CN113779735B - Planetary gear box three-dimensional tolerance analysis method based on jacobian rotation model - Google Patents
Planetary gear box three-dimensional tolerance analysis method based on jacobian rotation model Download PDFInfo
- Publication number
- CN113779735B CN113779735B CN202111194882.6A CN202111194882A CN113779735B CN 113779735 B CN113779735 B CN 113779735B CN 202111194882 A CN202111194882 A CN 202111194882A CN 113779735 B CN113779735 B CN 113779735B
- Authority
- CN
- China
- Prior art keywords
- characteristic
- tolerance
- deviation
- rotation
- assembly
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000004458 analytical method Methods 0.000 title claims abstract description 25
- 239000011159 matrix material Substances 0.000 claims abstract description 73
- 238000000034 method Methods 0.000 claims abstract description 38
- 230000005540 biological transmission Effects 0.000 claims abstract description 34
- 230000035945 sensitivity Effects 0.000 claims abstract description 25
- 238000000342 Monte Carlo simulation Methods 0.000 claims abstract description 11
- 238000004422 calculation algorithm Methods 0.000 claims abstract description 8
- 238000004364 calculation method Methods 0.000 claims description 30
- 238000012512 characterization method Methods 0.000 claims description 16
- 230000009466 transformation Effects 0.000 claims description 12
- 230000008569 process Effects 0.000 claims description 11
- 238000012546 transfer Methods 0.000 claims description 8
- 238000004088 simulation Methods 0.000 claims description 3
- 238000013461 design Methods 0.000 abstract description 5
- 238000005516 engineering process Methods 0.000 abstract description 5
- 230000009286 beneficial effect Effects 0.000 abstract description 2
- 238000012986 modification Methods 0.000 abstract description 2
- 230000004048 modification Effects 0.000 abstract description 2
- 230000033001 locomotion Effects 0.000 description 7
- 230000000694 effects Effects 0.000 description 2
- 238000009825 accumulation Methods 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 238000012360 testing method Methods 0.000 description 1
- 230000007704 transition Effects 0.000 description 1
- 238000013519 translation Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/17—Mechanical parametric or variational design
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Geometry (AREA)
- General Physics & Mathematics (AREA)
- Evolutionary Computation (AREA)
- General Engineering & Computer Science (AREA)
- Computer Hardware Design (AREA)
- Computational Mathematics (AREA)
- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- Numerical Control (AREA)
Abstract
The invention discloses a three-dimensional tolerance analysis method of a planetary gear box based on a jacobian rotation model, which comprises the steps of obtaining basic information of part characteristic tolerance information, assembly characteristic auxiliary information and pose information; generating a path characteristic deviation rotation based on a determined target through Monte Carlo simulation; acquiring a deviation transmission path based on assembly characteristic side information and by adopting a Dikk Tesla algorithm; based on the deviation transmission path, generating a jacobian matrix by combining pose information; the method comprises the steps of obtaining target functional characteristic parameters, path tolerance sensitivity and path tolerance contribution. The method has the beneficial effect that the three-dimensional tolerance analysis model based on the jacobian matrix is constructed based on the principle of robot mechanics. The method is particularly suitable for three-dimensional tolerance analysis of the planetary gear box, and computer aided design software can be formed by means of computer technology, so that the requirements of repeated modification of an assembly structure and tolerance distribution in a design stage are met.
Description
Technical Field
The invention relates to a planetary gear box accumulated error analysis technology, in particular to a planetary gear box three-dimensional tolerance analysis method based on a jacobian rotation model.
Background
The deviation of each assembly surface of each part of the large planetary gear box can be accumulated through assembly contact in the assembly process, and the deviation of key functional parts such as gear meshing parts and the like is affected. Tolerances are used in design and manufacture to control the deviations, and tolerance analysis is performed to predict the accumulation of deviations prior to assembly and to analyze the magnitude of the effects of each deviation to adjust the tolerance distribution. The large planetary gear box has the characteristics of high rigidity, three-dimensional spatial distribution of multiple parts, parallel connection of multiple parts and the like, and the assembly mode relates to plane fitting, cylindrical surface fitting, pin hole assembly, bolt assembly and the like with different spatial directions. The traditional size chain can only analyze one-dimensional and two-dimensional projection of the size of the part, so that the influence of the deviation of each assembly surface in the assembly body on the key functional part cannot be effectively expressed by means of the traditional size chain tolerance analysis, and the situation that the tolerance test of each part is qualified but the deviation of the key functional part is overlarge after the assembly is finished often occurs.
The existing tolerance analysis method is based on extreme value method and root method of the dimension chain method. A two-dimensional size chain cannot express the part rotation influence caused by form and position tolerance and clearance, and partial deviation sources on the three-dimensional size chain can be ignored for a planetary gear transmission system, so that the calculation accuracy is not high enough, and the source cannot be traced effectively. At present, there are two-dimensional size chain analysis software such as Chengzhipoeng DCC tolerance analysis software and DTAS chier software in China, but no three-dimensional deviation analysis software.
Disclosure of Invention
The invention aims to provide a planetary gear box three-dimensional tolerance analysis method based on a jacobian rotation model, which aims at the defect that the existing tolerance analysis means can not meet the three-dimensional tolerance of the planetary gear box, and the method is based on the joint motion principle and the pose transformation principle of robot mechanics, uses three-translation three-rotation six-degree-of-freedom rotation to represent the assembly surface deviation, and uses a 6X 6 jacobian matrix to reflect the influence of unit assembly surface deviation on the target key functional part deviation. Thereby constructing a three-dimensional tolerance analysis model comprising a tolerance characterization rotation model and a tolerance transfer jacobian matrix. The method is particularly suitable for the three-dimensional tolerance analysis requirement of the planetary gear box, which is characterized in that the number of parts is large, the assembly relation is complex, the assembly paths are connected in parallel to form a net, the selection of a deviation transmission path is difficult, computer aided design software can be formed by means of computer technology, and the requirement of the design stage of repeatedly modifying the assembly structure and the tolerance distribution scheme is met.
In order to achieve the above purpose, the present invention adopts the following technical scheme.
A planetary gear box three-dimensional tolerance analysis method based on a jacobian rotation model comprises the following steps:
S1, acquiring basic information of an assembly: acquiring part characteristic information, tolerance information, assembly characteristic pair information and pose information of an assembly based on the assembly of the planetary gear box; and a target functional feature pair and a target functional feature bias item determined based on the assembly;
S2, generating a path deviation rotation and a jacobian matrix: generating a path characteristic deviation rotation based on the target and capable of being used for calculating a path tolerance contribution by utilizing part characteristic tolerance information through Monte Carlo simulation; constructing an assembly undirected graph based on assembly characteristic side information and a shortest dimension chain principle, and obtaining a deviation transmission path based on the target by adopting a Dikk algorithm; generating a jacobian matrix based on the target and capable of being used for calculating path tolerance sensitivity based on the deviation transfer path in combination with pose information;
S3, obtaining target parameters: the target parameters comprise one or any two of target functional characteristic parameters, path tolerance sensitivity and path tolerance contribution; or all three; the target function characteristic parameters are target function parameters which are obtained by performing jacobian rotation model matrix calculation through the product of path characteristic deviation rotation and jacobian matrix, and are characterized according to a set vector characterization mode; the path tolerance sensitivity is calculated based on the jacobian matrix; the path tolerance contribution is calculated based on the path characteristic deviation spin.
According to the invention, through the joint motion principle and the pose transformation principle based on robot mechanics, the assembly surface deviation is represented by the rotation of three translational motions and three rotational motions with six degrees of freedom, and the influence of the unit assembly surface deviation on the target key functional part deviation is reflected by the 6X 6 Jacobian matrix. Thereby constructing a three-dimensional tolerance analysis model comprising a tolerance characterization rotation model and a tolerance transfer jacobian matrix. The method is particularly suitable for the three-dimensional tolerance analysis requirement of the planetary gear box, which is characterized in that the number of parts is large, the assembly relation is complex, the assembly paths are connected in parallel to form a network, the selection of a deviation transmission path is difficult, computer aided design software can be formed by means of computer technology, and the requirement that the assembly structure and the tolerance distribution scheme need to be repeatedly modified in the design stage is met.
Preferably, the feature tolerance information of the part comprises feature information and tolerance information of the part, wherein the feature information and the tolerance information belong to the set part; wherein, the characteristic is to index the assembly surface of the tolerance information; the characteristic information comprises characteristic geometric parameters belonging to characteristic types and pose information formed by characteristic positions and characteristic directions; the characteristic types are divided into cylindrical surfaces and plane surfaces; the characteristic geometric parameters comprise a cylindrical generatrix length corresponding to the cylindrical surface characteristic, and a plane maximum length and a plane maximum width corresponding to the plane characteristic; the feature position refers to the coordinate of the feature center in the assembly reference coordinate; wherein, the characteristic center of the cylindrical surface characteristic is the midpoint of the axis of the cylindrical surface; the feature center of the planar feature is a planar center point; the pose information is expressed by a4×4 homogeneous coordinate transformation matrix, and comprises a3×3 projection matrix and a3×1 position coordinate of a characteristic auxiliary coordinate relative to a reference coordinate, and the expression is as follows:
wherein,
Wherein: [ C 1i],[C2i],[C3i ] is the projection length of the unit direction vector of the three coordinate axes of the feature i coordinate system in the global coordinate system, and dx i,dyi,dzi is the coordinate of the origin of the feature i coordinate system in the global coordinate system;
The tolerance includes a non-reference tolerance and a reference tolerance; wherein, the tolerance without reference comprises a dimensional tolerance and a shape tolerance marked on one surface; the referenced tolerances include dimensional tolerances, orientation tolerances, positional tolerances and runout tolerances noted on the two faces with reference to at least one feature on the part.
Preferably, the assembly body characteristic pair consists of an internal pair and an assembly pair; the internal pair is two characteristic surfaces of the same part, and the condition for forming the internal pair is that one characteristic surface has a tolerance taking the other characteristic surface as a reference; the assembly pair is two characteristic surfaces assembled by different parts, and the condition for forming the assembly pair is that the two characteristic surfaces are tightly contacted through assembly.
Further preferably, the internal pair of the same component is a zero tolerance internal pair if there is no tolerance between the two feature surfaces including the reference, but there is a tolerance relationship secured by the precision of the machine tool.
Further preferably, in the constructed assembly undirected graph, the nodes represent characteristic faces of the assembly pairs, and the edges represent internal or assembly pairs of the same part; the assembly undirected graph is expressed by an adjacent matrix, wherein all the characteristic surfaces of the assembly are marked as rows and columns, the adjacent matrix has internal auxiliary relations on the same part or has corresponding rows and columns which form a pair of assembly auxiliary relations and are marked as 1, and the undirected relation is marked as 0.
Still more preferably, in the assembly relationship, the point contact of the assembly relationship which mainly plays a limiting role or the small surface contact relationship corresponding to the point contact, the corresponding position in the matrix is marked with a number higher than 1to indicate that the assembly relationship has a long path and a weak duty ratio in the shortest dimension chain principle calculation.
Still further preferably, in the process of adopting the diels tesla algorithm, a shortest path to one node in the assembly undirected graph is calculated with the node as a starting point, a deviation transmission path represented by a set of features is obtained, and a corresponding feature pair on the deviation transmission path is obtained by combining the deviation transmission path with feature pair information in the assembly.
Preferably, the generating process of the path characteristic deviation rotation in S2 includes:
s21, searching for tolerances of all the features on the deviation transmission path, and selecting a tolerance containing a reference and other non-reference tolerances of the reference on the path features;
S22, determining the upper limit and the lower limit of each tolerance according to the part characteristic tolerance information;
S23, converting a tolerance domain determined by the upper and lower tolerance limits into the upper and lower limits of each component of the six-degree-of-freedom characteristic deviation screw;
S24, determining the mean value and standard deviation of the normal distribution of each component of the characteristic auxiliary deviation screw according to the 3 sigma principle;
s25, generating characteristic deviation rotations for the characteristic tolerance on each deviation path according to Monte Carlo simulation times;
Wherein, for the combined tolerance containing a plurality of tolerance labels on the same feature, only one position tolerance or direction tolerance is considered, and the upper limit and the lower limit of the rotation component are determined according to the tolerance domain.
Further preferably, in S23, the expression of the six-degree-of-freedom characteristic minor deviation rotation is as follows:
T＝[u，v，w，α，β，γ]T (2)；
Wherein: the u, v and w components express the deviation of the characteristic in three directions of the local coordinate system, and the alpha, beta and gamma components express the deviation of the characteristic in three directions of rotation around the local coordinate system;
Wherein, the upper and lower limits of the rotation component of the plane tolerance domain are respectively determined as follows:
Wherein T is a plane tolerance parameter, and L 1 and L 2 are respectively a planeness length and width geometric parameters;
Wherein, the upper and lower limits of the rotation component of the cylindrical surface tolerance domain are respectively determined as follows:
wherein T is a cylindrical surface tolerance parameter, and L is a cylindrical surface length geometric parameter;
in S24, according to the 3 sigma principle, the mean and standard deviation are determined as follows:
wherein: TL is less than or equal to X is less than or equal to TU, and represents the upper limit and the lower limit of the component X.
Preferably, in the step S2, the characteristic deviation rotation on each deviation transmission path corresponds to a 6×6 jacobian matrix, and the deviation rotation generated by the characteristic unit deviation rotation in the target functional characteristic pair is expressed; the generation method of the jacobian matrix comprises the steps of corresponding to characteristic deviation rotation on each deviation transmission path, calculating to obtain the jacobian matrix of the deviation rotation by using a homogeneous coordinate transformation matrix of the characteristic and a homogeneous coordinate transformation matrix of a target functional characteristic pair;
the jacobian matrix expression is as follows:
Wherein:
wherein: A direction matrix of the i coordinate system relative to the global coordinate system; /(I) Is a matrix of positions of the coordinate system of the target point relative to the i coordinate system. dk n,dki (k=x, y, z) is the value of the k-axis of the target point coordinate system and the i-coordinate system in the global coordinate system;
In the step S3, the method for calculating the target function feature parameter includes:
S31, multiplying the characteristic auxiliary deviation rotation by the jacobian matrix according to the Monte Carlo simulation times to obtain a target functional characteristic deviation rotation;
s32, calculating to obtain target function feature deviation parameters based on the target function feature deviation rotation obtained in the S31;
S33, repeatedly executing simulation calculation for set times to obtain statistical distribution of target function characteristic deviation parameters;
the calculation for the characteristic deviation rotation is as follows:
TFR＝[[J]FE1…[J]FEn][TFEi…TFEn]T (5)；
Wherein: t FR＝[u,v,w,α,β,γ]T is the target characteristic deviation rotation, T FEi＝[ui,vi,wi,αi,βi,γi]T is the path deviation characteristic rotation;
the calculation formula for the target function feature deviation parameter is as follows:
x＝kx·TFR (6)；
Wherein: x is any target functional characteristic deviation parameter, and k x is a 1X 6 target functional parameter characterization vector corresponding to the parameter;
The calculation process of the path tolerance sensitivity comprises the following steps: taking the characteristic tolerance on the selected deviation transmission path as a unit tolerance, multiplying the deviation rotation determined by the unit tolerance parameter by the corresponding jacobian matrix, and multiplying the unit tolerance parameter by a target function parameter characterization vector to obtain a target function parameter obtained by the unit tolerance parameter; the calculation formula is as follows:
wherein: For the sensitivity of the deviation target functional parameter x to the unit tolerance at i, T FEi e is the deviation rotation of the i feature formed by the unit tolerance parameter;
The calculation of the path tolerance contribution degree comprises the following steps: calculating standard deviation of each component of deviation rotation based on the characteristic tolerance on the selected deviation transmission path, multiplying the standard deviation by a target function parameter characterization vector, and finally calculating the square sum duty ratio of the square of the standard deviation to all path tolerances; the calculation formula is as follows:
wherein: For the contribution degree of the sensitivity of the deviation at i to the deviation target functional parameter x, σ FEi is the six-component deviation rotation standard deviation of the i feature in the deviation rotation generation.
The invention has the beneficial effects that the assembly surface deviation is represented by the rotation of three translational motions and three rotational motions with six degrees of freedom based on the joint motion principle and the pose transformation principle of robot mechanics, and the influence of the unit assembly surface deviation on the target key functional part deviation is reflected by a 6X 6 jacobian matrix. Thereby constructing a three-dimensional tolerance analysis model comprising a tolerance characterization rotation model and a tolerance transfer jacobian matrix. The method is particularly suitable for the three-dimensional tolerance analysis requirement of the planetary gear box, which is characterized in that the number of parts is large, the assembly relation is complex, the assembly paths are connected in parallel to form a network, the selection of a deviation transmission path is difficult, computer aided design software can be formed by means of computer technology, and the requirement that the assembly structure and the tolerance distribution scheme need to be repeatedly modified in the design stage is met. The method is suitable for the situation of tight fit without gaps between fitting surfaces of parts, such as transition fit or interference fit, and is not suitable for the situation of larger fit gaps.
Drawings
Fig. 1 is a flow chart of the method of the present invention.
Fig. 2 is an assembly view of an embodiment of the present invention.
FIG. 3 is a component characteristic variation transfer path diagram of an embodiment of the present invention.
FIG. 4 is a target key function deviation profile of an embodiment of the present invention.
Detailed Description
The invention will be further described with reference to the accompanying drawings, which are not intended to limit the invention to the embodiments described.
Referring to fig. 1, a three-dimensional tolerance analysis method of a planetary gear box based on a jacobian rotation model comprises the following steps:
S1, acquiring basic information of an assembly: acquiring part characteristic tolerance information, assembly characteristic pair information and pose information of an assembly based on the assembly of the planetary gear box; and a target functional feature pair and a target functional feature bias item determined based on the assembly;
S2, generating a path deviation rotation and a jacobian matrix: generating a path characteristic deviation rotation based on the target and capable of being used for calculating a path tolerance contribution by utilizing part characteristic tolerance information through Monte Carlo simulation; constructing an assembly undirected graph based on assembly characteristic side information and a shortest dimension chain principle, and obtaining a deviation transmission path based on the target by adopting a Dikk algorithm; generating a jacobian matrix based on the target and capable of being used for calculating path tolerance sensitivity based on the deviation transfer path in combination with pose information;
S3, obtaining target parameters: the target parameters comprise one or any two of target functional characteristic parameters, path tolerance sensitivity and path tolerance contribution; or all three; the target function characteristic parameters are target function parameters which are obtained by performing jacobian rotation model matrix calculation through the product of path characteristic deviation rotation and jacobian matrix, and are characterized according to a set vector characterization mode; the path tolerance sensitivity is calculated based on the jacobian matrix; the path tolerance contribution is calculated based on the path characteristic deviation spin.
Wherein the part characteristic tolerance information comprises part, characteristic and tolerance information, which is characteristic information and tolerance information of the set part; wherein, the characteristic is to index the assembly surface of the tolerance information; the characteristic information comprises characteristic geometric parameters belonging to characteristic types and pose information formed by characteristic positions and characteristic directions; the characteristic types are divided into cylindrical surfaces and plane surfaces; the characteristic geometric parameters comprise a cylindrical generatrix length corresponding to the cylindrical surface characteristic, and a plane maximum length and a plane maximum width corresponding to the plane characteristic; the feature position refers to the coordinate of the feature center in the assembly reference coordinate; wherein, the characteristic center of the cylindrical surface characteristic is the midpoint of the axis of the cylindrical surface; the feature center of the planar feature is a planar center point; the pose information is expressed by a 4×4 homogeneous coordinate transformation matrix, and comprises a 3×3 projection matrix and a 3×1 position coordinate of a characteristic auxiliary coordinate relative to a reference coordinate, and the expression is as follows:
wherein,
Wherein: [ C 1i],[C2i],[C3i ] is the projection length of the unit direction vector of the three coordinate axes of the feature i coordinate system in the global coordinate system, and dx i,dyi,dzi is the coordinate of the origin of the feature i coordinate system in the global coordinate system;
The tolerance includes a non-reference tolerance and a reference tolerance; wherein, the tolerance without reference comprises a dimensional tolerance and a shape tolerance marked on one surface; the referenced tolerances include dimensional tolerances, orientation tolerances, positional tolerances and runout tolerances noted on the two faces with reference to at least one feature on the part.
Wherein, the assembly body characteristic pair consists of an internal pair and an assembly pair; the internal pair is two characteristic surfaces of the same part, and the condition for forming the internal pair is that one characteristic surface has a tolerance taking the other characteristic surface as a reference; the assembly pair is two characteristic surfaces assembled by different parts, and the condition for forming the assembly pair is that the two characteristic surfaces are tightly contacted through assembly. In the internal pair of the same part, if there is no tolerance containing a reference between two feature surfaces, but there is a tolerance relationship secured by the precision of the machine tool, the internal pair is denoted as a zero tolerance internal pair.
In the constructed undirected graph of the assembly, the nodes represent characteristic faces of assembly pairs, and the edges represent internal auxiliary relations or assembly auxiliary relations of the same part; the assembly undirected graph is expressed by an adjacent matrix, wherein all the characteristic surfaces of the assembly are marked as rows and columns, the adjacent matrix has internal auxiliary relations on the same part or has corresponding rows and columns which form a pair of assembly auxiliary relations and are marked as 1, and the undirected relation is marked as 0. And (3) marking numbers higher than 1 at corresponding positions in the matrix by using point contact or small surface contact relation which is equivalent to point contact of the assembly relation mainly playing a limiting role in the assembly relation so as to indicate that the assembly relation has long path and weak duty ratio in the shortest dimension chain principle calculation. In the process of adopting the Dikk Tesla algorithm, taking one node in the assembly undirected graph as a starting point, calculating the shortest path to the other node, obtaining a deviation transmission path characterized by a group of features, and obtaining a corresponding feature pair on the deviation transmission path by combining the deviation transmission path with feature pair information in the assembly body.
The generating process of the path characteristic deviation rotation in S2 includes:
s21, searching for tolerances of all the features on the deviation transmission path, and selecting a tolerance containing a reference and other non-reference tolerances of the reference on the path features;
S22, determining the upper limit and the lower limit of each tolerance according to the part characteristic tolerance information;
S23, converting a tolerance domain determined by the upper and lower tolerance limits into the upper and lower limits of each component of the six-degree-of-freedom characteristic deviation screw;
S24, determining the mean value and standard deviation of the normal distribution of each component of the characteristic auxiliary deviation screw according to the 3 sigma principle;
s25, generating characteristic deviation rotations for the characteristic tolerance on each deviation path according to Monte Carlo simulation times;
Wherein, for the combined tolerance containing a plurality of tolerance labels on the same feature, only one position tolerance or direction tolerance is considered, and the upper limit and the lower limit of the rotation component are determined according to the tolerance domain.
In S23, the expression of the six-degree-of-freedom characteristic sub-deviation rotation is as follows:
T＝[u，v，w，α，β，γ]T (2)；
Wherein: the u, v and w components express the deviation of the characteristic in three directions of the local coordinate system, and the alpha, beta and gamma components express the deviation of the characteristic in three directions of rotation around the local coordinate system;
Wherein, the upper and lower limits of the rotation component of the plane tolerance domain are respectively determined as follows:
Wherein T is a plane tolerance parameter, and L 1 and L 2 are respectively a planeness length and width geometric parameters;
Wherein, the upper and lower limits of the rotation component of the cylindrical surface tolerance domain are respectively determined as follows:
wherein T is a cylindrical surface tolerance parameter, and L is a cylindrical surface length geometric parameter;
in S24, according to the 3 sigma principle, the mean and standard deviation are determined as follows:
wherein: TL is less than or equal to X is less than or equal to TU, and represents the upper limit and the lower limit of the component X.
In the step S2, the characteristic deviation rotation on each deviation transmission path corresponds to a 6X 6 Jacobian matrix, and the deviation rotation generated by the characteristic unit deviation rotation in the target functional characteristic pair is expressed; the generation method of the jacobian matrix comprises the steps of corresponding to characteristic deviation rotation on each deviation transmission path, calculating to obtain the jacobian matrix of the deviation rotation by using a homogeneous coordinate transformation matrix of the characteristic and a homogeneous coordinate transformation matrix of a target functional characteristic pair;
the jacobian matrix expression is as follows:
Wherein:
wherein: A direction matrix of the i coordinate system relative to the global coordinate system; /(I) Is a matrix of positions of the coordinate system of the target point relative to the i coordinate system. dk n,dki (k=x, y, z) is the value of the k-axis of the target point coordinate system and the i-coordinate system in the global coordinate system;
In the step S3, the method for calculating the target function feature parameter includes:
S31, multiplying the characteristic auxiliary deviation rotation by the jacobian matrix according to the Monte Carlo simulation times to obtain a target functional characteristic deviation rotation;
s32, calculating to obtain target function feature deviation parameters based on the target function feature deviation rotation obtained in the S31;
S33, repeatedly executing simulation calculation for set times to obtain statistical distribution of target function characteristic deviation parameters;
the calculation for the characteristic deviation rotation is as follows:
TFR＝[[J]FE1…[J]FEn][TFEi…TFEn]T (5)；
Wherein: t FR＝[u,v,w,α,β,γ]T is the target characteristic deviation rotation, T FEi＝[ui,vi,wi,αi,βi,γi]T is the path deviation characteristic rotation;
the calculation formula for the target function feature deviation parameter is as follows:
x＝kx·TFR (6)；
Wherein: x is any target functional characteristic deviation parameter, and k x is a 1X 6 target functional parameter characterization vector corresponding to the parameter;
The calculation process of the path tolerance sensitivity comprises the following steps: taking the characteristic tolerance on the selected deviation transmission path as a unit tolerance, multiplying the deviation rotation determined by the unit tolerance parameter by the corresponding jacobian matrix, and multiplying the unit tolerance parameter by a target function parameter characterization vector to obtain a target function parameter obtained by the unit tolerance parameter; the calculation formula is as follows:
wherein: For the sensitivity of the deviation target functional parameter x to the unit tolerance at i, T FEi e is the deviation rotation of the i feature formed by the unit tolerance parameter;
The calculation of the path tolerance contribution degree comprises the following steps: calculating standard deviation of each component of deviation rotation based on the characteristic tolerance on the selected deviation transmission path, multiplying the standard deviation by a target function parameter characterization vector, and finally calculating the square sum duty ratio of the square of the standard deviation to all path tolerances; the calculation formula is as follows:
wherein: For the contribution degree of the sensitivity of the deviation at i to the deviation target functional parameter x, σ FEi is the six-component deviation rotation standard deviation of the i feature in the deviation rotation generation.
The three-dimensional tolerance analysis process of the planetary gear box shown in fig. 2 by applying the method of the invention is as follows: the planetary gearbox comprises a box body #1, a bearing #2, an input shaft #3 and a sun gear #4. For simplifying the case, the two bearings are regarded as one and the small plane contact such as a shaft sleeve is not considered, but the inner holes of the two bearings are still treated according to two on the box body #1, the 1 st inner hole and the 2 nd inner hole of the box body #1 are respectively provided with the two bearings #2, the 1 st outer circle of the input shaft #3 is matched with the inner holes of the bearings, and the 2 nd outer circle of the input shaft #3 is matched with the inner holes of the sun gear #4. The method comprises the following specific steps:
firstly, acquiring basic information of an assembly: acquiring part characteristic tolerance information and pose information tables constituting the assembly such as table 1, an assembly secondary characteristic information table such as table 2 and an internal secondary characteristic information table of table 3 based on the assembly of the planetary gear box such as fig. 2; and a target functional feature pair and a target functional feature deviation item composed of an axis angle deviation of the sun gear #4 with respect to the hole of the case #1, which are determined based on the assembly; the target functional characteristic pair is a2 nd inner hole of a characteristic 4-1 sun gear ring and a characteristic 1-2 box body, the target functional characteristic deviation parameter is a cylindrical characteristic axis angle deviation, and the characterization vector is (0 0001 1). All parts and tolerances can be considered using the method of the invention, and the feature pose omitted component is 0.
Secondly, generating path deviation rotation and jacobian matrix: generating a path characteristic deviation rotation based on the target and capable of being used for calculating a path tolerance contribution degree by using part characteristic tolerance information through 1000 Monte Carlo simulations; constructing an assembly undirected graph based on assembly characteristic side information and a shortest dimension chain principle, and adopting a Dikk algorithm to obtain a deviation transmission path based on the target as shown in fig. 3; generating a jacobian matrix based on the target and capable of being used for calculating path tolerance sensitivity based on the deviation transfer path in combination with pose information;
Thirdly, obtaining target parameters: the target parameters comprise target functional characteristic parameters, path tolerance sensitivity and path tolerance contribution; the target function characteristic parameters are obtained by performing jacobian rotation model matrix calculation through the product of path characteristic deviation rotation and jacobian matrix, and target function parameter distribution represented by a set vector representation mode is shown in fig. 4; the path tolerance sensitivity is calculated based on the jacobian matrix; the path tolerance contribution is calculated based on the path characteristic deviation spin. The results are shown in Table 4. According to table 4, it can be determined that the tolerance has the greatest contribution to the target effect, the ring gear runout and the coaxiality of the 2 nd inner hole of the box body, but the ring gear total runout and the size sensitivity of the sun gear inner hole are the greatest, so that the problem that the angle deviation of the sun gear teeth relative to the hole 2 is out of tolerance can be more effectively solved from the control of the tolerance.
TABLE 1 part characteristic tolerance information Table of the examples
TABLE 2 Assembly side characteristic information Table of the examples
| Assemble sub-name | Features (e.g. a character) | Features (e.g. a character) |
| Bearing and box | 1 St inner hole 1-1 of box body | Bearing excircle 2-1 |
| Bearing and input shaft | Bearing inner bore 2-2 | 1 St outer circle 3-1 of input shaft |
| Input shaft and sun gear | Input shaft 2 nd outer circle 3-2 | Inner hole 4-2 of sun gear |
Table 3-internal side characteristic information table in examples
| Internal pair | Features (e.g. a character) | Features (e.g. a character) |
| Box body | 1 St inner hole 1-1 | 2 Nd inner hole 1-2 |
| Bearing | Bearing excircle 2-1 | Bearing inner bore 2-2 |
| Input shaft | 1 St outer circle 3-1 of input shaft | Input shaft 2 nd outer circle 3-2 |
| Sun gear | Gear ring excircle 4-1 | Inner hole 4-2 of sun gear |
TABLE 4 sensitivity and contribution results for path tolerances in the examples
| Tolerance of | Sensitivity to | Contribution degree |
| Gear ring full run-out | 0.133 | 0.489 |
| Inner hole size of sun gear | 0.100 | 0.076 |
| Input shaft 2 nd outer circle size | 0.054 | 0.020 |
| Input shaft 1 st outer circle size | 0.060 | 0.005 |
| 1 St hole size of box | 0.061 | 0.039 |
| Coaxiality of 2 nd holes of box body | 0.058 | 0.370 |
The foregoing has shown and described the basic principles and main features of the present invention and the advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and that the above embodiments and descriptions are merely illustrative of the principles of the present invention, and various changes and modifications may be made without departing from the spirit and scope of the invention, which is defined in the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (7)
1. The planetary gear box three-dimensional tolerance analysis method based on the jacobian rotation model is characterized by comprising the following steps of:
S1, acquiring basic information of an assembly: acquiring part characteristic information, tolerance information, assembly characteristic pair information and pose information of an assembly based on the assembly of the planetary gear box; and a target functional feature pair and a target functional feature bias item determined based on the assembly;
S2, generating a path deviation rotation and a jacobian matrix: generating a path characteristic deviation rotation based on a target and capable of being used for calculating a path tolerance contribution degree by utilizing part characteristic tolerance information through Monte Carlo simulation; constructing an assembly undirected graph based on assembly characteristic side information and a shortest dimension chain principle, and obtaining a deviation transmission path based on the target by adopting a Dikk algorithm; generating a jacobian matrix based on the target and capable of being used for calculating path tolerance sensitivity based on the deviation transfer path in combination with pose information;
S3, obtaining target parameters: the target parameters comprise one or any two of target functional characteristic parameters, path tolerance sensitivity and path tolerance contribution; or all three; the target function characteristic parameters are target function parameters which are obtained by performing jacobian rotation model matrix calculation through the product of path characteristic deviation rotation and jacobian matrix, and are characterized according to a set vector characterization mode; the path tolerance sensitivity is calculated based on the jacobian matrix; the path tolerance contribution degree is obtained based on calculation of the path characteristic deviation rotation;
The generating process of the path characteristic deviation rotation in S2 includes:
s21, searching for tolerances of all the features on the deviation transmission path, and selecting a tolerance containing a reference and other non-reference tolerances of the reference on the path features;
S22, determining the upper limit and the lower limit of each tolerance according to the part characteristic tolerance information;
S23, converting a tolerance domain determined by the upper and lower tolerance limits into the upper and lower limits of each component of the six-degree-of-freedom characteristic deviation screw;
S24, determining the mean value and standard deviation of the normal distribution of each component of the characteristic auxiliary deviation screw according to the 3 sigma principle;
s25, generating characteristic deviation rotations for the characteristic tolerance on each deviation path according to Monte Carlo simulation times;
For the combined tolerance containing a plurality of tolerance labels on the same feature, only one position tolerance or direction tolerance is considered, and the upper limit and the lower limit of the rotation component are determined according to the tolerance domain;
in S23, the expression of the six-degree-of-freedom characteristic sub-deviation rotation is as follows:
T＝[u，v，w，α，β，γ]T (2)；
Wherein: the u, v and w components express the deviation of the characteristic in three directions of the local coordinate system, and the alpha, beta and gamma components express the deviation of the characteristic in three directions of rotation around the local coordinate system;
Wherein, the upper and lower limits of the rotation component of the plane tolerance domain are respectively determined as follows:
Wherein T is a plane tolerance parameter, and L 1 and L 2 are respectively a planeness length and width geometric parameters;
Wherein, the upper and lower limits of the rotation component of the cylindrical surface tolerance domain are respectively determined as follows:
wherein T is a cylindrical surface tolerance parameter, and L is a cylindrical surface length geometric parameter;
in S24, according to the 3 sigma principle, the mean and standard deviation are determined as follows:
wherein: TL is less than or equal to X is less than or equal to TU, and represents the upper limit and the lower limit of a component X;
In the step S2, the characteristic deviation rotation on each deviation transmission path corresponds to a 6X 6 Jacobian matrix, and the deviation rotation generated by the characteristic unit deviation rotation in the target functional characteristic pair is expressed; the generation method of the jacobian matrix comprises the steps of corresponding to characteristic deviation rotation on each deviation transmission path, calculating to obtain the jacobian matrix of the deviation rotation by using a homogeneous coordinate transformation matrix of the characteristic and a homogeneous coordinate transformation matrix of a target functional characteristic pair;
the jacobian matrix expression is as follows:
Wherein:
wherein: A direction matrix of the i coordinate system relative to the global coordinate system; [ W i n ] is the position matrix of the target point coordinate system relative to the i coordinate system; dk n,dki (k=x, y, z) is the value of the k-axis of the target point coordinate system and the i-coordinate system in the global coordinate system;
In the step S3, the method for calculating the target function feature parameter includes:
S31, multiplying the characteristic auxiliary deviation rotation by the jacobian matrix according to the Monte Carlo simulation times to obtain a target functional characteristic deviation rotation;
s32, calculating to obtain target function feature deviation parameters based on the target function feature deviation rotation obtained in the S31;
S33, repeatedly executing simulation calculation for set times to obtain statistical distribution of target function characteristic deviation parameters;
the calculation formula for the characteristic deviation rotation is as follows:
TFR＝[[J]FE1 … [J]FEn][TFEi … TFEn]T (5)；
Wherein: t FR＝[u,v,w,α,β,γ]T is the target characteristic deviation rotation, T FEi＝[ui,vi,wi,αi,βi,γi]T is the path deviation characteristic rotation;
the calculation formula for the target function feature deviation parameter is as follows:
x＝kx·TFR (6)；
Wherein: x is any target functional characteristic deviation parameter, and k x is a 1X 6 target functional parameter characterization vector corresponding to the parameter;
The calculation process of the path tolerance sensitivity comprises the following steps: taking the characteristic tolerance on the selected deviation transmission path as a unit tolerance, multiplying the deviation rotation determined by the unit tolerance parameter by the corresponding jacobian matrix, and multiplying the unit tolerance parameter by a target function parameter characterization vector to obtain a target function parameter obtained by the unit tolerance parameter; the calculation formula is as follows:
wherein: For the sensitivity of the deviation target functional parameter x to the unit tolerance at i, T FEi e is the deviation rotation of the i feature formed by the unit tolerance parameter;
The calculation of the path tolerance contribution degree comprises the following steps: calculating standard deviation of each component of deviation rotation based on the characteristic tolerance on the selected deviation transmission path, multiplying the standard deviation by a target function parameter characterization vector, and finally calculating the square sum duty ratio of the square of the standard deviation to all path tolerances; the calculation formula is as follows:
wherein: For the contribution degree of the sensitivity of the deviation at i to the deviation target functional parameter x, σ FEi is the six-component deviation rotation standard deviation of the i feature in the deviation rotation generation.
2. The method for analyzing three-dimensional tolerance of a planetary gear box based on a jacobian rotation model according to claim 1, wherein the part characteristic tolerance information comprises part, characteristic and tolerance information, namely characteristic information and tolerance information of a set part; wherein, the characteristic is to index the assembly surface of the tolerance information; the characteristic information comprises characteristic geometric parameters belonging to characteristic types and pose information formed by characteristic positions and characteristic directions; the characteristic types are divided into cylindrical surfaces and plane surfaces; the characteristic geometric parameters comprise a cylindrical generatrix length corresponding to the cylindrical surface characteristic, and a plane maximum length and a plane maximum width corresponding to the plane characteristic; the feature position refers to the coordinate of the feature center in the assembly reference coordinate; wherein, the characteristic center of the cylindrical surface characteristic is the midpoint of the axis of the cylindrical surface; the feature center of the planar feature is a planar center point; the pose information is expressed by a 4×4 homogeneous coordinate transformation matrix, and comprises a3×3 projection matrix and a3×1 position coordinate of a characteristic auxiliary coordinate relative to a reference coordinate, and the expression is as follows:
wherein,
Wherein: [ C 1i],[C2i],[C3i ] is the projection length of the unit direction vector of the three coordinate axes of the feature i coordinate system in the global coordinate system, and dx i,dyi,dzi is the coordinate of the origin of the feature i coordinate system in the global coordinate system;
The tolerance includes a non-reference tolerance and a reference tolerance; wherein, the tolerance without reference comprises a dimensional tolerance and a shape tolerance marked on one surface; the referenced tolerances include dimensional tolerances, orientation tolerances, positional tolerances and runout tolerances noted on the two faces with reference to at least one feature on the part.
3. The method for analyzing three-dimensional tolerance of a planetary gear box based on a jacobian rotation model according to claim 1, wherein the assembly body characteristic pair consists of an internal pair and an assembly pair; the internal pair is two characteristic surfaces of the same part, and the condition for forming the internal pair is that one characteristic surface has a tolerance taking the other characteristic surface as a reference; the assembly pair is two characteristic surfaces assembled by different parts, and the condition for forming the assembly pair is that the two characteristic surfaces are tightly contacted through assembly.
4. A method for three-dimensional tolerance analysis of a planetary gear box based on jacobian rotation model according to claim 3, characterized in that in the internal pair of the same part, if there is no tolerance containing a reference between the two characteristic faces, but there is a tolerance relation guaranteed by means of machine precision, it is noted as an internal pair of zero tolerance.
5. A method for three-dimensional tolerance analysis of a planetary gear box based on a jacobian rotation model according to claim 3, wherein in the constructed assembly undirected graph, the nodes represent characteristic faces of assembly pairs, and the edges represent internal or assembly pairs of the same part; the assembly undirected graph is expressed by an adjacent matrix, wherein all the characteristic surfaces of the assembly are marked as rows and columns, the adjacent matrix has internal auxiliary relations on the same part or has corresponding rows and columns which form a pair of assembly auxiliary relations and are marked as 1, and the undirected relation is marked as 0.
6. The method according to claim 5, wherein the point contact of the assembly relationship or the facet contact relationship corresponding to the point contact, which mainly plays a limiting role in the assembly relationship, marks a number higher than 1 at a corresponding position in the matrix to indicate that the assembly relationship has a long path and a weak duty ratio in the shortest dimension chain principle calculation.
7. The method for three-dimensional tolerance analysis of a planetary gear box based on a jacobian rotation model according to claim 5, wherein in the process of adopting a diecky tesla algorithm, a shortest path to one node in an assembly undirected graph is calculated by taking the node as a starting point, a deviation transmission path characterized by a set of features is obtained, and a corresponding feature pair on the deviation transmission path is obtained by combining the deviation transmission path with feature pair information in an assembly body.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202111194882.6A CN113779735B (en) | 2021-10-13 | 2021-10-13 | Planetary gear box three-dimensional tolerance analysis method based on jacobian rotation model |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202111194882.6A CN113779735B (en) | 2021-10-13 | 2021-10-13 | Planetary gear box three-dimensional tolerance analysis method based on jacobian rotation model |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN113779735A CN113779735A (en) | 2021-12-10 |
| CN113779735B true CN113779735B (en) | 2024-05-17 |
Family
ID=78873130
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202111194882.6A Active CN113779735B (en) | 2021-10-13 | 2021-10-13 | Planetary gear box three-dimensional tolerance analysis method based on jacobian rotation model |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN113779735B (en) |
Families Citing this family (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115033940B (en) * | 2022-07-01 | 2023-02-03 | 上海交通大学 | Blade dimension chain modeling method considering tenon-mortise connection |
| CN115096582B (en) * | 2022-07-08 | 2023-06-02 | 上海交通大学 | Transmission path analysis and gear fault tracing method based on in-situ measurement |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101710355A (en) * | 2009-12-17 | 2010-05-19 | 同济大学 | Actual-condition tolerance modeling method based on Jacobian spinors |
| CN104036102A (en) * | 2014-07-02 | 2014-09-10 | 北京理工大学 | Calculation method and device for product assembly deviation |
| CN106020147A (en) * | 2016-05-23 | 2016-10-12 | 北京理工大学 | Systematic analysis method for assembling precision of complex precise mechanical product |
| CN107992647A (en) * | 2017-11-16 | 2018-05-04 | 华中科技大学 | A kind of local parallel dimension chain error acquisition methods influenced by geometry |
| CN110516320A (en) * | 2019-08-06 | 2019-11-29 | 上海交通大学 | Match Analysis and device suitable for train body assembly components |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US11250184B2 (en) * | 2017-10-24 | 2022-02-15 | Enventive Engineering, Inc. | 3D tolerance analysis system and methods |
-
2021
- 2021-10-13 CN CN202111194882.6A patent/CN113779735B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101710355A (en) * | 2009-12-17 | 2010-05-19 | 同济大学 | Actual-condition tolerance modeling method based on Jacobian spinors |
| CN104036102A (en) * | 2014-07-02 | 2014-09-10 | 北京理工大学 | Calculation method and device for product assembly deviation |
| CN106020147A (en) * | 2016-05-23 | 2016-10-12 | 北京理工大学 | Systematic analysis method for assembling precision of complex precise mechanical product |
| CN107992647A (en) * | 2017-11-16 | 2018-05-04 | 华中科技大学 | A kind of local parallel dimension chain error acquisition methods influenced by geometry |
| CN110516320A (en) * | 2019-08-06 | 2019-11-29 | 上海交通大学 | Match Analysis and device suitable for train body assembly components |
Non-Patent Citations (1)
| Title |
|---|
| 基于雅可比旋量统计法的发动机三维公差分析;陈华等;哈尔滨工程大学学报;20141125;第35卷(第11期);第1397-1402页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN113779735A (en) | 2021-12-10 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN113779735B (en) | Planetary gear box three-dimensional tolerance analysis method based on jacobian rotation model | |
| Gao et al. | Generalized 3-D tolerance analysis of mechanical assemblies with small kinematic adjustments | |
| Bai et al. | On the comparison of trilinear, cubic spline, and fuzzy interpolation methods in the high-accuracy measurements | |
| Schleich et al. | A discrete geometry approach for tolerance analysis of mechanism | |
| Poniatowska | Deviation model based method of planning accuracy inspection of free-form surfaces using CMMs | |
| Bruyere et al. | Statistical tolerance analysis of bevel gear by tooth contact analysis and Monte Carlo simulation | |
| CN106774152B (en) | A kind of modeling method of numerically-controlled machine tool position correlation geometric error item | |
| Yan et al. | Tolerance analysis using skin model shapes and linear complementarity conditions | |
| Jin et al. | Point-based solution using Jacobian-Torsor theory into partial parallel chains for revolving components assembly | |
| Bastani et al. | Fault diagnosis using an enhanced relevance vector machine (RVM) for partially diagnosable multistation assembly processes | |
| CN110955979B (en) | Machine tool machining precision reliability sensitivity analysis method considering geometrical error bias correlation | |
| Bai et al. | On the comparison of bilinear, cubic spline, and fuzzy interpolation techniques for robotic position measurements | |
| CN111783249B (en) | Assembly precision analysis method, device and system | |
| CN104598697A (en) | Construction method of product simulation three-dimensional model | |
| Armillotta | Tolerance analysis of gear trains by static analogy | |
| CN104977816B (en) | The mechanical parameter flexible measurement method of mask aligner mask platform micropositioner based on Compact Particle Swarm Optimization algorithms | |
| Liu et al. | Optimal sensor placement for fixture fault diagnosis using Bayesian network | |
| Majstorovic et al. | Cyber-physical manufacturing metrology model (CPM3)–big data analytics issue | |
| Gou et al. | On the symmetric location problem | |
| Yin et al. | Influence of module on measurement uncertainty of gear tooth profile deviation on gear measuring center | |
| Zhao et al. | Monomer model: an integrated characterization method of geometrical deviations for assembly accuracy analysis | |
| CN106096099B (en) | Error transmission analysis method and device for mechanical product | |
| CN113656902A (en) | Error sensitivity analysis method for working end pose of multi-axis motion platform | |
| CN106802989B (en) | Hypoid gear contact calculation method considering influence of dislocation quantity | |
| Armillotta | A static analogy for 2D tolerance analysis |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |