JP2010151657A - Evaluation device of a pair of gears, and a pair of gears optimized by the same - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an evaluation device of a pair of gears for precisely and quantitatively grasping backlash of each kind of gear pair. <P>SOLUTION: In the evaluation device of a pair of gears, an operation section 6 mutually relate respective three-dimensional coordinates data on a gear tooth surface 102G and a pinion tooth surface 102P at a prescribed engagement rotary position for converting to three-dimensional coordinates data in a cylindrical coordinates system with a gear 101G as a reference. By two-dimensional parameters, functions for indicating respective points on the pinion tooth surface 102P are created, and respective points on the pinion tooth surface 102P corresponding to the respective points on the gear tooth surface 102G are computed by a Newton method. Information on gaps between tooth surfaces at drive and coast sides of a tooth surface is obtained by the computations, and backlash information is obtained based on the information on the gaps between the tooth surfaces. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to various gear pairs such as an external gear pair such as a spur gear, a bevel gear or a hypoid gear, or an internal gear pair such as a trochoid pump in which an inner rotor meshes with the inner periphery of an outer rotor. BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a gear pair evaluation device capable of analyzing backlash and a gear pair optimized using the evaluation device.

  In general, in a gear pair, backlash is required to smoothly and easily transmit rotation between gears regardless of whether the meshing form is an external tooth type or an internal tooth type. However, if the backlash is too large, it may cause vibration and noise. On the other hand, if the backlash is too small, the assembly error cannot be absorbed and may cause rotation failure, wear, or seizure. . Therefore, imparting optimal backlash to the gear pair is important in determining the performance of the gear pair.

For this reason, generally, when manufacturing a gear pair, the backlash is determined to some extent at the design stage, and the blade thickness of the tool at the time of tooth surface processing is adjusted according to the value. And, for example, in the case of a gear pair composed of helical gears, the tooth thickness of each gear whose tooth surface is processed is measured using a straddle tooth thickness method, an overpin method or the like, and based on the measured tooth thickness, Non-Patent Document 1 It is possible to evaluate (confirm) backlash using the disclosed method. Then, it is possible to optimize backlash by feeding back such an evaluation result to the blade thickness of the tool.
Ohara Gear Industry Co., Ltd., “Gear Intermediate Edition 4 Gear Backlash”, [Searched on November 6, 2008], Internet URL <http://www.khkgears.co.jp/gear_technology/intermediate_guide/KHK406_2.html >

  However, it is difficult to apply the backlash evaluation method disclosed in Non-Patent Document 1 described above to a limited gear pair such as a helical gear. Therefore, other than limited gear pairs, methods such as artificially measuring backlash using a dial gauge or the like on test machines and actual machines are still employed, and quantitative backlash without human error is still in use. It was difficult to grasp the rush.

  The present invention has been made in view of the above circumstances, and provides a gear pair evaluation device capable of accurately and quantitatively grasping the backlash of various gear pairs and a gear pair optimized using the evaluation device. The purpose is to do.

  The gear pair evaluation apparatus according to the present invention has three-dimensional coordinate data at each lattice point set on the tooth surface of the first gear and the tooth surface of the second gear meshing with the first gear. The set three-dimensional coordinate data at each lattice point is associated with each other at a predetermined meshing rotation position using the assembly specifications of the gear pair, and each of the three-dimensional coordinate data is associated with the first gear or the second gear. On the tooth surface of the second gear, using coordinate conversion means for converting into the three-dimensional coordinate data on the cylindrical coordinate system with reference to the two-dimensional parameter set on the tooth surface of the second gear Function generating means for generating a radial coordinate function, an axial coordinate function, and an angular coordinate function representing a point on the tooth surface of the second gear based on each of the three-dimensional coordinate data; and the first gear A point on the tooth surface of the second gear and the point on the same circumference on the cylindrical coordinate system The parameter shown is calculated from the radial coordinate function and the axial coordinate function, and based on the calculated parameter, the point on the tooth surface of the first gear and the second corresponding to the point. Inter-tooth surface gap information calculating means for calculating relative angle information indicating a gap between points on the tooth surface of the gear using the function of the angle coordinate, and the first calculated at a predetermined meshing rotation position. The minimum relative angle information is extracted from the relative angle information on the drive tooth surface side of the gear and the second gear, and the first gear calculated at the predetermined meshing rotational position and the The minimum relative angle information is extracted from the relative angle information on the coast tooth surface side with the second gear, and the minimum value of the relative angle information on the drive tooth surface side and the relative angle information on the coast tooth surface side are extracted. Based on the minimum value of the predetermined A backlash information calculating means for calculating a backlash information in meshing rotational position, characterized by comprising a.

  Further, the gear pair of the present invention is characterized in that specifications are optimized by using an evaluation result by the gear pair evaluation device.

  According to the gear pair evaluation apparatus of the present invention, it is possible to accurately and quantitatively grasp the backlash of various gear pairs.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings. FIG. 1 is a schematic configuration diagram of a gear pair evaluation device, FIG. 2 is a schematic configuration diagram showing an example of a computer system for realizing the gear pair evaluation device, and FIG. 3 is a gear configuration. FIG. 4 is a flowchart showing an inter-tooth gap calculation subroutine, FIG. 5 is a flowchart showing an envelope calculation subroutine, FIG. 6 is a flowchart showing a backlash calculation subroutine, and FIG. 7 is a perspective view of a hypoid gear. FIG. 8 is an explanatory view showing a cylindrical coordinate system for defining each lattice point on each tooth surface of the gear and pinion, and FIG. 9 is an explanation showing the relationship between the lattice point on the gear tooth surface and the convergence point on the pinion tooth surface. FIG. 10 is an explanatory diagram showing a method of calculating curved surface coordinates, FIG. 11 is an explanatory diagram showing a relative tooth surface based on the gear tooth surface, and FIG. 12 is a diagram showing the relative tooth surface at each pinion rotation step. FIG. 13 is an explanatory diagram showing an envelope surface obtained by synthesizing the respective relative tooth surfaces of FIG. 12, FIG. 14 is an explanatory diagram showing a tooth surface distance distribution of a gear pair, and FIG. 15 is an explanatory diagram showing an angle between tooth surfaces. FIG. 16 is an explanatory view showing the analysis result of backlash.

  In FIG. 7, reference numeral 100 denotes a gear pair. In the present embodiment, the gear pair 100 has a small diameter with, for example, a first gear (hereinafter also referred to as a gear) 101G that is one gear having a large diameter. The other gear is a hypoid gear that meshes with a second gear (hereinafter also referred to as a pinion) 101P.

  This gear pair 100 is evaluated using, for example, the evaluation apparatus 1 shown in FIG. The evaluation device 1 includes an input unit 5 for inputting three-dimensional coordinate data (measured values) and dimension data of each tooth surface of the gear 101G and the pinion 101P as information on the actual gear pair 100, and the input gear pair. A calculation unit 6 that performs various calculations based on the information, and a storage unit 7 that stores various programs executed by the calculation unit 6 and appropriately stores input gear pair information, calculation results by the calculation unit 6, and the like. And an output unit 8 that outputs a calculation result or the like in the calculation unit 6.

More specifically, the evaluation device 1 includes, for example, j × i pieces (for example, in the tooth height direction) set on the tooth surface (gear tooth surface) of interest of the gear 101G as actual tooth surface information of the gear 101G. Three-dimensional coordinate data (x _Gji , y _Gji , z _Gji ) measured at each grid point (15 × 15 in the tooth _{trace direction} ) is input. Further, the evaluation device 1 includes, for example, j × i pieces (for example, 15 pieces × tooth in the tooth height direction) set on the tooth surface of interest of the pinion 101P (pinion tooth surface) as the actual tooth surface information of the pinion 101P. The three-dimensional coordinate data (x _Pji , y _Pji , z _Pji ) measured at each lattice point (15 in the muscle direction) are input. More specifically, the evaluation apparatus 1 measures the actual tooth surface information of the gear 101G at each of j × i lattice points set on the drive-side gear tooth surface 102G _d of interest of the gear 101G. Three-dimensional coordinate data (x _Gji , y _Gji , z _Gji ) is input, and three-dimensional coordinate data (x is measured at each of j × i lattice points set on the coast side gear tooth surface 102G _{c. Gji} , _yGji , _zGji ) are input. Further, in the evaluation apparatus 1, as a real tooth surface information of the pinion 101P, 3-dimensional coordinate data measured respectively by the j × i pieces each lattice point of the set in the drive-side pinion tooth surface 102P on _d of interest of the pinion 101P (X _Pji , y _Pji , z _Pji ) are input, and three-dimensional coordinate data (x _Pji , y _Pji) respectively measured at j × i lattice points set on the coast side pinion tooth surface 102P _c. , Z _Pji ) is input. In the following description, the drive-side and coast-side gear tooth surfaces 102G _d and 102G _c are also collectively referred to as a gear tooth surface 102G. Similarly, the drive-side and coast-side pinion tooth surfaces 102P _d and 102P _c are also collectively referred to as a pinion tooth surface 102P.

Here, each of the three-dimensional coordinate data input to the evaluation device 1 as a real tooth surface information of the gear _{101G (x Gji, y Gji,} z Gji) is, X-Y having the origin _{O G} on the rotation axis of the gear 101G This is coordinate data defined by the orthogonal coordinate system of −Z, and in the present embodiment, the Z axis is set coaxially with the rotation axis of the gear 101G. Similarly, each three-dimensional coordinate data input to the evaluation device 1 as a real tooth surface information of the pinion _{101P (x Pji, y Pji,} z Pji) is, X-Y having the origin _{O P} on the rotation axis of the pinion 101P This is coordinate data defined by the orthogonal coordinate system of −Z, and in this embodiment, the Z axis is set coaxially with the rotation axis of the pinion 101P.

Here, in this embodiment, in order to standardize the rotation angle of the drive side and the coast side of each tooth surface, for example, each rotation angle of the drive side pinion tooth surface 102P _d and the coast side pinion tooth surface 102P _c is: As shown in FIG. 15 (b), a pinion tooth space is provided. Further, for example, the rotation angle of the drive gear tooth surface 102G _d and coast side gear tooth surface 102G _c, as shown in FIG. 15 (c), the gear tooth thickness is given.

  Further, the gear ratio ratio, the assembly specifications (offset Ε, crossing angle Σ), the respective deflection values δΕ, δΣ, δG, δP, etc. are input to the evaluation device 1 as dimension data of the gear pair 100. . Here, each deflection value is a deviation amount (an assembly error amount) caused by bending or the like when a predetermined torque is applied to the gear pair 100, δΕ is a deviation amount of the offset 、, and δΣ is a deviation of the crossing angle Σ. ΔG is the amount of deviation of the gear 101G in the direction of the rotation axis, and δP is the amount of deviation of the pinion 101P in the direction of the rotation axis (see FIG. 7).

The evaluation device 1, each three-dimensional coordinate data on the gear tooth surface _{102G (x Gji, y Gji,} z Gji) and each three-dimensional coordinate data on the pinion tooth surface _{102P (x Pji, y Pji,} z Pji ) _Are associated with each other at predetermined meshing rotational positions using the assembly specifications of the gear pair 100, and these are associated with three-dimensional coordinate data (r _Gji , _RZ -Θ on the cylindrical coordinate system with the gear 101G as a reference ₎ . z _Gji , θ _Gji ) and (r _Pji , z _Pji , θ _Pji ) (see FIG. 8). Here, the evaluation apparatus 1, each three-dimensional coordinate data on the gear tooth surface _{102G (x Gji, y Gji,} z Gji) and each three-dimensional coordinate data on the pinion tooth surface _{102P (x Pji, y Pji,} z _{When the Pji} ) is associated with each other, correction using the _deflection value is performed.

Further, the evaluation device 1 sets a two-dimensional parameter (j, i) on the pinion tooth surface 102P in association with the number of each lattice point on the pinion tooth surface 102P, and sets these parameter (j, i ), A radial coordinate function f _R (j, i) representing a point on the pinion tooth surface 102P and an axial coordinate function f _Z based on each three-dimensional coordinate data (r _Pji , z _Pji , θ _Pji ). (J, i) and an angular coordinate function f _Θ (j, i) are created.

Furthermore, the evaluation apparatus 1 includes each parameter (indicating each point on the pinion tooth surface 102P existing on the same circumference as each lattice point on the gear tooth surface 102G on the cylindrical coordinate system of RZ-Θ). j, i) is calculated from the functions f _R (j, i) and f _Z (j, i) using the Newton method, and the function f _Θ (j, i, j) is calculated using the calculated parameters (j, i). Based on the angle information θ _Pji obtained from i), a relative value indicating a gap between a point (lattice point) on the gear tooth surface 102G and a point on the pinion tooth surface 102P corresponding to the lattice point at a predetermined meshing rotation position. Angle information (interdental angle) is calculated.

Here, the evaluation apparatus 1 determines the rotation of the gear 101G and the pinion 101P defined by the pinion rotation angle θ _s for each rotation angle (pinion rotation angle) θ _{s obtained} by dividing one pitch of the pinion 101P by a predetermined number of divisions. For each meshing rotation position), relative tooth surface information with respect to each lattice point on the gear tooth surface 102G is calculated. In the present embodiment, the evaluation device 1 calculates each relative tooth surface information on the drive tooth surface side and each relative tooth surface information on the coast tooth surface side for each meshing rotation position.

Then, the evaluation device 1 combines the relative tooth surface information calculated at each meshing rotation position to thereby indicate an envelope surface indicating a relative clearance distance from the start to the end of meshing of the gear tooth surface 102G and the pinion tooth surface 102P. Is calculated. Further, the evaluation device 1 engages the gear tooth surface 102G and the pinion tooth surface 102G based on the relative tooth surface information on the drive tooth surface and the relative tooth surface information on the coast tooth surface calculated at each meshing rotational position. As backlash information at each meshing rotational position M from the start to the end, backlash angle information θ _BL (M) in the cylindrical coordinate system is calculated.

  In other words, the storage unit 7 of the evaluation apparatus 1 stores programs for performing the above-described various calculations. The calculation unit 6 executes coordinate programs, function generation units, Each function as a clearance information calculation means and a backlash information calculation means between tooth surfaces is realized.

  In addition, the evaluation apparatus 1 of this embodiment is implement | achieved by the computer system 10 shown, for example in FIG. In the computer system 10, for example, a keyboard 12, a display device 13 as an example of a display unit, and a printer 14 are connected to a computer main body 11 via a cable 15 to constitute a main part. In the computer system 10, for example, various drive devices, a keyboard 12, and the like disposed in the computer main body 11 function as the input unit 15, and a CPU, ROM, RAM, and the like built in the computer main body 11 are arithmetic units. 6 functions. Further, 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.

Next, the analysis of the gear pair executed by the calculation unit 6 will be described according to the flowchart of the gear pair evaluation routine shown in FIG. When this routine is started, the calculation unit 6 first, in step S101, the three-dimensional coordinate data (x _Gji , y _Gji , z _Gji ) measured at each lattice point on the tooth surface 102G of the gear 101G, the pinion 101P Three-dimensional coordinate data (x _Pji , y _Pji , z _Pji ) measured at each lattice point on the tooth surface 102P, gear ratio ratio, offset Ε, cross angle Σ, each assembly error amount δΕ, δΣ, δG, δP The gear pair information such as is read.

In subsequent step S102, the calculation unit 6 calculates the number of divisions per pitch of the pinion 101P and the pinion rotation angle θ _s per step using the following equations (1) to (4).
S _wagl = (2π / n _P ) · S _wn (1)
opn = Round ((2π / n _P ) / (S _wagl / max (j _max , i _max )) · c _hn )
... (2)
θ _s = (2π / n _P ) · (1 / opn) (3)
M _max = Round (S _wagl / θ _s ) + M _α (4)
Here, S _wagl is the pinion rotation angle between the mesh start point and end point, n _P is the number of pinion teeth, S _wn is the number of simultaneous mesh teeth (mesh rate), and opn is the number of angle steps per mesh pitch ( Integer), _Ch n is the number of angle steps per grid interval, and M _α is a correction value of the calculation range.

M _max indicates the range of angles to be calculated, and is the maximum gear rotation step number M _max .

Then, when the process proceeds from step S102 to step S103, the calculation unit 6 sets the gear rotation step number M = 1, and in the subsequent step S104, whether the gear rotation step number M has reached the gear rotation maximum step number _Mmax. Find out.

If the calculation unit 6 determines in step S104 that the gear rotation step number M has not yet reached the maximum gear rotation step number M _max , the operation unit 6 proceeds to step S105 and performs the following processing up to S111 M _max times. By repeating, the relative tooth surface data for each meshing rotation position where the pinion 101P rotates θ _s (rad) is calculated. In addition, although separate description is abbreviate | omitted, the calculating part 6 calculates the relative tooth surface data of a drive tooth surface side and a coast tooth surface side in the process of step S105 thru | or step S110, respectively. On the other hand, when it is determined in step S104 that the gear rotation step number M has reached the maximum gear rotation step number M _max , the arithmetic unit 6 proceeds to step S112.

When the process proceeds from step S104 to step S105, the calculation unit 6 uses the following equations (5) and (6) to calculate the rotation angles rotP and rotG of the pinion 101P and the gear 101G corresponding to the current gear rotation step number M. Calculate.
_{rotP = θ s · (M-} 1) - (θ s · M max) ... (5)
rotG = rotP · (−1 / ratio) (6)
In subsequent step S106, the calculation unit 6 moves the coordinates of the respective grid points on the orthogonal coordinate system of the pinion 101P by rotP (rad) around the Z axis, and the coordinates of the respective grid points on the orthogonal coordinate system of the gear 101G. Move rotG (rad) around the Z axis. Further, the calculation unit 6 moves the pinion's orthogonal coordinate system from the state where it coincides with the orthogonal coordinate system of the gear 101G (from the reference position of the cross point) by moving the offset Ε and rotating it by the intersection angle Σ. The relationship between the tooth surfaces 102G and 102P at the current step rotation position is set on the orthogonal coordinate system of the gear 101G. That is, the calculation unit 6 uses the coordinate data (x _Pji , y _Pji , z _Pji ) of each lattice point on the pinion tooth surface 102P at the current step rotation position as the coordinate data (x _{P ′} ) on the orthogonal coordinate system of the gear 101G. _ji , _yP'ji , _zP'ji ). At that time, calculating unit 6, the origin O _P of the coordinate systems of the pinion 101P and the gear _101G, O _G a deflection value [delta] P, is corrected by .delta.G, corrects the offset Ε in deflection value [Delta] [epsilon], the crossing angle Σ Is corrected with the deflection value δΣ.

In subsequent step S107, the calculation unit 6 obtains coordinate data of all measurement points (all gear lattice points and pinion lattice points) of the gear 101G and the pinion 101P represented on the orthogonal coordinate system based on the gear 101G in step S106 as follows. Using the equations (7) to (12), the data is converted into coordinate data of a cylindrical coordinate system of RZ-Θ with reference to the gear 101G.
r _Gji = (x _Gji ² + y _Gji ² ) ^1/2 (7)
z _Gji = z _Gji (8)
θ _Gji = tan ⁻¹ (y _Gji / x _Gji ) (9)
r _Pji = (x _P′ji ² + y _P′ji ² ) ^1/2 (10)
z _Pji = z _P'ji (11)
θ _Pji = tan ⁻¹ (y _P′ji / x _P′ji ) (12)
In subsequent step S108, the calculation unit 6 sets two-dimensional parameter variables j and i in association with the number of each grid point on the pinion tooth surface 102P, and uses these parameter variables j and i to set the pinion tooth surface 102P. Functions f _R (i, j), f _Z (i, j), f for interpolating between the grid points on the pinion tooth surface 102P based on the coordinate data (r _Pji , z _Pji , θ _Pji ) of each grid point _θ (i, j) is calculated. Here, each function _{f R (i, j),} f Z (i, j), f θ (i, j) , for example, respectively composed of a spline function.

Then, when the process proceeds from step S108 to step S109, the calculation unit 6 follows each of the lattice points on the gear tooth surface 102G and these lattice points on the pinion tooth surface 102P according to the flowchart of the inter-tooth surface gap calculation subroutine shown in FIG. The angle between teeth (relative tooth surface information) between the corresponding points is calculated. Here, in the following description, in order to distinguish the number of grids (j, i) defining each lattice point on the gear tooth surface 102G from that on the pinion tooth surface 102P, these are (j _G , i _G ). Is written.

When this subroutine starts, the calculation unit 6 sets initial values (j = j _ini , i = i _ini ) of parameters in step S201, and in step S202, the initial values j _ini and i _ini (for example, j _ini = i _ini = 8) The coordinates r ₁ (= R (j _ini , i _ini )), z ₁ (= Z (j _ini , i _ini )) of the defined pinion tooth surface 102P are obtained. .

In subsequent step S203, the calculation unit 6 performs calculation of an inter-tooth angle θ (j _G , i _G , M) described later on all the lattice points j _G , i _G on the gear tooth surface 102G. Find out. When it is determined that the calculation of the inter-tooth angle θ (j _G , i _G , M) for all the lattice points on the gear tooth surface 102G is not completed, the calculating unit 6 determines the inter-tooth surface angle θ (j _G , I _G , M) after updating the lattice point to be calculated to a new lattice point, the process proceeds to step S204, and the inter-tooth angle θ (j _G) using the Newton method by the processing up to step S209 below. , I _G , M). On the other hand, when it is determined in step S203 that the inter-tooth angle θ (j _G , i _G , M) is calculated for all the lattice points (j _G , i _G ) on the gear tooth surface 102G, the calculation unit 6 Exits the subroutine and returns to the main routine.

When proceeding from step S203 to step S204, the calculation unit 6 is the (j _G , i _G ) -th on the gear tooth surface 102G selected as the object of calculation of the tooth surface angle θ (j _G , i _G , M) this time. The three-dimensional coordinate data at the lattice point is (r ₀ , z ₀ , θ ₀ ), and this j _G , i _G- th lattice point and pinion existing on the same circumference on the RZ-Θ cylindrical coordinate system The three-dimensional coordinate data at the point (convergence point) on the tooth surface 102P is (r _c , z _c , θ _c ), and (r _c , z _c , θ _c ) = (r ₀ , z ₀ , θ) _c )), the three-dimensional coordinate data (r ₁ , z ₁ , θ ₁ ) of the reference point set on the pinion tooth surface 102P and the three-dimensional coordinate data (r ₀ , z ₀ , The following formulas (13) and (14) are created from θ _c ).
r ₀ = r ₁ + (∂r / ∂i) Δi + (∂r / ∂j) Δj (13)
z ₀ = z ₁ + (∂z / ∂i) Δi + (∂z / ∂j) Δj (14)
Here, the radial coordinate (R coordinate) component r on the cylindrical coordinate system of an arbitrary point (j, i) on the pinion tooth surface 102P can be calculated using the following equation (15). The inclination in the i direction (∂r / ∂i) and the inclination in the j direction (∂r / ∂j) at the coordinate r can be calculated using the following equations (16) and (17). Is possible.
r = − (j ₁ −j) · (i ₁ −i) · R (j ₀ , i ₀ )
− (J ₁ −j) · (i−i ₀ ) · R (j ₀ , i ₁ )
− (J−j ₀ ) · (i ₁ −i) · R (j ₁ , i ₀ )
− (J−j ₀ ) · (i−i ₀ ) · R (j ₁ , i ₁ )
+ (J ₁ −j) · f _Ri0 (i) + (j−j ₀ ) · f _Rj1 (i)
+ (I ₁ −i) · f _Ri0 (j) + (i−i ₀ ) · f _Ri1 (j)
... (15)
∂r / ∂i
= (J ₁ −j) · {R (j ₀ , i ₀ ) −R (j ₀ , i ₁ ) + (∂f _Rj0 (i) / ∂i)}
+ (J−j ₀ ) · {R (j ₁ , i ₀ ) −R (j ₁ , i ₁ ) + (∂f _Rj1 (i) / ∂i)}
−R (j, i ₀ ) + R (j, i ₁ )
... (16)
∂r / ∂j
= (I ₁ −i) · {R (j ₀ , i ₀ ) −R (j ₁ , i ₀ ) + (∂f _Ri0 (j) / ∂j)}
+ (I−i ₀ ) · {R (j ₀ , i ₁ ) −R (j ₁ , i ₁ ) + (∂f _Ri1 (j) / ∂j)}
−R (j ₀ , i) + R (j ₁ , i)
... (17)
In the equations (15) to (17), f _Rj0 (i), f _Rj1 (i), f _Rj0 (j), and f _Ri1 (j) are points (j, i ) Is a radial coordinate component at an arbitrary point on the function surrounding the function, and these are calculated based on the function created in step S108 described above. R (j ₀ , i ₀ ), R (j ₀ , i ₁ ), R (j ₁ , i ₀ ), R (j ₁ , i ₁ ) are at each lattice point surrounding the point (j, i) Radial coordinate component.

  Similarly, the axial coordinate (Z coordinate) component z on the cylindrical coordinate system of an arbitrary point (j, i) on the pinion tooth surface 102P can be calculated using the following equation (18). The inclination in the i direction (∂z / ∂i) and the inclination in the j direction (∂z / ∂j) at the coordinate z can be calculated using the following equations (19) and (20). Is possible.

z = − (j ₁ −j) · (i ₁ −i) · Z (j ₀ , i ₀ )
− (J ₁ −j) · (i−i ₀ ) · Z (j ₀ , i ₁ )
− (J−j ₀ ) · (i ₁ −i) · Z (j ₁ , i ₀ )
− (J−j ₀ ) · (ii ₀ ) · Z (j ₁ , i ₁ )
+ (J ₁ −j) · f _Zj0 (i) + (j−j ₀ ) · f _Zj1 (i)
+ (I ₁ −i) · f _Zi0 (j) + (i−i ₀ ) · f _Zi1 (j)
... (18)
∂z / ∂i
= (J ₁ −j) · {Z (j ₀ , i ₀ ) −Z (j ₀ , i ₁ ) + (∂f _Zj0 (i) / ∂i)}
+ (J−j ₀ ) · {Z (j ₁ , i ₀ ) −Z (j ₁ , i ₁ ) + (∂f _Zj1 (i) / ∂i)}
−Z (j, i ₀ ) + Z (j, i ₁ )
... (19)
∂z / ∂j
= (I ₁ −i) · {Z (j ₀ , i ₀ ) −Z (j ₁ , i ₀ ) + (∂f _Zi0 (j) / ∂j)}
+ (I−i ₀ ) · {Z (j ₀ , i ₁ ) −Z (j ₁ , i ₁ ) + (∂f _Zi1 (j) / ∂j)}
−Z (j ₀ , i) + Z (j ₁ , i)
... (20)
In the equations (18) to (20), f _Zj0 (i), f _Zj1 (i), f _Zi0 (j), and f _Zi1 (j) are on the function surrounding the point (j, i). These are axial coordinate components at arbitrary points, and these are calculated based on the function created in step S108 described above. Z (j ₀ , i ₀ ), Z (j ₀ , i ₁ ), Z (j ₁ , i ₀ ), and Z (i ₁ , j ₁ ) are at each lattice point surrounding the point (j, i). It is an axis coordinate component.

  And the calculating part 6 calculates | requires deviation (DELTA) i and (DELTA) j of the parameter from a reference point to a convergence point by solving simultaneous equations by (13), (14) Formula.

In subsequent step S205, the calculation unit 6 uses the deviations Δi and Δj obtained in step S204 to update the reference point parameter (j, i) using the following equations (21) and (22).
i = i + Δi (21)
j = j + Δj (22)
In step S206, the calculation unit 6 uses the above-described equations (15) and (18) and the following equation (23) based on the parameter (j, i) updated in step S205. The three-dimensional coordinate data (r ₁ , z ₁ , θ ₁ ) at the reference point is updated.
θ = − (j ₁ −j) · (i ₁ −i) · θ (j ₀ , i ₀ )
− (J ₁ −j) · (i−i ₀ ) · θ (j ₀ , i ₁ )
− (J−j ₀ ) · (i ₁ −i) · θ (j ₁ , i ₀ )
− (J−j ₀ ) · (i−i ₀ ) · θ (j ₁ , i ₁ )
+ (J ₁ −j) · f _θj0 (i) + (j−j ₀ ) · f _θj1 (i)
+ (I ₁ −i) · f _θi0 (j) + (i−i ₀ ) · f _θi1 (j)
... (23)
In the equation (23), f _θj0 (i), f _θj1 (i), f _θi0 (j), and f _θi1 (j) are angular coordinate components at each point surrounding the point (j, i). These are calculated based on the function created in step S108 described above. θ (j ₀ , i ₀ ), θ (j ₀ , i ₁ ), θ (j ₁ , i ₀ ), θ (j ₁ , i ₁ ) are the lattice points surrounding the point (j, i). It is an angular coordinate component.

When the process proceeds to step S207, the arithmetic unit 6, R-axis coordinate component _{r 1} and Z-axis coordinate component _{z 1} of the reference point calculated in step S206 is the convergence point R coordinate component _{r c} and Z-axis coordinate component _{z c} (That is, whether r ₁ and z ₁ and r ₀ and z ₀ match within a preset range, respectively). The process proceeds to S208, and if it is determined that the process has converged, the process proceeds to Step S208.

  When the process proceeds from step S207 to step S208, the calculation unit 6 determines whether or not the number of calculations in steps S204 to S206 performed on the lattice point on the currently selected gear tooth surface 102G is, for example, 10 times or more. If the number of calculations is less than 10, the process returns to step S204. If the number of calculations is 10 or more, the process proceeds to step S209.

Then, when the process proceeds from step S207 or step S208 to step S209, the calculation unit 6 uses the current gear grid j _G , i _G , the tooth face angle θ (j _G , i as the gear rotation step number M) as relative angle information. After calculating ( _G , M), the process returns to step S203. Here, proceeds to step S209 it is determined that the R-axis coordinate component _{r 1} and Z-axis coordinate component _{z 1} of the reference point is converged to R coordinate component _{r c} and Z-axis coordinate component _{z c} of the convergence point in step S207 In this case (that is, when a point corresponding to the lattice point on the currently selected gear tooth surface 102G exists in the pinion tooth surface 102P), the inter-tooth angle θ (j _G , i _G , M) is (24).
θ (j _G , i _G , M) = θ ₁ −θ ₀ (24)
On the other hand, when the process proceeds from step S208 to step S209, an angle value for determination (for example, θ indicating that a point corresponding to the lattice point on the currently selected gear tooth surface 102G exists outside the pinion tooth surface 102P). _{(j G, i G, M} ) = 2000) is set.

In the main routine, when the process proceeds from step S109 to step S110, the calculation unit 6 uses the gear tooth surface 102G as a reference based on the inter-tooth angle θ (j _G , i _G , M) calculated in step S109. Relative tooth surface data (see, for example, FIG. 11) is created, and in the subsequent step S111, the gear rotation step M is incremented (M = M + 1), and then the process returns to step S104.

  Further, when the process proceeds from step S104 to step S112, the calculation unit 6 determines the relative relationship between the tooth surfaces from the start to the end of meshing of the gear tooth surface 102G and the pinion tooth surface 102P according to the flowchart of the envelope surface calculation subroutine shown in FIG. Envelope surface calculation that shows a clear gap distance.

When this subroutine starts, the calculation unit 6 sets the gear rotation step M = 1 in step S301, and in subsequent step S302, determines whether or not the gear rotation step number M has reached the maximum gear rotation step number _Mmax. Investigate.

Then, calculating unit 6, in step S302, if it is determined that the gear rotation step number M has not yet reached the gear rotation maximum number of steps M _max, the process proceeds to step S303. On the other hand, when it is determined that the gear rotation step number M has reached the gear rotation maximum step number _Mmax , the arithmetic unit 6 proceeds to step S307.

When the process proceeds from step S302 to step S303, the calculation unit 6 performs the tooth surface angle θ (j _G , i _G , M) at all lattice points on the gear tooth surface 102G in the current gear rotation step number M. It is checked whether or not extraction calculation of the inter-tooth surface minimum angle θ _Smin (M) described later has been completed.

In step S303, when it is determined that the extraction calculation of the inter-tooth angle minimum value θ _Smin is not completed with respect to the inter-tooth angle θ (j _G , i _G , M) at all lattice points, the arithmetic unit 6 proceeds to step S304, and the inter-tooth angle minimum value θ _Smin (M) at the current gear rotation step number M is set to the inter-tooth angle θ of the currently selected lattice point by the following equation (25). _{(j G, i G, M} ) are appropriately updated at.
θ _Smin (M) = min (θ (j _G , i _G , M)) (25)
Further, when the inter-tooth surface angle minimum value θ _Smin (M) is updated with the inter-tooth surface angle θ (j _G , i _G , M) of the currently selected lattice point, the calculating unit 6 After updating the coordinates (POCj (M), POCi (M)) of the maximum convex point of the relative tooth surface in the gear rotation step M to (j _G , i _G ) of the current lattice point, the process returns to step S303.

On the other hand, when it is determined in step S303 that the extraction calculation of the inter-tooth angle minimum value θ _Smin is completed with respect to the inter-tooth angle θ (j _G , i _G , M) at all lattice points, the calculation unit 6 The process proceeds to step S305.

Then, in step S305, the arithmetic unit 6, following the equation (26), the tooth surface angle between the minimum value theta _minmin in all gear rotation step, between the teeth surface angle minimum value at the current gear rotation step M theta _Smin Update as appropriate.
θ _minmin = min (θ _Smin (M)) (26)
Furthermore, calculating unit 6, when the current gear rotation step M at the tooth surface angle between the minimum value theta _Smin total gear rotation step of the tooth surface between the angle minimum value theta _minmin is updated, relative in the total gear rotation step teeth The coordinates (APEXj, APEXi) of the most convex point of the surface (that is, the most convex point of the gear pair 100) are updated to the coordinates (POCj (M), POCi (M)) of the most convex point in the current gear rotation step M.

  And if it progresses to step S306 from step S305, the calculating part 6 will update the gear rotation speed step M (M = M + 1), and will return to step S302.

Further, when the process proceeds from step S302 to step S307, the calculation unit 6 uses the inter-tooth surface angles θ (j _G , i _G , M) calculated for each gear rotation step number M, and performs the processing up to step S312. Thus, relative tooth surface data θ indicating the relative gap distance from the start to the end of meshing of the gear tooth surface 102G and the pinion tooth surface 102P as an angle value for each lattice point (j _G , i _G ) on the gear tooth surface 102G. _EO (j _G , i _G ) is calculated.

More specifically, the calculation unit 6 sets the gear rotation step number M = 1 in step S307, and in the subsequent step S308, whether the gear rotation step number M has reached the gear rotation maximum step number _Mmax or not. Check out.

If it is determined in step S308 that the gear rotation step number M has not yet reached the gear rotation maximum step number _Mmax , the arithmetic unit 6 proceeds to step S309. On the other hand, when it is determined that the gear rotation step number M has reached the gear rotation maximum step number _Mmax , the arithmetic unit 6 proceeds to step S313.

When the process proceeds from step S308 to step S309, the calculation unit 6 performs relative tooth surface data θ _{EOM to be} described later with respect to all lattice points (j _G , i _G ) on the gear tooth surface 102G in the current gear rotation step number M. It is checked whether or not the calculation of (j _G , i _G , M) has been completed.

When it is determined in step S309 that the calculation of the relative tooth surface data θ _EOM (j _G , i _G , M) has not been completed for all grid points (j _G , i _G ), _Proceeding to step S310, the relative tooth surface data θ _EOM (Ease−Off) is calculated by using the following formula (27) as a reference.
θ _EOM (j _G , i _G , M) = θ (j _G , i _G , M) −θ _minmin (27)
In subsequent step S311, the calculation unit 6 uses the relative tooth surface data θ _EOM (j _G , i _G , M) of the currently selected lattice point (j _G , i _G ) according to the following equation (28). Then, the corresponding relative tooth surface data θ _EO (j _G , i _G ) is appropriately updated, and the process returns to step S309.
θ _EO (j _G , i _G ) = min (θ _EOM (j _G , i _G , M)) (28)
On the other hand, if it is determined in step S309 that the calculation of the relative tooth surface data θ _EOM (j _G , i _G , M) has been completed for all grid points (j _G , i _G ) at the current gear rotation step number M. The calculation unit 6 proceeds to step S312, increments the gear rotation step number M (M = M + 1), and then returns to step S308.

Further, when the process proceeds from step S308 to step S313, the arithmetic unit 6 calculates the relative tooth surface data θ _EO (j _G ) for each lattice point (j _G , i _G ) on the gear tooth surface 102G by the following equation (29). , I _G ) is converted into distance information (relative tooth surface data EO (j _G , i _G ), then the subroutine is exited and the process returns to the main routine.
_{EO (j G, i G)} = θ EO (j G, i G) · r 0 (j G, i G) ... (29)
Thus, an envelope surface (for example, see FIG. 13) is generated by combining the relative tooth surfaces (for example, see FIG. 12) for each gear rotation step number M. Here, the calculation unit 6 can also convert the generated three-dimensional envelope surface data into two-dimensional contour data (for example, see FIG. 14), and output the contour data to the display device 13 or the like. It is also possible to output through the section.

When the process proceeds from step S112 to step S113, the calculation unit 6 calculates the backlash information for each meshing rotation position M in accordance with the backlash calculation subroutine shown in FIG. In this subroutine, the calculation unit 6 calculates a backlash angle θ _BL on the cylindrical coordinate system (RZ-Θ) as backlash information.

When this subroutine is started, the calculation unit 6 sets the gear rotation step M = 1 in step S401, and in subsequent step S402, determines whether or not the gear rotation step number M has reached the maximum gear rotation step number _Mmax. Investigate.

Then, calculating unit 6, in step S402, if it is determined that the gear rotation step number M has not yet reached the gear rotation maximum number of steps M _max, the process proceeds to step S403. On the other hand, when it is determined that the gear rotation step number M has reached the gear rotation maximum step number _Mmax , the calculation unit 6 exits the subroutine and ends the main routine.

Proceeding from step S402 to step S403, the arithmetic unit 6, in the current gear rotation step number M, all the lattice points on the gear tooth surface 102G (on the drive side gear tooth surface 102G _d and coast side gear tooth surface 102G on _c respectively It is checked whether or not the extraction calculation of the inter-tooth angle minimum value θ _Smin (M), which will be described later, is completed with respect to the inter-tooth angle θ (j _G , i _G , M) at all grid points in FIG.

In step S403, when it is determined that the extraction calculation of the inter-tooth angle minimum value θ _Smin is not completed with respect to the inter-tooth angle θ (j _G , i _G , M) at all lattice points, the arithmetic unit 6 proceeds to step S404, and the inter-tooth angle minimum value θ _Smin (M) at the current gear rotation step number M is set to the inter-tooth angle θ of the currently selected lattice point according to the above equation (25). _{(j G, i G, M} ) are appropriately updated at.

Further, when the inter-tooth surface angle minimum value θ _Smin (M) is updated with the inter-tooth surface angle θ (j _G , i _G , M) of the currently selected lattice point, the calculating unit 6 After updating the coordinates (POCj (M), POCi (M)) of the most convex point of the relative tooth surface in the gear rotation step M to (j _G , i _G ) of the current lattice point, the process returns to step S403.

On the other hand, when it is determined in step S403 that the extraction calculation of the inter-tooth angle minimum value θ _Smin is completed with respect to the inter-tooth angle θ (j _G , i _G , M) at all lattice points, the calculation unit 6 The process proceeds to step S405.

In step S405, the calculation unit 6 uses the drive-side and coast-side minimum tooth surface angle values θ _Smind (M) and θ _Smin (M) extracted in step S404 (see FIG. 15A). The backlash angle θ _BL (M) at the current gear rotation step number M is calculated by the following equation (30).
θ _BL (M) = θ _Smind (M) + θ _Smin (M) _−2π (30)
Then, when the process proceeds from step S405 to step S406, the calculation unit 6 increments the gear rotation step number M (M = M + 1), and then returns to step S403.

Here, the calculation unit 6 multiplies each backlash angle θ _BL (M) calculated for each gear rotation step number M by, for example, the pitch circle radius r ′ _G of the gear 101, for each meshing rotation position. The backlash amount (distance) BL can be calculated (see, for example, FIG. 16), and the transition of the backlash amount can be output through an output unit such as the display device 13. .

According to this embodiment, the three-dimensional coordinate data on the gear tooth surface _{102G (x Gji, y Gji,} z Gji) and the 3-dimensional coordinate data on the pinion tooth surface _{102P (x Pji, y Pji,} z _Pji ) is associated with each other at a predetermined meshing rotational position using the assembly specifications of the gear pair 100, and three-dimensional coordinate data (r _Gji , z _Gji , θ _Gji ) and (r _Pji , z _Pji , θ _Pji ) and using two-dimensional parameters (j, i) set on the pinion tooth surface 102P, based on each three-dimensional coordinate data (r _Pji , z _Pji , θ _Pji ). By creating functions f _R (j, i), f _Z (j, i), f _Θ (j, i) representing points on the pinion tooth surface 102P, each point (grid) on the gear tooth surface 102G point The parametric (j, i) indicating the respective points on the corresponding pinion tooth surface 102P that in, easily and accurately calculated using Newton's method from the function _{f R (j, i),} f Z (j, i) be able to. Based on the angle information θ _Pji obtained from the function f _Θ (j, i) using each calculated parameter (j, i), a point (lattice point) on the gear tooth surface 102G at a predetermined meshing rotational position ) And the inter-tooth angle θ (j _G , i _G , M) indicating the gap between the point on the pinion tooth surface 102P corresponding to the lattice point and the information on the reference tooth surface of the gear pair as an index Therefore, accurate tooth surface analysis can be realized based on the measurement information of the actual tooth surface. Then, the minimum value θ _Smind (M) is extracted from the tooth surface angle θ (j _G , i _G , M) on the drive tooth surface side calculated at the predetermined meshing rotation position, and the coast tooth surface side The minimum value θ _Smin (M) is extracted from the inter-tooth surface angle θ (j _G , i _G , M), and based on these, backlash information (backlash angle θ _BL (M)) at the meshing rotation position is extracted. Thus, the backlash information of the gear pair can be grasped accurately and quantitatively without relying on artificial measurement or the like.

  At this time, the accuracy of the tooth surface analysis can be further improved by correcting the three-dimensional coordinate data associated with each other using the assembly specifications of the gear pair 100 with the deflection value of the gear pair 100.

  And, by feeding back the evaluation results of such backlash and optimizing the specifications of the gear pair, it is possible to suppress vibration and noise and to prevent rotation failure, wear or seizure. A compatible gear pair 100 can be obtained.

  Here, in the above-described analysis, an example in which backlash and the like are evaluated using the measured data on the tooth surfaces 102G and 102P of the gear pair 100 has been described. For example, theoretical teeth obtained at the design stage are described. It is also possible to evaluate backlash using surface data.

  By the way, the above-described gear pair evaluation can be applied to various external gear pairs other than hypoid gears, and can also be widely applied to various internal gear pairs. The present invention can also be applied to a trochoid oil pump 200 (see FIG. 17) classified as an internal gear pair in terms of meaning. Here, as shown in the drawing, the oil pump 200 is configured such that the inner rotor 201I as the second gear meshes with the inner periphery of the outer rotor 201O as the first gear.

  In the evaluation of the oil pump 200, for example, the outer rotor 201O is associated with the above-described gear 101G, and the inner rotor 201I is associated with the above-described pinion 101P. Then, for example, as shown in FIG. 18, the origin of the orthogonal coordinate system (XYZ) is set at the center of rotation and the center of the tooth width of the inner rotor 201I, and this orthogonal coordinate system (and based on the orthogonal coordinate system) is set. The Z axis of the cylindrical coordinate system (RZ-Θ) is set as the rotation axis of each rotor 201O, 201I.

The calculation unit 6 basically evaluates the oil pump 200 in accordance with the flowchart of the gear pair evaluation routine shown in FIG. However, when such an evaluation of the oil pump 200 is performed, in step S101, the calculation unit 6 reads the distance between the center axes of both the rotors 201O and 201I as the offset E, and reads “0” as the intersection angle Σ. In step S101, the calculation unit 6 uses, as a deflection value (assembly error amount), an error amount δX in the X axis direction, an error amount δY in the Y axis direction, an error amount δXR around the X axis, and an error amount around the Y axis. The error amount δYR (see FIG. 18) is read. In consideration of the fact that the outer rotor 201O and the inner rotor 201I of the oil pump 200 rotate in the same direction, in step S105, the calculation unit 6 determines the rotation angles rotP and rotG of the outer rotor 201O and the inner rotor 201I corresponding to the gear rotation step M. Is calculated using the following expressions (5) ′ and (6) ′.
rotP = θ _s · (M−1) − (θ _s · M _max ) (5) ′
rotG = rotP · (1 / ratio) (6) ′
For the other processes, the calculation unit 6 performs substantially the same process as the hypoid gear 100 described above. Thereby, also about the oil pump 200, the clearance gap information, backlash information, etc. can be grasped | ascertained accurately and quantitatively.

  Here, as described above, in order to realize not only hypoid gears but also various gear pairs such as oil pumps, for example, as shown in FIG. 19, the calculation unit 6 is displayed through an output unit such as a display 13 device. On the setting error amount setting screen, items for various assembling error amounts are displayed. Specifically, for example, the calculation unit 6 displays items E, P, G, and Σ corresponding to a gear pair having a staggered shaft such as a hypoid gear, and a parallel shaft such as an oil pump. X, Y, XR, and YR are displayed as items corresponding to the gear pair having. Further, the calculation unit 6 allows a user or the like to set a plurality of combinations of assembly error amounts for the corresponding gear pair, and thus a plurality of steps corresponding to each item on the assembly error amount setting screen. An input frame (for example, 10 levels) is displayed. The illustrated example describes an example of setting an assembly error amount for the oil pump 200. For example, in the first stage, all items (X, Y, XR corresponding to the oil pump 200) are described. , And YR), the case where no assembly error amount is set is shown. Further, for example, the second level shows a case where a predetermined assembly error amount is given only in the X-axis direction.

  By the way, the evaluation device 1 can use the above-described gear pair evaluation routine to search for a limit assembly error amount that is permitted when the gear pair to be evaluated secures backlash. In this search for the limit assembly error amount, the evaluation device 1 variably sets various assembly error amounts read in step S101 of the gear pair evaluation routine shown in FIG. 3, for example, for each set assembly error amount. The backlash information is sequentially calculated. Then, for example, the limit value for securing backlash is specified for the assembling error amount of each item. That is, the storage unit 7 of the evaluation apparatus 1 stores programs for performing the above-described various calculations. The calculation unit 6 executes these programs as a limit assembly error amount search unit. Realize the function.

  Moreover, the evaluation apparatus 1 can calculate the backlash characteristic with respect to various assembly errors of the gear pair to be evaluated using the above-described gear pair evaluation routine. In the calculation of the backlash characteristic, the evaluation apparatus 1 variably sets and sets various assembling error amounts to be read in step S101 of the gear pair evaluation routine shown in FIG. 3 described above, for example. Backlash information for each assembly error amount is calculated sequentially. Then, for example, the backlash characteristic information for the assembling error amount is generated based on the relationship between each assembling error amount variably set and the backlash information. That is, the storage unit 7 of the evaluation apparatus 1 stores programs for performing the various calculations described above, and the calculation unit 6 functions as a backlash characteristic calculation unit by executing these programs. Realize.

  Next, the limit assembly error search executed by the calculation unit 6 will be described with reference to the flowchart of the limit assembly error search routine shown in FIG. When this routine is started, the calculation unit 6 first checks in step S501 whether the backlash calculation has been completed for the assembly errors of all items. For example, when the above-described oil pump 200 shown in FIG. 17 is an evaluation target, it is checked whether or not the backlash calculation has been completed for all the assembly error amounts X, Y, XR, and YR.

If it is determined in step S501 that the backlash calculation for the assembly error amounts of all items has not been completed, the calculation unit 6 proceeds to step S502, and selects a predetermined item from items that have not yet been selected. And the plus side assembly error amount e ₁ and the minus side assembly error amount e ₂ for the selected item are set to “0”, respectively, and the process proceeds to step S503.

In step S503, the calculation unit 6 uses the plus and minus side assembly error amounts e ₁ and e ₂ set for the currently selected item, and follows the gear pair evaluation routine shown in FIG. Backlash information (backlash angle θ _BL (M)) is calculated. In this case, as the assembly error amount of the item not currently selected, for example, “0” is set uniformly. Alternatively, any assembly error amount set by the user or the like can be used. When the calculation of the backlash angle θ _BL (M) for each meshing rotational position M from the meshing start to the meshing end using the assembly error amounts e ₁ and e ₂ is completed, the calculation unit 6 The minimum values in the rush information θ _BL (M) are extracted, and values (backlash BL ₁ , BL ₂ ) obtained by converting them into distance information are calculated.

When the process proceeds from step S503 to step S504, the arithmetic unit 6 checks whether or not the backlashes BL ₁ and BL ₂ calculated in step S503 are both negative values.

In step S504, when at least _{one of} the backlash BL ₁ and BL ₂ is a positive value, the calculation unit 6 proceeds to step S505, and re-assembles the assembly error amount that is the positive value. After setting e (= e ± Δe), the process returns to step S503.

On the other hand, when the backlash BL ₁ and BL ₂ are negative values in step S504, the arithmetic unit 6 returns to step S501.

If it is determined in step S501 that the backlash calculation has been completed for the assembling error amounts of all items, the calculating unit 6 proceeds to step S506, and assembling when BL ₁ <0 is satisfied in each item. recognizes the error amount e ₁ as a plus side of the limit assembly error, and recognizes the assembling error amount e ₂ when a BL 2 _<0 as a limit assembly error of the minus side, the positive side of each item Then, after setting each limit assembly error on the minus side as output data, the routine is terminated.

  Next, the backlash characteristic calculation executed by the calculation unit 6 will be described according to the flowchart of the backlash characteristic calculation routine shown in FIG. When this routine is started, the calculation unit 6 first checks in step S601 whether the backlash calculation has been completed for the assembly errors of all items. For example, when the above-described oil pump 200 shown in FIG. 17 is an evaluation target, it is checked whether or not the backlash calculation has been completed for all the assembly error amounts X, Y, XR, and YR.

If it is determined in step S601 that the backlash calculation has not been completed for the assembling error amounts of all items, the calculation unit 6 proceeds to step S602 and selects a predetermined item from items not yet selected. Select. Here, when the backlash characteristic calculation is performed, the evaluation apparatus 1 analyzes the assembly error amount of each item by a user input or the like through the input unit 5 and the range of the assembly error amount (e _{min to} e _max ). The calculation unit 6 sets the lower limit value e _min of the assembling error amount of the selected item as the initial value of the assembling error amount e (e = e _min ), and then performs the step. The process proceeds to S603.

In step S603, the calculation unit 6 uses the assembly error amount e set for the currently selected item and performs backlash information (backlash angle θ _BL (M )) Is calculated. In this case, as the assembly error amount of the item not currently selected, for example, “0” is set uniformly. Alternatively, any assembly error amount set by the user or the like can be used. When the calculation of the backlash angle θ _BL (M) for each meshing rotational position M from the meshing start to the meshing end using the assembly error amount e is completed, the computing unit 6 calculates each backlash information θ _BL ( The minimum value in M) is extracted, and a value (backlash BL) obtained by converting this to distance information is calculated.

When the process proceeds from step S603 to step S604, the calculation unit 6 checks whether or not the current assembly error amount e is larger than a preset maximum value e _max .

Then, in step S604, the case where the current assembling error e is equal to or less than the maximum value e _max, calculating unit 6, the flow proceeds to step S605, and sets the amount Δe increase the current assembling error e After setting a new assembly error amount e (= e + Δe), the process returns to step S603.

On the other hand, if it is determined in step S604 that the current assembly error amount e is greater than the preset maximum value _emax , the arithmetic unit 6 returns to step S601.

  If it is determined in step S601 that the backlash calculation has been completed for the assembling error amounts of all items, the calculating unit 6 proceeds to step S606, and the back when the assembling error amount is changed for each item. After setting backlash information (for example, see FIGS. 22 and 23) indicating the transition of the rush BL as output data, the routine is terminated.

  Here, in the above-described embodiment, an example in which the actual measurement value is used as the three-dimensional coordinate data on each tooth surface of the gear pair has been described. However, the present invention is not limited to this example. It is also possible to use theoretical tooth surface data obtained at the design stage based on the design value of. And, for example, after evaluating the gear pair using the theoretical tooth surface data in this way and optimizing the specifications for backlash, etc., each tooth surface of the gear pair manufactured based on the specifications By re-evaluating the gear pair using the three-dimensional coordinate data actually measured above and optimizing the specifications for backlash and the like, the specification design of the gear pair can be realized efficiently.

Schematic configuration diagram of gear pair evaluation device Schematic configuration diagram showing an example of a computer system for realizing a gear pair evaluation device Flow chart showing gear pair evaluation routine Flow chart showing the inter-tooth gap calculation subroutine A flowchart showing an envelope surface calculation subroutine Flow chart showing backlash calculation subroutine Perspective view of hypoid gear Explanatory drawing which shows the cylindrical coordinate system which prescribes | regulates each lattice point on each tooth surface of a gear and a pinion Explanatory drawing which shows the relationship between the lattice point on a gear tooth surface and the convergence point on a pinion tooth surface Explanatory drawing showing the calculation method of curved surface coordinates Explanatory drawing showing relative tooth surface based on gear tooth surface Explanatory drawing which shows the relative tooth surface in each pinion rotation step Explanatory drawing which shows the envelope surface which synthesize | combined each relative tooth surface of FIG. Explanatory drawing showing tooth surface distance distribution of gear pair Explanatory drawing showing the angle between teeth Explanatory drawing showing the analysis result of backlash Cross section of the main part of the oil pump Explanatory drawing showing coordinates of inner rotor and outer rotor defined during backlash calculation Explanatory drawing showing the setting screen for assembly error Flow chart showing limit assembly error search routine Flow chart showing backlash characteristic calculation routine Explanatory drawing which shows the change of the backlash when an assembly | attachment error is given to the X-axis direction and the Y-axis direction of FIG. Explanatory drawing which shows the change of the backlash when an assembly | attachment error is given to the X-axis periphery and the Y-axis periphery of FIG.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 ... Evaluation apparatus 6 ... Calculation part (Coordinate conversion means, function preparation means, tooth gap clearance information calculation means, backlash information calculation means, limit assembly error calculation means, backlash characteristic calculation means)
100 ... Hypoid gear (gear pair)
101G ... Gear (first gear)
101P ... Pinion (second gear)
102G ... Gear tooth surface (tooth surface of the first gear)
102P ... Pinion tooth surface (tooth surface of the second gear)
200… Oil pump (gear pair)
201O ... Outer rotor (first gear)
201I ... Inner rotor (second gear)

Claims (5)

Three-dimensional coordinate data at each lattice point set on the tooth surface of the first gear and three-dimensional at each lattice point set on the tooth surface of the second gear meshing with the first gear The coordinate data is associated with each other at a predetermined meshing rotation position using the assembly specifications of the gear pair, and each of the three-dimensional coordinate data is defined as 3 on the cylindrical coordinate system based on the first gear or the second gear. Coordinate conversion means for converting to dimensional coordinate data;
Using a two-dimensional parameter set on the tooth surface of the second gear, a point on the tooth surface of the second gear is determined based on each three-dimensional coordinate data on the tooth surface of the second gear. A function creation means for creating a function of radius coordinates, a function of axis coordinates, and a function of angle coordinates;
The parametric variable indicating the point on the tooth surface of the first gear and the point on the tooth surface of the second gear existing on the same circumference on the cylindrical coordinate system is defined as a function of the radial coordinate and the axis. Calculated from a coordinate function, and based on the calculated parameter, indicates a gap between a point on the tooth surface of the first gear and a point on the tooth surface of the second gear corresponding to the point Tooth surface clearance information calculating means for calculating relative angle information using a function of the angle coordinate,
The minimum relative angle information is extracted from the relative angle information on the drive tooth surface side of the first gear and the second gear calculated at a predetermined meshing rotational position, and the predetermined meshing is performed. The minimum relative angle information is extracted from the relative angle information on the coast tooth surface side of the first gear and the second gear calculated at the rotational position, and the relative angle information on the drive tooth surface side is extracted. A backlash information calculating means for calculating backlash information at the predetermined meshing rotation position based on the minimum value of the relative angle information on the coast tooth surface side Evaluation device.   2. The gear pair evaluation according to claim 1, wherein the coordinate conversion means corrects the three-dimensional coordinate data associated with each other by using an assembly specification of the gear pair with an assembling error amount of the gear pair. apparatus.   The assembly error amount for correcting the three-dimensional coordinate data by the coordinate conversion unit is variably set, and the backlash information calculation unit is calculated for each of the three-dimensional coordinate data corrected by the variable assembly error amount. 3. A limit assembling error amount search means for searching for a limit assembling error amount allowed for the gear pair to secure backlash based on the backlash information calculated in step (2). The gear pair evaluation apparatus described.   The assembly error amount for correcting the three-dimensional coordinate data by the coordinate conversion unit is variably set, and the backlash information calculation unit is calculated for each of the three-dimensional coordinate data corrected by the variable assembly error amount. 4. The gear pair evaluation device according to claim 2, further comprising backlash characteristic calculation means for calculating a backlash characteristic with respect to an assembling error amount based on the backlash information calculated in step (4). .   5. A gear pair characterized in that specifications are optimized by using an evaluation result obtained by the gear pair evaluation device according to claim 1.