CN112131683A - Method for determining parameters of gear blank for gear cutting machining of split straight bevel gear - Google Patents
Method for determining parameters of gear blank for gear cutting machining of split straight bevel gear Download PDFInfo
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Abstract
A method for determining parameters of a gear blank for cutting and processing a split type straight bevel gear comprises the steps of respectively calculating equivalent stiffness of a split wheel blank when each tooth slot is processed according to equivalent wheel blank parameters when each tooth slot is processed, and calculating deformation in the process of processing each tooth slot 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 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 method can quickly and accurately predict the bending deformation of the gear blank after gear cutting processing, determine the design parameters of the gear blank which can meet the processing requirements of the bending deformation, and solve the problems of large processing deformation and unreasonable design of the split gear blank of the split straight bevel gear.
Description
Technical Field
The invention relates to a reasonable design method of a straight bevel gear blank, in particular to a method for determining parameters of a split type gear blank for gear cutting processing of a straight bevel gear.
Background
The super-huge straight bevel gear is one of the most important parts in large-scale heavy industrial equipment, is widely applied to a plurality of important fields such as mines, power generation and the like, and occupies an important position in industrial and economic development. The super-large bevel gear (with the diameter of more than 3000 mm) has high requirements on a forming method and processing equipment during processing, and a detection means after processing is complex, so that the manufacturing cost is high, the manufacturing time is long, and the processing difficulty is high.
At present, the tooth form of an oversize bevel gear in large-scale industrial equipment is mostly straight tooth. The integral oversize type straight bevel gear is small in structural rigidity and easy to deform during processing and assembling, the integral oversize type gear is limited greatly due to the specification of equipment during processing, and the processed gear is extremely difficult in the transportation process, so that a split type structure is selected for multiple times during processing and transportation of the existing oversize type straight bevel gear.
The existing research shows that the structural deformation of the split wheel blank is mainly bending deformation, the deformation depends on two aspects, namely the deformation caused by rigidity and internal stress change caused by material removal, the partial deformation accounts for 92.2 percent of the total deformation, and the structural deformation caused by processing stress accounts for 7.8 percent. Aiming at the process characteristics of first subdivision, then gear cutting and large deformation of an oversize wheel blank, how engineers design and reasonably subdivide the wheel blank lacks effective theoretical support, and the existing engineering practice has great blindness and randomness. The method for solving the wheel blank deformation problem mainly depends on applying external force to limit the wheel blank deformation or reserving machining allowance and then performing finish machining and the like. The split type straight bevel gear has the advantages of low manufacturing precision, long period, high assembly difficulty and high manufacturing cost.
Disclosure of Invention
The invention aims to overcome the defects and provides a method for determining parameters of a split type straight bevel gear cutting machining wheel blank, which can accurately determine wheel blank design parameters meeting the requirement of bending deformation after machining and fundamentally solve the problem of large wheel blank machining deformation.
The technical scheme adopted by the invention for solving the technical problems is as follows: a method for determining parameters of a cutting gear blank of a split straight bevel gear comprises the following steps:
(1) setting initial design parameters of the split wheel blank, defining a rectangular wheel blank with an equivalent equal cross section with the split wheel blank as an equivalent wheel blank, and setting the rigidity of the equivalent wheel blank as the equivalent rigidity of the split wheel blank;
(2) respectively calculating the equivalent stiffness of the split wheel blanks when each tooth slot is processed and finished according to the parameters of the equivalent wheel blanks when each tooth slot is processed and finished, and respectively calculating the deformation generated by the wheel blanks in the process of processing each tooth slot by using the equivalent stiffness and utilizing a moment area method;
(3) superposing the deformation generated in the process of machining each tooth socket to obtain the total deformation generated by splitting the wheel blank in the whole machining process;
(4) comparing the obtained total deformation with the allowable total deformation, and 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, and shortening the design length of the split wheel blanks to reduce the number of tooth grooves contained in each split wheel blank, or reduce the modulus of the 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 blank corresponding to the obtained total deformation of the split wheel blank as the design parameters for manufacturing the split wheel blank.
In the step (2), the tooth grooves are processed in sequence, namely, the tooth grooves in the middle positions of the split wheel blanks are processed firstly, then the tooth grooves on one side of the tooth grooves in the middle positions are processed in sequence, and finally the tooth grooves on the other side are processed in sequence.
Because the split plane of the split wheel blank is positioned in the middle of the tooth grooves, half tooth grooves are formed in the left end and the right end of the split wheel blank, and the half tooth grooves in the two ends of the split wheel blank do not calculate machining deformation.
In the step (5), when adjusting design parameters of the split wheel blank, the design length of the split wheel blank is shortened, and if the steps (2) to (5) are repeated until the total deformation amount does not meet the design requirement when the design length of the split wheel blank is shortened to an allowable limit value, the modulus of the gear is reduced, or the design thickness of the split wheel blank is increased.
The equivalent rigidity calculation formula of the split wheel blank is
Wherein E is the elastic modulus, L is the length of the split wheel blank, I2Is equivalent to the section moment of inertia of the wheel blank.
The calculation formula of the deformation generated by the wheel blank in the process of machining each tooth groove is as follows:
wherein: integration interval [ A, B ] with the length direction of the split wheel blank as the direction of the x axis]From one side of the top of the tooth socket to the other side, L is the length of the split wheel blank, and M is the additional moment borne in the wheel blank machining.
The formula for calculating the additional moment applied to the wheel blank in the wheel blank machining process is as follows:
wherein z is1The depth of the teeth of the split wheel blank is h the thickness of the split wheel blank, zcIs the distance between the neutral axis and the x axis of the section of the gear cutting back wheel blank, x1Is the distance, x, from the left end of the wheel blank to the left side surface of the tooth socket2Is the width, x, of the bottom of the tooth space3Width of the top of the tooth slot, m is gear module, σil(z) is.
The invention has the beneficial effects that: by the method, the bending deformation of the machined wheel blank can be rapidly and accurately predicted, and the wheel blank design parameters can be correspondingly adjusted according to the bending deformation, so that the wheel blank design parameters meeting the requirements of the bending deformation after machining can be accurately determined, and the problem of machining deformation of the split wheel blank is fundamentally solved. The method does not need to actually process the wheel blank for testing, and greatly improves the efficiency of designing and processing the split gear.
Drawings
FIG. 1 is a flow chart of a bending deformation calculation of a split wheel blank
FIG. 2 is a schematic view of a split wheel cogging analysis.
FIG. 3 is a graphical representation of a bend-imposed stress analysis during tooth cutting.
FIG. 4 is a schematic view of deflection analysis during gear cutting of a wheel blank.
FIG. 5 is a cloud of wheel blank deformations during single groove machining.
Fig. 6 is a graph showing comparative analysis of deformation in single-groove machining.
FIG. 7 is a schematic view of the deformation of the wheel blank during machining of the 1 st tooth slot.
FIG. 8 is a deformation schematic of a wheel blank after machining two tooth slots.
Fig. 9 is a schematic diagram showing a deformation of the right half of the split wheel blank after machining.
Fig. 10 is a schematic view of the split wheel blank after 4 th tooth machining.
Fig. 11 is a schematic view of a deformation of a fully finished wheel blank.
FIG. 12 is a finite element simulation result of a gear cutting process of a split wheel blank.
Detailed Description
The invention is further explained by the derivation of the figures and formulas.
The invention discloses a method for determining geometrical parameters of a split wheel blank for cutting machining of a split type straight bevel gear, which adopts the following technical ideas, design principles and specific schemes.
(1) Setting parameters
In the process of machining the cutting teeth, materials of the split straight bevel gear blank are continuously cut off, and the rigidity of the split gear blank changes along with the reduction of the materials. The slender structural characteristics of the split wheel blank determine that the main deformation mode is bending deformation. The inertia moment of the cross section of the split wheel blank to the neutral shaft in the length direction is different, the inertia moment of the cross section of the wheel blank at the gear cutting position is smaller, the corresponding rigidity is smaller, and the inertia moment of the cross section of the wheel blank at the gear non-cutting position is larger, and the corresponding rigidity is larger. In order to calculate the integral rigidity of the wheel blank in the process of cutting the teeth of the split wheel blank, the equivalent rigidity of the wheel blank is calculated by using a bending strain energy equivalent method. For an oversize split type straight bevel gear, the end surface of a split body after large gear splitting is close to a rectangle, and the split body can be analyzed by a rectangular section beam which is similar to a rectangular section beam when the length of the split body is smaller due to large diameter and small curvature of the split body.
In the method, firstly, initial design parameters of the split wheel blank are set, a rectangular wheel blank with an equivalent equal section with the split wheel blank is defined as an equivalent wheel blank, and the rigidity of the equivalent wheel blank is the equivalent rigidity of the split wheel blank.
(2) Calculating equivalent rigidity and processing deformation
And then, respectively calculating the equivalent stiffness of the split wheel blanks when each tooth slot is processed sequentially according to the parameters of the equivalent wheel blanks when each tooth slot is processed, and respectively calculating the deformation generated by the wheel blanks in the process of processing each tooth slot by using the equivalent stiffness and 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 blank is subjected to bending deformation due to internal stress change in machining, assuming that the bending moment acting on the two ends of the wheel blank is M, the bending moment causes the section corner of the split wheel blank to be theta, E is the elastic modulus, I is the inertia moment of the section of the wheel blank to a neutral axis, L is the length of the split wheel blank, and the unit of rigidity is Nm.
Obtaining the bending strain energy of the whole split wheel blank:
the bending strain energy of a complicated variable cross-section split wheel blank and a corresponding equivalent wheel blank (namely an equivalent equal cross-section beam) is respectively made to be U1And U2And make U ═ U1-U2Then, there are:
in the formula, y1(x)、y2(x) Equations of the deflection lines, I, for the split wheel blank and the equivalent wheel blank, respectively1、I2Respectively are the section moments of inertia of the split wheel blank and the equivalent wheel blank.
Wherein, the equation y of the deflection line of the equivalent uniform-section beam2(x) Can be easily obtained. Taking the equation y of the deflection line of the equivalent constant-section beam2(x) As equation y for the deflection line of the split wheel blank1(x) The first approximation of (2) is made to be 0 to obtain the equivalent section moment of inertia I of the split wheel blank2。
The equivalent stiffness of the split wheel blank is:
moment of inertia I of equivalent uniform-section wheel blank in actual calculation2For constant values to be solved, I1The cross section of the split wheel blank changes along with the change of different positions of the split wheel blank. As shown in fig. 2, the analysis is performed by taking the example of machining one tooth slot, and the size parameters of the tooth slots are taken according to the middle point of the tooth length of the equivalent gear. The unprocessed part section inertia moment of the left and right side wheel blanks of the tooth socket is I0The section inertia moment of the wheel blank on the left side surface of the tooth socket is I11Section moment of inertia I of tooth bottom surface12The section moment of inertia of the right side face of the tooth socket is I13(ii) a The horizontal distance from the left end of the split wheel blank to the top of the left tooth surface of the tooth socket is L1The horizontal distance from the top of the left side surface of the tooth socket to the bottom of the tooth socket is L2The level from the bottom of the left side surface of the tooth socket to the bottom of the right side surface of the tooth socketA distance L3The horizontal distance from the bottom of the right side surface of the tooth groove to the unprocessed part of the wheel blank is L4Then, there are:
in the formula (4), the reaction mixture is,
in actual calculation, one tooth groove is processed for analysis, a plurality of tooth grooves are similar, and the size parameter of the tooth groove is taken according to the middle point of the tooth length of the equivalent gear. According to the geometric parameters of the corresponding equivalent wheel blank when each tooth groove of the split wheel blank is processed, the equivalent section moment of inertia I of the split wheel blank at the moment when the tooth groove is finished can be calculated2And then calculating the equivalent stiffness K of the split wheel blank at the moment according to the formula (3).
And after the equivalent stiffness is calculated, respectively calculating the deformation of the wheel blank in the process of machining each tooth socket by using the equivalent stiffness and a moment area method.
The gear cutting simulation result of the split wheel blank shows that the gear cutting processing of the split wheel blank mainly generates bending deformation in a processing area, and the final deformation of the wheel blank in the processing process is a result of continuous superposition on the basis of the previous deformation. The sequence of the gear cutting has little influence on the deformation. And (3) obtaining the deformation of the split wheel blank when the tooth grooves at different positions are independently machined, and then superposing the deformations to obtain the integral deformation condition.
When the deformation of the split wheel blank relates to the superposition effect and the bidirectional stress, the calculation and the difficulty are directly solved by using an analytical method, and the stress change along the length direction of the wheel blank in the wheel blank machining process is the largest as seen from a finite element analysis result. Therefore, a method for generating and calculating the additional moment in the length direction of the wheel blank in the gear cutting machining process and the deformation condition of the wheel blank are researched by taking a single tooth groove which is used for removing the middle position of the split wheel blank as an analysis unit. The analytical calculation of the overall deformation of the entire section will be obtained by the accumulation of the deformations of the plurality of analytical units.
Starting from the machining of a single tooth groove in the middle of the split wheel blank, the length direction of the split wheel blank is taken as the direction of the x axis, and after the tooth groove in the middle of the wheel blank is cut, the section of the single-tooth grooved wheel blank is approximately U-shaped, as shown in fig. 3. Wherein x1The distance from the left end of the wheel blank to the left side surface of the tooth socket, L is the length of the split wheel blank, x2Is the width, x, of the bottom of the tooth space3Is the width of the top of the gullet, z1The gear cutting depth of the wheel blank, h the thickness of the divided wheel blank, and the distance between the neutral axis and the x axis of the section of the gear blank after gear cutting is zc. After the tooth grooves in the middle positions of the wheel blanks are cut off, residual stress contained in the material of the tooth groove parts is removed, and the original supporting stress sigma on the two side surfaces of the tooth grooves does not exist. In this case, a stress of- σ applied to the side walls of the gullets may achieve a force-equivalent effect. The structure of the split wheel blank determines that the main deformation is deformation in the x-axis direction, and that deformation in the y-axis direction (width direction of the wheel blank) is temporarily disregarded here.
According to the additional stress analysis, the equivalent effect in the tooth cutting process is analyzed by using a torque-area methodWheel blankThe bending moment between the left and right ends of the deformation is shown in FIG. 4. Taking any two sections m with infinite small distance on an equivalent wheel blank1、m2The distance between the two sections is ds, the two sections being bent by an additional momentThe angle of intersection of the perpendicular lines of the sections is d theta, and d theta is ds/rho, wherein rho is the curvature radius of the wheel blank. According to the mechanics of materials, the formula of the equivalent wheel blank bending is as follows:
in the formula, dx is the section m of the wheel blank after bending deformation1、m2Distance in the horizontal direction. When ds is very small, dx ≈ ds.
In FIG. 4, line segment m1ρ1Is a deformed section m of a wheel blank1Tangent line of (b), line segment m2ρ2Is a cross section m2The tangent line is the angle d theta, and the numerical value of the angle d theta obtained according to the formula (5) is the ratio of the bending moment diagram area Mdx to the bending rigidity EI. And integrating the wheel blank along the length direction to obtain the total included angle theta of the bending deflection rotation of the whole wheel blank. The equivalent wheel blank section m can be obtained by the geometric relation1To section m2The deflection between is:
in order to obtain the total deflection of the whole wheel blank, the equation (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 machining of the single-tooth-groove split wheel blank and various size parameters of the wheel blank, and according to an additional moment calculation principle, obtaining the additional moment applied to the machining of the wheel blank as follows:
wherein 2.25 is a fixed proportional relation between the tooth socket height and the modulus m obtained according to national standards.
Combining the formula (3) and the formula (7), 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 an x axis, an integral interval [ A, B ] is from one side of the top of the tooth socket to the other side, L is the length of the split wheel blank, and M is the additional moment borne in the wheel blank machining.
According to the equivalent stiffness calculation method of the split wheel blank, the equivalent stiffness of the split wheel blank can be obtained when the machining of tooth grooves at different positions is finished. The machining sequence of the tooth grooves can be set as that the tooth grooves at the middle positions of the split wheel blanks are machined firstly, then the tooth grooves at one side of the tooth grooves at the middle positions are machined in sequence, and finally the tooth grooves at the other side are machined in sequence. Set as K according to the processing sequence11、K12、K13、K14、K15And the like. And substituting the wheel blank rigidity into a wheel blank deformation formula (9), and adjusting an integral interval to obtain the deformation of the split wheel blank when a single tooth socket at different positions is machined.
The deformation of a single tooth socket at the middle position of the independently processed wheel blank is as follows:
in order to verify the accuracy of deformation calculation, materials in the tooth grooves of the wheel blank are cut off layer by layer, and the thickness of each cut is set to be 9 mm. Based on the set geometric dimension and material parameters of the wheel blank, the equivalent stiffness in the wheel blank machining process is solved according to an equivalent stiffness meter algorithm, and the calculation result is shown in the following table.
| Removing |
0 | 9 | 18 | 27 | 36 | 45 |
| Rigidity/105Nm | 8.998 | 8.701 | 8.471 | 8.243 | 8.021 | 7.808 |
As can be seen from the above table, as the gear cutting process proceeds, the rigidity of the split wheel blank gradually decreases, and the rate of decrease in rigidity accounts for about 13.2% of the rigidity before the wheel blank process. Research shows that in the whole processing process, the removal ratio of the wheel blank material is 4.6%, the reduction ratio of the rigidity is 13.2%, and the reduction speed of the volume of the wheel blank material is smaller than that of the rigidity of the wheel blank.
In finite element software ABAQUS, the material which is the same as the material calculated theoretically is selected, the wheel blank size parameters are the same, initial internal stress is applied, then the removal of the material in the tooth socket is simulated, the thickness of the cut tooth socket is set to be 9mm each time, and after the simulation is finished, a deformation cloud picture of each analysis step of the split wheel blank is output and is shown in figure 5.
The machining deformation was calculated by MATLAB, and a graph of the deformation amount of the wheel blank as a function of the removal thickness was drawn, and the result is shown in fig. 6. As can be seen from fig. 6, the calculation method is substantially consistent with the deformation result obtained by finite element analysis in the tooth cutting process of a single tooth socket.
Based on the wheel blank after the 1 st tooth groove is machined, the 2 nd tooth groove is continuously analyzed, the tooth groove is analyzed on the right side of the first tooth groove, and the deformation of the wheel blank after the second tooth groove is machined is as follows:
And (3) continuing to process the 3 rd tooth groove, taking the position on the right side of the 2 nd tooth groove as an example for analysis, and processing the deformation of the wheel blank after the third tooth groove is processed as follows:
then, the other half of the remaining tooth slots are machined, the tooth slot adjacent to the left side of the middle tooth slot is machined first, and the deformation of the wheel blank after the fourth tooth slot is machined is as follows:
and continuously analyzing the 2 nd tooth socket on the left half side, and processing the deformation of the wheel blank after a fifth tooth socket is processed into:
if there is a gullet at the left end, the same principle as the right part is used for the analysis and calculation.
It should be noted that, since the split plane of the split wheel blank is located in the middle of the tooth grooves, half of the tooth grooves are formed at both the left and right ends of the split wheel blank. Finite element analysis shows that the influence of the processing of the half tooth grooves at the two ends on the bending deformation of the whole wheel blank is very little and can be ignored, so that the calculation method is not embodied.
(3) Calculating the total deformation by superposing the deformations
And obtaining the wheel blank deformation when the tooth sockets at different positions are processed independently, and then superposing the deformation generated in the process of processing each tooth socket to obtain the total deformation generated by splitting the wheel blank in the whole processing process. The deformation of the wheel blank during machining of the 1 st tooth slot is shown in FIG. 7. The included angles between the bottom surfaces of the unprocessed areas on the left side and the right side of the deformed wheel blank and the horizontal line are theta respectively11、θ12The local deformation S can be calculated according to the previous theoretical calculation1Then, sin θ can be obtained11＝sinθ12When the angle of symmetry is 0.00035, the angle of symmetry is 0.02 °.
Earlier studies show that the sequence of cutting teeth has little influence on deformation. Here, the amount of local deformation of the blank when the tooth is continuously cut to the right side of the blank and the tooth groove is separately machined is set to S2The deformation causes the deflection angle theta of the right and left ends of the bottom surface of the wheel blank21、θ22. As shown in FIG. 8, a coordinate system S is established at the middle position of the split wheel blank1(o1-x1,z1) Coordinate axis z1Is a symmetry axis of the tooth socket at the middle position. Establishing a coordinate system at the position of the symmetrical axis of the second tooth socket, and rotating and deflecting the coordinate system anticlockwise by theta11The coordinate system S in FIG. 8 is obtained2(o2-x2,z2). After the first two tooth grooves are machined, the included angle between the horizontal line and the corresponding bottom surface of the unmachined area at the right end of the split wheel blank is theta11+θ21The deflection angle of the bottom surface of the left unprocessed area of the wheel blank is theta12+θ22The amount of deformation after the superposition is S'2＝S1+S2/cosθ21。
After the right half of the wheel blank is machined, the deformation of the split wheel blank is shown in FIG. 9. At this time, the angle between the straight line portion of the left end bottom surface of the wheel blank and the horizontal line is theta'32＝θ12+θ22+θ32And the included angle between the tangent line of the bottom surface of the right end of the wheel blank and the horizontal line is theta'31＝θ11+θ21+θ31And the distortion after superposition is S'3＝S'2+S3/cosθ31。
The deformation of the wheel blank after the fourth tooth slot is machined is shown in FIG. 10. An included angle between a straight line part of the bottom surface of the right end of the superposed rear wheel blank and the horizontal line is theta'41＝θ′31+θ41The included angle between the tangent line of the bottom surface at the left end of the wheel blank and the horizontal line is theta'42＝θ′32+θ42And the distortion after superposition is S'4＝S′3+S4/cosθ42。
Wheel blankAfter the machining is completed, the wheel blank is deformed as shown in fig. 11. Neglecting the deformation caused by machining the leftmost half of tooth socket, the included angles between the tangent lines of the bottom surfaces of the left and right ends and the horizontal line of the wheel blank after the deformation superposition are respectively theta'52＝θ′42+θ52、θ′52＝θ′42+θ52And the distortion after superposition is S'5＝S'4+S5/cosθ52。
The deflection angles at the above-mentioned working deformation and the individual working were calculated from the set dimensions of the wheel blank and the material parameters, and the calculation results are shown in the following table.
According to the above table, after the deformation superposition, the included angle between the right end tangent line of the bottom surface of the wheel blank and the horizontal line is theta'510.052 DEG, and the included angle of the left end is theta'520.052 DEG, and the superimposed distortion is S'5＝0.1301mm。
The simulation result of the above-described example is shown in fig. 12, and it can be seen that the average deformation of the maximum deformation region of the wheel blank is 0.1304mm, and the calculated bending deformation amount ratio is substantially the same as the simulation result by comparing the calculated result with the simulation result.
(4) And comparing the obtained total deformation with the total deformation allowed by engineering requirements, and if the obtained total deformation exceeds the allowed total deformation, performing the following step (5), otherwise, performing the step (7).
(5) And the deformation caused by the change of the rigidity and the internal stress is closely related to the specification size, the cross section design, the gear cutting process design and the like of the split body obtained after the whole wheel blank is cut. Therefore, when the obtained total deformation does not meet the engineering requirements, the final machining deformation can be influenced by adjusting parameters such as the size of the section of the split wheel blank and the size of the specification when the wheel blank is split.
For example, when the obtained total deformation amount does not meet the engineering requirements, design parameters of the split wheel blanks are adjusted, and the design length of each split wheel blank is shortened, so that the number of tooth grooves included in each split wheel blank is reduced, the modulus of the gear is reduced, or the design thickness of each split wheel blank is increased.
(6) And (5) repeating the steps (2) to (5) by using the adjusted design parameters of the split wheel blank until the total deformation obtained by calculation meets the engineering requirements.
(7) And taking the design parameters of the split wheel blank corresponding to the obtained total deformation of the split wheel blank as the design parameters for manufacturing the split wheel blank. According to the split wheel blank manufactured according to the design parameters, after all tooth grooves are machined, the machining deformation can meet engineering requirements, and then the gear meeting the requirements is 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 section shape of the wheel blank along the length direction is changed, and the section inertia moment I of the equivalent beam with the equal section is recalculated2Equivalent stiffness, etc. And (5) if the steps (2) to (5) are repeated until the total deformation amount does not meet the design requirement when the design length of the split wheel blank is shortened to the allowable limit value, properly reducing the modulus m of the gear or increasing the design thickness of the split wheel blank according to the design requirement of the gear pair, and then repeating the steps (2) to (5) until the total deformation amount meets the requirement.
Claims (7)
1. A method for determining parameters of a cutting gear blank of a split straight bevel gear is characterized by comprising the following steps: the method comprises the following steps:
(1) setting initial design parameters of the split wheel blank, defining a rectangular wheel blank with an equivalent equal cross section with the split wheel blank as an equivalent wheel blank, and setting the rigidity of the equivalent wheel blank as the equivalent rigidity of the split wheel blank;
(2) respectively calculating the equivalent stiffness of the split wheel blanks when each tooth slot is processed and finished according to the parameters of the equivalent wheel blanks when each tooth slot is processed and finished, and respectively calculating the deformation generated by the wheel blanks in the process of processing each tooth slot by using the equivalent stiffness and utilizing a moment area method;
(3) superposing the deformation generated in the process of machining each tooth socket to obtain the total deformation generated by splitting the wheel blank in the whole machining process;
(4) comparing the obtained total deformation with the allowable total deformation, and 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, and shortening the design length of the split wheel blanks to reduce the number of tooth grooves contained in each split wheel blank, or reduce the modulus of the 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 blank corresponding to the obtained total deformation of the split wheel blank as the design parameters for manufacturing the split wheel blank.
2. The method of determining cutting gear blank parameters for a divided straight bevel gear according to claim 1, wherein: in the step (2), the tooth grooves are processed in sequence, namely, the tooth grooves in the middle positions of the split wheel blanks are processed firstly, then the tooth grooves on one side of the tooth grooves in the middle positions are processed in sequence, and finally the tooth grooves on the other side are processed in sequence.
3. The method of determining cutting gear blank parameters for a divided straight bevel gear according to claim 2, wherein: and the half tooth grooves at the two ends of the split wheel blank do not calculate the machining deformation.
4. The method of determining cutting gear blank parameters for a divided straight bevel gear according to claim 1, wherein: in the step (5), when adjusting design parameters of the split wheel blank, the design length of the split wheel blank is shortened, and if the steps (2) to (5) are repeated until the total deformation amount does not meet the design requirement when the design length of the split wheel blank is shortened to an allowable limit value, the modulus of the gear is reduced, or the design thickness of the split wheel blank is increased.
5. The method of determining parameters of a gear blank for cutting machining of a straight bevel gear of a divided type as set forth in any one of claims 1 to 4, wherein: the equivalent rigidity calculation formula of the split wheel blank is
Wherein E is the elastic modulus, L is the length of the split wheel blank, I2Is equivalent to the section moment of inertia of the wheel blank.
6. The method of determining parameters of a gear blank for cutting machining of a divided straight bevel gear according to any one of claims 5, wherein: the calculation formula of the deformation generated by the wheel blank in the process of machining each tooth groove is as follows:
wherein: integration interval [ A, B ] with the length direction of the split wheel blank as the direction of the x axis]From one side of the top of the tooth socket to the other side, L is the length of the split wheel blank, and M is the additional moment borne in the wheel blank machining.
7. The method of determining parameters of a gear blank for cutting machining of a divided straight bevel gear according to any one of claims 6, wherein:
the formula for calculating the additional moment applied to the wheel blank in the wheel blank machining process is as follows:
wherein z is1The depth of the teeth of the split wheel blank is h, and the thickness of the split wheel blank is h，zcIs the distance between the neutral axis and the x axis of the section of the gear cutting back wheel blank, x1Is the distance, x, from the left end of the wheel blank to the left side surface of the tooth socket2Is the width, x, of the bottom of the tooth space3Width of the top of the tooth slot, m is gear module, σil(z) is the additional internal stress of the present 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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