Gear transmission device

Abstract

To provide a gear transmission device capable of reducing noise.SOLUTION: The gear transmission device includes a first gear pair, and a second gear pair for transmitting the rotation of the first gear pair. A first value as a ratio between a meshing frequency of the first gear pair and a meshing frequency of the second gear pair belongs to a consonance pitch, and a second value as a ratio between a frequency of gear sound which is caused by a tool mark of a first gear included the first gear pair or the second gear pair and a meshing frequency a gear pair including the first gear belong to a consonance pitch.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present invention relates to a gear transmission device that transmits power by gears.

Background Art

[0002] When there are tool marks (tool marks) on the tooth surface during machining of the gears in a gear transmission device, or when there are periodic undulations formed by the alignment of tool marks on the tooth surface, noise may occur when the gears mesh and transmit power. The prior art disclosed in Patent Document 1 forms tool marks on the gears that disrupt the periodicity of the undulations by adjusting the feed rate of the tool in order to reduce noise.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0004] There is a need for a technique to reduce noise when the gears transmit power as in the prior art.

[0005] The present invention has been made to meet this need, and an object thereof is to provide a gear transmission device capable of reducing noise.

Means for Solving the Problems

[0006] To achieve this object, a first aspect includes a first gear pair and a second gear pair that transmits the rotation of the first gear pair, and a first value that is the ratio of the meshing frequency of the first gear pair and the meshing frequency of the second gear pair belongs to a consonant interval, and a second value that is the ratio of the frequency of the gear noise generated by the tool marks of the first gear included in the first gear pair or the second gear pair and the meshing frequency of the gear pair including the first gear belongs to a consonant interval.

[0007] In a second aspect, in the first aspect, a third value, which is a ratio between the frequency of the gear sound generated by the tool marks of the second gear that mates with the first gear and the meshing frequency of the gear pair including the second gear, belongs to a consonant interval.

[0008] In a third aspect, in the second aspect, the third value is the same as the first value or the second value.

[0009] In a fourth aspect, in the second aspect, the third value is different from the first value or the second value.

[0010] In a fifth aspect, in any one of the first to fourth aspects, a fourth value, which is a ratio between the frequency of the gear sound generated by the tool marks of the third gear included in a gear pair not including the first gear and the meshing frequency of the gear pair including the third gear, belongs to a consonant interval.

[0011] In a sixth aspect, in the fifth aspect, a fifth value, which is a ratio between the frequency of the gear sound generated by the tool marks of the fourth gear that mates with the third gear and the meshing frequency of the gear pair including the fourth gear, belongs to a consonant interval.

[0012] In a seventh aspect, in the sixth aspect, the fifth value is the same as the first value or the fourth value.

[0013] In an eighth aspect, in the sixth aspect, the fifth value is different from the first value or the fourth value.

Advantages of the Invention

[0014] According to the present invention, since the frequency of the gear sound generated by the tool marks of the first gear and the meshing frequency of the gear pair including the first gear are in harmony, and further the meshing frequencies of the first gear pair and the second gear pair are in harmony, noise can be reduced.

Brief Description of the Drawings

[0015]

Figure 1

Figure 2

Embodiments for Carrying Out the Invention

[0016] Hereinafter, preferred embodiments of the present invention will be described with reference to the accompanying drawings. FIG. 1 is a skeleton diagram of a gear transmission device 10 according to the first embodiment. The gear transmission device 10 includes a first gear pair 11 and a second gear pair 12 that transmits the rotation of the first gear pair 11. The first gear pair 11 includes a gear 15 disposed on a first shaft 14 that is rotated by a prime mover 13 and a gear 17 disposed on a second shaft 16. The gear 17 meshes with the gear 15. The second gear pair 12 includes a gear 18 disposed on the second shaft 16 and a gear 20 disposed on a third shaft 19. The gear 20 meshes with the gear 18. The gears 15, 17, 18, and 20 can be various types such as spur gears, racks, internal gears, helical gears, helical racks, worm gears, straight bevel gears, spiral bevel gears, zero bevel gears, worm gears, cylindrical worm gears, etc., and can be used without limitation.

[0017] The rotation of the first shaft 14 is transmitted to the second shaft 16 by the meshing of the gears 15 and 17. If the rotation speed of the first shaft 14 is N (rpm), the number of teeth of the gear 15 is Z1, and the number of teeth of the gear 17 is Z2, then the rotation speed of the second shaft 16 is Z1 / Z2·N (rpm).

[0018] The rotation of the second shaft 16 is transmitted to the third shaft 19 by the meshing of the gears 18 and 20. If the number of teeth of the gear 18 is Z3 and the number of teeth of the gear 20 is Z4, then the rotation speed of the third shaft 19 is Z3 / Z4·Z1 / Z2·N (rpm).

[0019] Vibration occurs when the teeth of gear 15 come into contact with the teeth of gear 17 and force is transmitted from gear 15 to gear 17. The frequency of this vibration (the meshing frequency of the first gear pair 11) is Z1·N / 60 (Hz), which is obtained by multiplying the rotational speed N / 60 (Hz) of gear 15 by the number of teeth Z1 of gear 15.

[0020] Similarly, vibration occurs when the teeth of gear 18 come into contact with the teeth of gear 20 and force is transmitted from gear 18 to gear 20. The frequency of this vibration (the meshing frequency of the second gear pair 12) is Z1·Z3 / Z2·N / 60 (Hz), which is obtained by multiplying the rotational speed Z1 / Z2·N / 60 (Hz) of gear 18 by the number of teeth Z3 of gear 18.

[0021] When rotation is transmitted from the first gear pair 11 to the second gear pair 12, vibrations at the meshing frequency of the first gear pair 11 and vibrations at the meshing frequency of the second gear pair 12 occur simultaneously. The difference in the heights (intervals) of the two vibrations (sounds) is classified into consonant intervals and dissonant intervals based on the ratio of the frequencies of the two sounds. If the two sounds that sound simultaneously are in a pleasant harmony (consonance), it gives the impression that the noise is reduced. If the two sounds that sound simultaneously are in a dissonant state, it is noise.

[0022]

Table 1

[0023] Table 1 shows the ratios of two frequencies belonging to consonant intervals from a minor sixth to a 16 - fold perfect octave. The minor sixth to the 16 - fold perfect octave is part of the consonant intervals. Therefore, what is shown in Table 1 is an example of the ratio of consonant intervals. Consonant intervals continue as 16 - fold perfect octave, 16 - fold major third, 16 - fold perfect fourth, 16 - fold perfect fifth, 16 - fold major sixth, 32 - fold perfect octave, 32 - fold major third ···

[0024] The ratio 1:Z3 / Z2 (the first value) between the meshing frequency Z1·N / 60 (Hz) of the first gear pair 11 and the meshing frequency Z1·Z3 / Z2·N / 60 (Hz) of the second gear pair 12 belongs to a consonant interval. This can be achieved by setting the number of teeth Z2 of gear 17 and the number of teeth Z3 of gear 18 and determining the first value so as to belong to a consonant interval. Thereby, the noise of the composite sound composed of the vibration of the meshing frequency of the first gear pair 11 and the vibration of the meshing frequency of the second gear pair 12 can be reduced.

[0025] The tooth surfaces of gears 15, 17, 18, and 20 are generally produced by smoothly shaving the surface of the material with a tool. Due to the tool marks remaining on the tooth surfaces of gears 15, 17, 18, and 20, vibrations (gear sounds) occur when force is transmitted from gear 15 to gear 17 or when force is transmitted from gear 18 to gear 20. The order of the gear sound generated by the tool marks (a value expressed as a multiple with the frequency synchronized with the rotational speed of the gear as the first order) is referred to as the "tool mark order". The tool mark order can be estimated based on the machining conditions of the tooth surface. That the tool mark order can be estimated based on the machining conditions of the tooth surface is well known from "Mitsuru Egami, et al., Mechanism of Ghost Noise Generation due to Thread-Type Tool Gear Machining, Honda R&D Technical Review Vol.20 No.2", etc.

[0026] Since the tool mark order coincides with the order of the peak identified by performing a fast Fourier transform on the data obtained by measuring the shape of the tooth surface, the tool mark order can also be identified by performing a fast Fourier transform on the data of the shape of the tooth surface.

[0027] For example, when manufacturing a helical gear using a thread-shaped grinding wheel (tool), the tool is rotated so that the material and the tool mesh with each other, an involute shape is formed on the material, and the tool is fed in the axial direction of the material to form a tooth groove shape on the material. Since the tool intermittently acts in the axial direction of the material, undulations of tool marks occur in the axial direction of the gear depending on the feed pitch of the tool. The number of tool mark occurrences G1 caused by the undulation of the tool feed pitch is G1 = (N·Zw ± 1) / Zj, where N ≒ i·Lp / Fp. Here, Zw is the number of teeth of the gear, Zj is the number of threads of the thread-shaped grinding wheel (tool), i is the number of threads that strongly contact the gear among the tools, Lp is the lead length per pitch of the tool (the interval between the simultaneous contact lines of the gear), and Fp is the feed amount of the tool per one rotation of the material.

[0028] When each gear of the gear transmission device 10 is a helical gear and the number of teeth of each gear is set to Z1 = 19, Z2 = 60, Z3 = 20, and Z4 = 59, the ratio of the meshing frequency of the first gear pair 11 to the meshing frequency of the second gear pair 12 is a harmonious interval of 1:3 (a double-octave perfect fifth shown in Table 1). Thus, when vibrations occur in the meshing frequency of the first gear pair 11 and the meshing frequency of the second gear pair 12, the noise can be reduced.

[0029] When setting the number of tool mark occurrences G1 of the gear 18 to 16 times the number of teeth Z3 of the gear 18 (a 16-fold octave perfect eighth shown in Table 1) and making the gear noise caused by the tool marks into a harmonious interval, the feed amount Fp of the tool is obtained as follows. First, the interval Lp of the simultaneous contact lines of the gear 18 is obtained from the module m of the gear 18, the helix angle β of the gear 18, and the number of threads Zj of the tool. For example, when m = 2.5, β = 25°, and Zj = 3, Lp = π·m / (sin β) = 18.58 mm.

[0030] Next, substitute the values of Zw, Zj, and Lp into the algebraic expression of G1 so that the tool mark order G1 becomes 16 times the number of teeth Z3 of the gear 18, and obtain Fp. Note that i = 1 represents a state where one of the three tools strongly hits the material, and the generated vibration becomes large. i = 3 represents a state where all three of the three tools hit the material evenly, and the generated vibration becomes small. When Zj = 3, i can adopt any integer from 1 to 3. When each value is substituted, Fp = 0.387 mm / rev when i = 1. By appropriately setting the feed amount of the tool, the gear noise generated by the tool mark of the gear 18 can be made into a consonance.

[0031] In the present embodiment, for convenience, the gear 15 included in the first gear pair 11 is referred to as the first gear, the gear 17 paired with the first gear (gear 15) is referred to as the second gear, the gear 18 included in the second gear pair 12 that does not include the first gear (gear 15) is referred to as the third gear, and the gear 20 paired with the third gear (gear 18) is referred to as the fourth gear.

[0032] The material is machined so that the ratio (second value) of the frequency of the gear noise generated by the tool mark of the first gear (gear 15) (a multiple of the frequency obtained by multiplying the tool mark order by the rotational speed of the gear 15 (N / 60 (Hz))) to the meshing frequency (Z1·N / 60 (Hz)) of the first gear pair 11 including the gear 15 belongs to a consonant interval. Thereby, the noise of the composite sound composed of the gear noise generated by the tool mark of the gear 15 and the vibration of the meshing frequency of the first gear pair 11 can be reduced.

[0033] The ratio (third value) of the frequency of the gear noise generated by the tool mark of the second gear (gear 17) (a multiple of the frequency obtained by multiplying the tool mark order by the rotational speed of the gear 17 (Z1 / Z2·N / 60 (Hz))) to the meshing frequency (Z1·N / 60 (Hz)) of the first gear pair 11 including the gear 17 preferably belongs to a consonant interval. This is because the noise of the composite sound composed of the gear noise generated by the tool mark of the gear 17 and the vibration of the meshing frequency of the first gear pair 11 can be reduced.

[0034] The third value may be the same as the first value or the second value, or it may be a different value. If the third value is the same as the first value or the second value, a harmonic sound will ring, which can evoke an uplifting emotion. If the third value is different from the first value or the second value, the level of the harmonic sound can be lowered and the quietness can be enhanced.

[0035] The ratio (the fourth value) of the frequency of the gear sound generated by the tool marks of the third gear (gear 18) (a multiple of the frequency obtained by multiplying the tool mark order by the rotational speed of gear 18 (Z1 / Z2·N / 60 (Hz))) to the meshing frequency (Z1·Z3 / Z2·N / 60 (Hz)) of the second gear pair 12 including gear 18 preferably belongs to a consonant interval. This is because the noise of the complex sound composed of the gear sound generated by the tool marks of gear 18 and the vibration of the meshing frequency of the second gear pair 12 can be reduced.

[0036] The ratio (the fifth value) of the frequency of the gear sound generated by the tool marks of the fourth gear (gear 20) (a multiple of the frequency obtained by multiplying the tool mark order by the rotational speed of gear 20 (Z3 / Z4·Z1 / Z2·N / 60 (Hz))) to the meshing frequency (Z1·Z3 / Z2·N / 60 (Hz)) of the second gear pair 12 including gear 20 preferably belongs to a consonant interval. This is because the noise of the complex sound composed of the gear sound generated by the tool marks of gear 20 and the vibration of the meshing frequency of the second gear pair 12 can be reduced.

[0037] The fifth value may be the same as the first value or the fourth value, or it may be a different value. If the fifth value is the same as the first value or the fourth value, a harmonic sound will ring, which can evoke an uplifting emotion. If the fifth value is different from the first value or the fourth value, the level of the harmonic sound can be lowered and the quietness can be enhanced.

[0038] Note that since the first to fourth gears are for convenience, gear 17 is referred to as the first gear, gear 15 that mates with gear 17 is referred to as the second gear, gear 20 included in the second gear pair 12 that does not include gear 17 is referred to as the third gear, and gear 18 that mates with gear 20 is referred to as the fourth gear. Also, one of gears 18 and 20 included in the second gear pair 12 can be referred to as the first gear, the other of gears 18 and 20 that mates with the first gear can be referred to as the second gear, one of gears 15 and 17 included in the first gear pair 11 that does not include the first gear can be referred to as the third gear, and the other of gears 15 and 17 that mates with the third gear can be referred to as the fourth gear. In these cases as well, the second to fifth values are obtained in the same manner as in the above-described embodiment.

[0039] With reference to FIG. 2, the second to fourth embodiments will be described. In the first embodiment, the case where gears 18 and 20 different from gears 15 and 17 constituting the first gear pair 11 constitute the second gear pair 12 was described. In contrast, in the second embodiment, the case where one of the gears constituting the first gear pair 35 is common with one of the gears constituting the second gear pair 36 will be described (the same applies to the third and fourth embodiments). FIG. 2(a) is a skeleton diagram of the gear transmission device 30 in the second embodiment.

[0040] As shown in FIG. 2(a), the gear transmission device 30 is an epicyclic gear device and includes a sun gear 31, a pinion 32 that meshes with the sun gear 31, and a ring gear 33 that meshes with the pinion 32. The pinion 32 is supported by a carrier 34. In the gear transmission device 30, the rotation of the ring gear 33 is restricted, power is input to the sun gear 31, and power is output from the carrier 34. The first gear pair 35 includes the sun gear 31 and the pinion 32, and the second gear pair 36 includes the pinion 32 and the ring gear 33.

[0041] In this embodiment, for convenience, the sun gear 31 included in the first gear pair 35 is referred to as the first gear, the pinion 32 that mates with the sun gear 31 is referred to as the second gear, and the ring gear 33 included in the second gear pair 36 that does not include the first gear is referred to as the third gear.

[0042] Similar to the gear transmission device 10 in the first embodiment, for the gear transmission device 30, a first value, which is the ratio between the meshing frequency of the first gear pair 35 and the meshing frequency of the second gear pair 36, belongs to a consonant interval, and a second value, which is the ratio between the frequency of the gear noise generated by the tool marks of the first gear (sun gear 31) and the meshing frequency of the first gear pair 35 including the first gear, belongs to a consonant interval.

[0043] Also, a third value, which is the ratio between the frequency of the gear noise generated by the tool marks of the second gear (pinion 32) meshing with the first gear (sun gear 31) and the meshing frequency of the first gear pair 35 including the second gear, belongs to a consonant interval.

[0044] Furthermore, a fourth value, which is the ratio between the frequency of the gear noise generated by the tool marks of the third gear (ring gear 33) included in the second gear pair 36 that does not include the first gear (sun gear 31) and the meshing frequency of the second gear pair 36 including the third gear, belongs to a consonant interval.

[0045] Note that since the first - third gears are for convenience of naming, it is possible to refer to the ring gear 33 included in the second gear pair 36 as the first gear, the pinion 32 meshing with the ring gear 33 as the second gear, and the sun gear 31 included in the first gear pair 35 that does not include the first gear as the third gear. In this case, the second to fourth values can also be obtained in the same manner as in the above - described embodiment.

[0046] The third embodiment will be described with reference to FIG. 2(b). In the second embodiment, an epicyclic gear device in which the rotation of the ring gear 33 is restricted was described. In contrast, the third embodiment will describe the case where the rotation of the sun gear 31 is restricted. Parts that are the same as those described in the second embodiment will be given the same reference numerals and the following description will be omitted (the same also applies to the third embodiment). FIG. 2(b) is a skeleton diagram of the gear transmission device 40 in the third embodiment.

[0047] As shown in Fig. 2(b), in the gear transmission device 40, the rotation of the sun gear 31 is restricted, power is input to the ring gear 33, and power is output from the carrier 34. The first gear pair 41 includes the ring gear 33 and the pinion 32, and the second gear pair 42 includes the pinion 32 and the sun gear 31.

[0048] In this embodiment, for convenience, the ring gear 33 included in the first gear pair 41 is referred to as the first gear, the pinion 32 meshing with the ring gear 33 is referred to as the second gear, and the sun gear 31 included in the second gear pair 42 that does not include the first gear is referred to as the third gear.

[0049] Similar to the gear transmission device 10 in the first embodiment, in the gear transmission device 40, a first value that is the ratio of the meshing frequency of the first gear pair 41 to the meshing frequency of the second gear pair 42 belongs to a consonant interval, and a second value that is the ratio of the frequency of the gear noise generated by the tool marks of the first gear (ring gear 33) to the meshing frequency of the first gear pair 41 including the first gear belongs to a consonant interval.

[0050] Also, a third value that is the ratio of the frequency of the gear noise generated by the tool marks of the second gear (pinion 32) meshing with the first gear (ring gear 33) to the meshing frequency of the first gear pair 41 including the second gear belongs to a consonant interval.

[0051] Furthermore, a fourth value that is the ratio of the frequency of the gear noise generated by the tool marks of the third gear (sun gear 31) included in the second gear pair 42 that does not include the first gear (ring gear 33) to the meshing frequency of the second gear pair 42 including the third gear belongs to a consonant interval.

[0052] Note that since the first to third gears are for convenience of naming, it is possible to refer to the sun gear 31 included in the second gear pair 42 as the first gear, the pinion 32 meshing with the sun gear 31 as the second gear, and the ring gear 33 included in the first gear pair 41 that does not include the first gear as the third gear. Also in this case, the second to fourth values can be obtained in the same manner as in the above embodiment.

[0053] The fourth embodiment will be described with reference to FIG. 2(c). In the third embodiment, an epicyclic gear device in which the rotation of the sun gear 31 is restricted was described. In contrast, the fourth embodiment will describe the case where the rotation of the carrier 34 is restricted. FIG. 2(c) is a skeleton diagram of the gear transmission device 50 in the fourth embodiment.

[0054] As shown in FIG. 2(c), in the gear transmission device 50, the rotation of the carrier 34 is restricted, power is input to the sun gear 31, and power is output from the ring gear 33. The first gear pair 51 includes the sun gear 31 and the pinion 32, and the second gear pair 52 includes the pinion 32 and the ring gear 33.

[0055] In this embodiment, for convenience, the sun gear 31 included in the first gear pair 51 is referred to as the first gear, the pinion 32 meshing with the sun gear 31 is referred to as the second gear, and the ring gear 33 included in the second gear pair 52 that does not include the first gear is referred to as the third gear.

[0056] Similar to the gear transmission device 10 in the first embodiment, in the gear transmission device 50, a first value that is the ratio of the meshing frequency of the first gear pair 51 to the meshing frequency of the second gear pair 52 belongs to a consonant interval, and a second value that is the ratio of the frequency of the gear sound generated by the tool marks of the first gear (sun gear 31) to the meshing frequency of the first gear pair 51 including the first gear belongs to a consonant interval.

[0057] Also, a third value that is the ratio of the frequency of the gear sound generated by the tool marks of the second gear (pinion 32) meshing with the first gear (sun gear 31) to the meshing frequency of the first gear pair 51 including the second gear belongs to a consonant interval.

[0058] Furthermore, a fourth value that is the ratio of the frequency of the gear sound generated by the tool marks of the third gear (ring gear 33) included in the second gear pair 52 that does not include the first gear (sun gear 31) to the meshing frequency of the second gear pair 52 including the third gear belongs to a consonant interval.

[0059] Note that since the first to third gears are for convenience of naming, the ring gear 33 included in the second gear pair 52 may be referred to as the first gear, the pinion 32 meshing with the ring gear 33 may be referred to as the second gear, and the sun gear 31 included in the first gear pair 51 that does not include the first gear may be referred to as the third gear. Also in this case, the fourth value can be obtained from the second value in the same manner as in the above embodiment.

[0060] As described above, the present invention has been described based on the embodiments. However, it can be easily inferred that the present invention is not limited to these embodiments at all, and various improvements and modifications can be made without departing from the spirit of the present invention.

[0061] In the first embodiment, the gear transmission device 10 including the first gear pair 11 and the second gear pair 12 has been described. However, it is not necessarily limited to this. It is naturally possible to provide a gear on the third shaft, provide a fourth shaft on which the gears are arranged, and further provide a third gear pair by meshing the gear arranged on the third shaft with the gear arranged on the fourth shaft.

[0062] In the second to fourth embodiments, the gear transmission devices 30, 40, and 50 each including a single planetary gear train have been described. However, it is not necessarily limited to this. It is naturally possible to adopt a compound planetary gear train in which a plurality of single planetary gear trains are combined in the gear transmission device.

[0063] In the second embodiment, the case where power is input to the sun gear 31 and power is output from the carrier 34 has been described. However, it is naturally possible to reverse the relationship between the first gear pair 35 and the second gear pair 36, input power from the carrier 34, and output it from the sun gear 31.

[0064] In the third embodiment, the case where power is input to the ring gear 33 and power is output from the carrier 34 has been described. However, it is naturally possible to reverse the relationship between the first gear pair 41 and the second gear pair 42, input power from the carrier 34, and output it from the ring gear 33.

[0065] In the fourth embodiment, the case where power is input to the sun gear 31 and output from the ring gear 33 has been described. However, it is naturally possible to reverse the relationship between the first gear pair 51 and the second gear pair 52, input power from the ring gear 33, and output it from the sun gear 31.

Explanation of Signs

[0066] 10, 30, 40, 50 Gear transmission 11, 35, 41, 51 First gear pair 12, 36, 42, 52 Second gear pair

Claims

1. a first gear pair; a second gear pair configured to transmit the rotation of the first gear pair, and a first value, which is a ratio between the meshing frequency of the first gear pair and the meshing frequency of the second gear pair, belongs to a consonant interval, a gear transmission device, wherein a second value, which is a ratio between the frequency of the gear sound generated by the tool marks of a first gear included in the first gear pair or the second gear pair and the meshing frequency of the gear pair including the first gear, belongs to a consonant interval.

2. The gear transmission device according to claim 1, wherein a third value, which is a ratio between the frequency of the gear sound generated by the tool marks of a second gear meshing with the first gear and the meshing frequency of the gear pair including the second gear, belongs to a consonant interval.

3. The gear transmission device according to claim 2, wherein the third value is the same as the first value or the second value.

4. The gear transmission device according to claim 2, wherein the third value is different from the first value or the second value.

5. The gear transmission device according to claim 1 or 2, wherein a fourth value, which is a ratio between the frequency of the gear sound generated by the tool marks of a third gear included in a gear pair not including the first gear and the meshing frequency of the gear pair including the third gear, belongs to a consonant interval.

6. The gear transmission device according to claim 5, wherein a fifth value, which is a ratio between the frequency of the gear sound generated by the tool marks of a fourth gear meshing with the third gear and the meshing frequency of the gear pair including the fourth gear, belongs to a consonant interval.

7. The gear transmission device according to claim 6, wherein the fifth value is the same as the first value or the fourth value.

8. The gear transmission device according to claim 6, wherein the fifth value is different from the first value or the fourth value.

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