and layout of the three-stage cylindrical gear transmission system;

[0060] Figure 6a , Figure 6b A schematic diagram of the outer envelope bounding box of all cylindrical gears in the transmission system and the layout variables of the cylindrical gear pairs;

[0061] Figure 7 is the value of each design variable in the optimal solution of the embodiment. DETAILED DESCRIPTION

[0062] The present invention is described in more detail below with reference to the accompanying drawings:

[0063] Combination Figure 1-7 The present invention provides a method for coupling optimization design of scale and layout of a multi-stage cylindrical gear transmission system, and its specific implementation method includes the following steps:

[0064] Step (1): Establish a layout space model of the cylindrical gear pair, transmission shaft, and housing, and define the global coordinate system;

[0065] Step (2): Determine the scale and layout design requirements of the multi-stage cylindrical gear transmission system;

[0066] Step (3): Establish a combined scale and layout coupling optimization model for a multi-stage cylindrical gear transmission system;

[0067] Step (4): Substitute the above-established combined optimization model into the sorting-based particle swarm algorithm RPSO to solve the optimization problem and output the optimization result.

[0068] In step (1), the establishment of the layout space model of the cylindrical gear pair, the transmission shaft and the housing includes the definition of the layout space shape, the layout space scale and the positioning points. Figure 2 The figure shows the schematic diagram of the cylindrical gear pair layout space model. The layout space shape of the cylindrical gear pair in the figure is a combination of the main and driven gear outer envelope cylinders. The layout space scale is the sum of the volumes of the main and driven gear outer envelope cylinders V gp , the layout space positioning point is the geometric center P of the outer envelope cylinder of the main and driven wheels op \P ow ; Figure 3 The figure shows a schematic diagram of the transmission shaft layout space model. In this figure, the transmission shaft is simplified to an optical axis. Its layout space shape is the outer envelope cylinder of the optical axis. The layout space scale is the volume V of the cylinder. sh , the layout space positioning point is the geometric center P of the optical axis os ; Figure 4 The figure shows a schematic diagram of the box layout space model. In the figure, the box layout space is in the shape of a cuboid, and the layout space scale is the length L of the cuboid. box , Width W box , high H box The layout space positioning point is defined as the intersection point P of the input axis of the box and the front face of the rectangular layout space in , the intersection point P of the output axis of the box and the rear end surface of the rectangular layout space out , and the upper left vertex V of the rear end face of the box cuboid layout space lt and the lower right vertex V of the front face rb . Figure 4 Medium g -X g Y g Z gis the global coordinate system, which is a right-handed Cartesian rectangular coordinate system. As can be seen from the figure, the coordinate origin O of this coordinate system g Located at the lower right vertex of the rear end of the box cuboid layout space, Z g The X axis is located in the width direction of the box rectangular layout space and is parallel to the input / output axis of the box. g The axis direction is in the length direction of the box rectangular layout space, Y g The axis direction is in the height direction of the box cuboid layout space. Therefore, in this coordinate system, we have:

[0069]

[0070] Where: and P in X g Coordinate value and Y g Coordinate values, and Then they are P out X g Coordinate value and Y g Coordinate value.

[0071] In addition, in this coordinate system, the cylindrical gear is positioned in the spatial location point P op and P ow And the transmission shaft layout spatial positioning point P os The calculation method is:

[0072]

[0073]

[0074]

[0075] Where: and Respectively represent the i(j)th cylindrical gear pair P op,i (P op,j ) g Coordinate value and Y g Coordinate values, and and Then they represent the i(j)th cylindrical gear pair P respectively. ow,i (P ow,j ) g Coordinate value and Y g Coordinate value; L sh,j represents the length of the j-th transmission shaft. In this patent, the length of all transmission shafts is numerically equal to the width W of the rectangular layout space of the box body. box , that is, L sh,j =Wbox (j=1,…,N s ,N s+1 ).

[0076] In step (2), the multi-stage cylindrical gear transmission system size and layout design requirements include: the number of transmission stages N s , prime mover input power P and speed n r , total transmission ratio U tol , the length L of the box rectangular layout space box , Width W box , high H box and the positioning point P in and P out X g Coordinates and Y g Coordinates, i.e. In the embodiment, the value of each design requirement is: N s =4, P = 10kW, n r =4800r / min, U tol =100,L box =540mm, W box =150mm, H box =300mm,

[0077] In step (3), the establishment of the combined scale and layout coupling optimization model of the multi-stage cylindrical gear transmission system includes the definition of combined design variables, the definition of combined objective functions and the definition of combined design constraints.

[0078] The combined design variable X is defined as the sequential arrangement of the local variables of the cylindrical gear pair and the local variables of the transmission shaft, as shown below:

[0079]

[0080] Where: x gp,i represents the local variable of the i-th cylindrical gear pair, which consists of the scale variable and layout variable of the i-th cylindrical gear pair. Among them, the scale variable includes the number of teeth on the driving gear z p,i 、Number of teeth on the driven gear z w,i , normal modulus m n,i , tooth width coefficient ψ i ; The layout variables include the geometric center P of the driving wheel of the i-th cylindrical gear op,i Z g coordinate and the rotation angle θ of the cylindrical gear around the axis of the driving wheel i Composition, as shown in Figure 5.sh,i Represents the local variable of the j-th transmission shaft, that is, the minimum shaft diameter d of the j-th transmission shaft sh,j .

[0081] The combined objective function F(X) is defined as the minimum sum of the volume of the layout space of each level of cylindrical gears, the volume of the layout space of each transmission shaft, and the volume of the outer envelope bounding box of all cylindrical gears, as shown below:

[0082]

[0083] Where: V gp,i V is the volume of the layout space of the i-th cylindrical gear pair; sh,j V is the volume of the j-th transmission shaft layout space; bd is the outer envelope bounding box volume of all cylindrical gears in the transmission system. The smaller this volume is, the more compact the transmission system is. In addition, V gp,i 、V sh,j and V bd The calculation methods are:

[0084]

[0085]

[0086] V bd =L net W net H net (9)

[0087] Where: B i is the tooth width of the i-th cylindrical gear; d pa,i L is the diameter of the tooth top circle of the i-th cylindrical gear pair of the driving wheel; net , W net , H net are the length, width and height of the outer envelope bounding box of all cylindrical gears in the transmission system, as shown in Figure 5, and:

[0088]

[0089] Where: max({*}) means taking the maximum value in the set {*}, while min({*}) means taking the minimum value in the set {*}; x max,i With x min,i Respectively represent the points X on the outer envelope cylinder of the i-th cylindrical gear to the master and driven wheels g The maximum and minimum values ​​of the coordinates; y max,i With y min,i Respectively represent the points Y on the outer envelope cylinder of the i-th cylindrical gear to the master and driven wheels g The maximum and minimum values ​​of the coordinates; z max,iWith z min,i Respectively represent the points Z on the outer envelope cylinder of the i-th cylindrical gear to the master and driven wheels g The maximum and minimum values ​​of the coordinates, and:

[0090]

[0091] Where: d wa,i is the top circle diameter of the driven gear of the i-th cylindrical gear; max(* 1 ,* 2 ) means to take * 1 and* 2 The maximum value among them, while min(* 1 ,* 2 ) means taking * 1 and* 2 The minimum value in .

[0092] The combined design constraints are defined as the combination of the local constraints of the cylindrical gear pairs at each level, the local constraints of each transmission shaft, and the global constraints of the transmission system, as shown below:

[0093]

[0094] Where: represents the mth local constraint of the i-th cylindrical gear pair, N cgp Indicates the number of local constraints of the cylindrical gear pair; represents the nth local constraint of the jth transmission shaft, N csh Indicates the number of local constraints on the transmission shaft; represents the kth global constraint of the transmission system, N csys Represents the number of global constraints of the transmission system.

[0095] Among them, the local constraints of the cylindrical gear pair include x gp,i The upper and lower limit constraints, the non-root cutting constraint of the number of teeth of the driving wheel, the transmission ratio range constraint of the cylindrical gear pair, the contact fatigue strength of the tooth surface of the cylindrical gear pair and the bending fatigue strength constraint of the tooth root; the local constraints of the transmission shaft include x sh,i The upper and lower limit constraints and the torsional strength constraint of the transmission shaft; the global constraints of the transmission system include the total transmission ratio constraint, the non-interference constraint between gear pairs, the non-interference constraint between gear pairs and the transmission shaft, the non-interference constraint between gear pairs and the box rectangular layout space, and the box output axis position constraint.

[0096] The algorithm flow of RPSO in step (4) is:

[0097] Step (4.1): Map the combined design variable X to the position variable of the particle in RPSO;

[0098] Step (4.2): Set the maximum number of iterations G of the RPSO algorithm max =1000, particle swarm size S p =40, the acceleration factor c1=c2=1.4962, the maximum value of the inertia weight ω is ω max =0.9, the minimum value is ω min =0.4, then the nth (n=1, 2, ..., G max ) iteration inertia weight ω n The value of is max -n(ω max -ω min ) / G max ;

[0099] Step (4.3): Randomly initialize the velocity and position variable values ​​of each particle in the particle swarm;

[0100] Step (4.4): Calculate the fitness of each particle. The specific process is as follows:

[0101] (a) Calculate the objective function value F(X) and constraint violation degree value C of each particle val (X), the number of constraint violations C num (X), where the calculation method of F(X) value is shown in formula (6) to (9), C val (X) and C num The calculation method of (X) is as follows:

[0102]

[0103]

[0104] In the formula: <*> means when *≤0, <*>=0, otherwise <*>=|*|; [*] means when *≤0, [*]=0, otherwise [*]=1.

[0105] (b) The objective function value F(X) and constraint violation degree value C of each particle val (X), the number of constraint violations C num (X) Sort in ascending order.

[0106] (c) Calculate the fitness value Φ(X) of each particle according to the sorting results. The calculation method is:

[0107] Φ(X)=R fx +R cval +R cnum (15)

[0108] Where: R fx , R cval and R cnum Then they represent particles F(X), Cval (X) and C num (X) values ​​are sorted from small to large.

[0109] Step (4.5): Update the speed and position of each particle according to the fitness value Φ(X), where the particle speed is updated by:

[0110]

[0111] Where: is the velocity of the j-dimensional position variable of the ith particle in the n-th iteration; is the velocity of the j-dimensional position variable of the ith particle in the n-1th iteration; r 1 and r 2 is a random number between [0,1]; p best,i,j is the historical optimal position of the j-th dimension of the ith particle; g best,j Represents the global historical optimal position of the j-th dimension position variable of the entire particle group; is the position of the j-dimensional position variable of the ith particle in the n-1th iteration; N x is the dimension of the particle, which is numerically equal to the dimension of the combinatorial design variable X, with N x =7N s +1.

[0112] The particle position update method is:

[0113]

[0114] Where: is the position of the j-dimensional position variable of the ith particle in the n-th iteration.

[0115] Step (4.6): Determine whether the maximum number of iterations has been reached. If so, output the position of the optimal particle, which is also the optimal solution; otherwise, jump to step (4.4) to continue iterating and optimizing.

[0116] In step (4), according to the set RPSO algorithm parameters and the scale and layout design requirements of the embodiment determined in step (2), the optimal solution of the embodiment is finally obtained, that is, the optimal value of each variable in the combined design variable X, such as Figure 7 shown.

Claims

1. A method for coupling optimization design of scale and layout of a multi-stage cylindrical gear transmission system, characterized by: (1) Establish the layout space model of the cylindrical gear pair, transmission shaft, and housing, and define the global coordinate system; (2) Determine the size and layout design requirements of the multi-stage cylindrical gear transmission system; (3) Establish a combined scale and layout coupling optimization model for a multi-stage cylindrical gear transmission system; (4) Substitute the optimization model established above into the sorting-based particle swarm algorithm RPSO to solve the optimization problem and output the optimization result; The establishment of the combined scale and layout coupling optimization model of the multi-stage cylindrical gear transmission system includes the definition of the combined design variables, the definition of the combined objective function and the definition of the combined design constraints. The combined design variable X is defined as the sequential arrangement and combination of the local variables of the cylindrical gear pair and the local variables of the transmission shaft, as shown below: Where: x gp,i It represents the local variable of the i-th cylindrical gear pair, which consists of the scale variable and layout variable of the i-th cylindrical gear pair. The scale variable includes the number of teeth on the driving gear z p,i 、Number of teeth on the driven gear z w,i , normal modulus m n,i , tooth width coefficient ψ i , the layout variables include the driving wheel geometric center P op,i Z g coordinate and the rotation angle θ of the cylindrical gear around the axis of the driving wheel i Composition, x sh,i Represents the local variable of the j-th transmission shaft, which is determined by the minimum shaft diameter d of the transmission shaft scale variable sh,j composition; The combined objective function F(X) is defined as the minimum sum of the volume of the layout space of each level of cylindrical gears, the volume of the layout space of each transmission shaft, and the volume of the outer envelope bounding box of all cylindrical gears, as shown below: Where: V gp,i is the volume of the layout space of the i-th cylindrical gear pair, V sh,j is the volume of the j-th transmission shaft layout space, V bd The outer envelope bounding box volume of all cylindrical gears in the transmission system; The combined design constraints are defined as the combination of the local constraints of the cylindrical gear pairs at each level, the local constraints of each transmission shaft, and the global constraints of the transmission system, as shown below: Where: represents the mth local constraint of the i-th cylindrical gear pair, N cgp Indicates the number of local constraints of the cylindrical gear pair; represents the nth local constraint of the jth transmission shaft, N csh Indicates the number of local constraints on the transmission shaft; represents the kth global constraint of the transmission system, N csys Represents the number of global constraints of the transmission system.

2. The method for designing the coupled optimization of the scale and layout of a multi-stage cylindrical gear transmission system according to claim 1 is characterized by: Step (1) is specifically as follows: the establishment of the layout space model of the cylindrical gear pair, the transmission shaft and the housing includes the definition of the layout space shape, the layout space scale and the positioning point. The layout space shape of the cylindrical gear pair is defined as the combination of the outer envelope cylinders of the master and driven wheels, and the layout space scale is defined as the sum of the volumes of the outer envelope cylinders of the master and driven wheels V gp The layout space positioning point is defined as the geometric center P of the outer envelope cylinder of the master and driven wheels. op \P ow ; The transmission axis is simplified to the optical axis, and its layout space shape is defined as the outer envelope cylinder of the optical axis. The layout space scale is defined as the volume V of the cylinder. sh , the layout space positioning point is defined as the geometric center P of the optical axis os ; The box layout space shape is defined as a cuboid, and the layout space scale is defined as the length L of the cuboid box , Width W box , high H box The layout space positioning point is defined as the intersection point P of the input axis of the box and the front face of the rectangular layout space in , the intersection point P of the box output axis and the rear end surface of the rectangular layout space out , and the upper left vertex V of the rear end face of the box cuboid layout space lt and the lower right vertex V of the front face rb ; Global coordinate system O g -X g Y g Z g Use a right-handed Cartesian coordinate system and make Z g The axis direction is parallel to the input / output axis direction of the box, and the coordinate origin is O g Located at the lower right vertex of the rear end face of the box cuboid layout space, so in this coordinate system we have: Where: and P in X g Coordinate value and Y g Coordinate values, and Then they are P out X g Coordinate value and Y g Coordinate value.

3. The method for designing the coupled optimization of the dimensions and layout of a multi-stage cylindrical gear transmission system according to claim 2 is characterized by: The cylindrical gear pair layout space positioning point P op and P ow And the transmission shaft layout spatial positioning point P os The calculation method is: Where: and Respectively represent the i(j)th cylindrical gear pair P op,i (P op,j ) g Coordinate value and Y g Coordinate values, and Respectively represent the i(j)th cylindrical gear pair P ow,i (P ow,j ) g Coordinate value and Y g Coordinate value; L sh,j represents the length of the j-th transmission shaft. The lengths of all transmission shafts are numerically equal to the width of the box rectangular layout space. sh,j =W box .

4. The method for designing the coupled optimization of the dimensions and layout of a multi-stage cylindrical gear transmission system according to claim 1 is characterized by: The determination of the size and layout design requirements of the multi-stage cylindrical gear transmission system includes: the number of transmission stages N s Determination of the value, the prime mover input power P and speed n r Determination of the value, the total transmission ratio U tol Determination of the value, the length L of the box rectangular layout space box , Width W box , high H box as well as Determination of value.

5. The method for designing the coupled optimization of the dimensions and layout of a multi-stage cylindrical gear transmission system according to claim 1 is characterized by: Step (4) The algorithm flow of the sorting-based particle swarm algorithm RPSO is as follows: (4.1) Map the design variables to the position variables of the particles in RPSO; (4.2) Set the parameter values ​​of RPSO, including the maximum number of iterations, particle swarm size, acceleration factor, and inertia weight; (4.3) Randomly initialize the velocity and position variable values ​​of each particle in the particle swarm; (4.4) Calculate the fitness of each particle: calculate the objective function value, constraint violation degree value, and number of constraint violations of each particle; sort the objective function value, constraint violation degree value, and number of constraint violations of each particle; calculate the fitness value of each particle according to the sorting result; (4.5) Update the speed and position of each particle according to the fitness value; (4.6) Determine whether the maximum number of iterations has been reached. If so, output the position of the optimal particle, which is also the optimal solution. Otherwise, jump to step (4.4) to continue iterating and optimizing.

6. The method for designing the coupled optimization of the dimensions and layout of a multi-stage cylindrical gear transmission system according to claim 1 is characterized in that: V in the objective function F(X) gp,i 、V sh,j and V bd The calculation method is: V bd =L net W net H net Where: B i is the tooth width of the i-th cylindrical gear; d pa,i L is the diameter of the tooth top circle of the i-th cylindrical gear pair of the driving wheel; net , W net , H net are the length, width and height of the outer envelope bounding box of all cylindrical gears in the transmission system, and: Where: max({*}) means taking the maximum value in the set {*}, min({*}) means taking the minimum value in the set {*}; x max,i With x min,i Respectively represent the points X on the outer envelope cylinder of the i-th cylindrical gear to the master and driven wheels g The maximum and minimum values ​​of the coordinates; y max,i With y min,i Respectively represent the points Y on the outer envelope cylinder of the i-th cylindrical gear to the master and driven wheels g The maximum and minimum values ​​of the coordinates; z max,i With z min,i Respectively represent the points Z on the outer envelope cylinder of the i-th cylindrical gear to the master and driven wheels g The maximum and minimum values ​​of the coordinates, and: Where: d wa,i is the diameter of the tooth top circle of the driven wheel of the i-th cylindrical gear pair; max(*1,*2) means taking the maximum value of *1 and *2, while min(*1,*2) means taking the minimum value of *1 and *2.

7. The method for designing the coupled optimization of the dimensions and layout of a multi-stage cylindrical gear transmission system according to claim 1 is characterized by: In the combined design constraints, the local constraints of the cylindrical gear pair include x gp,i The upper and lower limit constraints, the non-root cutting constraint of the number of teeth of the driving wheel, the transmission ratio range constraint of the cylindrical gear pair, the contact fatigue strength of the tooth surface of the cylindrical gear pair and the bending fatigue strength constraint of the tooth root; the local constraints of the transmission shaft include x sh,i The upper and lower limit constraints and the torsional strength constraint of the transmission shaft; the global constraints of the transmission system include the total transmission ratio constraint, the non-interference constraint between gear pairs, the non-interference constraint between gear pairs and the transmission shaft, the non-interference constraint between gear pairs and the box rectangular layout space, and the box output axis position constraint.

8. The method for designing the coupled optimization of dimensions and layout of a multi-stage cylindrical gear transmission system according to claim 5 is characterized by: The calculation method of the particle constraint violation degree value, constraint violation number and fitness value in the RPSO algorithm process step (4.4) is: Φ(X)=R fx +R cval +R cnum Where: C val (X) and C num (X) represents the constraint violation degree and number of constraint violations of the particle respectively; <*> means when *≤0, <*>=0, otherwise <*>=|*|; [*] means when *≤0, [*]=0, otherwise [*]=1; Φ(X) represents the fitness value of the particle; R fx , R cval and R cnum They represent particles Φ(X), C val (X) and C num (X) values ​​are sorted from small to large.

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