Tooth surface shape design system

Abstract

To provide a tooth surface shape design system for improving the design accuracy of a gear to satisfy a desired performance.SOLUTION: A tooth surface shape design system 1 for designing a tooth surface shape of a gear includes: a misalignment calculation unit 20 for calculating misalignment corresponding to the misalignment of a center axis in a gear pair caused by rigidity and dimensional tolerances in the gear pair including at least the gear, a shaft connected to the gear pair, and a bearing supporting the shaft, and torque generated in the gear pair, thereby calculating a variation range of the misalignment; a performance calculation unit 30 for calculating meshing performance of the gear pair from gear dimensions of the gear pair, the misalignment, and calculation conditions of a tooth surface correction amount in the gear; and an optimum tooth surface correction amount derivation unit 40 for deriving an optimum solution of the tooth surface correction amount by an optimization method by setting the tooth surface correction amount as an explanatory variable and setting at least one of the calculated results of the performance calculation unit 30 as an objective function.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present invention relates to a tooth surface shape design system.

Background Art

[0002] As a method for designing the tooth surface shape of a machine gear, Patent Document 1 discloses a configuration for efficiently evaluating a complex tooth surface shape with a small amount of calculation by evaluating the tooth surface shape defined using a plurality of principal component shape data obtained by principal component analysis of a tooth surface shape sample data group.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] However, machine gears need to satisfy requirements for multiple performances such as quietness, strength, and efficiency, and the performance of machine gears is affected by slight differences in tooth surface shape. Therefore, after designers set the basic specifications of the gears, they set the amount of tooth surface shape trimming in units of μm. And, in order to accurately set the trimming amount, it is necessary to consider that misalignment occurs due to shaft displacement caused by the rigidity and tolerance of bearings and shafts provided on the gears, and that the misalignment changes due to the torque applied to the gear pair. However, since these are not considered in the configuration disclosed in Patent Document 1, there is room for improvement in improving the design accuracy of gears.

[0005] The present invention has been made in view of such problems, and aims to provide a tooth surface shape design system capable of improving the design accuracy of gears that satisfy desired performances.

Means for Solving the Problems

[0006] One aspect of the present invention is a tooth surface shape design system for designing the tooth surface shape of a gear, calculating misalignment corresponding to the deviation of the central axis of the gear pair caused by at least the gear pair including the gear, the rigidity and dimensional tolerance of the shaft connected to the gear pair, the rigidity, dimensional tolerance and internal clearance of the bearing supporting the shaft, and the torque generated in the gear pair, and calculating the variation range of the misalignment; a misalignment calculation unit, a performance calculation unit that calculates the meshing performance of the gear pair from the gear specifications of the gear pair, the misalignment, and the calculation conditions of the tooth surface dressing amount in the gear; an optimal tooth surface dressing amount derivation unit that sets the tooth surface dressing amount as an explanatory variable and sets at least one of the calculation results of the performance calculation unit as an objective function, and derives an optimal solution of the tooth surface dressing amount by an optimization method; It is in a tooth surface shape design system including

Advantages of the Invention

[0007] According to the above aspect, after calculating the variation range of misalignment in consideration of the rigidity and dimensional tolerance in the gear pair, shaft and bearing, and the torque generated in the gear pair, the meshing performance of the gear pair is calculated in consideration of the misalignment. Then, the tooth surface dressing amount is set as an explanatory variable, the meshing performance is set as an objective function, and an optimal solution of the tooth surface dressing amount is derived by an optimization method. As a result, since the misalignment that changes due to torque is considered in the tooth surface dressing amount, the design accuracy of the tooth surface shape according to the performance of the gear can be improved.

[0008] As described above, according to the above aspect, it is possible to provide a tooth surface shape design system capable of improving the design accuracy of a gear that satisfies desired performance.

Brief Description of the Drawings

[0009]

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Mode for Carrying Out the Invention

[0010] (Embodiment 1) 1. Tooth Surface Shape Design System 1 of Embodiment 1 The tooth surface shape design system 1 of Embodiment 1 will be described with reference to Fig. 1. The tooth surface shape design system 1 is configured by a computer and is composed of, for example, an arithmetic processing unit, a storage device, an interface, etc.

[0011] As shown in FIG. 1, the tooth surface shape design system 1 includes a gear device model 10, a misalignment calculation unit 20, a performance calculation unit 30, an optimal tooth surface finishing amount derivation unit 40, an optimal solution display unit 50, an input unit 60, and a tooth surface shape determination unit 70.

[0012] 1-1. Gear device model 10 The gear device model 10 shows a virtual gear device as shown in FIG. 2. As shown in FIG. 2, the gear device model 10 includes a first gear 111, a second gear 112, a first shaft 121, a second shaft 122, a first bearing 131, a second bearing 132, a third bearing 133, and a fourth bearing 134, and further includes a case (not shown). The first gear 111 and the second gear 112 form a gear pair 11 that meshes with each other. In the first embodiment, the first gear 111 is a driving gear and the second gear 112 is a driven gear. In the first embodiment, the first gear 111 and the second gear 112 are helical gears, but the present invention is not limited thereto, and spur gears may be used.

[0013] The first shaft 121 is connected to the first gear 111 and constitutes a first rotation axis C1. The second shaft 122 is connected to the second gear 112 and constitutes a second rotation axis C2. The first bearing 131 and the second bearing 132 rotatably support the first shaft 121. The third bearing 133 and the fourth bearing 134 rotatably support the second shaft 122. In an ideal state, the first rotation axis C1 and the second rotation axis C2 are parallel to each other. The case (not shown) houses the first gear 111, the second gear 112, the first shaft 121, the second shaft 122, the first bearing 131, the second bearing 132, the third bearing 133, and the fourth bearing 134.

[0014] The design target of the tooth surface shape in the tooth surface shape design system 1 may be either the first gear 111 or the second gear 112, or both may be the design targets. However, in the first embodiment, the tooth surface shape of the first gear 111 is the design target.

[0015] 1-2. Misalignment calculation unit 20 The misalignment calculation unit 20 shown in FIG. 1 calculates misalignment, which is the deviation (misalignment of the central axes) between the first rotation axis C1 and the second rotation axis C2 in the gear device model 10. The misalignment is caused by, for example, the interference error shown in FIG. 3(A) or the parallelism error shown in FIG. 3(B). The interference error is the inclination of the first rotation axis C1 with respect to the second rotation axis C2 when viewed from the overlapping direction of the first shaft 121 and the second rotation axis C2, as shown in FIG. 3(A). The parallelism error is the inclination of the first rotation axis C1 with respect to the second rotation axis C2 when viewed from the arrangement direction of the first shaft 121 and the second rotation axis C2, as shown in FIG. 3(B).

[0016] The misalignment calculation unit 20 calculates the misalignment at each torque when the torque is changed to a desired value based on at least the rigidity and dimensional tolerances of the gear pair 11, shafts 121 and 122 in the gear device model 10, the rigidity, dimensional tolerances and internal clearances of the bearings 131, 132, 133 and 134, and the deformation amounts of the shafts 121 and 122 due to the torque generated in the gear pair 11. In the first embodiment 1, further, considering the rigidity, dimensional tolerances, geometric tolerances and bearing internal clearances of a case (not shown), the misalignment at each torque when the torque is changed to a desired value is calculated. The calculation of the misalignment can be performed, for example, as shown in FIG. 4(a), by adopting a plurality of values within the range from the minimum value to the maximum value with the value of -3σ in the normal distribution as the minimum value and the value of +3σ as the maximum value for the dimensional tolerance (or geometric tolerance), and performing the calculation of the variation range of the misalignment for each torque. The calculation result will exhibit a variation range corresponding to the degrees of the interference error and the parallelism error, which are the elements of the misalignment, as shown in FIG. 4(b). The variation range includes the nominal point where all the dimensional tolerances and geometric tolerances are the mode values and a plurality of variation points other than the nominal point.

[0017] 1-3. Performance calculation unit 30 The performance calculation unit 30 shown in FIG. 1 calculates the meshing performance of the gear pair 11 based on the gear specifications, misalignment, and tooth surface finishing amount of the gear pair 11. The meshing performance can be, for example, the primary amplitude of the meshing transmission error, the maximum tooth surface pressure, the maximum tooth root stress, the maximum trochoid interference amount, the meshing efficiency, etc. in the gear pair 11. The primary amplitude of the meshing transmission error (also referred to as "T.E. primary" in this specification) is the primary amplitude in the periodic variation of the relative rotational delay of the driven gear with respect to the driving gear, and as shown in FIG. 5, it changes according to the magnitude of the torque and exhibits different change patterns depending on the value of the misalignment (e.g., the nominal point and the variation point).

[0018] In the above meshing performance, the maximum tooth surface pressure is the maximum value of the pressure generated on the tooth surface in the gear pair 11. The maximum tooth root stress is the maximum value of the pressure generated at the tooth root in the gear pair 11. Note that the maximum tooth surface pressure and the maximum tooth root stress are calculated for each of the first gear 111 and the second gear 112.

[0019] As shown by the arrow P in FIG. 6, the maximum trochoid interference amount is the maximum value of the penetration amount in the portion where the tooth tip locus 112a of the second gear 112, which is the driven gear in the driving state, penetrates into the tooth root of the first gear 111, which is the driving gear. Although geometrically there is no interference in the meshing of the gears, when a load acts on a certain tooth, the rotation of the driving gear advances slightly due to the elastic deformation of the tooth. When the tooth adjacent to the tooth on which the load acts is about to mesh, due to the advancement of the rotation caused by the above elastic deformation, it will deviate from the normal meshing position. The relative locus of the tooth tip at this time draws the trochoid curve shown by the dashed line as the tooth tip locus 112a in FIG. 6 and interferes with the tooth root of the other gear. The meshing efficiency is the ratio of the torque output from the second gear 112, which is the driven gear, to the torque input to the first gear 111, which is the driving gear.

[0020] The calculation of the meshing performance in the performance calculation unit 30 is performed based on the tooth contact state of the gear pair 11. The calculation method of the tooth contact state of the gear pair 11 is not limited. For example, by the finite element method (FEM), it can be performed by specifying the transition of the contact state of both gears 111 and 112 including the deformation when both gears 111 and 112 contact each other in the gear pair 11. Also, a gear meshing analysis method represented by "Journal of the Japan Society of Mechanical Engineers, Vol. 43, No. 371, 1977, Research on Load Transmission Characteristics of Cylindrical Gears with Errors: First Report, Fundamental Considerations, Aizo Kubo, Kiyohiko Umezawa" may be used.

[0021] 1-4. Optimal Tooth Surface Finishing Amount Derivation Unit 40 The optimal tooth surface finishing amount derivation unit 40 shown in FIG. 1 sets the tooth surface finishing amount of the gear pair 11 as an explanatory variable, and sets at least one of the calculation results of the performance calculation unit 30 as an objective function, and derives the optimal solution of the tooth surface finishing amount by an optimization method. In the first embodiment, the optimal solution of the tooth surface finishing amount of the first gear 111 among the gear pair 11 is derived. The optimization method is not limited, and known optimization methods such as genetic algorithms, annealing methods, particle optimization, and response surface methods based on experimental design can be adopted.

[0022] Tooth surface finishing can be performed by combining known tooth surface finishing elements on the tooth surface 15 before finishing shown in FIG. 7(a). As elements of tooth surface finishing, for example, the tooth flanks direction inclination (twist angle finishing) shown in FIG. 7(b), the pressure angle finishing shown in FIG. 7(c), the tooth profile crowning shown in FIG. 7(d), the tooth flanks crowning shown in FIG. 7(e), the bias finishing shown in FIG. 7(f), and the end relief shown in FIG. 7(g) can be combined with one or more of them. In FIGS. 7(b) to (g), the tooth surface 16 shows the tooth surface shape after being finished by the corresponding tooth surface finishing element. Also, although not shown, as elements of tooth surface finishing, in addition to these, tooth tip finishing and other arbitrary shape elements can be included. The tooth surface finishing amount of each tooth surface finishing element can be restricted in advance within a predetermined range based on processing conditions and gear specifications.

[0023] In deriving the optimal solution of the tooth surface finishing amount by the optimal tooth surface finishing amount derivation unit 40, at least one, preferably two or more, of the calculation results in the performance calculation unit 30 can be adopted. For example, the average value of the total torque nominal points, the average value of the maximum points of the total torque variation, the worst value of the specified torque variation points, etc. in the calculation results of the performance calculation unit 30 can be set as the objective function. In the first embodiment, at least two of the calculation results of the performance calculation unit 30 are set as the objective function.

[0024] The average value of the total torque nominal points defines the most frequent value in the variation range of misalignment as the nominal misalignment, and is the average value of the calculation results at the total torque in the nominal misalignment. Also, although the variation points of misalignment have different values depending on the torque, the combination of the input tolerances is the same even when the torque changes. Among the combinations of the tolerances, the point where the average value of the total torque of the meshing performance is the worst is defined as the maximum variation point, and the above average value is defined as the average value of the maximum variation points. Further, the worst value of the specified torque variation point is the worst value at the specified torque of the calculation results of the variation points other than the nominal point in the variation range of misalignment. Note that the specified torque can be set appropriately by the user.

[0025] The optimal tooth surface finishing amount derivation unit 40 can set at least one of the calculation results of the performance calculation unit 30 other than those set as the objective function as a constraint condition. For example, as the constraint condition, the primary amplitude of the meshing transmission error, the maximum tooth surface pressure, the maximum tooth root stress, the maximum trochoid interference amount, or the meshing efficiency can be limited to a predetermined range. Note that it is not always necessary to set the constraint condition, and there may be cases where the constraint condition is not set.

[0026] The optimal tooth surface finishing amount derivation unit 40 uses a predetermined optimization method, with the tooth surface finishing amount as an explanatory variable, and performs iterative calculations so that the objective function set as described above is maximized or minimized (under the constraint conditions if constraint conditions are set), thereby deriving the optimal solution of the tooth surface finishing amount. When a plurality of objective functions are set and are in a trade-off relationship with each other, since multi-objective optimization is required for the tooth surface finishing amount, the optimal solution of the tooth surface finishing amount can be derived as a Pareto solution. Note that the derivation of the optimal solution in the optimal tooth surface finishing amount derivation unit 40 may also be performed in multiple stages. That is, in the first stage, after deriving the first Pareto solution as the first optimal solution using a specific tooth surface finishing element as the first explanatory variable, in the second stage, after setting the value of the first explanatory variable in the first Pareto solution as a constant, other tooth surface finishing elements may be used as the second explanatory variable to derive the second Pareto solution as the second optimal solution.

[0027] 1-5. Optimal solution display unit 50 The optimal solution display unit 50 shown in FIG. 1 displays the optimal solution derived by the optimal tooth surface finishing amount derivation unit 40. The display mode in the optimal solution display unit 50 is not limited and can be displayed by a known method. For example, as shown in FIG. 8, the optimal solution display unit 50 can show an example of displaying the Pareto solution as the optimal solution when the nominal point of the meshing transmission error is adopted as the first objective function and the worst point of the meshing transmission error variation is adopted as the second objective function in the calculation of the optimal solution in the optimal tooth surface finishing amount derivation unit 40. Note that the nominal point of the meshing transmission error adopted as the first objective function reflects the basic NV performance related to noise and vibration in the gear pair 11, and the worst point of the meshing transmission error variation adopted as the second objective function reflects the robust performance of NV in the gear pair 11.

[0028] 1-6. Input unit 60 and tooth surface shape determination unit 70 The input unit 60 shown in FIG. 1 inputs the optimal solution selected by the user from the Pareto solutions displayed on the optimal solution display unit 50. The selection of the optimal solution can be appropriately determined by the user. In the tooth surface shape determination unit 70, the tooth surface finishing amount is determined based on the tooth surface finishing elements corresponding to the selection result of the optimal solution input to the input unit 60, and the tooth surface shape is determined.

[0029] 2. Flow of Tooth Surface Shape Design in Embodiment 1 Next, the tooth surface shape design flow using the tooth surface shape design system 1 in this Embodiment 1 will be described with reference to FIG. 9. In this tooth surface shape design flow, first, in step S1 shown in FIG. 9, the stiffness, dimensional tolerances, geometric tolerances, and bearing clearances of the gear pair 11, shafts 121 and 122, bearings 131, 132, 133, 134, and the case (not shown) in the gear device model 10 are set.

[0030] In step S2 shown in FIG. 9, the misalignment calculation unit 20 derives tolerance conditions for calculating misalignment. Then, in step S3, the misalignment calculation unit 20 calculates the shaft deformation amount at a desired torque based on the above tolerance conditions.

[0031] Thereafter, in step S4 shown in FIG. 9, the misalignment calculation unit 20 calculates the misalignment of the gear pair 11 from the shaft deformation amount. The calculation result of the misalignment has a variation range from a combination of the interference error and the parallelism error, which are the elements of the misalignment, as shown in, for example, FIG. 4(b). The variation range includes the nominal point, which is the most frequent value, and a plurality of other variation points.

[0032] Next, in step S5 shown in FIG. 9, the performance calculation unit 30 sets calculation conditions for calculating the meshing performance. The calculation conditions set the gear specifications and misalignment of the gear pair 11.

[0033] Next, in step S6 of FIG. 9, the optimal tooth surface finishing amount derivation unit 40 calculates candidate values for the tooth surface finishing amount. The calculation of the tooth surface finishing amount uses, as explanatory variables, the finishing amounts of the tooth surface finishing elements in the gear pair 11 shown in FIGS. 7(b) to 7(e) and FIG. 7(g), namely, the inclination finishing in the tooth trace direction, the pressure angle finishing, the tooth profile crowning, the tooth trace crowning, and the end relief. The first objective function is set to be the average value of the meshing transmission error primary amplitude (nominal point T.E. primary) at the nominal point of the misalignment of the total torque, and is set to minimize it. The second objective function is set to be the maximum average value of the variation point T.E. primary at the total torque (average value of the maximum variation point T.E. primary), and is set to minimize it. Further, as constraint conditions, it is set that the worst value of the T.E. primary of the specified torque is below a predetermined value, the worst value of the maximum tooth surface pressure of the specified torque is below a predetermined value, and the worst value of the maximum trochoid interference amount of the specified torque is below a predetermined value. Note that the initial candidate value of the tooth surface finishing amount can be arbitrarily determined within the range of the explanatory variables set in the optimal tooth surface finishing amount derivation unit 40.

[0034] Then, in step S7 shown in FIG. 9, the performance calculation unit 30 calculates the meshing performance based on the calculation conditions. In the meshing performance calculation in the first embodiment, the initial candidate values of the finishing amounts of the tooth surface finishing elements are input as input variables, and the meshing transmission error primary amplitude (nominal point T.E. primary) at the nominal point of the misalignment, the meshing transmission error primary amplitude (variation point T.E. primary) at the variation point of the misalignment, the maximum tooth surface pressure at the variation point, and the maximum trochoid interference amount at the variation point are respectively evaluated for each torque component. And as the meshing performance, the average value of the nominal point T.E. primary at the total torque, the maximum average value of the variation point T.E. primary at the total torque (average value of the maximum variation point T.E. primary), the worst value of the T.E. primary at the specified torque, the worst value of the maximum tooth surface pressure at the specified torque, and the worst value of the maximum trochoid interference amount at the specified torque are calculated. Note that the specified torque is set appropriately by the user.

[0035] As described above, the variation points of misalignment have different values depending on the torque, but the combination of tolerances to be input is the same even when the torque changes. Among the combinations of the tolerances, the point that becomes the worst average value of the first-order T.E. at all torques is defined as the maximum variation point, and the average value is defined as the average value of the worst first-order T.E.

[0036] Then, in step S8 of FIG. 9, the optimal flank modification amount derivation unit 40 determines whether or not the completion condition of the optimization calculation of the flank modification amount is satisfied. The completion condition can be set, for example, the number of calculations or the change rate of the Pareto solution. In step S8, if the completion condition of the optimization calculation of the flank modification amount is not satisfied, the process proceeds to No in step S8, and steps S6 and subsequent steps are performed again. Therefore, steps S6 and S7 are repeatedly performed while updating the candidate values of the modification amounts of the flank modification elements until the optimization of the flank modification amount is completed. On the other hand, in step S8 of FIG. 9, if the completion condition of the optimization calculation of the flank modification amount is satisfied, the process proceeds to Yes in step S8, and in step S9, the optimal solution of the flank modification amount shown in FIG. 8 is output to the optimal solution display unit 50.

[0037] Thereafter, in step S10 shown in FIG. 9, the user selects the flank modification amount that is the desired solution from the optimal solution output to the optimal solution display unit 50, and in step S11, the flank shape determination unit 70 determines the flank shape corresponding to the selected flank modification amount, and ends the flow. As a result, the NV performance and strength performance at important torques due to the constraint conditions are ensured, and the NV basic performance at the mating transmission error nominal point, which is the first objective function, and the NV robust performance at the mating transmission error variation worst point, which is the second objective function, are optimized so as to be compatible. The flank shape is designed.

[0038] 3. Operational effects of the flank shape design system 1 of Embodiment 1 According to the tooth surface shape design system 1 of the first embodiment, considering the rigidity, dimensional tolerances, geometric tolerances, bearing internal clearances in the gear pair 11, shafts 121, 122 and bearings 131, 132, 133, 134, and the torque generated in the gear pair 11, the variation range of misalignment is calculated. Then, considering the misalignment, the meshing performance of the gear pair 11 is calculated. And, the tooth surface finishing amount is set as an explanatory variable, and the meshing performance is set as an objective function, and the optimal solution of the tooth surface finishing amount is derived by an optimization method. Thereby, since the misalignment that varies depending on the torque is considered in the tooth surface finishing amount, the design accuracy of the tooth surface shape corresponding to the performance of the gear pair 11 can be improved.

[0039] Also, in the first embodiment, the misalignment calculation unit 20 further calculates the misalignment using the rigidity, dimensional tolerances, and geometric tolerances in the case where the bearings 131, 132, 133, 134 are mounted. Thereby, the calculation accuracy of the misalignment can be improved.

[0040] Also, in the first embodiment, the performance calculation unit 30 outputs at least one of the meshing transmission error, maximum tooth surface pressure, maximum tooth root stress, maximum trochoid interference amount, and meshing efficiency in the gear pair 11 as the meshing performance. Thereby, the design accuracy of the tooth surface shape can be improved.

[0041] Also, in the first embodiment, the tooth surface finishing of the gear 111 is performed by at least one of tooth flank direction inclination finishing (twist angle finishing), pressure angle finishing, tooth profile crowning, tooth flank crowning, bias finishing, end relief, and tooth tip finishing. Thereby, it becomes easy to finish the tooth surface of the gear 111 into a shape that exhibits a desired meshing performance.

[0042] Also, in the first embodiment, the optimal tooth surface finishing amount derivation unit 40 sets at least one of the calculation results of the performance calculation unit 30 as an objective function, and sets at least one of the calculation results other than the objective function as a constraint condition to derive the optimal solution of the tooth surface finishing amount. Thereby, the design accuracy of the tooth surface shape can be improved.

[0043] Also, in the first embodiment, at least two of the calculation results of the performance calculation unit 30 are set as the objective function. As a result, it becomes easy to design a tooth surface shape in which multi-objective optimization, which has been difficult in the past, is achieved.

[0044] Also, in the first embodiment, a tooth surface shape determination unit 70 is provided that determines the tooth surface shape by determining the tooth surface dressing amount based on the solution selected from the optimal solutions of the tooth surface dressing amount. As a result, for example, a user or the like can design a tooth surface shape with a desired tooth surface dressing amount.

[0045] As described above, according to the first embodiment, it is possible to provide a tooth surface shape design system 1 that improves the design accuracy of the gear pair 11 that satisfies the desired performance.

[0046] (Second Embodiment) 4. Tooth Surface Shape Design System 1 of the Second Embodiment In the tooth surface shape design system 1 of the second embodiment, as a configuration for deriving a performance calculation model described later, as shown in FIG. 10, a performance calculation model derivation unit 25 is provided. The performance calculation model derivation unit 25 uses the variation range of the misalignment calculated in the misalignment calculation unit 20 and the range of the tooth surface dressing amount set in the optimal tooth surface dressing amount derivation unit 40 as explanatory variables, and derives a performance calculation model having the meshing performance as the objective function. The performance calculation model can be derived by sampling so that the combinations of the explanatory variables are uniform within the variation range of the misalignment and the range of the tooth surface dressing amount, and repeatedly performing the calculation of the meshing performance in the performance calculation unit 30 according to the sampling for learning. In the second embodiment, the same components as those in the first embodiment are denoted by the same reference numerals and the description thereof is omitted.

[0047] In the tooth surface shape design system 1 of Embodiment 2, as shown in FIG. 11, as a configuration for executing the performance calculation model, a performance calculation model execution unit 26 is provided. The optimal tooth surface finishing amount derivation unit 40 derives the optimal solution of the tooth surface finishing amount by executing the performance calculation model derived in advance in the performance calculation model execution unit 26. As a result, by eliminating the repeated calculations of the performance calculation unit 30 in the optimization calculation, the time for deriving the optimal solution of the tooth surface finishing amount can be significantly reduced, and the total number of calculation times of the performance calculation unit 30 can also be significantly reduced. Therefore, the design of the tooth surface shape can be performed in a short time. Note that the same effects as those in Embodiment 1 are achieved in Embodiment 2 as well.

[0048] The present invention is not limited to the above-described Embodiments 1 and 2, and can be applied to various embodiments without departing from the gist thereof.

Explanation of Reference Numerals

[0049] 1 Tooth surface shape design system 10 Gear device model 11 Gear pair 20 Misalignment calculation unit 25 Performance calculation model derivation unit 26 Performance calculation model execution unit 30 Performance calculation unit 40 Optimal tooth surface finishing amount derivation unit 50 Optimal solution display unit 60 Input unit 70 Tooth surface shape determination unit 111 First gear 112 Second gear 121, 122 Shaft 131, 132, 133, 134 Bearing

Claims

1. A tooth surface shape design system for designing the tooth surface shape of a gear, comprising: a misalignment calculation unit that calculates misalignment corresponding to the deviation of the central axis of the gear pair due to at least the gear pair including the gear, the rigidity and dimensional tolerance of the shaft connected to the gear pair, the rigidity, dimensional tolerance and internal clearance of the bearing that supports the shaft, and the torque generated in the gear pair, and calculates the variation range of the misalignment; a performance calculation unit that calculates the meshing performance of the gear pair from the gear specifications of the gear pair, the misalignment, and the calculation conditions of the tooth surface finishing amount of the gear; an optimal tooth surface finishing amount derivation unit that sets the tooth surface finishing amount as an explanatory variable and sets at least one of the calculation results of the performance calculation unit as an objective function, and derives the optimal solution of the tooth surface finishing amount by an optimization method; A tooth surface shape design system including the above.

2. The tooth surface shape design system according to claim 1, wherein the misalignment calculation unit further calculates the misalignment using the rigidity, dimensional tolerance and geometric tolerance of the case for mounting the bearing.

3. The tooth surface shape design system according to claim 1 or 2, wherein the performance calculation unit calculates at least one of the meshing transmission error, maximum tooth surface pressure, maximum tooth root stress, maximum trochoid interference amount and meshing efficiency in the gear pair as the meshing performance.

4. The tooth surface shape design system according to claim 1 or 2, wherein the tooth surface finishing of the gear is performed by at least one of tooth trace direction inclination finishing, pressure angle finishing, tooth profile crowning, tooth trace crowning, bias finishing, end relief, and tooth tip finishing.

5. The tooth surface shape design system according to claim 1 or 2, wherein the optimal tooth surface finishing amount derivation unit sets at least one of the calculation results of the performance calculation unit as an objective function, sets at least one of the calculation results other than the objective function as a constraint condition, and derives the optimal solution of the tooth surface finishing amount.

6. The tooth surface shape design system according to claim 1 or 2, wherein at least two of the calculation results of the performance calculation unit are set as the objective function.

7. The optimal flank modification amount derivation unit uses, as explanatory variables, the variation range of the misalignment created in advance and the range of the flank modification amount set in the optimal flank modification amount derivation unit, and executes a performance calculation model having the meshing performance as an objective function, thereby deriving an optimal solution of the flank modification amount. The flank shape design system according to claim 1 or 2.

8. The flank shape design system according to claim 1 or 2, further comprising a flank shape determination unit that determines the flank shape by determining the flank modification amount based on a solution selected from the optimal solutions.

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