Tooth profile for differential gear

Abstract

To increase the meshing ratio of the tooth profile in a differential gear mechanism having a small difference in the number of teeth.SOLUTION: A reference circle centered on the axis of the external gear is defined as a circle passing through a center point Q of a contact point trajectory. Let α be the angle between the contact tooth profile normal direction N, which is from the point Q toward a rolling pitch point P, and the tangent T to the reference circle. Let β be the angle between the tangent to the contact point trajectory and the tangent T of the reference circle. Then, the contact point trajectory is designed such that the tangent to the contact point trajectory lies between the contact tooth profile normal N and the tangent T to the reference circle, i.e., such that the angle β is smaller than the angle α.SELECTED DRAWING: Figure 2

Description

Technical Field

[0001] The present invention relates to a method for designing the tooth profile of a parallel-axis gear.

Background Art

[0002] When the external gear is rotated around the internal gear axis while meshing with the fixed internal gear, a differential gear mechanism is formed in which the external gear rotates only corresponding to the difference between the number of teeth of the internal gear and the number of teeth of the external gear with respect to the internal gear.

[0003] As a tooth profile for a differential gear, a small circle may be given as the internal gear tooth profile, and a parallel curve of the trochoid curve drawn by the center point A of the small circle on the external gear may be used as the tooth profile of the external gear.

[0004] As a differential gear tooth profile, an involute tooth profile, which is said to be easier to machine than the above-mentioned trochoid-based curve, may be used. However, the trochoid-based tooth profile is considered advantageous because the involute tooth profile has a problem that the tooth contact ratio cannot be increased and the bending strength of the tooth is small. Also, in a differential gear mechanism, the difference between the number of teeth of the internal gear and the number of teeth of the external gear can be made small to obtain a large reduction ratio. However, when the tooth number difference is small, trochoid interference is likely to occur where the tooth profiles overlap at a position far from the tooth meshing position. Regarding this interference as well, interference is likely to occur with the involute tooth profile, and interference avoidance is easy with the trochoid-based tooth profile.

[0005] In the case of an involute tooth profile, in a stationary coordinate system formed by the center line C passing through the external gear axis O1 and the internal gear axis O2 and the rolling pitch point P of both gears on the center line, the tooth profiles having substantial portions within the tooth tip circle common region surrounded by the tooth tip circle of the external gear and the tooth tip circle of the internal gear come into contact with each other. However, the locus Z of the contact points where the tooth profiles come into contact within the tooth tip circle common region does not intersect the center line C, is located to the left or right of the center line C, and is also located closer to the gear axis than the rolling pitch point P of both gears (Non-Patent Document 1). In this gear, trochoid interference is easily avoided.

Prior Art Documents

Non-Patent Literature

[0006]

Non-Patent Literature 1

Non-Patent Literature 2

Summary of the Invention

Problems to be Solved by the Invention

[0007] In a differential gear mechanism with a small difference in the number of teeth, when an involute tooth profile that is easy to machine is used as the gear tooth profile, if the locus of the contact point is determined at a position closer to the gear axis than the rolling pitch point and away from the center line of the gear axis to the left or right, trochoid interference is easy to avoid, but there is a problem that the contact ratio cannot be increased. Solving this problem is the object of the present invention.

Means for Solving the Problems

[0008] Many conventional tooth profiles use a tooth profile design method of giving a tooth profile such as one gear tooth profile or a rack tooth profile and obtaining the locus of the contact point. In contrast, the present invention uses a means of giving the locus of the contact point and obtaining the tooth profile.

[0009] Further, in the present invention, the position of the locus of the contact point to be given is determined at a position away from the rolling pitch point. However, if it is within the tooth tip circle common region surrounded by the tooth tip circle of the external gear and the tooth tip circle of the internal gear, the substantial parts of the teeth can be in contact with each other, and it is considered that the locus of the contact point of the tooth profile can be freely given within this region.

[0010] However, the locus line of the contact point of the tooth profile cannot be given freely at all. It is necessary to avoid not only trochoid interference but also undercutting interference. For this purpose, there are restrictions on the shape of the locus line. Furthermore, although the tooth surface transmits the load in the direction of the contact tooth surface normal, there is also a restriction that as the angle formed by the radius line and the tooth profile tangent line, that is, the so-called tooth profile pressure angle, increases, the force cannot be transmitted at 90°.

Advantages of the Invention

[0011] According to the present invention, compared with the case of using an involute tooth profile, the contact ratio, which is the number of simultaneously meshing teeth, can be increased without extremely reducing the tooth profile pressure angle at the center point of the tooth profile, and an improvement in the bending strength of the teeth of the entire gear can be obtained.

Brief Description of the Drawings

[0012]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Embodiments for Carrying Out the Invention

[0013] In a differential gear mechanism that rotates an external gear around an internal gear axis while meshing with a fixed internal gear, in a gear pair having an involute tooth profile, when the difference between the number of teeth of the internal gear and the number of teeth of the external gear is small, trochoid interference is likely to occur. As shown in Fig. 1, by separating the tooth tip circle common area of the external gear tooth tip circle and the internal gear tooth tip circle closer to the gear axis from the rolling pitch point P, and moreover separating the locus of the tooth profile contact point leftward or rightward from the center line C passing through the external gear axis and the internal gear axis, it is known that trochoid interference can be easily avoided. However, in this case, there is a drawback that the number of simultaneously meshing teeth (meshing ratio) of the tooth profile does not increase.

[0014] In the method of separating the tooth tip circle common area closer to the gear axis from the rolling pitch point P, and moreover separating the tooth profile contact area leftward or rightward from the center line C passing through the external gear axis and the internal gear axis, the locus of the contact points between the teeth should be freely arranged within the tooth tip circle common area. However, even if it is said to be free, (1) since the point where the normal line of the contact point locus intersects the gear axis is the undercut interference limit, it is necessary to ensure that the normal lines of all points on the contact point locus line do not cross the gear axis. Also, (2) when the contact point locus intersects the center lines C of both gear axes, at the intersection point, the angle formed by the radius line from the gear axis and the tooth profile tangent line, that is, the tooth profile pressure angle, becomes 90°, so it is necessary to prevent the contact point locus from approaching the center line too much.

[0015] In Fig. 2, a circle passing through the center point Q of the contact point locus Z and centered on the outer gear shaft is defined as the reference circle. The angle (tooth profile pressure angle) α is the angle formed by the contact tooth profile normal direction N at the center point Q of the contact point locus Z with respect to the tangent T of the reference circle of the outer gear. Also, the angle β is the angle formed by the tangent B of the contact point locus at the center point Q of the contact point locus with respect to the tangent T of the reference circle of the outer gear passing through point Q. In order to improve the tooth engagement ratio at least more than in the case of an involute tooth profile, it is necessary to design the contact point locus such that the tangent B of the contact point locus is between the contact tooth profile normal N and the reference circle tangent T, in other words, such that the angle β is smaller than the angle α. Further, when extending the contact point locus along the slender tip circle common region, it is necessary to design the contact point locus line such that (1) at all points of the locus line within the tip circle common region, the normal of the locus line does not intersect the gear shaft, and (2) the contact point locus line does not approach too close to the center line connecting the two gear shafts.

Embodiment

[0016] The design procedure in the embodiment is shown below. A pitch circle where the tooth thickness and the tooth groove width are the same in the tooth row of the gear is called the tooth planting pitch circle for convenience. For a pair of gears with the number of teeth and the module given, the tooth planting pitch circle of the outer gear and the tip circle with the desired tip height are given. Also, the size of the rolling pitch circle of the outer gear is given by trial and error. As a result, the axial position of the rolling pitch circle of the inner gear is determined from the tooth number ratio, and the tooth planting pitch circle of the inner gear and the tip circle with the desired tip height are also determined. That is, the tip circle common region, the position of the rolling pitch point, and the position of the gear shaft are determined. In the design of the contact point locus, first, a point E slightly away from the gear shaft center line C is determined by trial and error on the outer gear tip circle forming the tip circle common region, and a point S is determined by trial and error at a position sufficiently far from the gear shaft center line C on the inner gear tip circle forming the tip circle common region. An arc with a radius equal to or larger than that of the outer gear tip circle and with the arc center closer to the gear shaft, passing through points E and S, is given as the contact point locus. Let the central point of the arc line segment ES be Q. By designing the contact point locus in this way, undercut interference does not occur, the tooth profile pressure angle does not become 90 degrees, and the engagement ratio can be increased. The main specifications regarding point Q in the trial calculation example are as follows. Number of teeth of internal gear: 100, number of teeth of external gear: 98 Module: 0.5 Tip height, root height: 1 module Angle formed by the tangent of the rolling pitch circle and the tooth profile normal N (operating line pressure angle): 41.1° Angle formed by the tangent of the reference circle T and the tooth profile normal N (tooth profile pressure angle): 23.5° Inclination angle of the contact point locus tangent from the tangent of the reference circle T: 3.6° An example of the contact point locus in the numerical example is shown in Fig. 3. For comparison, an example of the contact point locus in the case of an involute tooth profile is also shown. In the case of the involute tooth profile, the contact ratio is about 1.5, while the contact ratio of the design example is greatly improved to about 8.

[0017] There are several methods to obtain the tooth profile curve from the contact point locus line. Here, when the tooth profile is expressed in polar coordinates, the differential relationship between the contact point locus and the polar coordinates is known (Non-Patent Document 2), and this relationship is used.

[0018] Fig. 4 shows the trochoid curve drawn in the internal gear coordinate system as the tip points of the internal gear tooth profile and the external gear tooth profile in the above specifications accompany the meshing of the gears. For reference, the case of the involute tooth profile is also shown. In both cases, it can be confirmed that trochoid interference is avoided.

[0019] The relative curvature of the tooth profiles at the contact between the external gear tooth profile and the internal gear tooth profile is extremely small. For this reason, the clearance amount at the contact between the external gear tooth profile and the internal gear tooth profile is extremely small, and the two meshing tooth profiles appear to almost overlap. For this reason, the display of the external gear tooth profile is omitted here.

Example

[0020] The following shows a trial calculation example when the difference in the number of teeth is slightly increased. The main specifications regarding the central point Q of the contact point locus are as follows. Number of teeth of internal gear: 100, number of teeth of external gear: 94 Module: 0.5 Tip height, root height: 1 module The angle formed by the tangent to the rolling pitch circle and the tooth profile normal N (operating line pressure angle) is 61.6° The angle formed by the tangent T to the reference circle and the tooth profile normal N (tooth profile pressure angle) is 14.2° The inclination angle of the contact point locus tangent from the tangent T of the reference circle is 6.6° An example of the contact point locus in the numerical example is shown in Fig. 5. The contact ratio is approximately 4.5 If the contact point locus passes through the rolling pitch point and attempts to increase the contact ratio, the tooth profile pressure angle becomes extremely small. However, if the contact point locus is placed away from the pitch point, it can be seen that the contact ratio can be increased while ensuring a relatively large value of the tooth profile pressure angle to a certain extent.

Claims

1. In a differential gear mechanism where an external gear rotates around an internal gear axis while meshing with a fixed internal gear, the external gear rotates relative to the fixed internal gear by an amount corresponding to the difference between the number of teeth of the internal gear and the number of teeth of the external gear. In a stationary coordinate system defined by a center line C passing through the external gear axis O1 and the internal gear axis O2, and a rolling pitch point P of both gears on this center line, tooth forms having substantial portions within the tip circle common region surrounded by the tip circle of the external gear and the tip circle of the internal gear come into contact with each other. However, in a method of setting a locus Z of contact points where the tooth forms come into contact, which is defined within the tip circle common region, without intersecting the center line C, and being separated from the center line C to the left or right direction, and also being positioned closer to the gear axis than the rolling pitch point P, A circle centered on the external gear axis and passing through the center point Q of the contact point locus Z is arbitrarily referred to as a reference circle for convenience. When a tangent to the reference circle at point Q is designated as T, the normal direction N of the contact tooth form in the direction of the line connecting point Q and point P forms an angle α with respect to the tangent T. Also, When a tangent B to the contact point locus at the center point Q of the contact point locus forms an angle β with respect to the tangent T, A design method in which the tangent B to the contact point locus is installed at an angular position away from the tangent T between the normal N of the contact tooth form and the tangent T to the reference circle, in other words, the contact point locus is designed such that the angle β is smaller than the angle α.

2. As one of the design methods for the contact point locus of Claim 1, a point E slightly separated from the gear axis center line C is defined on the external gear tip circle, and a point S is defined at a position sufficiently far from the gear axis center line C on the internal gear tip circle. A line segment of an arc passing through points E and S, having a radius equal to or larger than the radius of the external gear tip circle, and with the center of the arc closer to the gear axis, is used as the contact point locus.

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