Method for calculating assembly error of spiral bevel gear pair by comprehensively counting bearing clearance and assembly relation

Abstract

According to the spiral bevel gear pair assembly error calculation method comprehensively reckoning the bearing clearance and the assembly relation, the error transmission relation between the bearing clearance and an assembly dimension chain is systematically represented by establishing a Jacobian spinor model. The method comprises the following steps: constructing an assembly size chain transfer relation graph, disassembling a clearance error of a parallel bearing assembly and calculating a spinor variation range; dynamically associating error transfer paths of all functional elements by adopting a Jacobian matrix, and combining parallel dimension chain error parameters; an axial separation amount (V), an intersection angle change amount (sigma), and an axial misalignment amount (H, GH) are calculated by an extreme value method. Innovation points include coupling modeling of the bearing clearance and the assembly relation, a spinor dynamic aggregation algorithm and error boundary quantification, comprehensiveness and accuracy of assembly precision analysis are remarkably improved, and the method is suitable for assembly process optimization of transmission systems of automobiles, aviation and the like.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of mechanical manufacturing and precision assembly, in particular to a kind of arc tooth bevel gear pair assembly error calculation method considering bearing play and assembly relationship. BACKGROUND

[0002] In mechanical transmission system, the assembly accuracy of arc tooth bevel gear pair directly affects the performance and life of transmission system. In the prior art, the assembly error calculation is mostly based on a single factor (such as gear geometric tolerance or bearing play), without considering the coupling effect between bearing play and assembly relationship, resulting in incomplete error accumulation analysis and difficulty in ensuring assembly accuracy. In addition, the traditional method mostly uses linear superposition or empirical correction, lacks mathematical modeling ability for complex size chain, and it is difficult to accurately quantify key parameters such as shaft angle deviation and axis separation. SUMMARY

[0003] In view of the problems existing in the prior art, the present application proposes a kind of arc tooth bevel gear pair assembly error calculation method considering bearing play and assembly relationship. By establishing a Jacobian screw model considering bearing play and assembly relationship, the axial displacement amount H of the driving bevel gear, the axial displacement amount GH of the driven bevel gear, the axis separation V and the axis angle change Σ are accurately calculated. The assembly error method is improved, the influence of bearing play is introduced, the calculation result is more real and reliable, and the problem of insufficient accuracy of the existing method is solved.

[0004] The technical scheme of the present application is as follows:

[0005] The arc tooth bevel gear pair assembly error calculation method considering bearing play and assembly relationship comprises the following steps:

[0006] Step 1: establish the size chain transmission relationship diagram of arc tooth bevel gear assembly, define the global coordinate system of output shaft system and input shaft system and functional requirements;

[0007] Step 2: analyze parallel size chain, disassemble bearing play error, and calculate screw variable range of functional features;

[0008] Step 3: use Jacobian screw model to represent error transmission and calculate screw parameters of parallel size chain;

[0009] Step 4: combine parallel size chain and calculate screw parameters of parallel functional features;

[0010] Step 5: rebuild the size chain transmission relationship of assembly, and correct the error accumulation path of input and output shaft system;

[0011] Step 6: calculate and output axis separation V, angle change Σ and axial displacement amount H, GH by extreme value method.

[0012] Further, in step 2, the decomposition of bearing clearance error includes:

[0013] The radial clearance and the axial clearance of the bearing are decomposed into translational and rotational degrees of freedom, and the minimum value of the axial clearance is taken as the limit condition of the offset under the clearance constraint of the parallel bearing assembly.

[0014] Further, in step 3, the specific implementation of the Jacobian wrench model includes:

[0015] The assembly error is decomposed into a translational vector and a rotational vector, the error wrench in the local coordinate system is converted to the global coordinate system through the Jacobian matrix, and the error transmission path of the bearing fit and the gear installation position is dynamically associated.

[0016] Further, in step 4, the merging method of the parallel dimension chain is:

[0017] Through the formula

[0018] T = T a = [ L 1 L ( u 1 + u 2 ) − u 2 0 L 1 L ( u 1 + u 2 ) − u 2 u 1 + u 2 L 0 u 1 + u 2 L ] T

[0019] Or

[0020] T = T b = [ ( L 1 − H 2 ) ( u 1 − u 2 ) L 2 + u 2 0 ( L 1 − H 2 ) ( u 1 − u 2 ) L 2 + u 2 u 1 − u 2 L 2 0 u 1 − u 2 L 2 ] T

[0021] The error wrench parameters of the parallel dimension chain are converted into the parameters of the serial dimension chain, wherein 、 is the wrench parameter of the parallel functional feature, is the geometric distance parameter.

[0022] Further, in step 6, the implementation of the extreme value method includes:

[0023] In the global coordinate system, the axial separation V and the intersection angle change Σ are solved by vector analysis method, and based on the intersection angle change Σ and the axial separation V of the shaft line, the axial misalignment H and GH of the driving bevel gear and the driven bevel gear are determined.

[0024] Further, in step 1, the functional requirements are the deviations of the center shaft lines of the driven bevel gear and the driving bevel gear in the global coordinate system, and the global coordinate system is consistent with the assembly datum of the output shaft system and the input shaft system.

[0025] Further, in step 5, the correction of the error accumulation path includes:

[0026] The wrench parameters of the parallel functional features are included in the serial dimension chain, and are uniformly mapped to the global coordinate system through coordinate transformation, so as to correct the error accumulation relationship between the input shaft system and the output shaft system.

[0027] Further, in step 6, the calculation formula of the axis separation amount V and the intersection angle change amount Σ is as follows:

[0028]

[0029] And

[0030] Wherein is a gear pitch cone radius, , is an offset amount of the axis in the global coordinate system.

[0031] Further, the method further comprises:

[0032] According to the constraint condition of the bearing clearance, the error screw parameters of the parallel size chain are dynamically adjusted, and the repeated calculation of the translational and rotational degrees of freedom is avoided.

[0033] Further, the method is suitable for assembly precision analysis and optimization of the spiral bevel gear pair in the automobile, aviation or industrial machinery transmission system.

[0034] Advantages

[0035] Compared with the prior art, the present application has the following advantages:

[0036] 1. The bearing clearance (radial, axial clearance) and the transmission relationship of the assembly size chain are combined for the first time, and the influence of the coupling effect of the two on the assembly error is quantified through the screw model. Specifically, for the clearance constraint of the parallel bearing assembly (such as the minimum axial clearance), a method of decomposing the radioactive error and the rotational error is proposed, which avoids repeated calculation and significantly improves the accuracy of error analysis.

[0037] 2. The Jacobian screw model is used to decompose the assembly error into translational and rotational vectors, and the error transmission path of each functional element (such as bearing fit, gear installation position) is dynamically associated through the Jacobian matrix (J). This method breaks through the limitations of traditional linear superposition and can accurately describe the error accumulation process of complex size chains (such as parallel size chains).

[0038] 3. The vector analysis method is used to solve the axis separation amount (V) and the intersection angle change amount (Σ). This method first realizes the boundary quantization of the assembly deviation and provides clear guidance for assembly process optimization.

[0039] Additional aspects and advantages of the application will be in part apparent and in part pointed out hereinafter. BRIEF DESCRIPTION OF DRAWINGS

[0040] The above and / or additional aspects and advantages of the present application will become apparent and more readily appreciated from the following description, taken in conjunction with the following drawings of which:

[0041] Figure 1 A method for calculating assembly error of an arc tooth bevel gear pair considering bearing clearance and assembly relationship;

[0042] Figure 2 An assembly drawing of an arc tooth bevel gear pair and a tolerance distribution diagram of parts (overall) ;

[0043] Figure 3 An assembly drawing of an arc tooth bevel gear pair and a tolerance distribution diagram of parts (part one) ;

[0044] Figure 4 An assembly drawing of an arc tooth bevel gear pair and a tolerance distribution diagram of parts (part two) ;

[0045] Figure 5 A schematic diagram of relative misalignment of gear axes;

[0046] As shown in Figure 5 , the driving bevel gear or the driven bevel gear is moved along the axis, and the axial displacement amounts are H and GH, respectively, +H and +GH represent the direction change of the installation distance in the increasing direction, -H and -GH represent the direction change of the installation distance in the decreasing direction; in the theoretical installation case, the axes of the two arc tooth bevel gears are vertically displaced by V=0, the movement of the axes of the two gears along the perpendicular direction, +V represents that the axis of the small gear is lower than that of the large gear; -V represents that the axis of the small gear is higher than that of the large gear; in theory, the two axes of the arc tooth bevel gears intersect at Γ (theoretical shaft intersection angle), +Σ represents the direction change of the shaft intersection angle of the two gears in the increasing direction, and -Σ represents the direction change of the shaft intersection angle in the decreasing direction.

[0047] Figure 6 An assembly body size chain transmission relationship diagram;

[0048] Figure 7 An assembly drawing of an input shaft system and an output shaft system component;

[0049] Figure 8 A position relationship diagram of a local coordinate system and a global coordinate system. DETAILED DESCRIPTION

[0050] Embodiments of the present application are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals represent the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by reference to the drawings are exemplary and are intended to explain the present application, and cannot be understood as limiting the present application.

[0051] In the description of the present application, it needs to be understood that the terms "center", "longitudinal", "transverse", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, which is only for the convenience of describing the present application and simplifying the description, and does not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the present application.

[0052] In addition, the terms "first", "second" are only for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the technical features indicated. Therefore, the features defined with "first", "second" can explicitly or implicitly include one or more of the features. In the description of the present application, the meaning of "multiple" is two or more, unless otherwise specifically limited.

[0053] The present embodiment takes Figures 2-4 The related parameters of the arc gear pair are shown in Table 1:

[0054] Table 1 Arc gear pair related parameters

[0055]

[0056] The assembly difference calculation process includes the following steps:

[0057] Step 1: Establish the size chain transmission relationship diagram of the arc gear assembly as shown in Figure 6 , define the global coordinate system of the output shaft system and the input shaft system and the functional requirements ).

[0058] As shown in Figures 2-4 , the arc gear pair in the present embodiment is composed of a box, an input shaft, an output shaft, a driven bevel gear, a driving bevel gear, a bearing 1, a bearing 2, a bearing 3 and a bearing 4. Among them, the driving bevel gear and the input shaft are integrated, supported by bearing 1 and bearing 2, the inner ring of bearing 1 cooperates with the input shaft, the outer ring cooperates with hole 1, the inner ring of bearing 2 cooperates with the input shaft, and the outer ring cooperates with hole 2; the driven bevel gear and the output shaft are integrated, supported by bearing 3 and bearing 4, the inner ring of bearing 3 cooperates with the output shaft, the outer ring cooperates with hole 3, the inner ring of bearing 4 cooperates with the output shaft, and the outer ring cooperates with hole 4.

[0059] The features in the assembly parts are represented by the numbers with rings, wherein feature ① is the reference line of the output shaft system; feature ② is the reference line of the input shaft system; feature ③ is the inner surface of hole 1, with a nominal size of Φ400, an upper deviation of +0.089, and a lower deviation of 0; feature ④ is the inner surface of hole 3, with a nominal size of Φ500, an upper deviation of +0.063, and a lower deviation of 0, and a radial runout error of 0.05 with respect to the reference line ②; feature ⑤ is the inner surface of hole 2, with a nominal size of Φ520, an upper deviation of +0.07, and a lower deviation of 0, and a radial runout error of 0.05 with respect to the reference line ①; feature ⑥ is the inner surface of hole 4, with a nominal size of Φ533.4, an upper deviation of +0.07, and a lower deviation of 0, and a positional error of 0.1 with respect to the reference line ②; feature ⑦ is the outer ring surface of bearing 1, with a nominal size of Φ400, an upper deviation of 0, a lower deviation of -0.036, and a length of 104; feature ⑧ is the outer ring surface of bearing 3, with a nominal size of Φ500, an upper deviation of 0, a lower deviation of -0.035, and a length of 200; feature ⑨ is the outer ring surface of bearing 2, with a nominal size of Φ520, an upper deviation of 0, a lower deviation of -0.044, and a length of 133; feature ⑩ is the outer ring surface of bearing 4, with a nominal size of Φ533.4, an upper deviation of +0.025, and a lower deviation of 0, and a length of 165; feature ⑪ is the inner ring surface of bearing 1, with a nominal size of Φ276, an upper deviation of 0, a lower deviation of -0.032, and a length of 104; feature ⑫ is the inner ring surface of bearing 3, with a nominal size of Φ288, an upper deviation of 0, a lower deviation of -0.032, and a length of 200; feature ⑬ is the inner ring surface of bearing 2, with a nominal size of Φ334, an upper deviation of 0, a lower deviation of -0.038, and a length of 133; feature ⑭ is the inner ring surface of bearing 4, with a nominal size of Φ233.4, an upper deviation of 0, a lower deviation of -0.027, and a length of 248; feature ⑮ is the surface on the output shaft that cooperates with the inner ring surface of bearing 1, with a nominal size of Φ276, an upper deviation of +0.011, and a lower deviation of -0.013; feature ⑯ is the surface on the input shaft that cooperates with the inner ring surface of bearing 3, with a nominal size of Φ288, an upper deviation of +0.014, and a lower deviation of -0.012; feature ⑰ is the surface on the output shaft that cooperates with the inner ring surface of bearing 2, with a nominal size of Φ334, an upper deviation of +0.015, and a lower deviation of -0.015; feature ⑱ is the surface on the input shaft that cooperates with the inner ring surface of bearing 4, with a nominal size of Φ233.4, an upper deviation of +0.012, and a lower deviation of -0.010; feature ⑲ is the rotational axis of the output shaft; feature ⑳ is the rotational axis of the input shaft; feature㉑ is the rotational axis of the driven bevel gear; feature㉒ is the rotational axis of the driving bevel gear; feature㉓ is the rotational axis of the tooth surface of the driven bevel gear, with a runout error of 0.04 with respect to feature㉑; and feature㉔ is the rotational axis of the tooth surface of the driven bevel gear, with a runout error of 0.04 with respect to feature㉒.

[0060] The above features are connected by arrows according to the matching relationship, forming an assembly size chain transmission relationship diagram, as shown in Figure 6 . Figure 6 Among them, CFEi (i=1, 2, 3…) represents the connecting function features formed by the matching of different part features; IFEi (i=1, 2, 3…) represents the internal function features formed by the matching of different parts in the same part; PFEi (i=1, 2, 3…) represents the parallel function features formed by the transformation of multiple parallel size chains into an equivalent serial size chain; is the deviation of the center axis of the driven gear in the reference coordinate system 1, and at the same time, the reference coordinate system is also the global coordinate system of the output shaft system assembly; is the deviation of the center axis of the driven gear in the reference coordinate system 1, and at the same time, the reference coordinate system is also the global coordinate system of the output shaft system assembly;

[0061] Step 2: Analyze the parallel size chain, disassemble the bearing clearance error, and calculate the range of the rotational volume of the function feature.

[0062] From Figure 6 , for the output shaft system assembly, the output shaft is connected with hole 1 and hole 2 through bearing 1 and bearing 2, respectively, forming local parallel size chains ( ) and ( ), FEi represents the function element represented by feature i, and parallel function feature is used to represent the rotational volume parameters of the two local parallel size chains. Similarly, for the input shaft system assembly, the input shaft is connected with hole 3 and hole 4 through bearing 3 and bearing 4, respectively, forming local parallel size chains ( ), ( ), and parallel function feature is used to represent the rotational volume parameters of the two local parallel size chains.

[0063] The present application uses a vector combining translational variable ( ) and rotational variable ( ) to represent the tolerance variation range of the function feature, which is like

[0064] T = [ u v w α β delta ] T (1)

[0065] Where u, v, w are translational vector parameters of x-axis, y-axis, and z-axis, respectively; α, β, δ are rotational vector parameters of x-axis, y-axis, and z-axis, respectively.

[0066] From Figure 6 , the function features involved in the local size chain are ; the function features involved in the local size chain are ; local dimension chain The functional features involved in the above-mentioned embodiment are ; local dimension chain The functional features involved in the above-mentioned embodiment are In combination with the tolerance value of the part, the calculation process and result of the functional feature screw motion range are as follows: Figures 2-4

[0067] CFE1 (the mating error of feature ③ and feature ⑦):

[0068] (2)

[0069] In the formula, and are the translation vectors of the functional feature CFE1 about the x-axis and the z-axis respectively; and are the rotation vectors of the functional feature CFE1 about the x-axis and the z-axis respectively. +0.089 is the size upper deviation of feature ③, -0.036 is the size lower deviation of feature ⑦, and 104 is the contact length of feature ③ and feature ⑦. , , , ,

[0070] CFE 1 = [ ± 0 . 0625 0 ± 0 . 0625 ± 0 . 0012 0 ± 0 . 0012 ] T (3)

[0071] IFE5 (the clearance between the outer ring and the inner ring of bearing 1):

[0072] Since bearing 1 and bearing 2 are used in pairs on the output shaft, their axial clearances are mutually restricted, the offset amount in the y-axis direction should take the minimum value of the offset amount of the two bearings in this direction, and the rotation amounts about the x-axis, the y-axis and the z-axis are affected by the overall length of the shaft system. The radial inner clearance of bearing 1 is 0.0005, the axial inner clearance is 0.0005; the radial inner clearance of bearing 2 is 0.0005, the axial inner clearance is 0.0005, the radial inner clearance has the freedom of variation in the x-axis and z-axis directions, and the axial inner clearance has the freedom of variation only in the y-axis direction, so

[0073] (4)

[0074] In the formula, and are the translation vectors of the functional feature IFE5 about the x-axis, the z-axis and the y-axis respectively; and are the rotation vectors of the functional feature IFE5 about the x-axis and the z-axis respectively. 1039.5 is the distance between bearing 1 and bearing 2. , , , , ,

[0075] [ ± 0 . 15 ± 0.4 ± 0 . 15 ± 0 . 000337 0 ± 0 . 000337 ] T ​​​​​ (5)

[0076] It is worth noting that the offset amount of IFE5 in the y-axis direction , the rotation amount around the x-axis , the rotation amount of the z-axis is affected by two bearings and the output shaft, in order to avoid repeated calculation, IFE5 is now disassembled into

[0077] = [ ± 0 . 15 0 ± 0 . 15 0 0 0 ] T (6)

[0078] and

[0079] = [ 0 ± 0.4 0 ± 0 . 000337 0 ± 0 . 000337 ] T (7)

[0080] are used for the calculation of and PFE13, respectively.

[0081] CFE9 (feature and feature mating error):

[0082] (8)

[0083] wherein, , are the translation vectors of functional feature CFE9 about the x-axis and the z-axis, respectively; , are the rotation vectors of functional feature CFE9 about the x-axis and the z-axis, respectively. 0 is the size deviation of feature , -0.013 is the size deviation of feature ; 104 is the contact length of feature and feature .

[0084] CFE 9 = [ ± 0 . 0065 0 ± 0 . 0065 ± 0 . 000125 0 ± 0 . 000125 ] T (9)

[0085] CFE3 (feature ⑤ and feature ⑨ mating error):

[0086] (10)

[0087] wherein, , are the translation vectors of functional feature CFE3 about the x-axis and the z-axis, respectively; , These are the rotation vectors of functional feature CFE3 about the x-axis and z-axis, respectively. +0.07 is the upper dimensional deviation of feature ⑤, -0.044 is the lower dimensional deviation of feature ⑨, 0.05 is the radial runout error of feature ⑤, and 133 is the contact length between feature ⑤ and feature ⑨.

[0088] CFE 3 = [ ± 0 . 082 0 ± 0 . 082 ± 0 . 001233 0 ± 0 . 001233 ] T (11)

[0089] IFE7 (Clearance between the outer and inner rings of bearing 2):

[0090] As can be seen from IFE5,

[0091] (12)

[0092] In the formula, , , These are the translation vectors of the functional feature IFE7 about the x-axis, z-axis, and y-axis, respectively. , These are the rotation vectors of functional feature IFE7 about the x-axis and z-axis, respectively; 1039.5 is the distance between bearing 1 and bearing 2.

[0093] [ ± 0 . 2 ± 0.4 ± 0 . 2 ± 0 . 000337 0 ± 0 . 000337 ] T

[0094] Therefore

[0095] = [ ± 0 . 2 0 ± 0 . 2 ± 0 0 ± 0 ] T (13)

[0096] = [ 0 ± 0.4 0 ± 0 . 000337 0 ± 0 . 000337 ] T (14)

[0097] CFE11 (features) With features (fitting error)

[0098] (15)

[0099] In the formula, , These are the translation vectors of the functional feature CFE11 about the x-axis and z-axis, respectively. , These are the rotation vectors of feature CFE11 about the x-axis and z-axis, respectively. 0 represents the feature. The dimensional deviation is -0.015 as a characteristic. Dimensional deviation; 133 is a feature With features The contact length.

[0100] CFE 11 = [ ± 0 . 0075 0 ± 0 . 0075 ± 0 . 0001128 0 ± 0 . 0001128 ] T (16)

[0101] CFE2 (feature 4 and feature 7 mating error) :

[0102] (17)

[0103] wherein, , are the translation vectors of the functional feature CFE2 with respect to the x-axis, z-axis, respectively; , are the rotation vectors of the functional feature CFE2 with respect to the x-axis, z-axis, respectively. +0.063 is the size upper deviation of feature 4, -0.035 is the size lower deviation of feature 7, 0.05 is the radial run-out error of feature 4; 200 is the contact length of feature 4 and feature 7.

[0104] CFE 2 = [ ± 0 . 074 0 ± 0 . 074 ± 0 . 00074 0 ± 0 . 0074 ] T (18)

[0105] IFE6 (clearance between the outer ring and the inner ring of bearing 3) :

[0106] Since bearing 3 and bearing 4 are used in pairs on the output shaft, their axial clearances are mutually constrained, and the offset amount in the y-axis direction should take the minimum value of the offset amount of the two bearings in this direction, and the rotation amounts around the x, y, and z axes are affected by the overall length of the shafting. The radial inner clearance of bearing 3 is , and the axial inner clearance is ; the radial inner clearance of bearing 4 is , and the axial inner clearance is The radial inner clearance has a degree of freedom in the x and z directions, and the axial inner clearance has a degree of freedom only in the y direction, so

[0107] (19)

[0108] wherein, , , are the translation vectors of the functional feature IFE6 with respect to the x-axis, z-axis, y-axis, respectively; , are the rotation vectors of the functional feature IFE6 with respect to the x-axis, z-axis, respectively; 754 is the distance between bearing 3 and bearing 4.

[0109] [ ± 0 . 18 ± 0.45 ± 0 . 18 ± 0 . 000531 0 ± 0 . 000531 ] T (20)

[0110] It is worth noting that the offset amount in the y-axis direction of IFE6 , and the rotation amount around the x-axis Rotation amount of the z-axis Affected by two bearings and the input shaft, to avoid repeated calculation, now IFE6 is disassembled into

[0111] = [ ± 0 . 18 0 ± 0 . 18 0 0 0 ] T (21)

[0112] And

[0113] = [ 0 ± 0.45 0 ± 0 . 000531 0 ± 0 . 000531 ] T (22)

[0114] Respectively used for And PFE14 calculation.

[0115] CFE10 (feature And feature Mating error):

[0116] (23)

[0117] In the formula, , Respectively the translation vector of functional feature CFE10 about x-axis, z-axis; , Respectively the rotation vector of functional feature CFE10 about x-axis, z-axis. 0 is the size of the feature The size of the feature Down deviation; 200 is the contact length of feature And feature .

[0118] CFE 10 = [ ± 0 . 006 0 ± 0 . 006 ± 0 . 00006 0 ± 0 . 00006 ] T (24)

[0119] CFE4 (feature ⑥ and feature ⑩ mating error):

[0120] (25)

[0121] In the formula, , Respectively the translation vector of functional feature CFE4 about x-axis, z-axis; , Respectively the rotation vector of functional feature CFE4 about x-axis, z-axis. +0.07 is the size of feature ⑥, 0 is the size of feature ⑩, 0.1 is the position error of feature ⑥; 165 is the contact length of feature ④ and feature ⑧.

[0122] CFE 4 = [ ± 0 . 085 0 ± 0 . 085 ± 0 . 00103 0 ± 0 . 00103 ] T (26)

[0123] IFE8 (Clearance between the outer and inner rings of bearing 4):

[0124] As can be seen from IFE6,

[0125] (27)

[0126] In the formula, , , These are the translation vectors of the functional feature IFE8 about the x-axis, z-axis, and y-axis, respectively. , These are the rotation vectors of functional feature IFE8 about the x-axis and z-axis, respectively; 754 is the distance between bearing 3 and bearing 4.

[0127] [ ± 0 . 22 ± 0.45 ± 0 . 22 ± 0 . 000531 0 ± 0 . 000531 ] T

[0128] Therefore

[0129] = [ ± 0 . 22 0 ± 0 . 22 ± 0 0 ± 0 ] T (28)

[0130] = [ 0 ± 0.45 0 ± 0 . 000531 0 ± 0 . 000531 ] T (29)

[0131] CFE12 (features) With features (fitting error)

[0132] (30)

[0133] In the formula, , These are the translation vectors of the functional feature CFE12 about the x-axis and z-axis, respectively. , These are the rotation vectors of feature CFE12 about the x-axis and z-axis, respectively. 0 represents the feature. The dimensional deviation is -0.010 as a characteristic. Dimensional deviation; 248 is a feature With features The contact length;

[0134] CFE 12 = [ ± 0 . 005 0 ± 0 . 005 ± 0 . 0000403 0 ± 0 . 0000403 ] T (31)

[0135] Step 3: Use the Jacobi spinor model to characterize error propagation and calculate the spinor parameters of the parallel dimensional chain.

[0136] This invention uses the Jacobi spinor model to characterize the propagation and accumulation of assembly errors, which can be expressed as:

[0137] FR = [ [ u ¯ , u ¯ ] [ v ¯ , v ¯ ] [ w ¯ , w ¯ ] [ α ¯ , α ¯ ] [ β ¯ , β ¯ ] [ delta ¯ , delta ¯ ] ] = [ [ J 1 ⋯ J 6 ] FEi ⋯ [ J 1 ⋯ J 6 ] FEn ] ⋅ [ [ [ u ¯ , u ¯ ] [ v ¯ , v ¯ ] [ w ¯ , w ¯ ] [ α ¯ , α ¯ ] [ β ¯ , β ¯ ] [ delta ¯ , delta ¯ ] ] FEi ⋯ [ [ u ¯ , u ¯ ] [ v ¯ , v ¯ ] [ w ¯ , w ¯ ] [ α ¯ , α ¯ ] [ β ¯ , β ¯ ] [ delta ¯ , delta ¯ ] ] FEn ] (32)

[0138] where are the functional requirements such as assembly gap, etc., represented by 6x1 small displacement screw; u, v, w are the translation vector parameters of x-axis, y-axis, z-axis, respectively; α, β, δ are the rotation vector parameters of x-axis, y-axis, z-axis, respectively, the underscore represents the lower deviation of the tolerance band, and the underscore represents the upper deviation of the tolerance band; [ J 1 ⋯ J 6 ] FEi is the Jacobian matrix of , which is used to represent the propagation path of the error in the assembly body; is the functional element, that is, the 6x1 small displacement screw of each part in the dimension chain, and i is 1 to , and n represents the total number of functional elements in the dimension chain.

[0139] Now calculate the error accumulation screw parameters of each local parallel dimension chain, assuming that the error accumulation screw parameters of the local dimension chain of the output shaft to hole 1 are ; the error accumulation screw parameters of the local dimension chain of the output shaft to hole 2 are ; the error accumulation screw parameters of the local dimension chain of the input shaft to hole 3 are ; and the error accumulation screw parameters of the local dimension chain of the input shaft to hole 4 are , and the calculation process is as follows:

[0140] As shown in Figure 7 , the present application regards the coordinate system of each connecting pair as being in the midpoint of the contact line on the projection of the gear axis, and now the error of CFE1 is converted to CFE9 by coordinate transformation using the Jacobian matrix:

[0141] S 1 = [ J CFE 1 J IFE 5 ′ J CFE 9 ] ⋅ [ [ CFE 1 ] [ IFE 5 ′ ] [ CFE 9 ] ] (33)

[0142] wherein , , are the Jacobian matrices corresponding to CFE1, IFE5 and CFE9, respectively:

[0143] J CFE 1 = [ 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 ] (34)

[0144] J IFE 5 ′ = [ 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 ] (35)

[0145] J CFE 9 = [ 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 ] (36)

[0146] Therefore

[0147] S 1 = [ ± 0 . 219 0 ± 0 . 219 ± 0 . 001325 0 ± 0 . 001325 ] T (37)

[0148] The error of CFE3 is transferred to CFE11 by coordinate transformation using Jacobian matrix:

[0149] S 2 = [ J CFE 3 J IFE 7 ′ J CFE 11 ] ⋅ [ [ CFE 3 ] [ IFE 7 ′ ] [ CFE 11 ] ] (38)

[0150] Wherein , , are the Jacobian matrices corresponding to CFE3, IFE7, CFE11 respectively:

[0151] J CFE 3 = [ 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 ] (39)

[0152] J IFE 7 ′ = [ 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 ] (40)

[0153] J CFE 11 = [ 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 ] (41)

[0154] Therefore

[0155] S 2 = [ ± 0 . 2895 0 ± 0 . 2895 ± 0 . 001346 0 ± 0 . 001346 ] T (42)

[0156] The error of CFE2 is transferred to CFE10 by coordinate transformation using Jacobian matrix:

[0157] S 3 = [ J CFE 2 J IFE 6 ′ J CFE 10 ] ⋅ [ [ CFE 2 ] [ IFE 6 ′ ] [ CFE 10 ] ] (43)

[0158] Wherein , , are the Jacobian matrices corresponding to CFE2, IFE6, CFE10 respectively:

[0159] J CFE 2 = [ 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 ] (44)

[0160] J IFE 6 ′ = [ 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 ] (45)

[0161] J CFE 10 = [ 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 ] (46)

[0162] Therefore

[0163] S 3 = [ ± 0 . 26 0 ± 0 . 26 ± 0 . 0008 0 ± 0 . 0008 ] T (47)

[0164] The error of CFE4 is transformed to CFE12 by Jacobian matrix

[0165] S 4 = [ J CFE 4 J IFE 8 ′ J CFE 12 ] ⋅ [ [ CFE 4 ] [ IFE 8 ′ ] [ CFE 12 ] ] (48)

[0166] Wherein 、 、 J4, J8, J12 are Jacobian matrix of CFE4, IFE8, CFE12 respectively

[0167] J CFE 4 = [ 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 ] (49)

[0168] J IFE 8 ′ = [ 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 ] (50)

[0169] J CFE 12 = [ 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 ] (51)

[0170] Therefore

[0171] S 4 = [ ± 0 . 31 0 ± 0 . 31 ± 0 . 00107 0 ± 0 . 00107 ] T (52)

[0172] Step 4: merge parallel size chain, calculate parallel function feature screw parameter.

[0173] In order to transform the complex parallel size chain into a simple serial size chain, the error screw parameter of the parallel size chain is transformed into the error screw parameter of the serial size chain by the following formula.

[0174] T = T a = [ L 1 L ( u 1 + u 2 ) − u 2 0 L 1 L ( u 1 + u 2 ) − u 2 u 1 + u 2 L 0 u 1 + u 2 L ] T (53)

[0175] T = T b = [ ( L 1 − H 2 ) ( u 1 − u 2 ) L 2 + u 2 0 ( L 1 − H 2 ) ( u 1 − u 2 ) L 2 + u 2 u 1 − u 2 L 2 0 u 1 − u 2 L 2 ] T (54)

[0176] Wherein, u1 is the larger screw parameter in the two parallel function features; u2 is the smaller screw parameter in the two parallel function features; L1 is the distance of the local coordinate system of the function requirement from the right end face of the connecting pair where u2 is located in the overall coordinate system; L is the distance between the two parallel function features; L2 is the distance between the connecting pair where u1 is located and the left end face of the connecting pair where u2 is located; H2 is the contact length of the connecting pair where u2 is located.

[0177] It is worth noting that if the function requirement The local coordinate system is located between two parallel dimension chains. Select equation (54) to calculate the axis separation amount required for the function; otherwise, select equation (53) to calculate the axis separation amount. At the same time, only equation (53) can be selected to calculate the change in the intersection angle required for the function.

[0178] Using equations (53) and (54) and Converted to PFE13, in order to calculate the axis separation V of the output shaft system assembly, the functional requirements are as follows: Local coordinate system It is located between two parallel dimension chains. Therefore, equation (54) is chosen for calculation. The range of spinor variation. However, if we want to calculate the change in angle... Equation (53) should be chosen for calculation. The range of spinor variation. For example... Figure 2 As shown, the measurements obtained The relevant parameter values ​​for the range of variation are shown in the table below.

[0179] Table 2 and Parameters related to the range of variation

[0180]

[0181] The range of variation is:

[0182] T PFE 13 = { [ ± 0 . 0436 0 ± 0 . 0436 ± 0.0004390 ± 0.000439 ] T ( for calculating ∑ ) [ ± 0 . 252 0 ± 0.252 ± 0.0000670 ± 0.000067 ] T ( for calculating V ) (55)

[0183] PFE 13 = T PFE 13 + PFE 5 ′ = { [ ± 0 . 0436 ± 0.4 ± 0 . 0436 ± 0.0007760 ± 0.000776 ] T ( for calculating ∑ ) [ ± 0 . 252 ± 0.4 ± 0.252 ± 0.0004040 ± 0.000404 ] T ( for calculating V ) (56)

[0184] For input shaft system components, Local coordinate system On the extension of the input shaft axis, such as Figure 7 This is shown. To calculate the final assembly deviation... And V, need to be calculated using Equation 3-1 The range of variation. To reduce the amount of calculation and facilitate calculation, a point on the nominal axis between bearing 3 and bearing 4 is selected. make It equals 0. For example... Figure 2 As shown, the measurements obtained are consistent with... The relevant parameter values ​​related to the change are shown in the table below.

[0185] Table 3 and Parameters related to the range of variation

[0186]

[0187] The variation range of

[0188] T PFE 14 = [ 0 0 0 ± 0.000610 ± 0.00061 ] T (57)

[0189] PFE 14 = T PFE 14 + PFE 6 ′ = [ 0 ± 0.45 0 ± 0.001140 ± 0.00114 ] T (58)

[0190] Step 5: Reestablish the dimension chain transmission relationship of the assembly, and correct the error accumulation path of the input and output shafts.

[0191] For the output shaft assembly, the variation range of the parallel functional feature is calculated, and the dimension chain relationship is reestablished as , where the interference fit between the output shaft and the driven bevel gear shaft hub is not considered, so the screw parameter of is 0. After calculating the variation range of the parallel functional feature , the dimension chain transmission relationship of the input shaft assembly is corrected as .

[0192] The distance between the origin of the local coordinate system of the output shaft and the origin of the local coordinate system of the driving bevel gear is , and the point is the intersection of the nominal axis of the driving gear and the midpoint section of the tooth width. The Jacobian matrix of the assembly function requirements and is shown in the following table.

[0193] Table 5 Jacobian matrix of FR1 and FR2

[0194]

[0195] For , if PFE 13 = [ ± 0 . 252 ± 0.4 ± 0.252 ± 0.0004040 ± 0.000404 ] T When calculating the axis separation amount, the calculation result is as follows:

[0196] FR 1 = [ J PFE 13 J IFE 15 ] ⋅ [ [ PFE 13 ] [ IFE 15 ] ] = [ ± 0 . 272 ± 0 . 4 ± 0 . 272 ± 0 . 000586 0 ± 0 . 000586 ] (59)

[0197] Similarly, when PFE 13 = [ ± 0 . 0436 ± 0.4 ± 0 . 0436 ± 0.0007760 ± 0.000776 ] T , the intersection angle variation of the sought is:

[0198] FR 1 = [ J PFE 13 J IFE 15 ] ⋅ [ [ PFE 13 ] [ IFE 15 ] ] = [ ± 0 . 0636 ± 0 . 4 ± 0 . 0636 ± 0 . 000958 0 ± 0 . 000958 ] (60)

[0199] For In this regard, the axial separation and the change in intersection angle can be obtained at the same location, therefore The calculation results are as follows:

[0200] FR 2 = [ J PFE 14 J IFE 16 ] ⋅ [ [ PFE 14 ] [ IFE 16 ] ] = [ ± 0 . 671 ± 0 . 45 ± 0 . 711 ± 0 . 00132 0 ± 0 . 00132 ] (61)

[0201] It is worth noting that, , The translational deviation along the y-axis can be used to calculate the axial misalignment GH of the driven bevel gear and the axial misalignment H of the driving bevel gear, respectively.

[0202] Step 6: Calculate and output the axis separation amount V, the angle change amount Σ, and the axial misalignment amounts H and GH through extreme value calculation.

[0203] Both the change in the axial angle ∑ and the axial separation V are affected by the final assembly deviation between the driven and driving bevel gears. Therefore, the maximum change in the axial angle ∑ of the gear axes is:

[0204] (62)

[0205] However, as Figure 8 As shown, due to the angular deviation between axis 1 and axis 2, the axis separation V is not equal to the sum of the positional deviations of the two axes. Here, the point... and These are relative to the local coordinate system. and In the global coordinate system The actual location within. In the extreme value method, if point... In plane Above, and simultaneously at the maximum positional deviation along the y-axis. Place; point In a plane Above, and simultaneously at the maximum positional deviation along the y-axis. Place, such as Figure 8 As shown, at this point, the axial separation amount V is at its maximum.

[0206] At a theoretical axis angle of 90°, and In the global coordinate system The coordinates are respectively and .at the same time, and The value of can be obtained through the following equation:

[0207] (63)

[0208] (64)

[0209] With the calculation results are as follows: , , and . The vector expressions of the axis 1 and the axis 2 are:

[0210] (65)

[0211] (66)

[0212] The common normal vector of the vectors and the normal vector ( , ) can be calculated as follows:

[0213] (67)

[0214] (68)

[0215] The axis separation V can be obtained by the following equation:

[0216] (69)

[0217] Therefore, the axis angle variation ∑ and the axis separation V of the arc tooth cone gear box are respectively: and , that is, the axis separation , the axis angle variation , the axial misalignment amount of the driving cone gear , and the axial misalignment amount of the driven cone gear .

[0218] Although the embodiments of the present application have been shown and described above, it should be understood that the above-mentioned embodiments are exemplary and should not be construed as limiting the present application, and those skilled in the art can make changes, modifications, replacements and variations to the above-mentioned embodiments without departing from the principles and purposes of the present application within the scope of the present application.

Claims

1. A method for calculating assembly errors of an arcuate-tooth bevel gear pair considering bearing play and assembly relationship, characterized in that, The method comprises the following steps: Step 1: Establish the size chain transmission relationship diagram of the spiral bevel gear pair assembly body, define the global coordinate system of the output shaft system and the input shaft system and the functional requirements ; Step 2: analyze the parallel size chain, disassemble the bearing clearance error, and calculate the range of variation of each functional feature; the range of variation of the vector is characterized by the translation variable and the rotation variable composed of Step 3: Jacobian spinor model is used to characterize the error propagation, and the spinor parameters of the parallel dimension chain are calculated by The Jacobian matrix dynamically associates the error propagation path of each functional element, and the spinor parameters of the parallel dimension chain are calculated Step 4: merging and combining the error screw parameters of the parallel size chain, converting them into the error screw parameters of the serial size chain, and calculating the screw variation range of the parallel functional features; Step 5: reconstructing the size chain transmission relationship of the assembly, and correcting the error accumulation path of the input shaft system and the output shaft system; Step 6: Calculate the output axis separation amount (V), the intersection angle change amount (θ), the driving bevel gear axial displacement amount (H), and the driven bevel gear axial displacement amount (GH) by the extremum method. ) 2. The method of claim 1, wherein, In the step 2, the disassembling of the bearing clearance error comprises: The radial clearance and the axial clearance of the bearing are decomposed into translational and rotational degrees of freedom, and the minimum value of the axial clearance is taken as the limit condition of the offset.

3. The method of claim 1, wherein, In the step 3, the specific implementation of the Jacobian screw model comprises: The assembly error is decomposed into a translational vector and a rotational vector, the error screw in the local coordinate system is converted into the global coordinate system through the Jacobian matrix, and the error transmission path of the bearing fit and the gear installation position is dynamically associated.

4. The method of claim 1, wherein, In the step 4, the merging mode of the parallel size chain is: Through the formula Or Transforming the error screw parameters of a parallel dimension chain into the parameters of a serial dimension chain, where , are the screw parameters of the parallel function feature, , , , are the geometric distance parameters.

5. The method of claim 1, wherein, In step 6, the implementation of the extremum method includes: solving the axis separation amount (V) and the intersection angle change amount (θ) in the global coordinate system by vector analysis method, and determining the axial misalignment amount (H, GH) of the driving bevel gear and the driven bevel gear based on the intersection angle change amount (θ) of the axis and the axis separation amount (V). ), and determining the axial misalignment amount (H, GH) of the driving bevel gear and the driven bevel gear based on the intersection angle change amount (θ) of the axis and the axis separation amount (V).​ 6. The method of claim 1, wherein, The functional requirements in step 1 are , ) are the deviations of the center axes of the driven bevel gear and the driving bevel gear in the global coordinate system, and the global coordinate system is consistent with the assembly reference of the output shaft system and the input shaft system.

7. The method of claim 1, wherein, In the step 5, the correction of the error accumulation path comprises: The screw parameters of the parallel functional features are included in the serial size chain, and are uniformly mapped to the global coordinate system through coordinate transformation, so as to correct the error accumulation relationship of the input shaft system and the output shaft system.

8. The method of claim 1, wherein, In the step 6, the calculation formula of the axis separation amount (V) and the intersection angle variation amount (Σ) is: And wherein , is the gear pitch cone radius, , is the offset of the axis in the global coordinate system.

9. The method of claim 1, wherein, The method further comprises: According to the constraint condition of the bearing clearance, the error screw parameters of the parallel size chain are dynamically adjusted to avoid repeated calculation of the translational and rotational degrees of freedom.

10. The method according to any one of claims 1 to 9, characterized in that, The method is suitable for assembly precision analysis and optimization of the spiral bevel gear pair in the automobile, aviation or industrial mechanical transmission system.

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