JP3693466B2 - Molded gear and method for determining tooth profile of molded gear - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a tooth profile of a molded spur gear such as a resin spur gear or a sintered gear.
[0002]
[Prior art]
Conventionally, not all designers knew that the tooth root shape of a formed spur gear is configured in an arc shape, so the allowable stress calculation is also the conventional Japan Gear Industry Association standard (hereinafter “ JGMA ”), and may not be compatible with actual parts. Furthermore, there is no algorithm for determining the tooth root arc radius, and there is no allowable stress calculation formula based on the above shape. Therefore, since the arbitrary tooth root arc radius has been determined from experience, a radius smaller than necessary is often set in order to prevent interference with the mating gear, which is often disadvantageous in terms of strength.
[0003]
The gear is standardized in JGMA401-01 as the tooth root shape is a trocolloid curved surface. Here, JGMA401-01 is unified with the goal of making it easy to understand the gears for general industrial machinery, not requiring excessive time and labor for calculation, and that there is no individual difference in the calculation results. In general, it is widely used for the purpose of gaining advantages such as technical improvement, labor saving, cost reduction and product unification throughout the design, manufacture and use of gears and gear transmissions. A standard for calculating the strength of gears was established with the goal of
[0004]
If a formed gear is required due to the configuration of the part, the arc radius R of the tooth base is numerically input when setting the machining conditions. In this case, the straight line from the base point of the involute to the gear center and the tooth bottom are connected by the arc having the radius R, or the involute surface and the tooth bottom are connected by the arc having the radius R. In this way, since the provisional proposal is made so that a radius R having a constant value is formed in the tooth base depending on the module and the number of teeth, the strength may be greatly lowered depending on the dislocation coefficient and the number of teeth. Actually, there are many parts lower than the calculation allowable stress, which may cause a problem. Moreover, in order to eliminate the point, it is necessary to set a large safety factor, which is uneconomical. Moreover, there is currently no algorithm for calculating the tooth profile strength of the tooth root arc.
[0005]
[Problems to be solved by the invention]
The present invention has been made to solve the above-mentioned problems, and sets the tooth profile shape of a molded gear that does not interfere with the counterpart gear under individual conditions and can obtain the maximum strength by the number of teeth, the dislocation coefficient, etc. can do.
[0006]
[Means for Solving the Problems]
In order to solve the above-mentioned problem, the invention according to claim 1 is an involute gear in which an arc tooth root surface having an arbitrary radius is formed from the tooth bottom surface, and the tooth root arc radius R of the arc tooth root surface is the same gear. based on the calculated dedendum arc half diameter R yf Japanese gear Manufacturers Association standards 4 01-01 tooth form factor and equal Kunar so by specifications, addendum modification coefficient of the positive reference shift coefficient a and the target gear X A molded gear characterized by being determined according to the following conditions using:
R = Ryf + f (X)
f (X) = (X−A) / 10
However, X <A → f (x) <0, X ≧ A → f (x) = 0
[0007]
According to a second aspect of the present invention, in the molded gear according to the first aspect , the upper limit Rmax of the root radius R is A = 0.3 to 0.5.
[0008]
According to a third aspect of the present invention, in the molded gear according to the second aspect, the lower limit Rmin of the root radius R is a value obtained by subtracting 0.2 modules from 0.1 modules to the Rmax. .
The invention according to claim 4 is the method for determining the shape of an involute gear in which an arc tooth root surface having an arbitrary radius is formed from the tooth bottom surface. If X ≧ A, the tooth root radius Ryf calculated to be equal to the tooth profile coefficient of the Japanese Gear Industry Association Standard 401-01 based on the same gear specifications as the above gear is set, and X < In the case of A, it is determined by R = Ryf + f (X), f (X) = (X−A) / 10.
According to a fifth aspect of the present invention, in the gear shape determining method according to the fourth aspect, the upper limit Rmax of the tooth root arc radius R of the gear is such that A is 0.3 to 0.5.
A sixth aspect of the present invention is the gear shape determining method according to the fifth aspect, wherein the lower limit Rmin of the tooth root arc radius R of the gear is a value obtained by subtracting 0.1 to 0.2 modules from the Rmax. and wherein the [0009]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, coefficients used for correcting the tooth root arc radius R will be described with reference to the drawings, and an embodiment of the tooth profile shape of the formed gear according to the present invention will be described.
[0010]
First, the tooth profile coefficient (tooth profile created by a tool) in JGMA 401-01 will be described. Tooth coefficient Y _F is a coefficient for relating the geometry and bending strength of the teeth of the gear, the overall load on the tooth surface is determined based on the weakest cross-sectional bending stress as applied to the tooth tip. Fig. 1 shows a tooth profile created by a tool. The weakest cross section is a section 6 connecting points 4 and 5 where the Hoofer 30 ° line, that is, the straight lines 2 and 3 inclined by 30 ° from the center line 1 of the tooth profile, contact the root surface. If the point where the weight line 7 perpendicular to the tooth tip surface intersects the center line 1 is 8, the weakest tooth thickness _Snf is the length of the cross section 6, and the weighted height hf is the distance between the cross section 6 and the point 8. It is expressed. Further, assuming that the angle between the weight line 7 and the cross section 6 is a tooth right angle tip load angle α _nF , a tooth right angle reference pressure angle α _n (not shown), and a tooth right angle module m _n , the tooth form coefficient Y _F is expressed by the following equation. It is expressed.
Y _F = {6 (hf / mn) cosαnF} / {(Snf / mn) 2cosαn}
[0011]
Next, the tooth profile coefficient of the tooth profile of the tooth root arc configuration of the formed gear will be described. The spur gear by the molding process has two cases as shown in FIG. 2 (a) and FIG. 2 (b) depending on the number of teeth, the dislocation coefficient, and the radius of the tooth root arc from the algorithm for mold processing. is there. As shown in FIG. 2A, when the tooth shape is formed by connecting a straight line 12 from the base point 10 of the involute surface on the basic circle 9 to the gear center 11 and a root circle 13 with a root arc 14 having an arbitrary radius. As shown in FIG. 2B, the tooth profile is formed by connecting the involute surface 15 and the root circle 16 with a root arc 17 having an arbitrary radius.
[0012]
The tooth profile coefficient Y _F ′ of the tooth arc constituting the tooth root arc is considered in the same manner as Y _F described above . In example FIG. 2 (a), the weakest cross-section is the section 22 connecting the _{Y F} as well as 20 and 21 that Hofer 30 ° line 18, 19 is in contact with the dedendum arc. Further, since the same and the Y _F with respect to weight, the tooth crest to the perpendicular weighted line 23 and 25 that intersects the center line 24, the weakest cross-section tooth thickness S _nf the dedendum circular arc configuration tooth _'is a cross-sectional The length 22 and the weighted height h _f ′ of the tooth profile constituting the root arc are expressed by the distance between the cross section 22 and the point 25. Therefore, the tooth profile coefficient Y _F ′ of the tooth profile constituting the tooth root arc is expressed by the following equation.
Y _F ′ = {6 (h _f ′ / m _n ) cos α _nF } / {(S _nf ′ / m _n ) 2 cos α _n }
The above formula is the same in FIG.
[0013]
Next, how to obtain the weighted height h _f ′ and the weakest tooth thickness S _nf ′ will be described. First, polar coordinates (Re, θ) of the center of the tooth root arc are obtained. In both cases of FIG. 2 (a) and FIG. 2 (b), Re represents the radius of the root circles 13 and 16 as Rs and the radius of the root of the root as Rz.
Re = Rs + Rz
It is represented by
The way of obtaining θ differs between FIG. 2A and FIG. 2B. In the case of FIG. 2A, the angle θ ′ between the straight line 12 and the root arc 26 of the root arc 14 is a perpendicular line from the center 26 to the straight line 12, this intersection and the gear center 11, and the gear center and the root arc. It is obtained by considering a right triangle consisting of the center 26. This is obtained by adding an angle θ ″ formed by the center line 24 and the base point 10 of the involute surface.
[0014]
In the case of FIG. 2B, the tooth root arc center 27 is an involute line having a base point 29 whose arc length on the base circle 28 is equal to the tooth root arc radius from the base point 29 of the involute surface 15 on the base circle 28. 31 is located. Accordingly, since the distance from the gear center 32 to the tooth root arc center 27 is obtained as described above, it can be calculated by obtaining the intersection 30 with the involute line 31. This can be obtained in the same manner as the tooth surface coordinates, as in the case of calculating the coordinates on the involute surface at an arbitrary radius.
[0015]
When the polar coordinates (Re, θ) of the tooth root arc center are obtained, the weakest sectional tooth thickness S _nf ′ of the tooth root constituting tooth profile and the weighted height h _f ′ of the tooth root constituting tooth profile are obtained by the following equations. . However, the distance between the point 25 and the gear center 11, the JG M A401-01 as a reference, repelled Sumiha destination load angle alpha _nF, the teeth perpendicular reference pressure angle is alpha _n.
S _nf ′ = 2 (Re × sin θ−Rz × cos 30 °)
_{h f 'Rz × cosα n /} cosα nF / 2- (Re × cosθ-Rz × sin30 °)
[0016]
Next, calculation and correction of the tooth root arc R that is equal to the tooth profile coefficient of JGMA 401-01 will be described. In JGMA401-01, a standard for calculating the strength of a gear is shown, but a method for calculating a tooth root arc radius is not described. Therefore, FIG. 3 shows an outline of a calculation flow in which the tooth root arc radius of the tooth root arc tooth profile in which the tooth profile coefficient of the tool generating tooth profile is substantially equal to the tooth profile coefficient of JGMA 401-01 is obtained and further corrected. The gear specification 32 is used to input the module, the number of teeth and the dislocation coefficient. The other specifications that affect the tooth profile coefficient, the tip end, the tip base, the tool tip radius R, etc. are fixed and set to standard values.
[0017]
In calculation block 33 on the basis of JGMA401-01, the calculation of the reference tooth profile factor _{Y F} as a reference for the tool creation teeth.
[0018]
Further, the calculation block 34 calculates the tooth profile coefficient Y _F ′ of the tooth base arc tooth profile. In this case, the calculation accuracy of the tooth root arc radius is set, the tooth root arc radius is changed within the range, and the tooth root when the tooth profile coefficient Y _F 'is larger than the reference tooth profile coefficient Y _F and the error is minimum. The arc radius Ryf is obtained. And Y _F ≦ Y _{F ',} the allowable stress the larger numbers as the tooth profile coefficient is small. If the reference tooth profile factor Y _F smaller, the interference between mating gear is assumed.
[0019]
The calculated tooth root radius Ryf is corrected by the calculation block 35, and the corrected tooth root radius is determined. In the present embodiment, the tooth root arc radius R with a plurality of correction factors is obtained in order to obtain the maximum tooth root radius Rmax without interference with the counterpart gear. The correction formula is shown below.
R = Ryf + (X−A) / 10
A = X: No correction A = 0.2 to 0.6
In this case, in order to prevent tooth profile interference, the precondition is that the tooth profile coefficient is equal to or smaller than the tooth root radius Ryf. Therefore, when the correction term is positive, the calculation is performed with the correction term = 0.
[0020]
In order to investigate the interference with the counter gear, the tooth profile coordinates of the position corresponding to the tooth tip of the counter gear and the height of 0.25 module from the tooth bottom are compared. Compare the tooth profile coordinates of the tool generating tooth profile at the radius of (tooth root radius + 0.25) from the gear center with the X coordinate of the tooth profile coordinates of the tooth root arc tooth profile of any radius. If the coordinate value is large, interference with the mating gear can be considered. For reference, the X-coordinate at a height of 0.2 module from the tooth bottom was compared with the assumption that the distance between the gear centers was reduced.
[0021]
For comparison, FIG. 4 shows the result of correction when the number of teeth is fixed at 25 and the dislocation coefficient is changed without correction. Numerical values are expressed as 0 in the case of [X coordinate of tool generating tooth profile]-[X coordinate of tooth root tooth profile] negative. Moreover, the result of FIG. 4 is shown as a graph in FIG. Furthermore, the actual tooth profile is shown in FIG. The left side is the shape without correction, and the right side is the shape according to the present invention.
[0022]
As shown in FIG. 4 and FIG. 5, without correction, when the dislocation coefficient is −0.5, the above numerical value is about 0.05, and tooth profile interference occurs. With correction I , 0.01 or less, and the backlash amount is taken into consideration. In this case, there is no practical problem. Further, in order to ensure against interference, the range up to the correction III is sufficient, and if the correction amount is larger than this, the tooth base becomes thin and a problem occurs in strength. Therefore, by setting the constant part of the correction term in the range of 0.3 to 0.5 as the upper limit value of the tooth root arc radius, it is possible to provide a tooth profile capable of obtaining possible strength without practical interference.
[0023]
As described above, the upper limit value of the tooth root arc radius is set. However, when the gear is actually used, accuracy (tolerance) in processing becomes a problem. In addition, the lower limit value of the tooth root radius equivalent to the tooth profile coefficient is 0.375 module when the dislocation coefficient is +0.9, but in principle, the tool tip radius R is set to 0.375 module. Since the tooth root is not created below that value, in order to form the arc R portion in the tooth root portion, the tolerance lower limit value needs to be −0.375 module or more. The tolerance width needs to be considered from the two aspects of processing and strength. As the tooth root arc radius decreases, the tooth root becomes thinner and the strength decreases. This influence on the strength can be judged by changing and comparing the tooth profile coefficient values. When the tool generating tooth profile is set to 1, the strength ratio of the tooth root arc tooth profile is considered as a strength coefficient, which is expressed by the following formula.
[Strength factor] = [Tooth profile of the tool generating tooth profile] / [Tooth profile of the tooth root arc tooth profile]
[0024]
Strength coefficient when the dislocation coefficient is 0 and the corrected tooth root arc radius is set to 0.05 module units, and the strength coefficient when the set tooth root arc radius is reduced by 0.05 module and 0.1 module Is shown in FIG. As the strength coefficient, a sawtooth change is shown, which shows a case where the set tooth root arc radius is rounded to 0.05 module units. The strength coefficient at the set radius is about 0.95 with 21 teeth (about 7% lower strength than the tool generating tooth profile). In addition, the strength coefficient when -0.1 module is reduced is about 0.06 lower than the set radius (about 13% lower strength than the tool generating tooth profile).
[0025]
If the strength reduction for the tool generating tooth profile is taken into consideration at the time of design, the strength reduction due to tolerance becomes a problem. Therefore, if an attempt is made to suppress a decrease in strength due to tolerance at about 10%, the approximate calculation is -0.16 module or more. For processing, if the module is small, for example, the module 0.2 has a tolerance width of 0.1 module and the actual size is 0.02 mm. In addition, the upper part of the upper part of the molding is thick, so that whiskers and the like are likely to appear, the accuracy becomes unstable, and this tolerance width is very difficult. In this case, an actual size of about 0.04 mm and 0.2 modules are required. From the above, by setting the lower limit value to -0.1 module to -0.2 module depending on the size of the module, an appropriate tooth root radius can be set from two surfaces in terms of processing and strength. For example, the module 0.6 or more may be set as required, such as a lower limit value of -0.1 module, or less than module 0.6, such as a lower limit value of -0.2 module.
[0026]
【The invention's effect】
According to the first aspect of the present invention, in an involute gear having an arc tooth root surface having an arbitrary radius from the tooth bottom surface, the tooth root arc radius R of the tooth root surface is the same as that of Japan Gear Industry. Kai standard (hereinafter referred to as "JGMA") gear coefficient of 401-01 and equal Kunar so the calculated dedendum arc half diameter R yf a reference, R rearrangement coefficient a becomes a dislocation coefficient X, reference = Ryf + f (X), f (X) = (X−A) / 10, where X <A → f (x) <0, X ≧ A → f (x) = 0 Applying the strength calculation (tooth profile coefficient calculation), it is possible to calculate the allowable stress up to the tooth root circular tooth profile, there is no tooth profile interference, the strength deterioration is small, and it is optimal for each condition depending on the number of teeth, the dislocation coefficient, etc. It is possible to set a correct root radius.
[0027]
According to the second aspect of the present invention, in the first aspect of the invention, the upper limit Rmax of the tooth root arc radius R satisfies the formula A = 0.3 to 0.5 . It is possible to set the upper limit value of the root radius so that interference does not become a problem.
[0028]
According to a third aspect of the present invention, in the second aspect of the present invention, the lower limit Rmin of the root radius R is satisfied to be a value obtained by subtracting 0.2 modules from 0.1 modules to the Rmax. because you, to set the lower limit on the basis of the upper limit value, Ki out to suppress the intensity difference between the upper and lower limits of the tolerance at practical extent possible, from processing problems, the width by the size of the module Since it is provided, a molded gear having a large tolerance width can be obtained for a small module that does not require much strength.
According to the fourth aspect of the present invention, in the method for determining the shape of an involute gear in which an arc tooth root surface having an arbitrary radius is formed from the tooth bottom surface, the tooth root arc radius R of the gear is set to a transfer coefficient X of the target gear. Comparison of the dislocation coefficient A used as a reference, and when X ≧ A, the tooth root arc radius Ryf calculated to be equal to the tooth profile coefficient of the Japan Gear Industry Association Standard 401-01 with the same gear specifications as the above gear, In the case of X <A, since R = Ryf + F (X), f (X) = (X−A) / 10, it is determined by applying the conventional strength calculation (tooth profile coefficient calculation), and the tooth root arc until the tooth form allows calculation of the allowable stress, and there is no tooth profile interference, less strength deterioration, the number of teeth, it is possible to optimal dedendum arc radius of determined for each condition by shift coefficient or the like.
According to the invention of claim 5, in the invention of claim 4, when the upper limit of the root radius is Rmax, the relational expression of A = 0.3 to 0.5 is satisfied. It is possible to set the upper limit value of the tooth root arc radius so that the interference with the gear does not become a problem.
According to the invention of claim 6, since the allowable value of the tooth root arc radius R is changed from 0.1 module to 0.2 module, the lower limit value is set on the basis of the upper limit value.・ The difference in strength at the lower limit can be suppressed within the practical range. Further, because of the processing problem, the width is given depending on the size of the module, so that the tolerance width can be set large when the module is small and does not require much strength.
[Brief description of the drawings]
FIG. 1 is a front view showing an example of a tooth profile of a formed gear according to the present invention.
FIG. 2 is a front view showing another example of the tooth profile of the formed gear according to the present invention.
FIG. 3 is a flowchart showing a calculation process of a tooth root arc radius of the formed gear according to the present invention.
FIG. 4 is a table showing a comparison of calculation results of tooth root arc radii of the formed gear according to the present invention.
FIG. 5 is a graph showing a comparison of calculation results of tooth root arc radii of the formed gear according to the present invention.
FIG. 6 is a front view showing a tooth profile of a formed gear according to the present invention.
FIG. 7 is a graph showing the strength coefficient of the formed gear according to the present invention.
[Explanation of symbols]
Rmax Upper limit of tooth root arc radius Rmin Lower limit of tooth root arc radius R tooth root arc radius Ryf tooth root arc radius when equal to JGMA401-01 tooth root radius RZ tooth root arc radius YF tooth profile coefficient X shift coefficient

Claims (6)

In involute gear circular arc flank any radius from the tooth bottom is configured, dedendum circular arc radius of the circular arc flank R is tooth profile of the same gear specifications of Japanese Gear Manufacturers Association standards 4 01-01 based on the coefficient and equal Kunar so the calculated dedendum arc half diameter R yf, molding and determining the positive reference shift coefficient a and the following conditions using a shift coefficient X of the target gear gear.
R = Ryf + f (X)
f (X) = (X−A) / 10
However, X <A → f (x) <0, X ≧ A → f (x) = 0 The formed gear according to claim 1, wherein a reference transition coefficient A is set to 0.3 to 0.5 at the root arc radius R. The formed gear according to claim 2, wherein the upper tolerance of the root radius R is 0 module and the lower tolerance is -0.1 module to -0.2 module. In the method for determining the shape of an involute gear in which an arc tooth root surface having an arbitrary radius is formed from the tooth bottom surface, the tooth root arc radius R of the gear is compared with the transition coefficient X of the target gear and the reference shift coefficient A, In the case of X ≧ A, the tooth root radius Ryf calculated to be equal to the tooth profile coefficient of the Japan Gear Industry Association Standard 401-01 with the same gear specifications as the above gear is used, and when X <A, R = Ryf + f (X), f (X) = (X−A) / 10. 5. The method for determining a tooth profile shape of a formed gear according to claim 4, wherein the tooth root arc radius R is determined by setting the reference transition coefficient A to 0.3 to 0.5. 6. The method of determining a tooth profile shape of a formed gear according to claim 5, wherein the upper tolerance of the root radius R is 0 module and the lower tolerance is -0.1 to -0.2 module.

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