JP2008175694A - Evaluation device of gear pair, evaluation program, and evaluation method of gear pair using this - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an evaluation device of a gear pair capable of calculating the distribution of a load or stress acting on the gear pair in detail over the whole tooth surface. <P>SOLUTION: An arithmetic section 6 calculates a unit distribution load P<SB>n</SB>(I, j) as a distribution load on a contact line C-C' at each mesh progression position I when a unit load is charged on mutually meshing tooth pair of the gear pair 100 and mesh rigidity value K<SB>0</SB>(I) based on each involute tooth surface shape of the tooth pair, calculates shared load f(I) at each mesh progression position I of the tooth pair when a predetermined load P<SB>s</SB>is charged on the gear pair 100 based on relative tooth surface error S(I, j) of the tooth pair and the mesh rigidity value K<SB>0</SB>(I), and calculates the real distributed load P(I, j) as the distribution load on the contact line C-C' at each mesh progression position I of the tooth pair when the predetermined load P<SB>s</SB>is charged on the gear pair 100 based on the unit distribution load P<SB>n</SB>(I, j) and the shared load f(I). <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a gear pair evaluation apparatus, an evaluation program, and a gear pair evaluation method using the spear gear, helical gear, and the like.

  In general, as the evaluation of the gear pair, for example, durability evaluation when the gear pair is engaged in a predetermined load state (for example, a maximum load state assumed when the gear pair is used) is performed. In this type of evaluation, generally, a tangential force on a pitch circle in a predetermined load state is calculated by a simulation using a calculation formula (for example, see Non-Patent Document 1) based on the ISO standard or JIS standard. Based on the force, a stress at the pitch point (tooth surface tangential stress) is calculated. Then, a margin set based on, for example, the experience of the operator is given to the stress at the calculated pitch point, and the stress value in consideration of this margin is an allowable value for the durability of the gear pair. It is determined whether or not.

By the way, in this type of gear pair, the point on the tooth surface where the tooth surface contact stress is maximum is not necessarily the pitch point, but rather may exist in the region where the tooth pair starts to mesh or ends. Many. This is largely due to the fact that the length of the meshing contact line is short at the beginning and end of meshing of the tooth pair, so the distributed load is large and the radius of curvature of the tooth surface is small.
"JGMA STANDARD Japan Gear Industry Association Standard-Conforms to ISO Standard-Spur Gear and Helical Gear Tooth Surface Strength Calculation Formula" Established March 8, 1989 Japan Gear Industry Association

  However, as for the calculation method of stress and the like acting on the gear pair, only the calculation method of stress and the like at the pitch point is known as described above, and the distribution of the load and stress acting on the gear pair is distributed over the entire tooth surface. It has been difficult to calculate in detail over a long period of time.

  The present invention has been made in view of the above circumstances, and an evaluation device, an evaluation program, and an evaluation program for a gear pair capable of calculating in detail the load and stress distribution acting on the gear pair over the entire tooth surface. An object of the present invention is to provide a method for evaluating a pair of gears.

  The gear pair evaluation device according to the present invention includes a relative tooth surface error calculating means for calculating relative tooth surface error distribution information, which is a relative error between the tooth surfaces of the tooth pairs engaged with each other, and the tooth pairs. Unit distributed load calculating means for calculating a unit distributed load which is a distributed load on the contact line at each meshing advance position of the tooth pair when a unit load is applied based on each involute tooth surface shape of the tooth pair; and the tooth A mesh stiffness value calculating means for calculating a mesh stiffness value at each mesh advance position of the pair based on each involute tooth surface shape of the tooth pair; and each mesh of the tooth pair when a predetermined load is applied to the gear pair. On the contact line at each meshing advance position of the tooth pair when a predetermined load is applied to the gear pair, and a share load calculating means for calculating the shared load at the advance position based on the relative tooth surface error and the meshing rigidity value And the actual load distribution calculation means for calculating on the basis of distribution is load actual load distribution in said unit distributed load and the shared load, characterized by comprising a.

  The gear pair evaluation program according to the present invention includes a relative tooth surface error calculating step for calculating distribution information of a relative tooth surface error, which is a relative error between tooth surfaces of the tooth pairs engaged with each other, and the tooth pairs. A unit distributed load calculating step for calculating a unit distributed load which is a distributed load on the contact line at each meshing advance position of the tooth pair when a unit load is applied based on each involute tooth surface shape of the tooth pair; and A mesh stiffness value calculating step for calculating a mesh stiffness value at each mesh advance position of the pair based on each involute tooth surface shape of the tooth pair; and each mesh of the tooth pair when a predetermined load is applied to the gear pair. A shared load calculating step of calculating a shared load at the advancing position based on the relative tooth surface error and the meshing rigidity value; and each meshing advance of the tooth pair when a predetermined load is applied to the gear pair And the actual distribution load calculating step of calculating, based the actual distributed load is distributed load of the contact line at a position in said shared load with the unit distributed load, characterized by comprising a.

  The gear pair evaluation method according to the present invention includes a relative tooth surface error calculating step for calculating a distribution information of a relative tooth surface error, which is a relative error between tooth surfaces of the tooth pairs engaged with each other, and the tooth pair. A unit distributed load calculating step of calculating a unit distributed load that is a distributed load on the contact line at each meshing advance position of the tooth pair when a unit load is applied based on each involute tooth surface shape of the tooth pair; and A mesh stiffness value calculating step for calculating a mesh stiffness value at each mesh advance position of the pair based on each involute tooth surface shape of the tooth pair, and each mesh of the tooth pair when a predetermined load is applied to the gear pair. On the contact line at each meshing advance position of the tooth pair when a predetermined load is applied to the gear pair, and a shared load calculating step for calculating the shared load at the advance position based on the relative tooth surface error and the meshing rigidity value And the actual distribution load calculating step of calculating, based the actual distributed load is distributed load and the unit distributed load and the shared load, characterized by comprising a.

  According to the present invention, the load and stress distribution acting on the gear pair can be calculated in detail over the entire tooth surface.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings. FIG. 1 is a schematic diagram of a gear pair evaluation device, FIG. 2 is a schematic diagram showing an example of a computer for realizing the gear pair evaluation device, and FIG. 3 is a stress distribution calculation. FIG. 4 is an explanatory diagram showing a working plane of a helical gear pair, FIG. 5 is an explanatory diagram showing correction amount input points set on the tooth surface, and FIG. 6 is a tooth tip correction amount and tooth base. 7A is an explanatory diagram of the crowning correction amount, FIG. 7B is an explanatory diagram of the tooth trace correction amount, FIG. 8 is an explanatory diagram of the bias correction amount, and FIG. 9A is a contour line. FIG. 10 is an explanatory diagram showing an example of the displayed relative tooth surface error distribution; FIG. 10B is an explanatory diagram showing an example of the stress distribution displayed by contour lines; and FIG. 10 shows the transition of the meshing rigidity value of each tooth pair at each meshing moment. Fig. 11 shows relative tooth surface error and equivalent tooth profile error on the contact line. FIG. 12 is an explanatory diagram showing an analysis model of a helical gear pair, FIG. 13 is an explanatory diagram showing a stress distribution in a direction perpendicular to the contact line, and FIG. 14 is a stress distribution of each tooth pair at each meshing moment. FIG. 15 is an explanatory diagram showing the transition of the maximum tooth surface stress. Note that the present invention can be applied to both the engagement on the drive side and the engagement on the coast side of the gear pair, but in the present embodiment, the engagement on the drive side will be described below as an example.

  The gear pair evaluation apparatus 1 shown in FIG. 1 includes, for example, a gear pair 100 (helical gear pair: FIGS. 4 and 13) in which the driving gear 101 and the driven gear 102 that mesh with each other are each a helical gear. Evaluation). Specifically, the evaluation device 1 is, for example, a distributed load (actual distribution) that actually acts on the contact line of the tooth pair at the moment of meshing when the driving gear 101 and the driven gear 102 are meshed while applying a predetermined load. Load), a stress distribution is calculated based on the calculated actual distribution load, and durability evaluation of the gear pair 100 is performed based on these.

  Here, in the helical gear pair 100 to be evaluated by the evaluation apparatus 1, the tooth surfaces of the driving gear 101 and the driven gear 102 are, for example, macro-shaped tooth surfaces defined based on basic specifications. It is formed by performing three-dimensional tooth surface correction based on various tooth surface correction amounts (set tooth surface correction amounts) on (involute tooth surfaces as reference tooth surfaces).

The basic specifications of the gear pair 100 include, for example, the number of teeth z of each gear 101, 102, the tooth right angle module m _n , the tooth height coefficient K _s , the pressure angle α _n , the tooth width b, and the torsion angle β. ₀ etc. are set. As the set tooth surface correction amount, for each tooth surface, for example, the tip correction amount T _m , the tooth root correction amount R _m , the crowning correction amount C _m , the tooth trace Taole amount L _m , and the left and right bias Correction amounts Bl _m , Br _{m and the} like (see FIGS. 6 to 8) are set. In the following description, the suffix “ _Dv ” is attached to the tooth surface correction amount set on the tooth surface of the drive gear 101 as necessary, and the tooth surface correction set on the tooth surface of the driven gear 102 is added. Subscript ' _Dn ' is added to the quantity etc. as necessary.

  The evaluation apparatus 1 is an input unit 5 for inputting various information about the gear pair 100 and the like, and an operation for evaluating the gear pair 100 (calculation of actual distribution load and stress distribution, etc.) based on the input information from the input unit 5 A storage unit 7 for storing a program such as a stress distribution calculation routine executed by the calculation unit 6 and the information input from the input unit 5 and a calculation result by the calculation unit 6 as appropriate; and a calculation unit 6 And an output unit 8 for outputting a calculation result or the like.

  The evaluation apparatus 1 is realized by a computer system 10 shown in FIG. 2, for example. The computer system 10 has, for example, a computer main body 11, a keyboard 12, a display device 13 as a display means, and a printer 14, which are connected via a connection cable 15 to constitute a main part. Yes. In the computer system 10, for example, various drive devices, CPU, ROM, RAM, and the like arranged in the computer main body 11 function as the calculation unit 6. A hard disk or the like built in the computer main body 11 functions as the storage unit 7, and the display device 13, the printer 14, and the like function as the output unit 8.

  Here, in addition to the basic specifications of the gear pair 100 and the set tooth surface correction amount, the evaluation device 1 assumes the maximum torque assumed when using the gear pair 100 (that is, acting on the gear pair 100). Information such as the maximum load) is input through the input unit 5. And the calculating part 6 performs the program of the stress distribution calculating routine memorize | stored in the memory | storage part 7, for example, and performs a calculation based on said each input information, A relative tooth surface error calculating means, a unit distribution load calculating means The functions as the meshing rigidity value calculating means, the shared load calculating means, the actual distributed load calculating means, and the stress distribution calculating means are realized.

  That is, the calculation unit 6 performs, for example, a simulation based on the basic specifications, the design tooth surface correction amount, and the like on the distribution information of the relative tooth surface error, which is a relative error between the tooth surfaces of the tooth pairs meshing with each other. Calculate by The relative tooth surface error is caused by scanning the stylus with respect to each tooth surface of the actual gear pair as disclosed in, for example, Japanese Patent Application Laid-Open No. 2005-193560 by the present applicant. The tooth surface error data with respect to the reference tooth surface of the surface may be measured and calculated based on the tooth surface error data.

In addition, the calculation unit 6 performs, for example, a simulation based on each involute tooth surface shape of the tooth pair on the assumption that a unit load (1N load) is applied to the tooth pair engaged with each other of the gear pair 100. While calculating the unit distribution load P _n (I, j) which is the distribution load on the contact line (mesh contact line) CC ′ at each meshing advance position I when the unit load is applied to the tooth pair, the tooth pair The meshing rigidity value K (I) at each meshing advance position I is calculated. Here, j indicates coordinates on the contact line CC ′. As shown in FIG. 4, since the contact line CC ′ of the helical gear pair 100 is twisted with respect to the gear shaft, the meshing thereof starts from point contact unlike the spur gear. That is, the meshing of the helical gear pair 100 starts from the point S, the oblique meshing contact line CC ′ advances in parallel on the working plane 103 while changing the length, and finally ends at the point E. The action plane 103 indicates an effective meshing region on each tooth surface of the tooth pair. In this embodiment, the action plane 103 is defined with reference to the tooth surface (drive tooth surface) of the drive gear 101, for example. Has been.

In addition, the calculation unit 6 assigns a predetermined load (for example, a maximum load assumed when the gear pair 100 is used) P _s to the gear pair 100, and a shared load f at each meshing advance position I of the tooth pair. (I) is calculated based on the relative tooth surface error and the meshing rigidity value K (t). In the calculation of the shared load f (I), when the calculation unit 6 first applies a predetermined load P _s to the gear pair 100, each tooth that the load P _s meshes simultaneously at each meshing instant t of the gear pair 100. A load acting on each pair (shared load f _{q (q = 1, 2,..., Q)} (t)) is calculated based on the relative tooth surface error and the meshing rigidity value K (t). Here, the meshing instant t of the gear pair 100 is, for example, a parameter for representing each meshing progress position of a plurality of tooth pairs meshing simultaneously, and the meshing progress position of the target tooth pair extracted from each tooth pair. I is set in association with I. Therefore, at the meshing instant t, the meshing progress position of the target tooth pair is I, and the meshing progress positions of the front and rear tooth pairs are I ± N (N = 1 pitch). The subscript 'q' is a number for identifying each tooth pair that meshes simultaneously at the meshing instant t, and the maximum value 'Q' varies depending on the meshing state (meshing moment t) of the gear pair 100. For example, when the meshing rate is 3.5, the gear pair 100 has three tooth pairs meshing (three tooth meshing) and four tooth pair meshing (four tooth meshing) according to the meshing state. Since Q is repeated, the possible value of Q is 3 or 4 depending on the meshing instant t. Based on these relationships, the calculation unit 6 is based on the shared load f _q (t) of each tooth pair at each meshing moment, and the shared load f ((1 tooth pair) at each meshing advance position I ( I) is determined.

Further, the calculation unit 6 is an actual distributed load P (I, j) that is a distributed load on the contact line CC ′ at each meshing advance position I of the tooth pair when the predetermined load P _s is applied to the gear pair 100. Is calculated based on the unit distribution load P _n (I, j) and the shared load f (I).

Further, the calculation unit 6 calculates the stress distribution H (I, j) when the predetermined load P _s is applied to the gear pair 100 based on the actual distribution load P (I, j).

Next, the calculation process of the stress distribution of the gear pair 100 executed by the calculation unit 6 will be described in detail according to the flowchart of the stress distribution calculation routine shown in FIG.
When this routine is started, the calculation unit 6 first reads various information such as the basic specifications of the gear pair 100 and the set tooth surface correction amount input from the input unit 5 by the operator or the like from the storage unit 7 in step S101. .

In subsequent step S102, the calculation unit 6 calculates the distribution information of the relative tooth surface error S (I, j) between the tooth surfaces of the tooth pair by simulation based on the basic specifications of the gear pair 100 and the set tooth surface correction amount. To do.
In the calculation of the relative tooth surface error, first, as tooth surface error distribution information of each tooth surface of the gear pair 100 (each tooth surface of the driving gear 101 and the driven gear 102), the tooth surface error distribution of 3 rows × 3 columns, respectively. Information is calculated. That is, as shown in FIG. 5, the calculation unit 6 calculates the center of the effective tooth surface (D (1, 1)) on each reference tooth surface and the four corners (D (0, 0), D ( 0,2), D (2,0), D (2,2)) and the center (D (0,1), D (1,0)), D (1,2) surrounding each effective tooth surface ), D (2, 1)), the tooth surface error distribution information of 3 rows × 3 columns for each reference tooth surface is calculated by assigning each corresponding tooth surface correction amount.

Specifically, when the drive gear 101 is right-handed, the tooth trace correction amount is positive in the direction of strong twisting, and the bias correction amount is positive in bias-in. The amount is
D _Dv (0,0) = T _Dv + C _Dv + L _Dv / 2-Bl _Dv / 2
D _Dv (0,1) = T _Dv
D _Dv (0,2) = T _Dv + C _Dv −L _Dv / 2 + Br _Dv / 2
D _Dv (1, 0) = C _Dv + L _Dv / 2
D _Dv (1,1) = 0
D _Dv (1,2) = C _Dv −L _Dv / 2
D _Dv (2, 0) = R _Dv + C _Dv + L _Dv / 2 + Bl _Dv / 2
D _Dv (2,1) = R _Dv
D _Dv (2, 2) = R _Dv + C _Dv −L _Dv / 2
It becomes. On the other hand, the tooth surface correction amount at each point on the drive side tooth surface of the driven gear 102 is
D _Dn (0,0) = T _Dn + C _Dn + L _Dn / 2-Bl _Dn / 2
D _Dn (0,1) = T _Dn
D _Dn (0,2) = T _Dn + C _Dn -L _Dn / 2 + Br _Dn / 2
D _Dn (1, 0) = C _Dn + L _Dn / 2
D _Dn (1,1) = 0
D _Dn (1,2) = C _Dn -L _Dn / 2
D _Dn (2,0) = R _Dn + C _Dn + L _Dn / 2 + Bl _Dn / 2
D _Dn (2,1) = R _Dn
D _Dn (2, 2) = R _Dn + C _Dn −L _Dn / 2
It becomes. When the drive gear 101 is left-handed, the addition / subtraction related to the tooth trace correction amount and the bias correction amount is reversed at each point described above.

Further, the calculation unit 6 performs, for example, interpolation calculation using a well-known multipoint spline interpolation method on the calculated tooth surface error distribution information of each 3 rows × 3 columns, and thereby samples of each tooth trace direction. Each tooth surface error distribution information of 3 rows × l _Dv column, 3 rows × l _Dn column with an interval of 0.1 mm, for example, is generated.

Then, the calculation unit 6 calculates the effective meshing region of each drive side tooth surface of the drive gear 101 and the driven gear 102, and the tooth surface error distribution information (distribution information of 3 rows × l _Dv column) and the driven gear 101 Tooth surface error distribution information (3 row × l ′ column distribution information) existing in the effective meshing region is extracted from the tooth surface error distribution information of the gear 102 (3 row × l _Dn column distribution information). .

  Next, the computing unit 6 generates relative tooth surface error distribution information that is a relative tooth surface error at the time of meshing between the driving tooth surface and the driven tooth surface based on the extracted tooth surface error distribution information. . Here, in this embodiment, the calculating part 6 calculates the relative tooth surface error distribution information in a no-load state, for example on the basis of a drive tooth surface.

Specifically, in each tooth surface error distribution information of 3 rows × l ′ columns, the tooth surface error data of the m-th row and the n-th column on the driving tooth surface side is represented by D _Dv (m, n), and the tooth surface error data on the driven tooth surface side. When the tooth surface error data in the m-th row and the n-th column is D _Dn (m, n), the relative tooth surface error S (m, n) at each point (m, n) on the tooth surface is, for example, (1) It is calculated using the calculation formula shown in the formula.
S (m, n) = D _Dv (m, n) + D _Dn (3-1-m, n) + Gosa (m, n) (1)
Here, Gosa (m, n) is a correction value reflecting the assembly error and deflection of the gear pair 100 on the tooth surface.

For example, when each tooth surface error distribution information extracted is 3 rows × 161 columns, based on the above equation (1),
S (0,0) = D _Dv (0,0) + D _Dn (2,0) + Gosa (0,0),
S (0,1) = D _Dv (0,1) + D _Dn (2,1) + Gosa (0,1),.
S (2,159) = D _Dv (2,159) + D _Dn (0,159) + Gosa (2,159),
S (2,160) = D _Dv (2,160) + D _Dn (0,160) + Gosa (2,160)
A data group (relative tooth surface error distribution information) of the relative tooth surface error S (m, n) of 3 rows × 161 columns is calculated.

  Further, the calculation unit 6 performs row complementation and column complementation on the relative tooth surface error distribution information using a multipoint spline interpolation method, and more detailed relative tooth surface error distribution information (for example, 241 rows × 241 columns). Distribution information). The calculation unit 6 can also display the relative tooth surface error distribution information in a contour line through the output unit 8 (for example, the display device 13) as shown in FIG. 9A, for example.

In the subsequent step S103, the calculation unit 6 calculates the unit distribution load P _n (I, j) at each meshing advance position I of the tooth pair, and the meshing rigidity value K ₀ (I) at each meshing progress position I of the tooth pair. ) Is calculated.

These unit distributed loads P _n (I, j) and meshing rigidity values K (I) are based on, for example, the macro shape of each tooth surface determined based on the basic specifications of the gear pair 100 at each meshing advance position I. Then, an integral equation of tooth bending deflection and tooth surface contact deflection shown in the following equations (2) to (4) is created, and obtained by solving the integral equation.

More specifically, the calculation unit 6 assumes that the load P _s = 1N (unit load), and solves the equations (2) to (4) using a Gaussian process, whereby the meshing contact line C -C units distributed loads P _c (ξ) on 'calculates a and deflection amount [delta] _I. Then, the calculation unit 6 divides and normalizes the unit distribution load P _c (ξ) by the calculated division width ΔB set on the contact line CC ′, thereby finalizing the unit distribution load P _n (I , J) (P _n (I, j) = P _c (ξ) / ΔB) and a meshing rigidity value K ₀ (I) which is the reciprocal of the deflection amount δ _I.

δ _I = ∫K _b (x, ξ) · P _c (ξ) dξ + K _c (x = ξ) · P _c (ξ) dξ (2)
P _s = ∫P _c (ξ) dξ (3)
K (I) = P _s / δ _I (4)
Here, in equation (2), the K _c is the effect function of the deflection surface contact, Suzuki et al. (Suzuki Umezawa "unapproachable by tooth surface contact gears per piece", Japan Society of Mechanical Engineers (C ed 52) No. 481 (1986), P2449). It is possible to use a theoretical formula between rollers in consideration of the influence of the free end load distribution.
K _c [x = ξ, y = η = fuc (x)]
= 25 · (1-γ ² ) · ∫ (1-x ⁴ ) ^1/4 dx
/ Π · E · ΔB · (1-x ⁴ ) ^1/4 (5)
(However, the integration range is 0 to 1)
In addition, K _b , which is the bending bending influence function of the tooth, is Kano et al. (Kano / Saiki, “New bending bending influence function of gear rack”, Japanese Society of Mechanical Engineers 2002 Annual Conference Proceedings (V) No. 2314, It is possible to use a high-accuracy formula that takes into account the flexural characteristics that differ between the tooth width direction and the tooth height direction proposed by P27).
K _b (x, y, ξ, η)
= U · G (η) · [ν (r) / ν (η)]
・ [[F (x) · F (ξ)] / F (| x−ξ |)] ^1/2 (6)
γ = η + [[λ · (x−ξ)] ² + (y−η) ² ] ^1/2 (7)
Here, variables and the like in the equations (2) to (7) are as follows.
(X, y): coordinate value of deflection observation point (ξ, η): coordinate value of unit concentrated load point P _c (ξ): load distribution on meshing contact line E: Young's modulus [2.068 × 10 ¹¹ N / m ² ]
γ: Poisson's ratio [0.3]
I: Coordinate value U on the equivalent action line of the helical gear pair (see FIG. 4) with the center of the contact tooth width being 0: Absolute value of the deflection at the origin at the origin concentrated load λ: Concentric circle of the deflection elliptical distribution Coordinate conversion coefficient to distribution r: Radius ν (r) of deflection concentric distribution with tooth tip as origin: Deflection characteristic function G (η) of equivalent concentric distribution: Deflection characteristic function F (immediately below concentrated load point in tooth height direction) ξ): Deflection characteristic function just below the concentrated load point in the tooth width direction In this embodiment, the unit distributed load P _n (I, j) and the meshing rigidity value K ₀ (I) are expressed by the bending bending of the tooth and the tooth surface. Although an example of calculation using the integral equation of contact deflection has been described, the unit distribution load P _n (I, j) and the meshing rigidity value K ₀ (I) may be obtained individually.

In the subsequent step S104, the calculation unit 6 loads the helical gear pair load meshing equation (static) shown in the following equations (8) to (11) based on the helical gear pair analysis model shown in FIG. Load meshing equation) is created at each meshing moment t, and by solving this load meshing equation, the shared load f _q (t) of each tooth pair meshing simultaneously at each meshing moment t is calculated.

Here, in the equations (8) to (11), k _q (t) is the meshing rigidity value of each tooth pair that meshes simultaneously at the meshing instant t, and each meshing rigidity value k _q (t) It is obtained based on the meshing rigidity value K ₀ (I) per tooth pair obtained in step S103. Specifically, for example, as shown in FIG. 10, the calculation unit 6 is arranged by shifting the characteristic line of the meshing rigidity value K ₀ (I) per tooth pair by one pitch in association with each tooth pair. The search map is generated, and each tooth-to-tooth meshing stiffness value k _q (t) at the meshing instant t is retrieved based on the search map. In addition, the search map shown in FIG. 10 shows a search map when the meshing rate of the gear pair 100 is 3.5.

Further, e _q (t) is an equivalent tooth profile error of each tooth pair, and each equivalent tooth profile error e _q (t) is a relative tooth surface error S (m, n) of the tooth pair and a substantial static of the gear pair. Calculated based on the deflection x _s '. More specifically, the calculation unit 6 first calculates the relative tooth surface error S (m, n) obtained in step S102 as a coordinate axis with the tooth pair meshing direction and the contact line CC ′ direction as coordinate axes. The relative tooth surface error S (I, j) in the orthogonal coordinate system is converted. For example, as shown in FIGS. 11A to 11C, the relative information on the contact line CC ′ of each tooth pair at the meshing instant t is obtained from the distribution information of the relative tooth surface error S (I, j). Tooth surface errors S _{q = 1} (j),..., S _{q = Q} (j) are extracted, and the average value of each relative tooth surface error S _q (j) in the actual contact range on each contact line (ie, The area of the region of the relative tooth surface error S _q (j) where the actual static deflection is greater than or equal to x _s ′ is calculated as the equivalent tooth profile error e _q (t). Also, t _Z is the time required to pass one front normal pitch of the helical gear pair and is called the meshing cycle. In this case, the calculation unit 6 sets, for example, a static deflection amount x _s0 that does not consider an error as an initial value of the substantial static deflection x _s ′ based on the following equations (12) and (13).

Then, the calculation unit 6 solves the above formulas (8) to (11) by substituting the meshing rigidity value k _q (t) and the equivalent tooth profile error e _q (t) of each tooth pair, thereby obtaining each tooth pair. A shared load f _q (t) is calculated, and a new substantial static deflection x _s ′ is calculated.

Then, has the arithmetic unit 6 converged so that the newly calculated substantial static deflection x _s ′ satisfies the relationship of the following expression (14) with respect to the previous substantial static deflection x _s ′ _(n−1) ? Check for no.

| (X _s ′ −x _s ′ _(n−1) ) / x _s ′ _(n−1) | <10 ⁻⁶ (14)
As a result, when it is determined that the substantial static deflection x _s ′ (t) has not converged, the calculation unit 6 recalculates the equivalent tooth profile error e _q (t) using the newly calculated x _s ′. . Then, by solving the above equations (8) to (11) in which the recalculated equivalent tooth profile error e _q (t) is substituted, the shared load f _q (t) and the substantial static deflection x _s ′ for each tooth pair are obtained. Calculate again. These processes are repeated, for example, up to three times until the substantially static deflection x _s ′ converges. Then, the calculation unit 6 sets the shared load f _q (t) of each tooth pair when the substantial static deflection x _s ′ is converged as the final shared load f _q (t).

Furthermore, the calculating part 6 calculates | requires the sharing load f (I) of the tooth pair in each meshing advance position I from the sharing load _fq (t) of each tooth pair calculated in each meshing moment t. The shared loads f _q (t) calculated simultaneously from the above equations (8) to (11) are the shared loads of the respective tooth pairs meshing at the meshing advance position shifted by 1 pitch, and therefore the calculation unit 6 Merely calculates the shared load f _q (t) at each meshing instant t within the meshing section for one pitch preset in the gear pair 100, and each meshing advance position I from the start to the end of meshing of the toothpairs. The shared load f (I) can be obtained.

In subsequent step S105, the calculation unit 6 uses the unit distribution load P _n (I, j) and the shared load f (I), and each meshing advance position I when the predetermined load P _s is applied to the gear pair 100. The actual distribution load P (I) on the contact line CC ′ at is calculated based on the following equation (15).

P (I, j) = P _n (I, j) × f (I) (15)
For example, the calculation unit 6 uses all the actual distribution loads P (I, j) calculated for each contact line CC ′ as information on the actual distribution loads over the entire tooth surface, for example, the output unit 8 (for example, It is also possible to display contour lines through the display device 13).

In the subsequent step S106, the calculation unit 6 uses the actual distribution load P (I, j) and calculates the Hertz tooth surface contact stress calculation formula (contact line CC ′) shown in the following formulas (16) and (17). after calculating the stress distribution in the vertical direction on the basis of (see FIG. 13)), the stress distribution H at each meshing advancing position I when imparted with a predetermined load P _s to a gear pair 100 (I, j) for the routine Exit.

Here, in the equations (16) and (17), Ν is Poisson's ratio. Ρ _Dv (I, j) is the radius of curvature of the point on the driving tooth surface, and ρ _Dn (I, j) is the radius of curvature of the point on the driven tooth surface. These are the basic specifications of the gear pair 100. It is determined based on.

  For example, as shown in FIG. 9B, the calculation unit 6 calculates all stress distributions H (I, j) calculated for each contact line CC ′ to the stress distribution over the entire tooth surface. As information, it is also possible to display contour lines through the output unit 8 (for example, the display device 13).

  Further, for example, as shown in FIG. 14, the calculation unit 6 processes the information of the obtained stress distribution H (I, j) to thereby obtain the tooth pairs simultaneously meshed at each meshing instant t of the gear pair 100. It is also possible to display each stress distribution.

  Further, for example, as shown in FIG. 15A, the calculation unit 6 can also display the relationship between the meshing advance position I and the maximum stress in one tooth pair, and further, in FIG. 15B. As shown, it is also possible to display the relationship with the maximum stress at the meshing instant t as the gear pair 100 as a whole.

According to such an embodiment, the unit distributed load P _n (I) which is a distributed load on the contact line CC ′ at each meshing advance position I when the unit load is applied to the tooth pairs engaged with each other of the gear pair 100. , J) and the meshing rigidity value K ₀ (I) based on each involute tooth surface shape of the tooth pair, and at each meshing advance position I of the tooth pair when a predetermined load P _s is applied to the gear pair 100. The shared load f (I) is calculated based on the relative tooth surface error S (I, j) of the tooth pair and the meshing rigidity value K ₀ (I), and the tooth pair when the predetermined load P _s is applied to the gear pair 100. The actual distribution load P (I, j), which is the distribution load on the contact line CC ′ at each meshing advance position I, is based on the unit distribution load P _n (I, j) and the shared load f (I). By calculating, the load acting on the tooth pair of the gear pair 100 that is difficult to actually measure is calculated. It can be calculated in detail over the entire tooth surface.

At that time, an integral equation of the bending bending of the tooth and the contact bending of the tooth surface is set based on the macro shape of each tooth surface determined based on the basic specifications of the gear pair 100, and the load acting between the tooth pairs is a unit load. The unit distribution load P _n (I, j) and the meshing rigidity value K ₀ (I) can be easily obtained by solving the integral equation assuming that

In this case, the unit distribution load P _n (I, j) is calculated based on the macro shape of the tooth surface where each tooth surface error (relative tooth surface error S (I, j)) is not considered. However, the relative tooth surface error S (I, j) is reflected in the calculation of the shared load f (I), and such shared load f (I) is used in the calculation of the actual distribution load P (I, j). As a result, a highly accurate actual distribution load P (I, j) can be obtained. In other words, by simplifying the calculation of the unit distribution load P _n (I, j), the accuracy of reflecting the relative tooth surface error S (I, j) suitably without performing an unnecessarily complicated calculation. A high actual distribution load P (I, j) can be obtained.

  Further, by calculating the stress distribution H (I, j) of the tooth pair based on the actual distribution load P (I, j) calculated with high accuracy as described above, the stress distribution H (I, j, with high accuracy is calculated. j) can be obtained.

  Then, by using the highly accurate actual distribution load P (I, j) and stress distribution H (I, j) obtained in detail over the entire tooth surface in this way, various evaluations are accurately performed by simulation. be able to. For example, by using the above-described stress distribution H (I, j), the same results as the endurance test using the actually created gear pair 100 can be obtained with respect to the presence / absence of pitching, the position where pitching occurs, and the like.

  Furthermore, by processing the actual distribution load P (I, j) and stress distribution H (I, j) into various forms and displaying them (for example, by displaying contour lines), information meaningful to the user is visualized. Can be presented.

Schematic configuration diagram of gear pair evaluation device Schematic which shows an example of the computer for implement | achieving the evaluation apparatus of a gear pair Flow chart showing stress distribution calculation routine Explanatory drawing showing the working plane of the helical gear pair Explanatory drawing which shows the correction amount input point set on the tooth surface Explanation of tooth tip correction amount and tooth base correction amount (A) is explanatory drawing of crowning correction amount, (b) is explanatory drawing of tooth trace taole correction amount. Illustration of bias correction amount (A) is explanatory drawing which shows an example of relative tooth surface error distribution displayed by contour line, (b) is explanatory drawing which shows an example of stress distribution displayed by contour line Explanatory drawing which shows transition of the meshing rigidity value of each tooth pair at each meshing moment Explanatory drawing showing relative tooth surface error and equivalent tooth profile error on contact line Explanatory drawing showing analysis model of helical gear pair Explanatory drawing showing the stress distribution in the direction perpendicular to the contact line Explanatory drawing which shows stress distribution of each tooth pair at each meshing moment Explanatory drawing showing transition of maximum tooth surface stress

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 ... Evaluation apparatus 5 ... Input part 6 ... Calculation part (Relative tooth surface error calculation means, unit distribution load calculation means, meshing rigidity value calculation means, shared load calculation means, actual distribution load calculation means, stress distribution calculation means)
7: Storage unit 8: Output unit (display means)
DESCRIPTION OF SYMBOLS 100 ... Gear pair 101 ... Drive gear 102 ... Driven gear

Claims (6)

A relative tooth surface error calculating means for calculating distribution information of a relative tooth surface error, which is a relative error between the tooth surfaces of the tooth pairs meshing with each other;
Unit distributed load calculating means for calculating a unit distributed load that is a distributed load on the contact line at each meshing advance position of the tooth pair when a unit load is applied to the tooth pair based on each involute tooth surface shape of the tooth pair. When,
A meshing rigidity value calculating means for calculating a meshing rigidity value at each meshing advance position of the tooth pair based on each involute tooth surface shape of the tooth pair;
A shared load calculating means for calculating a shared load at each meshing advance position of the tooth pair when a predetermined load is applied to the gear pair based on the relative tooth surface error and the meshing rigidity value;
Actual distributed load calculating means for calculating an actual distributed load, which is a distributed load on the contact line at each meshing advance position of the tooth pair when a predetermined load is applied to the gear pair, based on the unit distributed load and the shared load. And a gear pair evaluation device.   The unit distribution load and the meshing stiffness value are set by integrating integral equations of tooth bending deflection and tooth surface contact deflection based on the macro shape of each tooth surface determined based on the basic specifications of the gear pair. 2. The gear pair evaluation device according to claim 1, wherein the gear pair evaluation device is obtained by solving an equation.   2. A stress distribution calculating means for calculating a stress distribution at each meshing advance position of the tooth pair when the predetermined load is applied to the gear pair based on the actual distribution load. The gear pair evaluation apparatus according to claim 2.   4. The gear pair evaluation apparatus according to claim 3, further comprising display means for displaying the actual distribution load and the stress distribution in contour lines. A relative tooth surface error calculating step for calculating distribution information of a relative tooth surface error, which is a relative error between the tooth surfaces of the tooth pairs meshing with each other;
A unit distributed load calculating step for calculating a unit distributed load that is a distributed load on the contact line at each meshing advance position of the tooth pair when a unit load is applied to the tooth pair based on each involute tooth surface shape of the tooth pair. When,
A meshing rigidity value calculating step for calculating a meshing rigidity value at each meshing advance position of the tooth pair based on each involute tooth surface shape of the tooth pair;
A shared load calculation step of calculating a shared load at each meshing advance position of the tooth pair when a predetermined load is applied to the gear pair based on the relative tooth surface error and the meshing rigidity value;
An actual distributed load calculation step of calculating an actual distributed load that is a distributed load on the contact line at each meshing advance position of the tooth pair when a predetermined load is applied to the gear pair based on the unit distributed load and the shared load. And a gear pair evaluation device. A relative tooth surface error calculating step for calculating distribution information of a relative tooth surface error, which is a relative error between tooth surfaces of the tooth pairs engaged with each other in the gear pair;
Unit distributed load calculation step of calculating a unit distributed load that is a distributed load on the contact line at each meshing advance position of the tooth pair when a unit load is applied to the tooth pair based on each involute tooth surface shape of the tooth pair When,
A meshing rigidity value calculating step of calculating a meshing rigidity value at each meshing advance position of the tooth pair based on each involute tooth surface shape of the tooth pair;
A shared load calculating step of calculating a shared load at each meshing advance position of the tooth pair when a predetermined load is applied to the gear pair based on the relative tooth surface error and the meshing rigidity value;
An actual distributed load calculating step of calculating an actual distributed load that is a distributed load on the contact line at each meshing advance position of the tooth pair when a predetermined load is applied to the gear pair based on the unit distributed load and the shared load. And a gear pair evaluation device.