CN112131683B - Gear blank parameter determination method for gear cutting machining of split straight bevel gear - Google Patents
Gear blank parameter determination method for gear cutting machining of split straight bevel gear Download PDFInfo
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Abstract
According to the equivalent wheel blank parameters when each tooth slot is machined, the equivalent rigidity of the split wheel blank when each tooth slot is machined is calculated respectively, and the deformation of each tooth slot in the machining process is calculated by using a moment area method; superposing the deformation to obtain the total deformation in the whole processing process; if the obtained total deformation exceeds the allowable total deformation, adjusting the design parameters of the split wheel blanks, shortening the design length of the split wheel blanks, reducing the number of tooth grooves contained in each split wheel blank, or reducing the gear modulus, or increasing the design thickness of the split wheel blanks, repeating the operation until the requirements are met, and taking the corresponding design parameters as the design parameters for manufacturing the split wheel blanks. The bending deformation of the gear blank after gear cutting processing can be rapidly and accurately predicted, the design parameters of the gear blank which can meet the bending deformation processing requirement are determined, and the problems of large processing deformation of the split straight bevel gear and unreasonable design of the split gear blank are solved.
Description
Technical Field
The invention relates to a reasonable design method of a straight bevel gear blank, in particular to a gear blank parameter determining method for gear cutting processing of a split straight bevel gear.
Background
The ultra-large straight bevel gear is one of the most important parts in large and heavy industrial equipment, has wide application in a plurality of important fields such as mines, power generation and the like, and takes an important place in industrial and economic development. The ultra-large bevel gear (with the diameter of more than 3000 mm) has higher requirements on a forming method and processing equipment during processing, and the detection means after processing are more complex, so that the manufacturing cost is higher, the manufacturing time is longer and the processing difficulty is higher.
At present, the tooth shape of an oversized bevel gear in large industrial equipment is mostly straight teeth. The integral super-large straight bevel gear has small structural rigidity, is easy to deform during processing and assembling, is often greatly limited due to the specification of equipment during processing the integral super-large gear, and is extremely difficult to process during transportation, so that the existing super-large straight bevel gear is in a split structure during processing and transportation.
The prior study shows that the structural deformation of the split wheel blank is mainly bending deformation, and the deformation depends on two aspects, namely the deformation caused by rigidity and internal stress change due to material removal, the deformation of the part accounts for 92.2% of the total deformation, and the structural deformation caused by processing stress accounts for 7.8%. Aiming at the technical characteristics of the oversized wheel blank, such as first splitting, gear cutting and large deformation, engineers perform reasonable wheel blank design and reasonable wheel blank splitting, and lack effective theoretical support, and in the existing engineering practice, great blindness and randomness exist. The method for solving the problem of deformation of the wheel blank mostly depends on the method of limiting the deformation of the wheel blank by applying external force or reserving machining allowance and then carrying out finish machining. This results in low precision, long cycle, difficult assembly and high manufacturing cost of the existing split straight bevel gears.
Disclosure of Invention
The invention aims to overcome the defects, and provides a method for determining parameters of a gear blank for cutting teeth of a split straight bevel gear, which can accurately determine design parameters of the gear blank meeting the requirement of bending deformation after machining, thereby fundamentally solving the problem of large machining deformation of the gear blank.
The technical scheme adopted by the invention for solving the technical problems is as follows: a gear blank parameter determining method for gear cutting processing of a split straight bevel gear comprises the following steps:
(1) Setting initial design parameters of a split wheel block, and defining a rectangular wheel block with an equivalent equal section with the split wheel block as an equivalent wheel block, wherein the rigidity of the equivalent wheel block is the equivalent rigidity of the split wheel block;
(2) According to parameters of an equivalent wheel blank when each tooth groove is machined by the split wheel blank, respectively calculating the equivalent rigidity of the split wheel blank when each tooth groove is machined in turn, and respectively calculating the deformation quantity generated by the wheel blank in the process of machining each tooth groove by using the equivalent rigidity and utilizing a moment area method;
(3) Superposing the deformation produced in the process of machining each tooth slot to obtain the total deformation produced by splitting the wheel blank in the whole machining process;
(4) Comparing the obtained total deformation with the allowable total deformation, if the obtained total deformation exceeds the allowable total deformation, performing the step (5), otherwise, performing the step (7);
(5) Adjusting design parameters of the split wheel blanks, shortening the design length of the split wheel blanks, so that the number of tooth grooves contained in each split wheel blank is reduced, or the modulus of a gear is reduced, or the design thickness of the split wheel blanks is increased;
(6) Repeating the steps (2) to (5) by utilizing the adjusted design parameters of the split wheel blank;
(7) And taking the design parameters of the split wheel block corresponding to the current time of obtaining the total deformation of the split wheel block as the design parameters for manufacturing the split wheel block.
In the step (2), the machining sequence of the tooth grooves is that firstly machining the tooth grooves at the middle position of the split wheel blank, then sequentially machining the tooth grooves at one side of the tooth grooves at the middle position, and finally sequentially machining the tooth grooves at the other side.
Since the split plane of the split wheel block is positioned in the middle of the tooth grooves, half tooth grooves are formed at the left end and the right end of the split wheel block, and the half tooth grooves at the two ends of the split wheel block do not calculate the processing deformation.
In the step (5), when the design parameters of the split wheel block are adjusted, the design length of the split wheel block is shortened, and if the total deformation does not meet the design requirement when the design length of the split wheel block is shortened to the allowable limit value by repeating the steps (2) to (5), the modulus of the gear is reduced or the design thickness of the split wheel block is increased.
The equivalent stiffness calculation formula of the split wheel blank is as followsWherein E is elastic modulus, L is length of the split wheel blank, and I 2 is section moment of inertia of the equivalent wheel blank.
The calculation formula of the deformation amount generated by the wheel blank in the process of processing each tooth slot is as follows: Wherein: the length direction of the split wheel blank is taken as the direction of the x axis, the integration interval [ A, B ] is from one side to the other side of the top of the tooth groove, L is the length of the split wheel blank, and M is the additional moment applied to the wheel blank during processing.
The calculation formula of the additional moment applied in the wheel blank processing is as follows: Wherein z 1 is the tooth cutting depth of the split wheel blank, h is the thickness of the split wheel blank, z c is the distance between the neutral axis and the x axis of the cross section of the wheel blank after cutting, x 1 is the distance from the left end of the wheel blank to the left side surface of the tooth slot, x 2 is the width of the bottom of the tooth slot, x 3 is the width of the top of the tooth slot, m is the gear module, and sigma il (z) is.
The beneficial effects of the invention are as follows: the method can rapidly and accurately predict the bending deformation of the machined wheel blank, correspondingly adjust the wheel blank design parameters according to the bending deformation, accurately determine the wheel blank design parameters which can meet the requirement of the bending deformation after machining, and further fundamentally solve the problem of machining deformation of the split wheel blank. The method does not need to actually process wheel blanks for testing, and greatly improves the efficiency of designing and processing the split gears.
Drawings
FIG. 1 is a flow chart of calculation of bending deformation of a split wheel block
FIG. 2 is a schematic illustration of a split wheel block tooth slot analysis.
Fig. 3 is a schematic view of the analysis of bending additional stress during tooth cutting.
Fig. 4 is a schematic illustration of deflection analysis during tooth cutting of a wheel blank.
Fig. 5 is a cloud image of wheel blank deformation during single tooth slot machining.
Fig. 6 is a graph showing the analysis of deformation in the single tooth slot process.
Fig. 7 is a schematic diagram showing deformation of the wheel base when the 1 st tooth slot is machined.
Fig. 8 is a schematic representation of the deformation of the wheel blank after machining two tooth slots.
Fig. 9 is a schematic diagram of deformation after machining of the right half of the split wheel block.
Fig. 10 is a schematic diagram showing deformation of the split wheel base after machining of the 4 th tooth.
Fig. 11 is a schematic diagram of the deformation of the wheel base after the complete processing.
Fig. 12 is a finite element simulation result of the split wheel block tooth cutting process.
Detailed Description
The invention is further described below with reference to the drawings and the formula derivation.
The invention relates to a method for determining geometric parameters of a split wheel blank for cutting teeth of a split straight bevel gear, which adopts the following technical ideas, design principles and adopted specific schemes.
(1) Parameter setting
In the process of machining the gear cutting teeth, the gear blank material is continuously cut off, and the rigidity of the split gear blank changes along with the reduction of the material. The structural characteristics of the slender shape of the split wheel blank determine that the main deformation mode is bending deformation. The section of the split wheel blank in the length direction is different from the moment of inertia of the central shaft, the smaller section moment of inertia of the wheel blank tooth cutting position corresponds to smaller rigidity, and the larger section moment of inertia of the non-tooth cutting position corresponds to larger rigidity. In order to calculate the integral rigidity of the wheel blank in the tooth cutting process of the split wheel blank, the equivalent rigidity of the wheel blank is calculated by using a bending strain energy equivalent method. For an oversized split straight bevel gear, the end face of a split body after the large wheel is split is close to a rectangle, and the split body has small curvature due to the large diameter, and when the length of the split body is smaller, the split body can be analyzed by being similar to a rectangular cross-section beam.
In the method of the present invention, first, initial design parameters of the split wheel block are set, a rectangular wheel block having an equivalent cross section to the split wheel block is defined as an equivalent wheel block, and the rigidity of the equivalent wheel block is the equivalent rigidity of the split wheel block.
(2) Calculating equivalent rigidity and processing deformation
And then, according to parameters of an equivalent wheel blank when each tooth groove is machined by the split wheel blank, respectively calculating the equivalent rigidity of the split wheel blank when each tooth groove is machined in turn, and respectively calculating the deformation quantity of the wheel blank in the process of machining each tooth groove by using the equivalent rigidity and utilizing a moment area method.
And the equivalent rigidity of the split wheel blank is calculated by adopting a bending strain energy method. When the split wheel block is deformed by bending due to internal stress change during processing, the bending moment acting on both ends of the wheel block is assumed to be M, the bending moment causes the cross-sectional rotation angle of the split wheel block to be θ, E is the elastic modulus, I is the moment of inertia of the cross-section of the wheel block to the neutral axis, L is the length of the split wheel block, and the unit of rigidity is Nm.
Obtaining bending strain energy of the whole split wheel blank:
Let the bending strain energy of the complex variable cross-section split wheel block and the corresponding equivalent wheel block (i.e. equivalent isosurface beam) be U 1 and U 2, respectively, and let ε=u 1-U2, then there are:
Where y 1(x)、y2 (x) is the flex line equation for the split wheel and the equivalent wheel, respectively, and I 1、I2 is the cross-sectional moment of inertia for the split wheel and the equivalent wheel, respectively.
Wherein the flex line equation y 2 (x) for an equivalent constant cross-section beam is relatively easy to determine. Regarding the bending line equation y 2 (x) of the equivalent isosurface beam as the first approximation of the bending line equation y 1 (x) of the split wheel base, the equivalent section moment of inertia I 2 of the split wheel base is obtained by using ε=0 in the equation (2).
The equivalent stiffness of the split wheel block is:
In actual calculation, the moment of inertia I 2 of the equivalent constant-section wheel blank is a fixed value to be solved, and I 1 changes along with the change of sections of different positions of the split wheel blank. As shown in fig. 2, the analysis is performed here by taking one tooth slot as an example, and the size parameters of the tooth slots are similar when a plurality of tooth slots are processed, and the size parameters of the tooth slots are valued according to the midpoint of the tooth length of the equivalent gear. The unprocessed partial section moment of inertia of the wheel blanks on the left side and the right side of the tooth groove is I 0, the section moment of inertia of the wheel blank on the left side surface of the tooth groove is I 11, the section moment of inertia of the bottom surface of the tooth groove is I 12, and the section moment of inertia of the right side surface of the tooth groove is I 13; the horizontal distance from the left end of the split wheel blank to the top of the tooth surface on the left side of the tooth groove is L 1, the horizontal distance from the top of the left side of the tooth groove to the bottom of the tooth groove is L 2, the horizontal distance from the bottom of the left side of the tooth groove to the bottom of the right side of the tooth groove is L 3, the horizontal distance from the bottom of the right side of the tooth groove to the unprocessed part of the wheel blank is L 4, and the method comprises the following steps:
in the formula (4), the amino acid sequence of the compound,
In actual calculation, an example of processing a tooth slot is taken for analysis, the time of processing a plurality of tooth slots is similar, and the dimension parameter of the tooth slot is valued according to the midpoint of the tooth length of the equivalent gear. And calculating the equivalent section moment of inertia I 2 of the split wheel blank at the moment of finishing the tooth slot according to the geometric parameters of the corresponding equivalent wheel blank when finishing the machining of each tooth slot of the split wheel blank, and then calculating the equivalent rigidity K of the split wheel blank at the moment according to the formula (3).
After the equivalent rigidity is calculated, the deformation quantity of the wheel blank in the process of machining each tooth slot is calculated by using the equivalent rigidity and utilizing a moment area method.
From the simulation result of cutting teeth of the split wheel blank, it is found that the cutting teeth of the split wheel blank are mainly bent and deformed in a machining area, and the final deformation of the wheel blank in the machining process is a result of continuous superposition on the basis of the previous deformation. The sequence of the cutting teeth has little influence on deformation. And obtaining deformation of the split wheel blank when the tooth grooves at different positions are processed independently, and then superposing the deformation to obtain the overall deformation condition.
When the deformation of the split wheel block involves the superposition effect and the bidirectional stress, the calculation and the difficulty thereof are directly solved by using an analytic method, and the result of finite element analysis shows that the stress variation along the length direction of the wheel block is the largest in the wheel block processing process. Therefore, a single tooth slot with the middle position of the split wheel blank removed is taken as an analysis unit to study the generation and calculation method of the additional moment in the length direction of the wheel blank and the deformation condition of the wheel blank in the gear cutting process. The analytical calculation of the overall deformation of the whole split body will be available by the accumulation of the deformations of the multiple analysis units.
Starting from processing a single tooth groove at the middle position of the split wheel block, taking the length direction of the split wheel block as the direction of the x axis, and cutting the tooth groove at the middle position of the wheel block, wherein the cross section of the single tooth groove wheel block is approximately U-shaped, as shown in figure 3. Wherein x 1 is the distance from the left end of the wheel blank to the left side surface of the tooth groove, L is the length of the split wheel blank, x 2 is the width of the bottom of the tooth groove, x 3 is the width of the top of the tooth groove, z 1 is the cutting depth of the wheel blank, h is the thickness of the split wheel blank, and the distance between the neutral axis and the x axis of the section of the wheel blank after cutting is z c. After the tooth groove in the middle of the wheel blank is cut off, residual stress contained in the material of the tooth groove part is removed, and the original supporting stress sigma on the two side surfaces of the tooth groove is not existed. In this case, the stress of-sigma applied to the side wall of the tooth slot can achieve the equivalent effect of stress. The configuration of the split wheel block determines that the main deformation is in the x-axis direction, and the deformation in the y-axis direction (the width direction of the wheel block) is temporarily disregarded here.
According to the additional stress analysis, the deformation condition of the equivalent wheel blank in the tooth cutting process is analyzed by using a moment-area method, and the bending moment between the left end and the right end of the equivalent wheel blank is shown as a figure 4. Taking any two sections m 1、m2 with infinite small distance on an equivalent wheel blank, wherein the distance between the two sections is ds, the angle at which the perpendicular lines of the two sections intersect after being bent by an additional moment is dθ, dθ=ds/ρ, and ρ is the curvature radius of the wheel blank. According to the material mechanics, the formula of the equivalent wheel blank bending is as follows:
wherein dx is the distance in the horizontal direction of the section m 1、m2 of the wheel blank after bending deformation. When ds is very small, dx≡ds.
In fig. 4, a line segment m 1ρ1 is a tangent line at a section m 1 of the deformed wheel blank, a line segment m 2ρ2 is a tangent line at a section m 2, an intersecting angle of the two tangent lines is dθ, and a value of the dθ angle obtained according to the formula (5) is a ratio of a bending moment diagram area Mdx to bending stiffness EI. Integrating the wheel blank along the length direction to obtain the total included angle theta of the whole wheel blank in bending deflection rotation. From the geometrical relationship, the deflection between the section m 1 and the section m 2 of the equivalent wheel blank is as follows:
In order to obtain the total deflection of the whole wheel blank, the formula (6) can be integrated from the point A to the point B of the split wheel blank, and the total deflection of the wheel blank can be obtained as follows:
combining the processing of a single tooth space split wheel blank and each dimension parameter of the wheel blank, and obtaining the additional moment born in the wheel blank processing according to an additional moment calculation principle as follows:
Wherein 2.25 is a fixed proportional relationship between the tooth space height and the modulus m according to national standards.
The calculation formula of the deformation amount of the wheel blank generated in the process of processing each tooth slot is as follows by combining the formula (3) and the formula (7):
Wherein: the length direction of the split wheel blank is taken as the direction of the x axis, the integration interval [ A, B ] is from one side to the other side of the top of the tooth groove, L is the length of the split wheel blank, and M is the additional moment applied to the wheel blank during processing.
According to the equivalent stiffness calculation method of the split wheel blank, the equivalent stiffness of the split wheel blank when the tooth grooves at different positions are machined can be obtained. The processing sequence of the tooth grooves can be set as that firstly, the tooth grooves at the middle position of the split wheel blank are processed, then the tooth grooves at one side of the tooth grooves at the middle position are sequentially processed, and finally the tooth grooves at the other side are sequentially processed. K 11、K12、K13、K14、K15 and the like are set according to the processing sequence. Substituting the rigidity of the wheel blank into a wheel blank deformation formula (9), and adjusting an integration interval to obtain the deformation of the split wheel blank when processing the single tooth grooves at different positions.
The deformation of a single tooth groove at the middle position of the single machining wheel blank is as follows:
in order to verify the accuracy of deformation calculation, the materials in the tooth grooves of the wheel blank are removed in a layered mode, and the thickness of each removal is set to be 9mm. Based on the set geometry size and material parameters of the wheel blank, solving the equivalent stiffness in the wheel blank processing process according to an equivalent stiffness calculation method, wherein the calculation result is shown in the table below.
| Removing tooth slot thickness | 0 | 9 | 18 | 27 | 36 | 45 |
| Rigidity/10 5 Nm | 8.998 | 8.701 | 8.471 | 8.243 | 8.021 | 7.808 |
From the above table, as the gear cutting process proceeds, the rigidity of the split wheel block gradually decreases, and the rate of decrease in rigidity is about 13.2% of the rigidity of the wheel block before the gear cutting process. The research shows that the removal proportion of the wheel blank material is 4.6%, the rigidity reduction proportion is 13.2% and the volume reduction speed of the wheel blank material is smaller than the rigidity reduction speed of the wheel blank in the whole processing process.
In finite element software ABAQUS, selecting the same material as the theoretically calculated material, the same wheel blank size parameter, applying initial internal stress, simulating removal of the material in a tooth slot, setting the thickness of each cut tooth slot to be 9mm, and outputting a deformation cloud chart of each analysis step of the split wheel blank after the simulation is finished as shown in figure 5.
The deformation was calculated by MATLAB and plotted as a wheel stock deformation versus removal thickness, the results are shown in fig. 6. As can be seen from fig. 6, in the cutting tooth processing of the single tooth slot, the calculation method is substantially consistent with the deformation result obtained by finite element analysis.
Based on the wheel blank after the 1 st tooth slot is processed, continuously analyzing the 2 nd tooth slot, analyzing the right side of the first tooth slot by using the tooth slot, and processing the deformation of the wheel blank after the second tooth slot is processed as follows:
Wherein x 4 is the thickness of the machined gear tooth tip.
Continuing to process the 3 rd tooth groove, analyzing by taking the right side of the 2 nd tooth groove as an example, wherein the deformation of the wheel blank after the third tooth groove is processed is as follows:
next, the remaining half of the tooth slot is machined, first the tooth slot immediately to the left of the middle tooth slot, and the deformation of the wheel blank after the fourth tooth slot is machined is:
continuously analyzing the 2 nd tooth groove on the left half side, and processing the deformation of the wheel blank after the fifth tooth groove is processed into the following steps:
if there is a tooth slot at the left end, the analysis and calculation principle is the same as that of the right part.
Since the split plane of the split wheel block is located in the middle of the tooth space, half tooth spaces are provided at both the left and right ends of the split wheel block. Finite element analysis shows that the processing of half tooth grooves at two ends has little influence on the bending deformation of the whole wheel blank and can be ignored, so that the method is not embodied in the calculation method.
(3) The total deformation is calculated by superposition of deformation
And obtaining the deformation of the wheel blank when the tooth grooves at different positions are processed independently, and then superposing the deformation amount generated in the process of processing each tooth groove to obtain the total deformation amount generated by splitting the wheel blank in the whole processing process. The deformation of the wheel blank when machining the 1 st tooth slot is shown in fig. 7. The included angles between the bottom surfaces of the unprocessed areas on the left and right sides and the horizontal line after the wheel blank is deformed are respectively theta 11、θ12, the local deformation S 1 can be obtained according to the previous theoretical calculation, then sin theta 11＝sinθ12 =0.00035 can be obtained, and the symmetrical included angle is further obtained to be 0.02 degrees.
Earlier studies show that the sequence of cutting teeth has little influence on deformation. Here, the partial deformation amount of the wheel blank when the tooth groove is machined alone is set to S 2 by continuing the tooth cutting to the right side of the wheel blank, and the deformation causes the deflection angles θ 21、θ22 of the right and left ends of the bottom surface of the wheel blank. As shown in fig. 8, a coordinate system S 1(o1-x1,z1 is established at the intermediate position of the split wheel block), and the coordinate axis z 1 is the symmetry axis of the tooth slot at the intermediate position. A coordinate system is established at the position of the second tooth slot symmetry axis, and the coordinate system is rotated counterclockwise by θ 11 to obtain a coordinate system S 2(o2-x2,z2 in fig. 8. And after the first two tooth grooves are machined, the included angle between the corresponding bottom surface of the unprocessed area at the right end of the split wheel blank and the horizontal line is theta 11+θ21, the deflection angle of the bottom surface of the unprocessed area at the left end of the wheel blank is theta 12+θ22, and the deformation after superposition is S' 2＝S1+S2/cosθ21.
After the right half of the wheel block is finished, the deformation of the split wheel block is shown in fig. 9. At this time, the included angle between the straight line part of the bottom surface of the left end of the wheel blank and the horizontal line is θ ' 32＝θ12+θ22+θ32, the included angle between the tangent line of the bottom surface of the right end of the wheel blank and the horizontal line is θ ' 31＝θ11+θ21+θ31, and the deformation after superposition is S ' 3＝S'2+S3/cosθ31.
When the fourth tooth slot is finished, the deformation of the wheel blank is as shown in fig. 10. The included angle between the straight line part of the bottom surface of the right end of the wheel blank and the horizontal line after superposition is theta ' 41＝θ′31+θ41, the included angle between the tangent line of the bottom surface of the left end of the wheel blank and the horizontal line is theta ' 42＝θ′32+θ42, and the deformation after superposition is S ' 4＝S′3+S4/cosθ42.
After the wheel base is fully processed, the wheel base is deformed as shown in fig. 11. Neglecting deformation caused by processing the leftmost half tooth slot, wherein included angles between bottom surface tangents of the left end and the right end of the deformed and overlapped wheel blank and a horizontal line are respectively theta '52＝θ′42+θ52、θ′52＝θ′42+θ52, and the overlapped deformation is S' 5＝S'4+S5/cosθ52.
The above-mentioned processing deformation and deflection angle at the time of individual processing are calculated respectively based on the set wheel blank size and material parameters, and the calculation results are shown in the following table.
According to the table above, after deformation and superposition, the included angle between the right tangent line of the bottom surface of the wheel blank and the horizontal line is θ ' 51 =0.052°, the included angle between the left end is θ ' 52 =0.052°, and the deformation after superposition is S ' 5 = 0.1301mm.
As shown in FIG. 12, the simulation results of the above calculation example show that the average deformation of the maximum deformation region of the wheel blank is 0.1304mm, and the calculated bending deformation ratio is substantially identical to the simulation result by comparing the calculated result with the simulation result.
(4) And (3) comparing the obtained total deformation with the total deformation allowed by the engineering requirement, if the obtained total deformation exceeds the allowed total deformation, performing the following step (5), otherwise, performing the step (7).
(5) Deformation caused by rigidity and internal stress changes is closely related to the specification size, cross section design, gear cutting process design and the like of a split body obtained after the integral wheel blank is cut. Therefore, when the obtained total deformation does not meet the engineering requirements, the final processing deformation can be influenced by adjusting parameters such as the cross-sectional dimension of the split wheel blank and the specification and the size of the wheel blank when the wheel blank is split.
For example, when the obtained total deformation does not meet the engineering requirements, the design parameters of the split wheel blanks are adjusted, the design length of the split wheel blanks is shortened so that the number of tooth grooves contained in each split wheel blank is reduced, the modulus of the gear is reduced, or the design thickness of the split wheel blanks is increased.
(6) And (3) repeating the steps (2) to (5) by utilizing the adjusted design parameters of the split wheel block until the calculated total deformation meets the engineering requirement.
(7) And taking the design parameters of the split wheel block corresponding to the current time of obtaining the total deformation of the split wheel block as the design parameters for manufacturing the split wheel block. After all tooth grooves are machined, the machining deformation of the split wheel blank manufactured according to the design parameters can meet engineering requirements, and then gears meeting the requirements are produced in a combined mode.
When the design parameters of the split wheel blanks are adjusted in the step (5), the design length L of the split wheel blanks is preferentially shortened, so that the number of tooth grooves contained in each split body is reduced, the cross section of the wheel blanks along the length direction is changed, and the section moment of inertia I 2, the equivalent rigidity and the like of the equivalent equal-section beam are recalculated. If the steps (2) to (5) are repeated until the total deformation amount still does not meet the design requirement when the design length of the split wheel block is shortened to the allowable limit value, the module m of the gear is properly reduced or the design thickness of the split wheel block is increased in combination with the design requirement of the gear pair, and then the steps (2) to (5) are repeated until the total deformation amount meets the requirement.
Claims (5)
1. A method for determining parameters of a gear blank for gear cutting processing of a split straight bevel gear is characterized by comprising the following steps of: the method comprises the following steps:
(1) Setting initial design parameters of a split wheel block, and defining a rectangular wheel block with an equivalent equal section with the split wheel block as an equivalent wheel block, wherein the rigidity of the equivalent wheel block is the equivalent rigidity of the split wheel block;
(2) According to parameters of an equivalent wheel blank when each tooth groove is machined by the split wheel blank, respectively calculating the equivalent rigidity of the split wheel blank when each tooth groove is machined in turn, and respectively calculating the deformation quantity generated by the wheel blank in the process of machining each tooth groove by using the equivalent rigidity and utilizing a moment area method;
the equivalent stiffness calculation formula of the split wheel blank is as follows Wherein/>Is elastic modulus,/>To divide the length of the wheel block,/>Is the section moment of inertia of the equivalent wheel blank;
The calculation formula of the deformation amount generated by the wheel blank in the process of processing each tooth slot is as follows: Wherein: the length direction of the split wheel blank is taken as the direction of the x axis, the integration interval [ A, B ] is taken as one side to the other side of the top of the tooth slot,/> To divide the length of the wheel block,/>The additional moment applied in the wheel blank processing is applied;
(3) Superposing the deformation produced in the process of machining each tooth slot to obtain the total deformation produced by splitting the wheel blank in the whole machining process;
(4) Comparing the obtained total deformation with the allowable total deformation, if the obtained total deformation exceeds the allowable total deformation, performing the step (5), otherwise, performing the step (7);
(5) Adjusting design parameters of the split wheel blanks, shortening the design length of the split wheel blanks so as to reduce the number of tooth grooves contained in each split wheel blank, or reduce the modulus of a gear, or increase the design thickness of the split wheel blanks;
(6) Repeating the steps (2) to (5) by utilizing the adjusted design parameters of the split wheel blank;
(7) And taking the design parameters of the split wheel block corresponding to the current time of obtaining the total deformation of the split wheel block as the design parameters for manufacturing the split wheel block.
2. The method for determining parameters of gear cutting machining gear blanks of split straight bevel gears according to claim 1, wherein the method comprises the following steps of: in the step (2), the machining sequence of the tooth grooves is that firstly machining the tooth grooves at the middle position of the split wheel blank, then sequentially machining the tooth grooves at one side of the tooth grooves at the middle position, and finally sequentially machining the tooth grooves at the other side.
3. The method for determining parameters of gear cutting machining gear blanks of split straight bevel gears according to claim 2, wherein the method comprises the following steps of: the half tooth grooves at the two ends of the split wheel blank do not calculate the processing deformation.
4. The method for determining parameters of gear cutting machining gear blanks of split straight bevel gears according to claim 1, wherein the method comprises the following steps of: in the step (5), when the design parameters of the split wheel block are adjusted, the design length of the split wheel block is shortened, and if the total deformation does not meet the design requirement when the design length of the split wheel block is shortened to the allowable limit value by repeating the steps (2) to (5), the modulus of the gear is reduced or the design thickness of the split wheel block is increased.
5. The method for determining gear blank parameters for cutting a split straight bevel gear according to any one of claim 1, wherein: the calculation formula of the additional moment applied in the wheel blank processing is as follows: Wherein/> For subdividing the tooth depth of the wheel block,/>To divide the thickness of the wheel block,/>Is the distance between the neutral axis and the x axis of the cross section of the gear blank after gear cutting,/>Is the distance from the left end of the wheel blank to the left side surface of the tooth groove,/>Is the width of the tooth slot bottom,/>Is the width of the top of the tooth slot,For gear modulus,/>Is an additional internal stress of the layer material corresponding to the parameter z.
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Citations (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| RU1793988C (en) * | 1991-05-20 | 1993-02-07 | Малое Научно-Внедренческое Предприятие "Елсипмаш" | Method of forming billets having cross-section of regular polygon |
| CN102357531A (en) * | 2011-10-18 | 2012-02-22 | 武汉理工大学 | Composite roll forming process of thick-wall deep-groove ring member |
| CN103084639A (en) * | 2013-01-21 | 2013-05-08 | 西北工业大学 | Method for strengthening process rigidity of thin-wall blade based on non-uniform allowance |
| CN103128514A (en) * | 2013-03-01 | 2013-06-05 | 吴敬 | Machining method and tool for large-modulus large-diameter small-width gears |
| CN104077442A (en) * | 2014-06-24 | 2014-10-01 | 南京晨光集团有限责任公司 | Method for controlling machining accuracy of large integrated thin-walled parts based on finite element analysis |
| CN104384428A (en) * | 2014-12-01 | 2015-03-04 | 重庆理工大学 | Warm precise forging forming method for hollow gear shaft blank |
| CN105912793A (en) * | 2016-04-18 | 2016-08-31 | 清华大学 | Finite element method obtaining hypoid gear teeth bending deformation |
| CN108446524A (en) * | 2018-05-14 | 2018-08-24 | 天津大学 | A kind of modeling method of spiral bevel gear for digital control processing |
| CN108804783A (en) * | 2018-05-25 | 2018-11-13 | 南昌航空大学 | A kind of assessment method of blank initial residual stress |
-
2020
- 2020-09-22 CN CN202011002766.5A patent/CN112131683B/en active Active
Patent Citations (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| RU1793988C (en) * | 1991-05-20 | 1993-02-07 | Малое Научно-Внедренческое Предприятие "Елсипмаш" | Method of forming billets having cross-section of regular polygon |
| CN102357531A (en) * | 2011-10-18 | 2012-02-22 | 武汉理工大学 | Composite roll forming process of thick-wall deep-groove ring member |
| CN103084639A (en) * | 2013-01-21 | 2013-05-08 | 西北工业大学 | Method for strengthening process rigidity of thin-wall blade based on non-uniform allowance |
| CN103128514A (en) * | 2013-03-01 | 2013-06-05 | 吴敬 | Machining method and tool for large-modulus large-diameter small-width gears |
| CN104077442A (en) * | 2014-06-24 | 2014-10-01 | 南京晨光集团有限责任公司 | Method for controlling machining accuracy of large integrated thin-walled parts based on finite element analysis |
| CN104384428A (en) * | 2014-12-01 | 2015-03-04 | 重庆理工大学 | Warm precise forging forming method for hollow gear shaft blank |
| CN105912793A (en) * | 2016-04-18 | 2016-08-31 | 清华大学 | Finite element method obtaining hypoid gear teeth bending deformation |
| CN108446524A (en) * | 2018-05-14 | 2018-08-24 | 天津大学 | A kind of modeling method of spiral bevel gear for digital control processing |
| CN108804783A (en) * | 2018-05-25 | 2018-11-13 | 南昌航空大学 | A kind of assessment method of blank initial residual stress |
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