Reverse differential planetary roller screw uniform load optimization design method

Abstract

The invention provides a reverse differential planetary roller screw uniform load optimization design method, and belongs to the technical field of planetary roller screw transmission uniform load design optimization, and the method comprises the following steps: step 1, on the basis of a reverse differential planetary roller screw thread tooth meshing deformation coordination relationship, a reverse differential planetary roller screw transmission uniform load design is established; constructing a deformation coordination formula of the roller ring groove and the nut ring groove and a deformation coordination formula of the roller thread and the lead screw thread; step 2, acquiring importance of thread tooth structure parameters and the like on uniform load performance by adopting a random forest algorithm, and extracting key influence parameters; step 3, establishing a key parameter and uniform load performance prediction model by using a GA-BP neural network; and step 4, constructing a mass loss and tolerance sensitivity multi-objective optimization algorithm based on NSGA-II, and realizing reverse differential planetary roller screw uniform load multi-objective optimization design taking the processing cost as a constraint condition. By means of the method, the uniform load effect between threads of the reverse differential planetary roller screw can be improved, the bearing capacity is improved, and the service life is prolonged.

Description

Technical Field

[0001] The invention belongs to the design optimization of load balancing of planetary roller screw transmission, and specifically belongs to a method for optimizing the design of load balancing of reverse differential planetary roller screw. Background Art

[0002] Planetary roller screw is a transmission device that realizes the conversion between linear motion and rotational motion. It is mainly composed of screw rod, nut, roller, cage and other parts, and realizes load distribution through numerous thread meshing points. It has the characteristics of high load, high precision, high rigidity and long life. The reverse differential planetary roller screw is a kind of planetary roller screw. It can use the differential effect generated by the segmented meshing of roller, screw and nut to convert the rotary motion of the nut into the linear displacement of the screw.

[0003] At present, for planetary roller screws, the uneven load between thread teeth is an inherent characteristic of planetary roller screws, which makes their load life significantly reduced, especially under heavy load conditions, the thread teeth with the highest eccentric load coefficient are very likely to fail prematurely. Therefore, the research on the optimization method of the load distribution of the thread teeth of the planetary roller screw pair has been one of the research focuses in related fields in recent years.

[0004] The existing planetary roller screw thread teeth inter-teeth load balancing technology is usually based on the standard planetary roller screw pair thread meshing deformation coordination equation, and the qualitative analysis results of the load distribution are obtained. Then a simple thread diameter taper modification is performed to achieve that the thread teeth of the synchronous gears at both ends of the roller do not participate in the thread surface meshing transmission, thereby avoiding premature failure of the thread at the low-strength roller synchronous gear due to excessive eccentric load.

[0005] However, for the reverse differential planetary roller screw pair, since the rollers and the nut and screw thread mesh in a segmented meshing form, the deformation coordination relationship is different from the standard roller continuous meshing. At the same time, the characteristics of the ring groove meshing also make it possible to perform load-balancing repair on a single ring groove meshing pair.

[0006] Therefore, in order to better improve the load-sharing design effect of the segmented meshing helical transmission, a load-sharing optimization design method for a reverse differential planetary roller screw is urgently needed. Summary of the invention

[0007] In view of the above problems, the present invention provides a reverse differential planetary roller screw load balancing optimization design method, through which the load balancing effect between the thread teeth of the reverse differential planetary roller screw can be improved, and the load-bearing capacity and life can be improved.

[0008] The technical solution adopted by the present invention is as follows:

[0009] A method for optimizing the load-sharing design of a reverse differential planetary roller screw comprises the following steps:

[0010] Step 1: Based on the meshing deformation coordination relationship of the reverse differential planetary roller screw thread teeth, the deformation coordination formulas of the roller ring groove and the nut ring groove, the roller thread and the screw thread are constructed;

[0011] Step 2: Use the random forest algorithm to obtain the importance of thread structure parameters and other parameters on load-sharing performance, and extract key influencing parameters;

[0012] Step 3: Use GA-BP neural network to establish a prediction model for key parameters and load balancing performance;

[0013] Step 4: Based on NSGA-II, a multi-objective optimization algorithm for mass loss and tolerance sensitivity is constructed to realize the multi-objective optimization design of the reverse differential planetary roller screw with processing cost as the constraint.

[0014] As a further improvement of the present invention, step one specifically includes:

[0015] S1. According to the meshing deformation coordination relationship between the roller, the screw and the nut, the contact between the roller shaft segment and the thread teeth is equivalent to a spiral spring, and the thread teeth are equivalent to a leaf spring. A stiffness deformation association model is established for all contacts of the reverse differential planetary roller screw.

[0016] S2, thread segment stiffness is the tensile and compressive stiffness of the two adjacent load-bearing thread teeth of the screw, roller or nut. This stiffness is solved by the tensile and compressive stiffness formula of the material mechanics axis. In the reverse differential planetary roller screw, the segment stiffness of the screw, roller and nut is:

[0017]

[0018] In the formula, k XB E is the shaft stiffness of the screw / nut / roller of the reverse differential planetary roller screw. X is the elastic modulus of the material, P is the pitch, A X is the cross-sectional area of ​​the shaft segment, S is the screw, R is the roller, and N is the nut;

[0019] S3. When the reverse differential planetary roller screw is subjected to load, the roller thread teeth are meshed with the screw and nut thread teeth respectively to bear the load, and each thread tooth will deform along the screw axis after being subjected to force; wherein, the axial deformation of the thread teeth includes deformation δ1 caused by bending, deformation δ2 caused by shearing, deformation δ3 caused by root tilting, deformation δ4 caused by root shearing, and deformation δ5 caused by radial force component;

[0020] The thread profile is a trapezoidal thread profile of the screw and nut. The radial component of the normal contact load of the thread teeth and the axial component of the normal contact load of the thread teeth satisfy the following relationship:

[0021]

[0022] In the formula, F r is the radial separation of the normal contact load, F a is the axial component of the normal contact load;

[0023] The calculation method of each deformation is as follows:

[0024]

[0025] Where, μ is the Poisson's ratio of the material of the screw, roller and nut; E is the elastic modulus of the screw, roller and nut, a is the thread root thickness, b is the thread thickness, c is the thread crest thickness, and hf is the thread root height;

[0026] Due to the different structures of internal and external threads, the deformation of thread teeth caused by radial force is not the same; the external thread is equivalent to the diameter d w Solid cylinder, the internal thread is equivalent to the outer diameter d n , inner diameter d ni The hollow cylinder is 5w Indicates external thread deformation, using δ 5n Indicates the deformation of the internal thread;

[0027] For external threads, the deformation caused by the radial force is:

[0028]

[0029] For internal threads, the thread deformation caused by the radial force is:

[0030]

[0031] Thus, the total axial deformation δ of the thread teeth of the reverse differential planetary roller screw under the axial load is obtained: XT for:

[0032] δ XT =δ1+δ2+δ3+δ4+δ5

[0033] Corresponding thread stiffness k XT That is:

[0034]

[0035] S4. Based on the established stiffness-deformation correlation model and the axial load on the screw, it is first assumed that the axial load is evenly borne by all meshing contact points. The deformation of each shaft segment, thread tooth, and contact area is calculated based on the stiffness obtained from the material properties. The axial load of each contact point is then reversed based on the deformation to perform the next round of iteration. Finally, when the difference between the previous round of calculation results and the current calculation results is less than 10 -5 When , the iteration ends and the current calculation result is defined as the final calculation value of the thread tooth distribution result;

[0036] Among them, the deformation of the threaded shaft section of the screw, roller and nut can be obtained through the shaft section load and shaft section stiffness. From the established relationship, it can be known that the axial deformation of the i-th shaft section of the nut is:

[0037]

[0038] In the formula, F NRj k is the axial load at the jth meshing position between the nut and the roller from the free end to the fixed end; NB is the nut shaft end stiffness, the free end is defined as the end close to the force direction when the screw is compressed, and the fixed end is defined as the end away from the force direction.

[0039] Similarly, the axial deformation of the i-th shaft segment of the screw is:

[0040]

[0041] In the formula, F A is the axial load of the screw; F SRj is the axial load at the jth meshing point of the screw roller meshing position; k SB is the axial stiffness of the nut,

[0042] Similarly, the axial deformation of the i-th roller segment is:

[0043]

[0044] Where p is the number of thread pairs that the roller-screw has engaged from the free end to the fixed end at the i-th meshing point of the roller; q is the number of thread pairs that the roller-nut has engaged from the free end to the fixed end at the i-th meshing point of the roller;

[0045] Without considering the error, the threads between the roller and the nut before and after deformation always maintain the meshing relationship, that is:

[0046]

[0047] Where P N is the nut lead, P R is the roller lead, n is the number of thread starts, ∑l Niis the total deformation of the nut, ∑l Ri is the total deformation of the roller, compression is positive and tension is negative,

[0048] For the reverse differential planetary roller screw, the pitch of the roller and nut are equal. Simplifying the above equation, we get

[0049] Δl NBi +ΔL NTi -Δl NTi+1 +Δl RNCi =Δl RBi -Δl RTi +Δl RTi+1 +Δl RNCi+1

[0050] In the formula, Δl NBi is the deformation of the nut and the i-th shaft end of the screw, Δl NTi is the deformation of the thread at the ith contact point of the nut, Δl NTi+1 is the deformation of the thread at the i+1th contact point of the nut, Δl RNCi is the axial component of the contact deformation of the nut roller at the i-th contact point, Δl RBi is the deformation of the i-th shaft segment of the roller nut, Δl RTi is the axial deformation of the ith contact thread pair of the roller nut, Δl RNCi+1 is the axial component of the contact deformation of the roller-nut i+1th thread,

[0051] And substitute the stiffness for calculation, namely:

[0052]

[0053] Where p is the meshing pair number of rollers and screws before the i-th shaft segment, q is the meshing pair number of rollers and nuts before the i-th shaft segment, and k is NT Indicates the nut thread stiffness, k NRC Indicates the nut-roller contact stiffness, k RT Indicates the roller thread stiffness, F NRi is the axial load at the i-th meshing point;

[0054] Similarly, the threads between the roller and the lead screw before and after deformation always maintain a meshing relationship, that is:

[0055]

[0056] In the formula, ∑l Si is the total deformation of the screw, ∑l Ri is the total deformation of the roller, compression is positive and tension is negative,

[0057] For the reverse differential planetary roller screw, the pitch of the roller and the screw are also equal. Simplifying the above formula, we get:

[0058] Δl SBi -Δl STi +Δl STi+1 -Δl RSCi =Δl RBi +Δl RTi -Δl RTi+1 -Δl RSCi+1

[0059] In the formula, Δl SBi is the deformation of the i-th shaft end where the screw and roller mesh, Δl STi is the deformation of the thread teeth at the i-th contact point of the screw, Δl STi+1 is the deformation of the thread at the i+1th contact point of the screw, Δl RSCi is the axial component of the contact deformation of the i-th contact point of the screw roller, Δl RBi is the deformation of the i-th shaft segment of the roller screw, Δl RTi is the axial deformation of the ith contact thread pair of the roller screw, Δl RSCi+1 is the axial component of the contact deformation of the roller-screw thread tooth i+1,

[0060] And substitute the stiffness for calculation, namely:

[0061]

[0062] In the formula, F A k is the axial load on the screw divided evenly onto a single roller, ST k is the thread stiffness of the screw thread, SRC k is the contact stiffness of the screw-roller thread engagement, RT is the roller thread stiffness.

[0063] As a further improvement of the present invention, in step S2, if only a single roller engagement is considered, the cross-sectional area of ​​the screw shaft segment is:

[0064]

[0065] In the formula, A S is the cross-sectional area of ​​the screw shaft, d S is the middle diameter of the screw, hf is the tooth bottom height, and m is the number of rollers;

[0066] For the nut, the cross-sectional area of ​​the shaft segment is:

[0067]

[0068] In the formula, A N is the cross-sectional area of ​​the nut shaft section, D N is the outer diameter of the nut, d Nis the nut median diameter, hf is the tooth bottom height, and m is the number of rollers;

[0069] For rollers, the cross-sectional area of ​​the shaft segment is:

[0070]

[0071] In the formula, A R is the cross-sectional area of ​​the roller-nut shaft section, d R h is the median diameter of the roller-nut meshing section, fR d is the bottom height of the roller-nut segment ring groove, r h is the median diameter of the roller-screw meshing section, fr It is the bottom height of the annular groove of the roller-screw meshing section.

[0072] As a further improvement of the present invention, step 2 specifically includes:

[0073] The random forest algorithm is used to establish a relevant model with the main structural parameters of the thread as input and the Euclidean distance of the eccentric load coefficient of the contact point as output. The Euclidean distance of the eccentric load coefficient is defined as follows:

[0074]

[0075] In the formula, xi represents the axial load of the i-th thread, and y represents the mean axial load of the thread;

[0076] Then, by adding interference factors to each structural parameter, the influence of interference factors on the prediction error of the Euclidean distance of the partial load coefficient is analyzed. Then, the importance of each structural parameter is compared and the corresponding contribution is calculated. The average descent precision algorithm is used to evaluate the importance of various structural parameters to the Euclidean distance of the partial load coefficient. The variable importance measure VIM(X) is expressed as follows:

[0077]

[0078] Where m is the number of trees in the random forest algorithm, ER j is the error rate of the jth tree before variable j is replaced, ER' j is the error rate of the jth tree after variable j is replaced;

[0079] If there is no significant change in the error rate before and after replacement, it is considered that the structural parameters are not very important to the eccentric load coefficient.

[0080] As a further improvement of the present invention, step three specifically includes:

[0081] Based on the Latin hypercube sampling method, the input parameter set of each structural parameter is obtained, the sampling range is determined by the design tolerance, the normal distribution is determined by the actual engineering experience, and the eccentric load coefficient of the corresponding data set is obtained by the analytical model, and finally the training data set used by the GA-BP and random forest algorithms is generated; the genetic algorithm (GA) is used to optimize the initial weight value and bias of the BP neural network to predict the eccentric load coefficient; the inverse of the sum of the squares of the error between the predicted value and the actual value of the eccentric load coefficient is used as the fitness function, as shown below:

[0082]

[0083] Where F represents the fitness function, yt is the initial value of the eccentric load coefficient calculated by the analytical model, is the predicted value of the neural network, z is the number of simulations of the eccentric load coefficient in the data set;

[0084] Finally, the GA-BP neural network parameter settings are obtained by fitting the structural parameters and the Euclidean distance of the eccentric load coefficient through the training data set, and the inherent correlation law is obtained.

[0085] As a further improvement of the present invention, step 4 specifically includes:

[0086] Taking the minimum Euclidean distance of the eccentric load coefficient as the goal, the optimal solution of each structural parameter is obtained by the NSGA-II algorithm, and then the tolerance band is optimized and allocated by the quality loss function and tolerance sensitivity; quality loss is defined as the deviation between the quality characteristic value of the product and the design target value, resulting in the loss of product quality; the quality loss model is as follows:

[0087]

[0088] In the formula, g represents the quality loss function, C(u i ,l i ) is the cost loss caused by the i-th tolerance exceeding the tolerance. The more the actual value exceeds the tolerance range, the greater the cost loss. It is determined by the actual project. ui represents the upper deviation of the i-th tolerance, and li represents the lower deviation of the i-th tolerance. For geometric tolerance, the lower deviation is always 0. i is the importance weight of the i-th tolerance deviation on the performance of the whole machine, U L , U T , U E Represent load, accuracy, and efficiency weights respectively, L i , T i , E represent the importance coefficient of the ith tolerance to load, accuracy, and efficiency, respectively;

[0089] Based on the neural network model trained in step 3, the normal distribution of each structural parameter actually detected in the project is used as input, Latin hypercube sampling is performed within each tolerance band, and the Euclidean distance of the eccentric load coefficient is used as the output. Based on the random forest algorithm, the sensitivity index of the standard deviation of the Euclidean distance distribution of the eccentric load coefficient to the tolerance width is obtained, that is, the average load sensitivity is used as the tolerance sensitivity function, in order to obtain higher accuracy stability and consistency within the tolerance range, as shown below:

[0090] h=Δσ(u1,u2,…u i ,l1,l2,…l i )

[0091] Where h represents the tolerance sensitivity function, Δσ represents the sensitivity function of the standard deviation of the Euclidean distance of the eccentric load coefficient to the tolerance;

[0092] The final multi-objective optimization fitness function is as follows:

[0093] min f=[g(u1,u2,…u i ,l1,l2,…l i ),h(u1,u2,…u i ,l1,l2,…l i )]

[0094] Where f is the weighted result of quality loss and precision consistency caused by machining under specified tolerance, g(u1,u2,…u i ,l1,l2,…l i ) is the processing quality fitness function, h(u1,u2,…u i ,l1,l2,…l i ) is the load-balancing sensitivity fitness function.

[0095] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0096] The present invention fully considers the deformation coordination relationship caused by the meshing between thread teeth, introduces the stiffness matrix and random forest algorithm, extracts key structural parameters, and introduces the precision level of dimensional tolerance and form and position tolerance limited by processing cost, thereby improving the feasibility and economy of the optimization result. The stiffness of the annular groove teeth is affected by adjusting the structural parameters, thereby affecting the axial load distribution, and realizing the multi-objective optimization design of the reverse differential planetary roller screw for load sharing and processing cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0097] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0098] Figure 1 It is a schematic diagram of the structure of the reverse differential planetary roller screw in the present invention;

[0099] Figure 2 for Figure 1 Schematic diagram of the structure of the middle roller;

[0100] Figure 3 for Figure 1 Schematic diagram of the structure of the middle lead screw;

[0101] Figure 4 The figure is the thread engagement deformation coordination relationship diagram of the reverse differential planetary roller screw;

[0102] Figure 5 This is the stiffness-deformation correlation model diagram of the reverse differential planetary roller screw;

[0103] Figure 6 It is a schematic diagram of the deformation of the thread teeth of the reverse differential planetary roller screw after being subjected to force;

[0104] Figure 7 This is the flow chart for calculating the load between threads;

[0105] Figure 8 The figure is a flow chart of the method of the present invention. DETAILED DESCRIPTION

[0106] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. The components of the embodiments of the present invention generally described and shown in the drawings herein can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0107] In the description of the present invention, it should be noted that if the terms "center", "up", "down", "left", "right", "vertical", "horizontal", "inside", "outside" and the like appear, the orientation or position relationship indicated is based on the orientation or position relationship shown in the accompanying drawings, or is the orientation or position relationship in which the product of the application is usually placed when used. It is only for the convenience of describing the present invention and simplifying the description, and does not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention.

[0108] Combine the following Figure 1-Figure 8 The present invention is described in detail.

[0109] Example

[0110] The structure of the reverse differential planetary roller screw mentioned in this method is as follows Figure 1 As shown in the figure, the rollers are meshed with the lead screw and nut in sections. By introducing the differential effect through different meshing motion relationships, the actual lead can be made much lower than the theoretical lead, achieving high reduction ratio precision transmission. In addition, the reverse differential planetary roller screw eliminates the synchronous meshing gears between the lead screw and the rollers, which reduces the processing difficulty, avoids the synchronous gear eccentricity caused by processing errors, and improves the overall reliability.

[0111] Among them, the roller structure is as follows Figure 2 As shown in the figure, the roller and the screw meshing section is the ring groove meshing, while the roller and the nut meshing section is the thread meshing. The schematic diagram of the screw structure is as follows Figure 3 shown.

[0112] A method for optimizing the load-sharing design of a reverse differential planetary roller screw comprises the following steps:

[0113] Step 1: Based on the meshing deformation coordination relationship of the reverse differential planetary roller screw thread teeth, the deformation coordination formulas of the roller ring groove and the nut ring groove, the roller thread and the screw thread are constructed;

[0114] Step 2: Use the random forest algorithm to obtain the importance of thread structure parameters and other parameters on load-sharing performance, and extract key influencing parameters;

[0115] Step 3: Use GA-BP neural network to establish a prediction model for key parameters and load balancing performance;

[0116] Step 4: Based on NSGA-II, a multi-objective optimization algorithm for mass loss and tolerance sensitivity is constructed to realize the multi-objective optimization design of the reverse differential planetary roller screw with processing cost as the constraint.

[0117] In the above method, step one specifically includes the following steps:

[0118] S1, such as Figure 4As shown in the figure, according to the meshing deformation coordination relationship between the roller, the screw and the nut, the contact between the roller shaft segment and the thread teeth is equivalent to a spiral spring, and the thread teeth are equivalent to a leaf spring. The following is established for all contacts of the reverse differential planetary roller screw: Figure 5 The stiffness-deformation correlation model shown;

[0119] S2, thread segment stiffness is the tensile and compressive stiffness of the two adjacent load-bearing thread teeth of the screw, roller or nut. This stiffness is solved by the tensile and compressive stiffness formula of the material mechanics axis. In the reverse differential planetary roller screw, the segment stiffness of the screw, roller and nut is:

[0120]

[0121] In the formula, k XB E is the shaft stiffness of the screw / nut / roller of the reverse differential planetary roller screw. X is the elastic modulus of the material, P is the pitch, A X is the cross-sectional area of ​​the shaft segment, S is the screw, R is the roller, and N is the nut;

[0122] S3. When the reverse differential planetary roller screw is subjected to load, the roller thread teeth are engaged with the screw and nut thread teeth respectively to bear the load. Each thread tooth will deform along the screw axis after being subjected to force; among them, if Figure 6 As shown, the axial deformation of the thread teeth includes deformation δ1 caused by bending, deformation δ2 caused by shearing, deformation δ3 caused by root tilting, deformation δ4 caused by root shearing, and deformation δ5 caused by radial force.

[0123] The thread profile is a trapezoidal thread profile of the screw and nut. The radial component of the normal contact load of the thread teeth and the axial component of the normal contact load of the thread teeth satisfy the following relationship:

[0124]

[0125] In the formula, F r is the radial separation of the normal contact load, F a is the axial component of the normal contact load.

[0126] The calculation method of each deformation is as follows:

[0127]

[0128] Where, μ is the Poisson's ratio of the material of the screw, roller and nut; E is the elastic modulus of the screw, roller and nut, a is the thread root thickness, b is the thread thickness, c is the thread crest thickness, and hf is the thread root height;

[0129] Due to the different structures of internal and external threads, the deformation of thread teeth caused by radial force is not the same; the external thread is equivalent to the diameter dw Solid cylinder, the internal thread is equivalent to the outer diameter d n , inner diameter d ni The hollow cylinder is 5w Indicates external thread deformation, using δ 5n Indicates the deformation of the internal thread;

[0130] For external threads, the deformation caused by the radial force is:

[0131]

[0132] For internal threads, the thread deformation caused by the radial force is:

[0133]

[0134] Thus, the total axial deformation δ of the thread teeth of the reverse differential planetary roller screw under the axial load is obtained: XT for:

[0135] δ XT =δ1+δ2+δ3+δ4+δ5

[0136] Corresponding thread stiffness k XT That is:

[0137]

[0138] S4. Based on the established stiffness-deformation correlation model and the axial load on the screw, it is first assumed that the axial load is evenly borne by all meshing contact points. The deformation of each shaft segment, thread tooth, and contact area is calculated based on the stiffness obtained from the material properties. The axial load of each contact point is then reversed based on the deformation to perform the next round of iteration. Finally, when the difference between the previous round of calculation results and the current calculation results is less than 10 -5 When , the iteration ends and the current calculation result is defined as the final calculation value of the thread tooth distribution result; the specific process is as follows Figure 7 shown.

[0139] Among them, the deformation of the threaded shaft section of the screw, roller and nut can be obtained through the shaft section load and shaft section stiffness. From the established relationship, it can be known that the axial deformation of the i-th shaft section of the nut is:

[0140]

[0141] In the formula, F NRj k is the axial load at the jth meshing position between the nut and the roller from the free end to the fixed end; NB is the nut shaft end stiffness, the free end is defined as the end close to the force direction when the screw is compressed, and the fixed end is defined as the end away from the force direction.

[0142] Similarly, the axial deformation of the i-th shaft segment of the screw is:

[0143]

[0144] In the formula, F A is the axial load of the screw; F SRj is the axial load at the jth meshing point of the screw roller meshing position; k SB is the axial stiffness of the nut.

[0145] Similarly, the axial deformation of the i-th roller segment is:

[0146]

[0147] Where p is the number of thread pairs that the roller-screw has engaged from the free end to the fixed end at the i-th meshing point of the roller; q is the number of thread pairs that the roller-nut has engaged from the free end to the fixed end at the i-th meshing point of the roller.

[0148] Without considering the error, the threads between the roller and the nut before and after deformation always maintain the meshing relationship, that is:

[0149]

[0150] Where P N is the nut lead, P R is the roller lead, n is the number of thread starts, ∑l Ni is the total deformation of the nut, ∑l Ri is the total deformation of the roller, compression is positive and tension is negative.

[0151] For the reverse differential planetary roller screw, the pitch of the roller and nut are equal. Simplifying the above equation, we get

[0152] Δl NBi +ΔL NTi -Δl NTi+1 +Δl RNCi =Δl RBi -Δl RTi +Δl RTi+1 +Δl RNCi+1

[0153] In the formula, Δl NBi is the deformation of the nut and the i-th shaft end of the screw, Δl NTi is the deformation of the thread at the ith contact point of the nut, Δl NTi+1 is the deformation of the thread at the i+1th contact point of the nut, Δl RNCi is the axial component of the contact deformation of the nut roller at the i-th contact point, Δl RBi is the deformation of the i-th shaft segment of the roller nut, Δl RTiis the axial deformation of the ith contact thread pair of the roller nut, Δl RNCi+1 It is the axial component of the contact deformation of the i+1th thread of the roller-nut.

[0154] And substitute the stiffness for calculation, namely:

[0155]

[0156] Where p is the meshing pair number of rollers and screws before the i-th shaft segment, q is the meshing pair number of rollers and nuts before the i-th shaft segment, and k is NT Indicates the nut thread stiffness, k NRC Indicates the nut-roller contact stiffness, k RT Indicates the roller thread stiffness, F NRi is the axial load at the i-th meshing point.

[0157] Similarly, the threads between the roller and the lead screw before and after deformation always maintain a meshing relationship, that is:

[0158]

[0159] In the formula, ∑l Si is the total deformation of the screw, ∑l Ri is the total deformation of the roller, compression is positive and tension is negative.

[0160] For the reverse differential planetary roller screw, the pitch of the roller and the screw are also equal. Simplifying the above formula, we get:

[0161] Δl SBi -Δl STi +Δl STi+1 -Δl RSCi =Δl RBi +Δl RTi -Δl RTi+1 -Δl RSCi+1

[0162] In the formula, Δl SBi is the deformation of the i-th shaft end where the screw and roller mesh, Δl STi is the deformation of the thread teeth at the i-th contact point of the screw, Δl STi+1 is the deformation of the thread at the i+1th contact point of the screw, Δl RSCi is the axial component of the contact deformation of the i-th contact point of the screw roller, Δl NBi is the deformation of the i-th shaft segment of the roller screw, Δl RTi is the axial deformation of the ith contact thread pair of the roller screw, Δl RSCi+1 It is the axial component of the contact deformation of the i+1th thread of the roller-screw.

[0163] And substitute the stiffness for calculation, namely:

[0164]

[0165] In the formula, F A k is the axial load on the screw divided evenly onto a single roller, ST k is the thread stiffness of the screw thread, SRC k is the contact stiffness of the screw-roller thread engagement, RT is the roller thread stiffness.

[0166] In step S2 of this embodiment, if only a single roller engagement is considered, the cross-sectional area of ​​the screw shaft segment is:

[0167]

[0168] In the formula, A S is the cross-sectional area of ​​the screw shaft, d S is the middle diameter of the screw, hf is the tooth bottom height, and m is the number of rollers;

[0169] For the nut, the cross-sectional area of ​​the shaft segment is:

[0170]

[0171] In the formula, A N is the cross-sectional area of ​​the nut shaft section, D N is the outer diameter of the nut, d N is the middle diameter of the nut, hf is the tooth bottom height, and m is the number of rollers.

[0172] For rollers, the cross-sectional area of ​​the shaft segment is:

[0173]

[0174] In the formula, A R is the cross-sectional area of ​​the roller-nut shaft section, d R h is the median diameter of the roller-nut meshing section, fR d is the bottom height of the roller-nut segment ring groove, r h is the median diameter of the roller-screw meshing section, fr It is the bottom height of the annular groove of the roller-screw meshing section.

[0175] In the above method, step 2 specifically includes the following steps:

[0176] The random forest algorithm is used to establish a relevant model with the main structural parameters of the thread as input and the Euclidean distance of the eccentric load coefficient of the contact point as output. The Euclidean distance of the eccentric load coefficient is defined as follows:

[0177]

[0178] Where xi represents the axial load of the i-th thread, and y represents the mean axial load of the thread.

[0179] Then, by adding interference factors to each structural parameter, the influence of interference factors on the prediction error of the Euclidean distance of the partial load coefficient is analyzed. Then, the importance of each structural parameter is compared and the corresponding contribution is calculated. The average descent precision algorithm is used to evaluate the importance of various structural parameters to the Euclidean distance of the partial load coefficient. The variable importance measure VIM(X) is expressed as follows:

[0180]

[0181] Where m is the number of trees in the random forest algorithm, ER j is the error rate of the jth tree before variable j is replaced, ER' j is the error rate of the jth tree after variable j is replaced;

[0182] If there is no significant change in the error rate before and after replacement, it is considered that the structural parameters are not very important to the eccentric load coefficient.

[0183] In the above method, step three specifically includes the following steps:

[0184] Based on the Latin hypercube sampling method, the input parameter set of each structural parameter is obtained, the sampling range is determined by the design tolerance, the normal distribution is determined by the actual engineering experience, and the eccentric load coefficient of the corresponding data set is obtained by the analytical model, and finally the training data set used by the GA-BP and random forest algorithms is generated; the genetic algorithm (GA) is used to optimize the initial weight value and bias of the BP neural network to predict the eccentric load coefficient; the inverse of the sum of the squares of the error between the predicted value and the actual value of the eccentric load coefficient is used as the fitness function, as shown below:

[0185]

[0186] Where F represents the fitness function, yt is the initial value of the eccentric load coefficient calculated by the analytical model, is the predicted value of the neural network, z is the number of simulations of the eccentric load coefficient in the data set;

[0187] Finally, the GA-BP neural network parameter settings are obtained by fitting the structural parameters and the Euclidean distance of the eccentric load coefficient through the training data set, and the inherent correlation law is obtained.

[0188] In the above method, step 4 specifically includes the following steps:

[0189] Taking the minimum Euclidean distance of the eccentric load coefficient as the goal, the optimal solution of each structural parameter is obtained by the NSGA-II algorithm, and then the tolerance band is optimized and allocated by the quality loss function and tolerance sensitivity; quality loss is defined as the deviation between the quality characteristic value of the product and the design target value, resulting in the loss of product quality; the quality loss model is as follows:

[0190]

[0191] In the formula, g represents the quality loss function, C(u i ,l i ) is the cost loss caused by the i-th tolerance exceeding the tolerance. The more the actual value exceeds the tolerance range, the greater the cost loss. It is determined by the actual project. ui represents the upper deviation of the i-th tolerance, and li represents the lower deviation of the i-th tolerance. For geometric tolerance, the lower deviation is always 0. i is the importance weight of the i-th tolerance deviation on the performance of the whole machine, U L , U T , U E Represent load, accuracy, and efficiency weights respectively, L i , T i , E represent the importance coefficient of the ith tolerance to load, accuracy, and efficiency, respectively.

[0192] Based on the neural network model trained in step 3, the normal distribution of each structural parameter actually detected in the project is used as input, Latin hypercube sampling is performed within each tolerance band, and the Euclidean distance of the eccentric load coefficient is used as the output. Based on the random forest algorithm, the sensitivity index of the standard deviation of the Euclidean distance distribution of the eccentric load coefficient to the tolerance width is obtained, that is, the average load sensitivity is used as the tolerance sensitivity function, in order to obtain higher accuracy stability and consistency within the tolerance range, as shown below:

[0193] h=Δσ(u1,u2,…u i ,l1,l2,…l i )

[0194] Where h represents the tolerance sensitivity function, and Δσ represents the sensitivity function of the standard deviation of the Euclidean distance of the eccentric load coefficient to the tolerance.

[0195] The final multi-objective optimization fitness function is as follows:

[0196] min f=[g(u1,u2,…u i ,l1,l2,…l i ),h((u1,u2,…u i ,l1,l2,…l i )].

[0197] Where f is the weighted result of quality loss and precision consistency caused by machining under specified tolerance, g(u1,u2,…u i ,l1,l2,…l i ) is the processing quality fitness function, h((u1,u2,...u i ,l1,l2,...l i ) is the load-balancing sensitivity fitness function.

[0198] The present invention fully considers the deformation coordination relationship caused by the meshing between thread teeth, introduces the stiffness matrix and random forest algorithm, extracts key structural parameters, and introduces the precision level of dimensional tolerance and form and position tolerance limited by processing cost, thereby improving the feasibility and economy of the optimization result. The stiffness of the annular groove teeth is affected by adjusting the structural parameters, thereby affecting the axial load distribution, and realizing the multi-objective optimization design of the reverse differential planetary roller screw for load sharing and processing cost.

[0199] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for optimizing the load-sharing of a reverse differential planetary roller screw, characterized in that: The following steps are involved: Step 1: Based on the meshing deformation coordination relationship of the reverse differential planetary roller screw thread teeth, the deformation coordination formulas of the roller ring groove and the nut ring groove, the roller thread and the screw thread are constructed; Step 2: Use the random forest algorithm to obtain the importance of thread structure parameters and other parameters on load-sharing performance, and extract key influencing parameters; Step 3: Use GA-BP neural network to establish a prediction model for key parameters and load balancing performance; Step 4: Based on NSGA-II, a multi-objective optimization algorithm for mass loss and tolerance sensitivity is constructed to realize the multi-objective optimization design of the reverse differential planetary roller screw with processing cost as the constraint.

2. The load-sharing optimization design method for a reverse differential planetary roller screw according to claim 1, characterized in that: Step 1 specifically includes: S1. According to the meshing deformation coordination relationship between the roller, the screw and the nut, the contact between the roller shaft segment and the thread teeth is equivalent to a spiral spring, and the thread teeth are equivalent to a leaf spring. A stiffness deformation association model is established for all contacts of the reverse differential planetary roller screw. S2, thread segment stiffness is the tensile and compressive stiffness of the two adjacent load-bearing thread teeth of the screw, roller or nut. This stiffness is solved by the tensile and compressive stiffness formula of the material mechanics axis. In the reverse differential planetary roller screw, the segment stiffness of the screw, roller and nut is: In the formula, k XB E is the shaft stiffness of the screw / nut / roller of the reverse differential planetary roller screw. X is the elastic modulus of the material, P is the pitch, A X is the cross-sectional area of ​​the shaft segment, S is the screw, R is the roller, and N is the nut; S3. When the reverse differential planetary roller screw is subjected to load, the roller thread teeth are meshed with the screw and nut thread teeth respectively to bear the load, and each thread tooth will deform along the screw axis after being subjected to force; wherein, the axial deformation of the thread teeth includes deformation δ1 caused by bending, deformation δ2 caused by shearing, deformation δ3 caused by root tilting, deformation δ4 caused by root shearing, and deformation δ5 caused by radial force component; The thread profile is a trapezoidal thread profile of the screw and nut. The radial component of the normal contact load of the thread teeth and the axial component of the normal contact load of the thread teeth satisfy the following relationship: In the formula, F r is the radial separation of the normal contact load, F a is the axial component of the normal contact load; The calculation method of each deformation is as follows: Where, μ is the Poisson's ratio of the material of the screw, roller and nut; E is the elastic modulus of the screw, roller and nut, a is the thread root thickness, b is the thread thickness, c is the thread crest thickness, and hf is the thread root height; Due to the different structures of internal and external threads, the deformation of thread teeth caused by radial force is not the same; the external thread is equivalent to the diameter d w Solid cylinder, the internal thread is equivalent to the outer diameter d n , inner diameter d ni The hollow cylinder is 5w Indicates external thread deformation, using δ 5n Indicates the deformation of the internal thread; For external threads, the deformation caused by the radial force is: For internal threads, the thread deformation caused by the radial force is: Thus, the total axial deformation δ of the thread teeth of the reverse differential planetary roller screw under the axial load is obtained: XT for: d XT =δ1+δ2+δ3+δ4+δ5 Corresponding thread stiffness k XT That is: S4. Based on the established stiffness-deformation correlation model and the axial load on the screw, it is first assumed that the axial load is evenly borne by all meshing contact points. The deformation of each shaft segment, thread tooth, and contact area is calculated based on the stiffness obtained from the material properties. The axial load of each contact point is then reversed based on the deformation to perform the next round of iteration. Finally, when the difference between the previous round of calculation results and the current calculation results is less than 10 -5 When , the iteration ends and the current calculation result is defined as the final calculation value of the thread tooth distribution result; Among them, the deformation of the threaded shaft section of the screw, roller and nut can be obtained through the shaft section load and shaft section stiffness. From the established relationship, it can be known that the axial deformation of the i-th shaft section of the nut is: In the formula, F NRj k is the axial load at the jth meshing position between the nut and the roller from the free end to the fixed end; NB is the nut shaft end stiffness, the free end is defined as the end close to the force direction when the screw is compressed, and the fixed end is defined as the end away from the force direction. Similarly, the axial deformation of the i-th shaft segment of the screw is: In the formula, F A is the axial load of the screw; F SRj is the axial load at the jth meshing point of the screw roller meshing position; k SB is the axial stiffness of the nut, Similarly, the axial deformation of the i-th roller segment is: Where p is the number of thread pairs that the roller-screw has engaged from the free end to the fixed end at the i-th meshing point of the roller; q is the number of thread pairs that the roller-nut has engaged from the free end to the fixed end at the i-th meshing point of the roller; Without considering the error, the threads between the roller and the nut before and after deformation always maintain the meshing relationship, that is: Where P N is the nut lead, P R is the roller lead, n is the number of thread starts, ∑l Ni is the total deformation of the nut, ∑l Ri is the total deformation of the roller, compression is positive and tension is negative, For the reverse differential planetary roller screw, the pitch of the roller and nut are equal. Simplifying the above equation, we get Δl NBi +ΔL NTi -Δl NTi+1 +Δl RNCi =Δl RBi -Δl RTi +Δl RTi+1 +Δl RNCi+1 In the formula, Δl NBi is the deformation of the nut and the i-th shaft end of the screw, Δl NTi is the deformation of the thread at the ith contact point of the nut, Δl NTi+1 is the deformation of the thread at the i+1th contact point of the nut, Δl RNCi is the axial component of the contact deformation of the nut roller at the i-th contact point, Δl RBi is the deformation of the i-th shaft segment of the roller nut, Δl RTi is the axial deformation of the ith contact thread pair of the roller nut, Δl RNCi+1 is the axial component of the contact deformation of the roller-nut i+1th thread, And substitute the stiffness for calculation, namely: Where p is the meshing pair number of rollers and screws before the i-th shaft segment, q is the meshing pair number of rollers and nuts before the i-th shaft segment, and k is NT Indicates the nut thread stiffness, k NRC Indicates the nut-roller contact stiffness, k RT Indicates the roller thread stiffness, F NRi is the axial load at the i-th meshing point; Similarly, the threads between the roller and the lead screw before and after deformation always maintain a meshing relationship, that is: In the formula, ∑l Si is the total deformation of the screw, ∑l Ri is the total deformation of the roller, compression is positive and tension is negative, For the reverse differential planetary roller screw, the pitch of the roller and the screw are also equal. Simplifying the above formula, we get: Δl SBi -Δl STi +Δl STi+1 -Δl RSCi =Δl RBi +Δl RTi -Δl RTi+1 -Δl RSCi+1 In the formula, Δl SBi is the deformation of the i-th shaft end where the screw and roller mesh, Δl STi is the deformation of the thread teeth at the i-th contact point of the screw, Δl STi+1 is the deformation of the thread at the i+1th contact point of the screw, Δl RSCi is the axial component of the contact deformation of the i-th contact point of the screw roller, Δl RBi is the deformation of the i-th shaft segment of the roller screw, Δl RTi is the axial deformation of the ith contact thread pair of the roller screw, Δl RSCi+1 is the axial component of the contact deformation of the roller-screw thread tooth i+1, And substitute the stiffness for calculation, namely: In the formula, F A k is the axial load on the screw divided evenly onto a single roller, ST k is the thread stiffness of the screw thread, SRC k is the contact stiffness of the screw-roller thread engagement, RT is the roller thread stiffness.

3. The load-sharing optimization design method for a reverse differential planetary roller screw according to claim 2, characterized in that: In step S2, if only a single roller meshing is considered, the cross-sectional area of ​​the screw shaft segment is: In the formula, A S is the cross-sectional area of ​​the screw shaft, d S is the middle diameter of the screw, hf is the tooth bottom height, and m is the number of rollers; For the nut, the cross-sectional area of ​​the shaft segment is: In the formula, A N is the cross-sectional area of ​​the nut shaft section, D N is the outer diameter of the nut, d N is the nut median diameter, hf is the tooth bottom height, and m is the number of rollers; For rollers, the cross-sectional area of ​​the shaft segment is: In the formula, A R is the cross-sectional area of ​​the roller-nut shaft section, d R h is the median diameter of the roller-nut meshing section, fR d is the bottom height of the roller-nut segment ring groove, r h is the median diameter of the roller-screw meshing section, fr It is the bottom height of the annular groove of the roller-screw meshing section.

4. The method for optimizing the load-sharing design of a reverse differential planetary roller screw according to claim 1, characterized in that: Step 2 specifically includes: The random forest algorithm is used to establish a relevant model with the main structural parameters of the thread as input and the Euclidean distance of the eccentric load coefficient of the contact point as output. The Euclidean distance of the eccentric load coefficient is defined as follows: In the formula, xi represents the axial load of the i-th thread, and y represents the mean axial load of the thread; Then, by adding interference factors to each structural parameter, the influence of interference factors on the prediction error of the Euclidean distance of the partial load coefficient is analyzed. Then, the importance of each structural parameter is compared and the corresponding contribution is calculated. The average descent precision algorithm is used to evaluate the importance of various structural parameters to the Euclidean distance of the partial load coefficient. The variable importance measure VIM(X) is expressed as follows: Where m is the number of trees in the random forest algorithm, ER j is the error rate of the jth tree before variable j is replaced, ER' j is the error rate of the jth tree after variable j is replaced; If there is no significant change in the error rate before and after replacement, it is considered that the structural parameters are not very important to the eccentric load coefficient.

5. The load-sharing optimization design method for a reverse differential planetary roller screw according to claim 1, characterized in that: Step three specifically includes: Based on the Latin hypercube sampling method, the input parameter set of each structural parameter is obtained, the sampling range is determined by the design tolerance, the normal distribution is determined by the actual engineering experience, and the eccentric load coefficient of the corresponding data set is obtained by the analytical model, and finally the training data set used by the GA-BP and random forest algorithms is generated; the genetic algorithm (GA) is used to optimize the initial weight value and bias of the BP neural network to predict the eccentric load coefficient; the inverse of the sum of the squares of the error between the predicted value and the actual value of the eccentric load coefficient is used as the fitness function, as shown below: Where F represents the fitness function, yt is the initial value of the eccentric load coefficient calculated by the analytical model, is the predicted value of the neural network, z is the number of simulations of the eccentric load coefficient in the data set; Finally, the GA-BP neural network parameter settings are obtained by fitting the structural parameters and the Euclidean distance of the eccentric load coefficient through the training data set, and the inherent correlation law is obtained.

6. A load-balanced optimization design method for a reverse differential planetary roller screw according to claim 5, characterized in that: Step 4 specifically includes: Taking the minimum Euclidean distance of the eccentric load coefficient as the goal, the optimal solution of each structural parameter is obtained by the NSGA-II algorithm, and then the tolerance band is optimized and allocated by the quality loss function and tolerance sensitivity; quality loss is defined as the deviation between the quality characteristic value of the product and the design target value, resulting in the loss of product quality; the quality loss model is as follows: In the formula, g represents the quality loss function, C(u i ,l i ) is the cost loss caused by the i-th tolerance exceeding the tolerance. The more the actual value exceeds the tolerance range, the greater the cost loss. It is determined by the actual project. ui represents the upper deviation of the i-th tolerance, and li represents the lower deviation of the i-th tolerance. For geometric tolerance, the lower deviation is always 0. i is the importance weight of the i-th tolerance deviation on the performance of the whole machine, U L , U T , U E Represent load, accuracy, and efficiency weights respectively, L i 、T i , E represent the importance coefficient of the ith tolerance to load, accuracy, and efficiency, respectively; Based on the neural network model trained in step 3, the normal distribution of each structural parameter actually detected in the project is used as input, Latin hypercube sampling is performed within each tolerance band, and the Euclidean distance of the eccentric load coefficient is used as the output. Based on the random forest algorithm, the sensitivity index of the standard deviation of the Euclidean distance distribution of the eccentric load coefficient to the tolerance width is obtained, that is, the average load sensitivity is used as the tolerance sensitivity function, in order to obtain higher accuracy stability and consistency within the tolerance range, as shown below: h=Δσ(u1,u2,…u i ,l1,l2,…l i ) Where h represents the tolerance sensitivity function, Δσ represents the sensitivity function of the standard deviation of the Euclidean distance of the eccentric load coefficient to the tolerance; The final multi-objective optimization fitness function is as follows: <h2 style=";text-align:left;direction:ltr">min f=[g(u1,u2,…u<h2 style=";text-align:left;direction:ltr"> i <h2 style=";text-align:left;direction:ltr"> ,l1,l2,…l<h2 style=";text-align:left;direction:ltr"> i <h2 style=";text-align:left;direction:ltr"> ),h(u1,u2,...u<h2 style=";text-align:left;direction:ltr"> i <h2 style=";text-align:left;direction:ltr"> ,l1,l2,...l<h2 style=";text-align:left;direction:ltr"> i <h2 style=";text-align:left;direction:ltr"> )] Where f is the weighted result of quality loss and precision consistency caused by machining under specified tolerance, g(u1,u2,...u i ,l1,l2,…l i ) is the processing quality fitness function, h(u1,u2,…u i ,l1,l2,...l i ) is the load-balancing sensitivity fitness function.

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