JP3084912B2 - Gear motion characteristics evaluation method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for evaluating the motion characteristics of a gear from an error in the tooth profile of the gear.

[0002]

2. Description of the Related Art An example of a method of obtaining a tooth profile error in a direction perpendicular to each tooth surface of a gear is described in the document "Gear 2 (published by Nikkan Kogyo Shimbun, October 1, 1961, 6th edition)". 34
It is described on pages 5-354. Hereinafter, a brief description will be given with reference to FIG.

A base disk 10 having the same diameter as an ideal base circle of a measurement gear is fixed coaxially to an involute spur gear (hereinafter simply referred to as a measurement gear) to be measured. Further, a straight ruler 20 having a straight edge 18 is brought into contact with the cylindrical surface of the base disc 10 by the straight edge 18,
In addition, it is provided so as to be freely linearly movable in the direction of the straight edge 18. A contact 24 is attached to the straight ruler 20 so as to be freely displaceable in a direction substantially parallel to the straight edge 18. In this state, when the base disc 10 is rotated integrally with the measurement gear while the contact 24 is in contact with the tooth surface of the measurement gear, the straightedge 20 is linearly moved without slipping with the base disc 10. Contact 24 has tooth curve 2
6 is made to follow. Therefore, if the tooth profile curve 26 deviates from the involute curve, the contact 24 swings from the normal position by a tooth profile error, and this deflection can be acquired as a tooth profile error.

[0004]

Conventionally, the motion characteristics (for example, vibration characteristics, dynamic load characteristics) of the gear have been evaluated based on the tooth profile error thus obtained. However, since there is no clear relationship between the tooth profile error and the gear motion characteristics, the gear motion characteristics must be evaluated from the tooth profile errors based on years of experience and intuition. There was a limit to improving accuracy.

[0005] In view of such circumstances, the present inventor has conducted research to find parameters that can accurately evaluate the motion characteristics of gears. As a result, the amount of change in the load acting on each tooth surface when the pair of meshing gears rotates (hereinafter, referred to as the variable load) is the base circle radius error of the gear (this is the difference between the radius of the instantaneous base circle described in detail later). , Which means the deviation of the gear from the radius of the base circle based on the general definition). Hereinafter, the relationship between the fluctuating load and the base circle radius error will be described by taking as an example a case where a pair of involute helical gears are rotated in a state of meshing with one tooth surface.

First, of a pair of involute helical gears, a drive gear having no error is a helical gear,
The driven gear is assumed to be a helical gear with an involute having an error. The pair of involutes assumes that the resultant value of the actual error of each of the helical gears is present on the driven gear. Further, the involute replaces the helical gear pair with an equivalent spur gear pair for rotational movement. Hereinafter, a spur gear equivalent to a helical gear with no error is referred to as a first gear, and a spur gear equivalent to a helical gear with an error is referred to as a second gear. Under such an assumption, the present inventor has determined that the fluctuating load F _d (θ ₂ ) is M · [T ₂ ΔR _b (θ ₂ ) / J ₂ −ΔR _b ′ (θ ₂ )
・ Ω ₂₀ ² ] was found. Where M: J ₁ · J ₂ / [R _b10 ² · [i ² · J ₁ + J ₂ ]] J ₁ : Moment of inertia of the first gear J ₂ : Moment of inertia of the second gear R _b10 : First I: gear ratio T ₂ : torque transmitted to the second gear θ ₂ : rotation angle of the second gear ΔR _b (θ ₂ ): base circle radius error of the second gear ΔR _b ′ (θ ₂ ): basic circular error radius error differential obtained by differentiating ΔR _b (θ ₂ ) with the rotation angle θ ₂ of the second gear ω ₂₀ : average angular velocity of the second gear

The process of deriving the formula for calculating the variable load is described in the report of the present inventor, "Vibration generating mechanism of a helical gear having a modified tooth surface" (contributed to the Japan Society of Mechanical Engineers on March 13, 1991). Then, it was announced at the 69th Annual Meeting of the Japan Society of Mechanical Engineers on October 16 of the same year.
Vol. 543 (1991-1-11) 3634-3644
No. 544 (1991-1) No. 3947-3
Page 956. ), The description is omitted here.

[0008] In summary, involute fluctuating load F _d of the helical gear is a low-speed rotation and high load region of the gear depends strongly on base circle radius error ΔR _b (θ _2), whereas, high-speed rotation and low-load region Then, the basic circle radius error differential ΔR _b ′
(Θ ₂ ). Further, since the involute motion characteristics of the helical gear is strongly dependent on the fluctuating load F _d, after all, the base circle radius error ΔR _b (θ _2), the base circle radius error differential ΔR _b '(θ ₂₎ is if obtaining them Therefore, the motion characteristics of the involute helical gear can be accurately evaluated.

Based on the above findings, it is an object of the present invention to provide a method for accurately evaluating the gear movement characteristics from a tooth profile error.

[0010]

SUMMARY OF THE INVENTION In order to solve this problem, the present invention obtains a tooth profile error in a direction substantially perpendicular to each tooth surface of a gear in association with a rotation angle of the gear, and obtains each tooth profile error. It is an object of the present invention to provide a gear motion characteristic evaluation method for obtaining a tooth profile error differential by differentiating the tooth profile with a rotation angle, and evaluating the gear motion characteristics based on the tooth profile error differential.

In this case, the tooth shape error differential is defined as a tooth shape error obtained by differentiating the tooth shape error only once with a rotation angle, or a tooth shape error obtained by differentiating the tooth shape error once with a rotation angle. It can also be the second derivative of the error.

[0012]

For example, as shown in FIG. 1, a tooth profile curve of the equivalent spur gear (hereinafter simply referred to as a gear) is shown in FIG. 1, with the rotation angle θ of the gear as an auxiliary variable, and a tooth profile tangent L tangent to the tooth profile curve and a center O of the gear. And the instantaneous basic circle radius R _b (θ) as a variable. Here, the instantaneous basic circle is a circle that is tangent to the normal line at each point on the tooth profile curve and is centered on the center O of the gear, and actually acts on each gear when a pair of gears mesh and rotate. A circle whose tangent is the line of action of the force. As shown in the figure, when the rotation angle θ of the gear is 0, the tooth tangent at point P on the tooth curve is L ₀ , the distance between the tooth tangent and the center O of the gear is q ₀ , Let the circle be C ₀ .

From this state, when the gear rotates counterclockwise in the figure by an angle θ, the tooth tangent changes from L ₀ to L, the contact point between the tooth tangent and the tooth curve changes from P to T, and the tooth tangent and the center O of the gear. Is changed from q ₀ to q (θ), and the instantaneous base circle changes from C ₀ to C. At this time, q (θ) is q ₀ +
It can be approximated by R _b0 · θ + Δp (θ). Here, R _b0 is the ideal base circle radius of the gear, and Δp (θ) is the tooth profile error which is the deviation of the tooth profile from the involute curve. FIG. 2 is a graph showing an example of this relationship. In the figure, the broken line graph corresponds to the involute curve, and the solid line graph corresponds to the tooth profile curve having an error.

Further, when the gear rotates counterclockwise by a small angle Δθ from this state, as shown in FIG. 3, the instantaneous basic circle changes from C to C ′, and the basic circle tangent, which is the tangent to the instantaneous basic circle, changes from U. U ′, the intersection of the basic circle tangent with the tooth profile curve is from T to T ′, and the distance between the intersection and the center O of the gear in the direction of the basic circle tangent is q (θ) to q (θ + Δθ), that is, q (Θ) + Δq. At this time, if it is noted that the value of Δθ is minute, the instantaneous basic circle radius R _b (θ
+ Δθ) and R _b (θ) are equal to each other, and the base circular tangents U and U ′ are substantially parallel to each other.
_b (θ) · Δθ. As a result, the instantaneous basic circle radius R _b (θ) is expressed as dq / dθ.

By utilizing the relationship of R _b (θ) = dq / dθ and the relationship of q (θ) = q ₀ + R _b0 · θ + Δp (θ), the instantaneous basic circle radius R _b (θ) becomes R _b0 + D (Δ
p (θ)) / dθ. That is, the radius of the instantaneous base circle at the rotation angle θ is d (Δp (θ)) from the ideal base circle.
/ D [theta], i.e., there than that for the value obtained by differentiating the tooth profile error Δp in the rotation angle theta, which is the base circle radius error [Delta] R _b. An example of the base circle radius error [Delta] R _b in FIG.

[0016] Thus, during the present invention the base circle radius error [Delta] R _b if carried out on involute gear can be obtained as an embodiment of the tooth profile error Differential, also a base circle radius error [Delta] R _b and fluctuating load F _d since the relationship represented by the fluctuating load calculation formula described above is satisfied, it is possible to accurately evaluate the kinetic properties of the involute gear from the base circle radius error [Delta] R _b considering the relationship.

[0017] It is also possible to get the value of the variable load F _d by substituting appropriate values to varying load calculation formula, evaluating the motion characteristics from this value.

The present invention can be applied to a cylindrical gear, a bevel gear, a hypoid gear and the like having a tooth profile other than the involute. Because the tooth surface normal of the contact point of the gear pair at any moment touches the instantaneous basic circle (cylinder) centered on the gear axis, and the tooth surface displacement in the normal direction of the contact point depends on the instantaneous basic circle. This is because the relational expression R _b (θ) = dq / dθ shown for the involute gear basically holds for a cylindrical gear, bevel gear, or hypoid gear having a tooth profile other than involute.

[0019]

As described above, according to the present invention, there is obtained an effect that the motion characteristics of the gear can be accurately evaluated from the tooth profile error.

[0020]

Embodiments of the present invention will be described below. The gear motion characteristic evaluation method according to one embodiment of the present invention uses a basic disk type tooth profile error measuring device (hereinafter simply referred to as a measuring device) 8 shown in FIG.

In this measuring device 8, a base disk 10 having the same diameter as an ideal base circle of an involute spur gear (hereinafter simply referred to as a measurement gear) to be measured can be rotated around its axis and at a fixed position. It is supported by. The base disk 10 is rotated by rotation drive means 12 including a motor. The rotation angle θ of the base disk 10 is detected by a rotation angle detecting means 14 including a rotary encoder. A straight edge 20 having a straight edge 18 in contact with the cylindrical surface of the base disk 10 is supported so as to be able to move in a straight line in the direction of the straight edge 18. A measuring tool 23 that is rotatable around a pin 22 is attached to the straight ruler 20 along a plane parallel to the surface of the base disk 10. Measuring tool 23
Has a spherical contact 24, which is
It is in contact with the straight edge 18 and is freely rotatable along a circumference around the axis of the pin 22. The amount of displacement of the contact 24 is detected by the tooth shape error detecting means 28 as a tooth shape error Δp which is a deviation from the involute curve of the tooth profile curve 26 of the measurement gear mounted coaxially and integrally rotatable on the base disk 10. Is done.

The tooth shape error detecting means 28 and the rotation angle detecting means 14 are connected to a basic circle error calculating means 30. The basic circle error calculating means 30 stores the data representing the tooth shape error Δp in association with the data representing the rotation angle θ of the basic disk 10, and based on the data, differentiates the tooth profile error Δp by the rotation angle θ. Circle radius error Δ
_Rb is calculated.

If the operator calculates the basic circle radius error ΔR _b in such a manner that the rotational noise is not expected to increase when the measurement gear is actually used this time, the operator is in a proper range. The quality of the measurement gear is determined to be appropriate. This determination can be made automatically.

In the above embodiment, the measuring device 23
Is a pivot type, but when it is necessary to more accurately measure the base circle radius error ΔR _b , a contact is provided which comes into straight contact with the tooth profile of the measuring gear, and this contact is It is desirable to use a measuring tool that moves linearly while maintaining a posture in which the line is perpendicular to the direction of the straight edge 18. This is because the normal at each position of the tooth profile curve 26 can be assumed with higher accuracy.

A gear motion characteristic evaluation method according to another embodiment of the present invention uses a meshing type gear error measuring device (hereinafter simply referred to as a measuring device) 48 shown in FIG. The measuring device 48 rotates the pair of involute spur gears (hereinafter simply referred to as “gears”) at a low speed in a meshing state with one tooth surface and no load, and transmits a rotation transmission error of the driven gear for each rotation angle θ of the driven gear. Is provided with a rotation transmission error calculating means 50 for measuring the rotation transmission error. Since the rotation transmission error calculating means 50 is well known, a detailed description thereof will be omitted. The measuring device 48 has a tooth profile error calculating means (described later in detail) 52 for calculating a tooth profile error Δp from the rotation transmission error, and differentiates the tooth profile error Δp with the rotation angle θ to obtain a basic circle radius error. A basic circle error calculating means 54 for calculating ΔR _b is connected.

Here, a specific description will be given of a method in which the tooth profile error calculating means 52 calculates the tooth profile error Δp from the rotation transmission error. A gear pair to be measured has a first gear that is a drive gear having no tooth profile error, and a second gear that is a driven gear having the same tooth profile error as the composite value of the actual tooth profile error of the gear pair. Substitute equivalently so that the same rotational movement is realized. In this state, when the first gear is rotated by the minute angle Δθ ₁ in a no-load state, the second gear is rotated by the minute angle Δθ ₂
If only the rotation is made, the following equation is established. R _b10 · Δθ ₁ = R _b2 (θ ₂ ) · Δθ ₂ where R _{b10 is} the radius of the ideal base circle of the first gear R _b2 (θ ₂ ) is the instantaneous base of the second gear at the rotation angle θ ₂ Here, the instantaneous basic circle radius R _b2 (θ ₂ ) is the sum of the ideal base circle radius R _{b20 of} the second gear and the error of the instantaneous basic circle, that is, the basic circle radius error ΔR _b2 (θ ₂ ). Therefore, by integrating the above equation, the following equation is obtained. R _b10 · θ ₁ = R _b20 · θ ₂ + ∫ΔR _b2 (θ ₂ ) dθ ₂ However, it is assumed that θ ₂ = 0 when θ ₁ = 0. As described above, ΔR _b2 (θ ₂ ) in the second term on the right side of the above equation
Is equal to d (Δp (θ ₂ )) / dθ ₂ based on the above definition, so the above equation can be modified as follows. R _b10 · θ ₁ = R _b20 · θ ₂ + Δp (θ ₂ ) On the other hand, the second gear has an ideal rotation angle (actual rotation angle θ ₂ + rotation transmission error Δθ _{2K with} respect to the rotation angle θ ₁ of the first gear). ), The following equation holds. R _b10 · θ ₁ = R _b20 · [θ ₂ + Δθ _2K ]

Therefore, the rotation transmission error Δθ _2K is as follows. Δθ _2K = Δp (θ ₂ ) / R _b20 And, based on this fact, the tooth profile error calculating means 52
Is the rotation transmission error Δθ between the first gear and the second gear.
By multiplying _2K (θ ₂ ) by the radius R _b20 of the ideal base circle of the second gear, the tooth shape error Δp (θ ₂ ) is calculated by the rotation angle θ
Calculate every _two .

[0028] represents an example of the computed base circle radius error [Delta] R _b by the base circle error calculating unit 54 in the graph of FIG. Operator, if this way is calculated the base circle radius error [Delta] R _b is within a proper range, it is determined that the current gear pair for proper combinations rotation noise is small. This determination can also be made automatically.

Therefore, in the present embodiment, the basic circle radius error ΔR _b can be continuously obtained for a plurality of teeth of the gear and the motion characteristics can be continuously evaluated, so that the required evaluation time of the motion characteristics can be reduced. .

As described above, as two embodiments of the present invention, a single-type embodiment in which the tooth profile error Δp is measured independently for one gear and the motion characteristics of the gear are evaluated, and a gear pair in a no-load state is evaluated. Although the embodiment of the meshing type in which the gear pair is rotated at a low speed and the tooth profile error Δp is measured to evaluate the motion characteristics of the gear pair has been described, the present invention can be applied to other embodiments.

For example, the gear pair is rotated at a low speed in a light load state which is not a no-load state but is lighter than a load in an actual use state, and a tooth profile error Δp is measured. The circular radius error ΔR _b2 (θ ₂ ) and its differential value ΔR _b2 ′ (θ ₂ ) are obtained, and are obtained by calculating the average angular velocity ω of the second gear in the actual use state.
₂₀ into equation of the fluctuating load F _d with fluctuating load F _d
Another meshing embodiment in which (θ ₂ ) is calculated and the motion characteristics of the gear pair are evaluated using the calculated value may be used.

[0032] However, this embodiment measures the tooth profile error Δp at light load conditions, using the same, and vary from the impact force generated between the mating tooth surfaces is very small ignore it load F _d because calculates a, is estimated to be difficult to sufficiently increase the accuracy of the true value of the variable load F _d in the actual use state. Tooth profile error Δ
This is because a load as large as the actual one is not applied to the tooth profile for which p is to be measured.

Therefore, the following embodiment can be adopted. Hereinafter, this embodiment will be described. However, since this embodiment has many portions common to the embodiment described with reference to FIGS. 6 and 7, only different portions will be described in detail.

This embodiment uses substantially the same measuring equipment as the previous embodiment of the meshing type, and uses an involute helical gear pair (hereinafter simply referred to as a helical gear pair, and an involute helical gear). (Referred to simply as a helical gear) is rotated at a low speed in a single-tooth meshing rotation state to measure the tooth profile error Δp. However, unlike the previous embodiment, the same load as in the actual use state is applied. This is for measuring the tooth profile shape error Δp.

Also in this embodiment, of the helical gear pair, the helical gear on the driving side is replaced with the helical gear without tooth profile error, and the helical gear on the driven side with the actual tooth profile error. It is assumed that the helical gear has a combined value with the actual tooth profile error of the driving helical gear. Further, as described above, each tooth surface of the helical gear can be replaced with an equivalent tooth profile that transmits exactly the same rotational motion (a spur gear tooth profile in which the helical gear is equivalently replaced with respect to the rotational motion). That is, also in the present embodiment, in the helical gear pair to be measured, the driving gear is a first gear which is a spur gear having no tooth profile error, and the driven gear is a second gear which is a spur gear having a tooth profile error. Are equivalently replaced.

The tooth profile of the second gear includes a tooth profile whose base circle radius error ΔR _b2 (θ ₂ ) is maintained at the base circle variation coefficient a ₀ irrespective of the rotation angle θ ₂ , and a base circle radius. Error ΔR _b2
(Θ ₂ ) is the primary base circle variation coefficient a ₁ (≧ 0) and the rotation angle θ
₂ , a symmetrical mid-convex tooth profile equal to the product of ₂ and a base circle radius error ΔR
_Although there is a symmetrical central concave tooth shape in which _b2 (θ ₂ ) is equal to the product of the primary base circle variation coefficient a ₁ (<0) and the rotation angle θ ₂ , since the symmetrical central convex tooth shape is most important in practical use, In this case, it is assumed that each tooth profile of the helical gear can be equivalently replaced with a symmetric middle convex tooth profile. Here, the base circle variation coefficient a ₀ and the primary base circle variation coefficient a ₁ respectively have a base circle radius error ΔR _b2 (θ) of a ₀ + a ₁ · θ ₂ + a ₂ · θ ₂ ² + ...
A ₀ and a ₁ assuming that the rotation angle θ ₂ can be approximated by a polynomial.

It is further assumed that each tooth of the gear pair passes through a single-mesh section, an impact section, a two-mesh section and an impact section in that order, and makes a steady motion with one pitch. That is, this time, it is assumed that the meshing ratio is less than 2. When the meshing ratio is assumed to be, for example, 2 or more and less than 3, the two-meshing section, the shock section, the three-meshing section, and the shock section are referred to as those. And if it is assumed to be 3 or more and less than 4, the vehicle passes through the three-meshing section, the impact section, the four-meshing section, and the impact section in that order.

Then, for this equivalent gear pair, 1
As described above, the fluctuating load F _dx in the sheet meshing section is M · [T ₂ ΔR _bx (θ ₂ ) / J ₂ −ΔR _bx ′ (θ ₂ )
· Ω ₂₀ ² ]. However, here, “ΔR
_bx (θ ₂ ) ”and“ ΔR _bx ′ (θ ₂ ) ”
It means the base circle radius error and the base circle radius error differential of the second gear in the single mesh section. Also, the variable load F _dy in the two-meshing section is M · [T ₂ · ΔR _by (θ ₂ ) / J ₂ -ΔR _by '(θ ₂ ), as in the one-meshing section.
· Ω ₂₀ ² ]. However, here, “ΔR
_by (θ ₂ ) ”and“ ΔR _by ′ (θ ₂ ) ”
This means the base circle radius error and the base circle radius error differential of the second gear in the two-meshing section.

The impact section is a section between one meshing section of the equivalent gear pair and another meshing section, in which the locus of the contact point between the tooth surfaces is discontinuous. for that reason,
This impact section, the impact force F _ds and F _de is generated between the tooth surface meshing to be a discontinuous equivalent gear angular velocity. The impact forces F _ds and F _de can be calculated from the difference in angular momentum before and after the impact section. Accordingly, variable load F _d acting on the tooth surface between one pitch can be expressed as follows. F _d = F _dx (one-mesh section) = F _ds (impact section) = F _dy (two-mesh section) = F _de (impact section)

[0040] Based on these assumptions, if the Fourier expansion of the variable load F _d acting on the tooth surface of this equivalent gear, amplitude F _dn of each order n of fluctuating load F _d is as follows. _{F dn = 2 · M · √} ( [omega ₂₀ ² · U _n] ² + [[T ₂ · theta
_2p / J _2] · V _n] ²⁾ However, theta _2p: half U _n of angular pitch of the second gear: [[a _1x -a _1y] · ζ + a _1y] · cos (n · π ·
ζ)-[[a _1x -a _1y ] / [n · π]] · sin (n · π ·
ζ) V _n : [1 / [n · π]] · [[a _1y −a _1x ] · ζ−a
_1y ] · cos (n · π · ζ) + [[a _1y −a _1x ] · [ζ ² /
3-1 / [n ² · π ² ] + a _1y · [1-2 · ζ] / 3]
Sin (n · π · ζ) a _1x : Coefficient of primary base circle variation of the second gear in one meshing section a _1y : Primary base circle variation coefficient of second gear in the meshing section of two gears ζ : 1 Ratio of the length of one meshing section to one pitch

Since the process of deriving the formula for calculating the variable load amplitude is also described in detail in the report, the description is omitted here.

Therefore, in this embodiment, as shown in FIG. 8, which conceptually shows the configuration of the signal processing section (mainly a computer), first, the rotation transmission error calculating means 60 performs the The rotation transmission error θ _2K of the gear pair is measured for each rotation angle θ ₂ , and the tooth profile shape error calculating means 62 calculates
Calculate the tooth shape error Δp from the rotation transmission error θ _2K ,
The basic circle error calculating means 64 calculates the tooth shape error Δp
Is once differentiated by a rotation angle θ ₂ to calculate a basic circle radius error ΔR _b2 . Next, the primary base circle variation coefficient calculating means 70 differentiates once the base circle radius error ΔR _b2 in one meshing section (ΔR _bx ) with the rotation angle θ ₂ once to thereby obtain the basic circle radius error ΔR _{b2 in} the single meshing section. The primary base circle variation coefficient a _1x is calculated, and the base circle radius error ΔR
_The primary base circle variation coefficient a _1y in the two-meshing section is calculated by differentiating the _{b2 in} the two-meshing section (ΔR _by ) once with the rotation angle θ ₂ . This time, each tooth surface of the helical gear is a symmetrical mid-convex tooth profile, that is, a tooth profile whose base circle radius error ΔR _b2 (θ ₂ ) is equal to the product of the primary base circle variation coefficient a ₁ and the rotation angle θ _2. This is because it is assumed that it can be replaced. Finally, the variable load calculating means 72 calculates the primary base circle variation coefficient numbers a _1x and a _1x.
It calculates the amplitude F _dn of fluctuating load F _d by the _1y with other parameters of M such that the above equation yields the amplitude F _dn. Then, if the amplitude _Fdn calculated in this manner is within an appropriate range, the operator determines that the current helical gear pair is an appropriate combination with low rotational noise. This determination can also be made automatically.

As is apparent from the above description, in the present embodiment, the gear load shifts from one meshing section to another meshing section while taking into account the impact force generated on the tooth surface while taking into account the impact load _Fd . The amplitude F _dn is calculated, and the gear pair is provided with a tooth profile as close as possible to the actual use state, and the amplitude F _dn is calculated.
_{Since dn} is calculated, the effect of accurately predicting the amplitude _Fdn in an actual use state can be obtained.

In addition, in this embodiment, by rotating the gear pair while applying the same load as that in the actual use state, the tooth profile error Δp is measured in a state as close as possible to the actual use state. The result was used to accurately calculate the amplitude _Fdn in the actual use _state.For example, by rotating the gear pair at no load at low speed, the tooth profile error Δp in the no-load state was measured, By adding the effect of the elastic deformation of the gear pair expected to occur in the actual use state to the result, the amplitude _Fdn in the actual use state can be accurately calculated. Hereinafter, the embodiment will be described. However, since this embodiment has many portions common to the embodiment described with reference to FIG. 8, the description of the common portions will be omitted, and only different portions will be described in detail.

Also in this embodiment, it is assumed that both the first gear, which is a drive gear having no tooth profile error, and the second gear, which is a driven gear having a tooth profile error, are symmetric center convex gears. That is, it is assumed that the base circle radius error ΔR _b2 (θ ₂ ) of the second gear in the loaded state can be approximated by a ₁ · θ ₂ .

Further, it is assumed that the first gear is a rigid gear and the second gear is an elastic gear. In other words, each tooth surface of each gear by the gear pair is an elastic body, bending occurs under quiescent and load state (hereinafter, simply electrostatic deflection as) x _s is only the second gear is elastic gear It is assumed that it will occur. In addition, it is assumed that the static deflection x _s can be approximated by F _S / K (θ ₂ ). However, in this equation,
“F _S ” means a static load on the tooth surface (a load applied to the tooth surface in a stationary state), and “K (θ ₂ )” means a spring constant of a pair of teeth. _{P · exp (-C P · |} θ 2 3 |) in can be approximated. However, in this equation, “K _P ” and “C _P ” are constants determined from the specifications of the gear pair.

Based on these assumptions, a tooth profile error (hereinafter, referred to as a “tooth profile”) of the second gear in a single-mesh section and in a load state.
Δp _x (θ ₂ ), which is simply referred to as load tooth profile error, is described by the following equation: Δp _X (θ ₂ ) = Δp (θ ₂ ) −x _S (θ ₂ ). Here, “Δp (θ ₂ )” is a tooth profile error of the second gear in the no-load state (hereinafter, referred to as “tooth error”).
Simply referred to as tooth profile error). Tooth profile error Δp
(Θ ₂ ) is equal to the measurement result by the meshing gear error measuring device 48, and the static deflection x _S (θ ₂ ) is the above-mentioned equation x _S (θ ₂ ) = F _S / K (θ ₂ ) And K (θ ₂ ) = K _P · exp (−C _P || θ ₂ ³ |).
From the tooth profile error Δp (θ ₂ ), the static load F _{S on the} tooth surface and the spring constant K (θ ₂ ), the loaded tooth profile error Δp _x (θ ₂ )
Can be calculated.

On the other hand, the load tooth profile error Δp _x (θ ₂ )
As described above, d (Δp _x (θ ₂ )) / dθ ₂ = ΔR _bx (between the base circle radius error ΔR _bx (θ ₂ ) in the single gear meshing section of the second gear. θ ₂ ) and ΔR _bx (θ ₂ )
As described above, there is a relationship between ΔR _bx (θ ₂ ) = a _1x · θ ₂ between the primary base circle variation coefficient a _1x and the tooth shape error Δp ( θ ₂ ), the primary base circle variation coefficient a _1x can be calculated.

The theory for calculating the primary base circle variation coefficient a _1x of the second gear in the one-mesh section and in the load state has been described. The theory for calculating the next basic circle variation coefficient a _1y will be described.

In the two-meshing section, one tooth (rotation angle θ) meshing in the one-meshing section is used.
₂ not only teeth) corresponding to meshes teeth) also corresponds to the next tooth by one pitch from the teeth ((rotation angle theta ₂ -2 · angle pitch half theta _2P). Therefore, unlike the case of the primary base circle variation coefficient a _1x , the primary base circle variation coefficient a _1y is affected not only by the shape error and static deflection of one tooth, but also by the shape error of the adjacent tooth. It is necessary to calculate in consideration of the influence of static deflection.

When one tooth shifts from the one-meshed section to the two-meshed section, a part of the load that the one tooth has been taking up is carried by the adjacent tooth. . Therefore, if it represented as two meshing section and load conditions tooth profile error load tooth profile error Delta] p _y in, reduction of the load the teeth of one that is responsible, i.e., K (theta ₂₎ · [-Δp and _{x (θ 2) + Δp y} (θ 2) ], load teeth neighboring responsible newly, _{i.e., K (θ 2 -2 · θ} 2p) · _{[-Δp y (θ 2) + Δp} (θ
Since ₂ -2 · _{θ 2p)]} and are equal to each other, after all, the load tooth profile error Delta] p _y
Is _{[K (θ 2 -2 · θ 2p} ) · Δp (θ 2 -2 · θ 2p) + K
(Θ ₂ ) · Δp _x (θ ₂ )] / [K (θ ₂ -2 θ _2p )
+ K (θ ₂ )].

[0052] On the other hand, load tooth profile error Δp _y (θ ₂₎
When, in the second gear, also between the two intermeshing base circle radius error [Delta] R _By in the interval _{(θ 2), d (Δp} y (θ 2)) / dθ 2 = ΔR by (θ 2) becomes formula , And ΔR _by (θ ₂ )
And the primary base circle variation coefficient a _1y , there is a relationship represented by the following formula: ΔR _by (θ ₂ ) = a _1y · θ _2. (Θ ₂ ) and the tooth profile shape error Δp (θ ₂ -2 ·
θ _2p ), the primary base circle variation coefficient a _1y can be calculated.

The calculation theory of the primary base circle variation coefficients a _1x and a _1y is also described in detail in the report.

Then, the primary base circle variation coefficients a _1x ,
a _1y of the _{foregoing, F dn = 2 · M ·} √ ( [omega ₂₀ · U _n] ² + [[T ₂ · theta _2p
/ J ₂ ] · V _n ] ² ), the amplitude F _dn of the variable load F _d can be calculated.

Therefore, in this embodiment, as shown in FIG. 9 which conceptually shows the configuration of the signal processing unit (mainly a computer), first, the rotation transmission error calculating means 100 performs the The rotation transmission error Δθ _2K of the gear pair is measured for each rotation angle θ ₂ , and the tooth profile error calculating means 102 calculates the tooth profile error Δp from the rotation transmission error Δθ _2K.
(Θ ₂ ) is calculated.

Next, based on the tooth profile error Δp (θ ₂ ), the load tooth profile error calculating means 104 calculates
The load tooth profile shape error Δp _x (θ ₂ ) in the single-meshing section is calculated for each rotation angle θ ₂ using the above relationship.

Subsequently, the load tooth profile shape error Δp _x (θ ₂ ) is converted by the basic circle error calculating means 106 into the rotation angle θ _2.
Is calculated once to calculate the basic circle radius error ΔR _bx (θ ₂ ) in the single-meshing section. In addition, 1
The primary base circle variation coefficient a _1x in the single-mesh section is calculated by differentiating the basic circle radius error ΔR _bx (θ ₂ ) once with the rotation angle θ ₂ by the next basic circle variation coefficient calculation means 108.

The method of calculating the primary base circle variation coefficient a _1x in the single meshing section has been described above.
The primary base circle variation coefficient a _1y in the sheet meshing section is calculated in substantially the same manner. That is, first, the load tooth profile error calculating means 104 calculates the load tooth profile error Δp _x (θ ₂ ) in the single meshing section and the tooth profile error Δp (θ ₂ −2 · θ) of the adjacent tooth in the no-load state. based on a _2p), and, using the aforementioned relationship, and calculates the load tooth profile in two meshing section shape error Δp _y (θ _2),
Subsequently, the base circle error calculating means 106 calculates a base circle radius error ΔR _by (θ ₂₎ by differentiating the load tooth profile error Delta] p _y a (theta _2), further, the primary base circle variation coefficient calculation The means 108 calculates the primary base circle variation coefficient a _1y by differentiating the base circle radius error ΔR _by (θ ₂ ).

After the primary base circle variation coefficients a _1x and a _1y have been calculated as described above, the variation load calculating means 11
By 0, those primary base circle variation coefficient numbers a _1x and a _1y
The computed amplitudes F _dn of fluctuating load F _d by substituting with other parameters M such as expression of the amplitude F _dn.

Then, if the amplitude _Fdn calculated in this way is within an appropriate range, the operator determines that the current helical gear pair is an appropriate combination with small rotational noise. This determination can also be made automatically.

As is clear from the above description, in this embodiment, even if the measurement result under no load condition is used,
Effect that actual amplitude F _dn of fluctuating load F _d in the use state, that the heavy load state can be predicted accurately.

As described above with reference to some embodiments, the tooth profile error is obtained from the rotation transmission error of the gear pair, and the tooth profile error differential is obtained by differentiating the error with the rotation angle. The method of evaluating the gear motion characteristics of the meshing type based on which the gear motion characteristics are evaluated is based on the basic disk type tooth profile error such as involute helical gear, non-involute cylindrical gear, bevel gear, hypoid gear, etc. The measurement device 8 is particularly effective when evaluating the motion characteristics of gears of a type for which a tooth profile error cannot be easily measured.

Although several embodiments of the present invention have been described in detail above, various modifications and improvements can be made based on the knowledge of those skilled in the art without departing from the scope of the claims. It is needless to say that the present invention can be implemented in the above-described embodiment.

[Brief description of the drawings]

FIG. 1 is a diagram for explaining the principle of a gear motion characteristic evaluation method according to the present invention.

FIG. 2 is a graph showing an example of a tooth profile error Δp in the present invention.

FIG. 3 is a diagram for explaining the principle of the gear motion characteristic evaluation method according to the present invention.

4 is a graph showing an example of a base circle radius error [Delta] R _b is an example of a tooth profile error Differential of the present invention.

FIG. 5 is a diagram showing a device used to execute a single-type gear motion characteristic evaluation method according to an embodiment of the present invention.

FIG. 6 is a view showing a device used to execute a meshing gear motion characteristic evaluation method according to another embodiment of the present invention.

7 is a graph showing an example of the acquired base circle radius error [Delta] R _b using the gear motion characteristics evaluating method of the meshing type.

FIG. 8 is a view showing a device used for executing a meshing type gear motion characteristic evaluation method which is still another embodiment of the present invention.

FIG. 9 is a view showing a device used for carrying out a meshing type gear motion characteristic evaluation method which is still another embodiment of the present invention.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 10 Basic disk 18 Straight edge 20 Straightedge 24 Contact 26 Tooth profile curve 28 Tooth profile error detecting means 30 Basic circular error calculating means 50, 60, 100 Rotation transmission error calculating means 52, 62, 102 Tooth profile error calculating means 54, 64, 106 Basic circle error calculation means 70, 108 Primary base circle variation coefficient calculation means 72, 110 Fluctuating load calculation means 104 Load tooth profile shape calculation means

Claims (1)

(57) [Claims] 1. A tooth profile error in a direction substantially perpendicular to each tooth surface of a gear is obtained in association with a rotation angle of the gear, and the tooth profile error is obtained by differentiating each tooth profile error by the rotation angle. A gear motion characteristic evaluation method comprising: evaluating a gear motion characteristic based on the differential of the tooth profile error.