Toothed gear surface shape design system

Abstract

To provide a toothed gear surface shape design system that can achieve improvement in design accuracy of a toothed gear meeting a desired performance, and can suppress increase in cost.SOLUTION: A gear surface shape design system 1, which designs a gear surface shape of a gear machinable by creation machining, includes: a performance computation unit 30 that computes a meshing performance of the gear on the basis of a computation condition including at least gear specifications of the gear and a modification amount of a gear surface of the gear; a corresponding relationship storage unit 45 that stores a corresponding relationship between at least two modification amounts out of a vias modification amount, a crowning modification amount and a tooth strip inclination modification serving as a modification amount in a gear tooth strip direction in the modification amount of the gear surface; and an optimization gear surface modification amount derivation unit 40 that sets the gear surface modification amount to an explanatory variable, sets meeting the corresponding relationship to a constraint condition, sets at least one of computation results of the performance computation unit to an objective function, and derives an optimized solution of the gear surface modification amount by an optimization method.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 mechanical 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, mechanical gears need to satisfy requirements for multiple performances such as quietness, strength, and efficiency, and the performance of mechanical 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 misalignment 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] Furthermore, when performing crowning finishing in the tooth trace direction during tooth surface finishing, an unintended bias finishing amount (natural bias) occurs as an error in the tooth surface shape. In the processing method for mass-producing gears, it is difficult to apply an arbitrary bias finishing amount, and a tooth surface shape with the natural bias remaining as an error is manufactured. When the tooth surface shape is such a shape, a deviation occurs from the performance at the time of tooth surface finishing amount design, so it is necessary to redesign the tooth surface shape to a mass-producible one, leading to an increase in the cost of tooth surface shape design.

[0006] 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 performance and suppressing an increase in cost.

Means for Solving the Problems

[0007] One aspect of the present invention is A tooth surface shape design system for designing the tooth surface shape of a gear that can be machined by generative machining, A performance calculation unit that calculates the meshing performance of the gear based on calculation conditions including at least the gear specifications of the gear and the tooth surface finishing amount of the gear, A correspondence relationship storage unit that stores the correspondence relationship of at least two of the bias finishing amount, crowning finishing amount, and tooth trace inclination finishing, which are the finishing amounts in the tooth trace direction in the tooth surface finishing amount, An optimal tooth surface finishing amount derivation unit that sets the tooth surface finishing amount as an explanatory variable, sets satisfying the correspondence relationship as a constraint condition, 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 finishing amount by an optimization method, is in a tooth surface shape design system including.

Effects of the Invention

[0008] According to the above aspect, the meshing performance of a gear pair is calculated based on the gear specifications of the gear and the calculation conditions including the tooth surface finishing amount of the gear. Then, 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, the design accuracy of the tooth surface shape according to the meshing performance of the gear can be improved.

[0009] Furthermore, when deriving the optimal solution, it is a constraint condition that the crowning finishing amount and the bias finishing amount in the tooth surface finishing element have a corresponding relationship. Thereby, all the derived optimal solutions can be made into tooth surface shapes that can be formed by the processing method during mass production. Therefore, no matter which optimal solution is selected, it is not necessary to redesign the tooth surface shape again for mass production processing, and an increase in cost can be suppressed.

[0010] As described above, according to the above aspect, it is possible to provide a tooth surface shape design system that can improve the design accuracy of a gear that satisfies desired performance and can suppress an increase in cost.

Brief Description of the Drawings

[0011]

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Mode for Carrying Out the Invention

[0012] (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. The tooth surface shape design system 1 includes a machining simulation unit 1a and a performance simulation unit 1b.

[0013] 1-1. Machining simulation unit 1a The machining simulation unit 1a has a machine tool model 100 including a tool T, a driving device 101, a control device 102, and a machining condition input unit 103. The machine tool model 100 models a machine tool that performs grinding or cutting as the generation machining of gears. In the first embodiment, the machine tool model 100 models a machine tool that performs continuous generation grinding of gears, and the tool T constitutes a screw-shaped grinding wheel. The driving device 101 rotationally drives the tool T and the workpiece W. The control device 102 controls the operation of the driving device 101. The machining condition input unit 103 receives the machining conditions for tooth surface machining. The machine tool model 100 performs tooth surface machining based on the machining conditions input to the machining condition input unit 103.

[0014] As shown in FIG. 2, the workpiece W has a substantially cylindrical shape, and a gear shape of an initial shape is created in advance on the circumferential surface, and it can be rotated about the central axis Wa by the driving device 101. Further, the tool T made of a screw-shaped grinding wheel can be rotated about the central axis Ta by the driving device 101, and when giving a crowning dressing amount, it can be moved along a predetermined orbit Tb so as to be able to grind the circumferential surface of the workpiece W.

[0015] 1-2. Performance simulation unit 1b As shown in FIG. 1, the performance simulation unit 1b includes a gear device model 10, a misalignment calculation unit 20, a performance calculation unit 30, an optimal tooth surface dressing amount derivation unit 40, a correspondence relationship storage unit 45, a correspondence relationship creation unit 46, an optimal solution display unit 50, an input unit 60, and a tooth surface shape determination unit 70.

[0016] 1-2-1. Gear device model 10 The gear device model 10 shows a virtual gear device shown in FIG. 3. As shown in FIG. 3, 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. The first gear 111 and the second gear 112 are formed by grinding a workpiece W in the machining simulation unit 1a. In the first embodiment, the first gear 111 is a driving gear and the second gear 112 is a driven gear.

[0017] 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, and 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.

[0018] 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.

[0019] 1-2-2. Misalignment calculation unit 20 The misalignment calculation unit 20 shown in FIG. 1 calculates the misalignment, which is the deviation between the first rotating shaft C1 and the second rotating shaft C2 in the gear device model 10. The misalignment is caused by, for example, the interference error shown in FIG. 4(A) or the parallelism error shown in FIG. 4(B). The interference error is the inclination of the first rotating shaft C1 with respect to the second rotating shaft C2 when viewed from the overlapping direction of the first shaft 121 and the second rotating shaft C2, as shown in FIG. 4(A). The parallelism error is the inclination of the first rotating shaft C1 with respect to the second rotating shaft C2 when viewed from the arrangement direction of the first shaft 121 and the second rotating shaft C2, as shown in FIG. 4(B).

[0020] The misalignment calculation unit 20 calculates the misalignment at each torque when the torque is changed to a desired value, based on the rigidity, dimensional tolerance, geometric tolerance, and bearing internal clearance of the gear pair 11, shafts 121, 122, bearings 131, 132, 133, 134, and the case (not shown) in the gear device model 10, and the deformation amounts of the shafts 121, 122 due to the torque generated in the gear pair 11. The calculation of the misalignment can be performed, for example, as shown in FIG. 5(a), by adopting a plurality of values within the range from the minimum value to the maximum value, with the dimensional tolerance (or geometric tolerance) having a minimum value of -3σ and a maximum value of +3σ in the normal distribution, 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. 5(b). The variation range includes the nominal point where all the dimensional tolerances and geometric tolerances are the mode value and a plurality of variation points other than the nominal point.

[0021] 1-2-3. 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 the primary amplitude of the meshing transmission error, the maximum tooth surface pressure, the maximum tooth root stress, 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. 6, it changes according to the magnitude of the torque and exhibits different change patterns depending on the value of the misalignment (for example, the nominal point and the variation point).

[0022] 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 the first gear 111 and the second gear 112 respectively. 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.

[0023] 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, but for example, 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 come into contact with each other in the gear pair 11 by the finite element method (FEM).

[0024] 1-2-4. 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 1, 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, and particle optimization can be adopted.

[0025] Tooth surface finishing can be performed on the tooth surface 15 before finishing shown in Fig. 7(a) by combining known tooth surface finishing elements. The tooth surface finishing elements are classified into tooth groove direction finishing and tooth profile direction finishing. Examples of tooth groove direction finishing include bias finishing shown in Fig. 7(b), tooth groove crowning shown in Fig. 7(c), and tooth groove inclination finishing (twist angle finishing) shown in Fig. 7(d). Examples of tooth profile direction finishing include pressure angle finishing shown in Fig. 7(e) and tooth profile rounding (tooth groove crowning) shown in Fig. 7(f). The tooth surface finishing amount of each tooth surface finishing element can be preliminarily restricted within a predetermined range based on processing conditions and gear specifications.

[0026] As the objective function 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 point, the average value of the total torque variation maximum point, the worst value of the specified torque variation point, 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.

[0027] The average value of the total torque nominal point is the average value of the calculation results of the total torque at the nominal point, which is the most frequent value in the misalignment variation range. Also, although the values of the misalignment variation points themselves differ 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 with the worst average value at the total torque is defined as the variation maximum point, and the above average value is defined as the average value of the variation maximum point described above. Also, the worst value of the specified torque variation point is the worst value of the specified torque in the calculation results of the variation points other than the nominal point in the misalignment variation range. Note that the specified torque can be set appropriately by the user.

[0028] The optimal flank modification amount derivation unit 40 is set to satisfy the correspondence relationship stored in the correspondence relationship storage unit 45 described later as a constraint condition. In addition to the correspondence relationship described later, the constraint conditions can limit the first-order amplitude of the meshing transmission error, the maximum flank pressure, the maximum tooth root stress, or the meshing efficiency within a predetermined range, excluding those set in the objective function. Note that the constraint conditions do not necessarily have to be set, and there may be cases where the constraint conditions are not set.

[0029] The optimal flank modification amount derivation unit 40 uses a predetermined optimization method, with the flank modification amount as an explanatory variable, and repeatedly performs calculations so that the objective function set as described above is maximized or minimized (under the constraint conditions if the constraint conditions are set), thereby deriving the optimal solution of the flank modification amount. When multiple objective functions are set and are in a trade-off relationship with each other, since multi-objective optimization is required for the flank modification amount, the optimal solution of the flank modification amount can be derived as a Pareto solution. Note that the derivation of the optimal solution in the optimal flank modification 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 flank modification element as the first explanatory variable, in the second stage, with the value of the first explanatory variable in the first Pareto solution as a constant, other flank modification elements may be used as the second explanatory variable to derive the second Pareto solution as the second optimal solution.

[0030] 1-2-5. Correspondence Relationship Storage Unit 45 The correspondence relationship storage unit 45 shown in FIG. 1 stores the correspondence relationship of at least two of the bias modification amount, which is the modification amount in the tooth line direction in the flank modification amount, the crowning modification amount, and the tooth line inclination modification. In the first embodiment, the correspondence relationship between the bias modification amount and the crowning modification amount is stored.

[0031] Here, the relationship between the bias dressing amount and the crowning dressing amount will be described in detail below. First, in gear grinding using a helical grinding wheel as the tool T, when crowning dressing is performed as tooth surface dressing, the formed tooth surface shape has the relationship shown in Fig. 8(b) when comparing the errors with respect to the involute tooth profile for cross-section A at one position in the tooth trace direction shown in Fig. 8(a), cross-section C at the other position, and cross-section B at a position between the two. That is, in cross-section A at one position in the tooth trace direction and cross-section C at the other position, the errors in the tooth profile direction are symmetric, and bias dressing has occurred.

[0032] Also, when crowning dressing is performed as tooth surface dressing, as shown in Fig. 2, during machining, correction of the center distance, which is the distance between the center axis Wa of the workpiece W and the center axis Ta of the tool T consisting of a helical grinding wheel, is performed so that the orbit Tb of the center axis Ta of the tool T draws an arc with respect to the center axis Wa of the workpiece W. Here, as shown in Fig. 9, the relationship between the correction amount (center distance correction amount) y and the feed amount x of the tool T in the workpiece axis direction X has the relationship of the following formula (1).

[0033] y = ηx 2 …(1)

[0034] And the center distance change coefficient η in the above formula (1) and the bias dressing amount have the relationship shown in Fig. 10(a). Also, the center distance change coefficient η and the crowning dressing amount have the relationship shown in Fig. 10(b). And from these, it is derived that the bias dressing amount and the crowning dressing amount have the linear relationship shown in Fig. 10(c). Therefore, when the bias dressing amount is BS and the crowning dressing amount is CR, the following relational formula (2) holds as the correspondence relationship between the two.

[0035] CR = α × BS …(2) (α is a coefficient)

[0036] Therefore, in optimizing the tooth surface finishing amount, by setting as a constraint condition that the crowning finishing amount and the bias finishing amount satisfy the above relationship, the bias finishing amount when the crowning finishing amount is given can be made to match the so-called natural bias. Thus, the tooth surface finishing amount can be designed according to the processing method for mass production, and high-precision performance prediction becomes possible.

[0037] 1-2-6. Corresponding relationship creation unit 46 The corresponding relationship creation unit 46 shown in FIG. 1 creates the corresponding relationship stored in the corresponding relationship storage unit 45. The creation of the corresponding relationship creates Equation (2) of the above relational expression based on the specifications of the gears of the gear pair 11 and the specifications of the tool T. In Equation (2), CR and BS have a linear relationship, and when CR = 0, BS = 0. Therefore, for the creation of Equation (2) of the above relational expression, it is only necessary to calculate one point for each of the crowning finishing amount CR and the bias finishing amount BS from the machining simulation.

[0038] 1-2-7. 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 it can be displayed by a known method. For example, as shown in FIG. 11, in the operation of the optimal solution in the optimal tooth surface finishing amount derivation unit 40, the optimal solution display unit 50 adopts the meshing transmission error nominal point as the first objective function, adopts the meshing transmission error variation worst point as the second objective function, and sets the constraint condition to satisfy CR = α × BS in the above Equation (2), and an example of displaying the Pareto solution as the optimal solution can be shown. Note that the meshing transmission error nominal point adopted as the first objective function reflects the basic NV performance regarding noise and vibration in the gear pair 11, and the meshing transmission error variation worst point adopted as the second objective function reflects the robust NV performance in the gear pair 11.

[0039] 1-2-8. Input unit 60 and tooth surface shape determination unit 70 The input unit 60 shown in FIG. 1 inputs the optimal solution selected from the Pareto solutions displayed on the optimal solution display unit 50 by the user. 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 based on the tooth surface finishing element corresponding to the selection result of the optimal solution input to the input unit 60 is determined, and the tooth surface shape is determined.

[0040] 2-1. Corresponding Relationship Creation Flow of Embodiment 1 Next, the corresponding relationship creation flow using the tooth surface shape design system 1 in the present Embodiment 1 will be described with reference to FIG. 12. The corresponding relationship creation flow is executed before the tooth surface shape design flow described later.

[0041] In the corresponding relationship creation flow, in step S1 shown in FIG. 12, the workpiece specifications including the gear pair 11, shafts 121 and 122, bearings 131, 132, 133, and 134 in the gear device model 10 and the rigidity, dimensional tolerances, geometric tolerances, and bearing internal clearances of the case (not shown), the tool specifications of the tool T, and the machining conditions are set.

[0042] In step S2 shown in FIG. 12, the center distance change coefficient η in the above formula (1) is set. Then, in step S3, machining simulation is performed by the machining simulation unit 1a, and the workpiece shape is calculated by the machining simulation.

[0043] Next, in step S4 shown in FIG. 12, each tooth surface finishing amount is calculated from the workpiece shape calculated by the machining simulation, and the crowning finishing amount CR and the bias finishing amount BS are extracted by the corresponding relationship creation unit 46. In step S5, the above formula (2) which is the corresponding relationship between CR and BS is created. Then, in step S6, the created corresponding relationship is stored in the corresponding relationship storage unit 45, and the flow is terminated.

[0044] 2-2. Tooth Surface Shape Design Flow of Embodiment 1 Next, a tooth surface shape design flow using the tooth surface shape design system 1 in the first embodiment will be described with reference to FIG. 13. In this tooth surface shape design flow, first, in step S11 shown in FIG. 13, the rigidity, dimensional tolerances, geometric tolerances, and bearing clearances of the gear pair 11, shafts 121 and 122, bearings 131, 132, 133, 134, and a case (not shown) in the gear device model 10 are set.

[0045] In step S12 shown in FIG. 13, a tolerance condition for calculating misalignment is derived by the misalignment calculation unit 20. Then, in step S13, the misalignment calculation unit 20 calculates the shaft deformation amount at a desired torque under the above tolerance condition.

[0046] Thereafter, in step S14 shown in FIG. 13, 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 elements of the misalignment, as shown in, for example, FIG. 5(b). The variation range includes the nominal point, which is the most frequent value, and a plurality of other variation points.

[0047] Next, in step S15 shown in FIG. 13, the performance calculation unit 30 sets calculation conditions for calculating the meshing performance. The calculation conditions are set based on the gear specifications and misalignment of the gear pair 11.

[0048] Next, in step S16 of FIG. 13, the optimal flank modification amount derivation unit 40 calculates candidate values for the flank modification amount. The calculation of the flank modification amount uses, as explanatory variables, the modification amounts of the flank modification elements in the gear pair 11 shown in FIGS. 7(b) to 7(f). 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 a constraint condition, it is set to satisfy the above formula (2), which is the relational expression between CR and BS, stored in the correspondence relation storage unit 45, and it is set that the worst value of the T.E. primary at the specified torque is below a predetermined value, and the worst value of the maximum flank pressure at the specified torque is below a predetermined value. Note that the first candidate value of the flank modification amount can be arbitrarily determined within the range of the explanatory variables set in the optimal flank modification amount derivation unit 40.

[0049] Then, in step S17 shown in FIG. 13, the performance calculation unit 30 calculates the meshing performance based on the calculation conditions. In the meshing performance calculation in the first embodiment, the first candidate value of the modification amount of the flank modification element is input as an input variable, and the meshing transmission error primary amplitude (nominal point T.E. primary) at the nominal point of misalignment, the meshing transmission error primary amplitude (variation point T.E. primary) at the variation point of misalignment, the maximum flank pressure at the variation point, and the maximum trochoid interference amount at the variation point are respectively evaluated as torque components. Then, 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 flank 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 as appropriate by the user.

[0050] As described above, although the variation points of misalignment have different values depending on the torque, the combination of tolerances as input is the same even when the torque changes. Among the combinations of such tolerances, the point that becomes the average value of the worst T.E. primary at all torques is defined as the maximum variation point, and the said average value is defined as the average value of the maximum T.E. primary.

[0051] Then, in step S18 of FIG. 13, the optimal flank modification amount derivation unit 40 determines whether or not the completion condition for the optimization calculation of the flank modification amount is satisfied. As the completion condition, for example, the number of calculations and the change rate of the Pareto solution can be set. In step S18, if the completion condition for the optimization calculation of the flank modification amount is not satisfied, the process proceeds to No in step S18, and steps S16 and subsequent steps are performed again. Therefore, until the optimization of the flank modification amount is completed, steps S16 and S17 are repeatedly performed while updating the candidate values of the modification amounts of the flank modification elements. On the other hand, in step S18 of FIG. 13, if the completion condition for the optimization calculation of the flank modification amount is satisfied, the process proceeds to Yes in step S18, and in step S19, the optimal solution of the flank modification amount shown in FIG. 8 is output to the optimal solution display unit 50.

[0052] Thereafter, in step S20 shown in FIG. 13, the user selects the flank modification amount, which is the desired solution, from the optimal solution output to the optimal solution display unit 50. In step S21, the flank shape determination unit 70 determines the flank shape corresponding to the selected flank modification amount, and ends the said flow. As a result, an optimized flank shape is designed so as to achieve both the NV basic performance at the nominal point of the contact transmission error, which is the first objective function, and the NV robust performance at the worst point of the contact transmission error variation, which is the second objective function, while also ensuring the NV performance and strength performance at the important torque due to the constraint conditions.

[0053] 2-3. Performance confirmation flow of the gear pair 11 having the determined flank shape Next, a performance confirmation flow for confirming the meshing performance of the gear pair 11 having the flank shape determined by the above-described flank shape design flow will be described with reference to FIG. 14.

[0054] First, in step S30 in FIG. 14, input the machining conditions for forming the tooth surface shape determined by the above tooth surface shape design flow into the machining condition input unit 103 in the machining simulation unit 1a. Then, in step S31, based on the machining conditions, perform a machining simulation using the machine tool model 100 with the tool T.

[0055] After that, in step S32, in the machining simulation unit 1a, determine whether the machining has ended normally. For example, when all the machining corresponding to the machining conditions is completed within a predetermined time, a determination of normal end can be made. When all the machining corresponding to the machining conditions is not completed even after the elapse of the predetermined time, or when the machining stops, a determination of abnormal end can be made. And in step S32, if it is determined that the machining has ended normally, proceed to Yes in step S32.

[0056] Then, for the formed gear 111, calculate the meshing performance in step S40. The calculation of the meshing performance in step S40 is performed by the performance simulation unit 1b in the same manner as steps S11 to S16 shown in FIG. 13, and end the control flow. Thereby, the performance of the gear pair 11 having the determined tooth surface shape can be confirmed.

[0057] In this performance confirmation flow, since the machining is simulated based on the machining conditions for forming the tooth surface shape determined by the above tooth surface shape design flow, the tooth surface can include the undulation and machining marks of the tooth surface that can occur during machining. Thereby, a more detailed performance simulation can be performed.

[0058] 3. Operational Effects of the Tooth Surface Shape Design System 1 of Embodiment 1 According to the tooth surface shape design system 1 of the first embodiment, the meshing performance of the gear pair 11 is calculated based on the specifications of the gear 111 and the calculation conditions including the tooth surface finishing amount of the gear 111. Then, 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, the design accuracy of the tooth surface shape according to the performance of the gear pair 11 can be improved.

[0059] Furthermore, when deriving the optimal solution, it is a constraint condition that the crowning finishing amount CR and the bias finishing amount BS in the tooth surface finishing element have a corresponding relationship. Thereby, since all the derived optimal solutions can be tooth surface shapes that can be formed by the processing method during mass production, no matter which optimal solution is selected, it is not necessary to redesign the tooth surface shape again for mass production processing, and an increase in cost can be suppressed.

[0060] Also, in the first embodiment, it further includes a correspondence relationship creation unit 46 that creates a correspondence relationship between the crowning finishing amount CR and the bias finishing amount BS based on the specifications of the gear pair 11 and the specifications of the tool T. Thereby, based on the correspondence relationship between the crowning finishing amount CR and the bias finishing amount BS created by the correspondence relationship creation unit 46, a tooth surface shape that can be mass-produced can be designed with high precision.

[0061] Also, in the first embodiment, the tool T is a screw-shaped grinding wheel, and the above correspondence relationship is represented by a relational expression of CR = α × BS (α is a coefficient) when the bias finishing amount is BS and the crowning finishing amount is CR. As described above, in the gear grinding process using a screw-shaped grinding wheel as the tool T, since the bias finishing amount BS and the crowning finishing amount CR have a linear relationship, by using the above relational expression of BS and CR, a tooth surface shape that can be mass-produced can be designed with high precision.

[0062] Also, in the first embodiment, it has a tooth surface shape determination unit 70 that determines a tooth surface shape according to the tooth surface finishing amount selected from the Pareto solutions of the tooth surface finishing amount derived by the optimal tooth surface finishing amount derivation unit 40. Thereby, a tooth surface shape that can be mass-produced can be designed.

[0063] As described above, according to the above-described Embodiment 1, it is possible to improve the design accuracy of the gear pair 11 that satisfies the desired performance, and it is possible to provide the tooth surface shape design system 1 that can suppress the cost increase.

[0064] (Embodiment 2) In the above-described Embodiment 1, the machine tool model 100 in the machining simulation unit 1a shown in FIG. 1 is a model of a machine tool that performs continuous generation grinding of gears, and the tool T is configured as a helical grinding wheel. Instead, in the tooth surface shape design system 1 of the present Embodiment 2, the machine tool model 100 is a model of a machine tool that performs skiving machining for generating cutting of gears, and the tool T is a skiving cutter that is a cutting tool.

[0065] In the above-described Embodiment 1, the correspondence relationship storage unit 45 stores the correspondence relationship between the bias dressing amount BS and the crowning dressing amount CR. However, in the present Embodiment 2 that performs gear skiving machining, the correspondence relationship storage unit 45 stores the correspondence relationship between the bias dressing amount BS, the crowning dressing amount CR, and the tooth flank inclination dressing amount CL.

[0066] As shown in FIG. 15(a), in gear skiving machining using a skiving cutter as the tool T, the bias dressing amount BS and the crowning dressing amount CR have a linear relationship. Further, as shown in FIG. 15(b), in gear skiving machining using a skiving cutter as the tool T, the tooth flank inclination dressing amount CL and the crowning dressing amount CR also have a linear relationship. Therefore, as the correspondence relationship between the bias dressing amount BS, the crowning dressing amount CR, and the tooth flank inclination dressing amount CL, the following relational expressions (3) and (4) are established.

[0067] CR = β × BS …(3) CR = γ × CL …(4) (β and γ are coefficients)

[0068] And the correspondence creation flow and tooth surface shape design flow by the tooth surface shape design system 1 of the second embodiment can be implemented in the same manner as in the case of the first embodiment by replacing the correspondence with the above formulas (3) and (4) in the case shown in FIGS. 12 and 13.

[0069] Moreover, the tooth surface shape design system 1 of the second embodiment also exhibits the same operational effects as in the case of the first embodiment. Also, the above formulas (3) and (4) of the relational expressions also hold true in hobbing using a hob cutter as the cutting tool T, and the correspondence creation flow and tooth surface shape design flow can be made the same as in the case of gear skiving.

[0070] The present invention is not limited to the above first and second embodiments, and can be applied to various embodiments without departing from the gist thereof.

Explanation of Reference Numerals

[0071] 1 Tooth surface shape design system 1a Machining simulation unit 1b Performance simulation unit 10 Gear device model 11 Gear pair 20 Misalignment calculation unit 30 Performance calculation unit 40 Optimal tooth surface dressing amount derivation unit 45 Correspondence storage unit 46 Correspondence creation 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 T Tool (thread grinding wheel, skiving cutter, hob cutter)

Claims

1. A tooth surface shape design system for designing the tooth surface shape of a gear that can be machined by generative machining, a performance calculation unit that calculates the meshing performance of the gear based on calculation conditions including at least the gear specifications of the gear and the tooth surface finishing amount of the gear, a correspondence relationship storage unit that stores the correspondence relationship of at least two of the bias finishing amount, crowning finishing amount, and tooth trace inclination finishing amount, which are the finishing amounts in the tooth trace direction in the tooth surface finishing amount, an optimal tooth surface finishing amount derivation unit that sets the tooth surface finishing amount as an explanatory variable, sets satisfying the correspondence relationship as a constraint condition, 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:

2. The tooth surface shape design system according to claim 1, further comprising a correspondence relationship creation unit that creates the correspondence relationship based on the gear specifications of the gear and the tool specifications of the tool for machining the gear.

3. The tool for machining the gear is a helical grinding wheel, The tooth surface shape design system according to claim 1 or 2, wherein the correspondence relationship is expressed by a relational expression of CR = α × BS (α is a coefficient) when the bias finishing amount is BS and the crowning finishing amount is CR.

4. The tool for machining the gear is a cutting tool for performing skiving or hobbing, The tooth surface shape design system according to claim 1 or 2, wherein the correspondence relationship is expressed by relational expressions of CR = β × BS and CR = γ × CL (β and γ are coefficients) when the bias finishing amount is BS, the crowning finishing amount is CR, and the tooth trace inclination finishing amount is CL.

5. The tooth surface shape design system according to claim 1 or 2, having a tooth surface shape determination unit that determines a tooth surface shape corresponding to the tooth surface finishing amount selected from the Pareto solutions of the tooth surface finishing amount derived by the optimal tooth surface finishing amount derivation unit.

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