CN202048161U - Involute helical gear - Google Patents

Abstract

The utility model provides an involute helical gear which can improve the anti-fatigue strength of the dedendum and basically does not affect its anti-impact performance. The tooth surface with the larger pressure angle is the meshing surface, and the tooth surface with the smaller pressure angle is the non-meshing surface. The gear is an involute helical gear with displacement and different pressure angles on the tooth profile surface on both sides. According to the generation characteristics of the tooth profile surface of the involute helical cylindrical gear, the tooth profile surface on both sides of the tooth is given Design ideas of involute helical spur gears with different pressure angles, and deduce the calculation formulas of gear geometric parameters and dimensions in the case of displacement processing. Compared with conventional involute helical gears, the new involute helical gears have the advantages of large load capacity, small size, light weight, long service life and low noise.

Description

A kind of involute helical gear

technical field

The utility model relates to the technical field of gear design, in particular to an involute helical gear.

Background technique

Gear transmission is widely used because of its advantages of high power, high efficiency and long life. The pros and cons of its performance and quality ultimately affect the quality of machine products. Therefore, in order to adapt to the rapid development of modern mass production and technology, the performance of gear transmission is required to be continuously optimized. Especially in recent decades, great progress has been made in the meshing theory of gears, calculation and test of bearing capacity, vibration and noise, and new gear transmission.

The tooth shape not only affects the kinematic characteristics of the gear pair, but also affects the dynamic characteristics of the gear pair. In order to conform to the development trend of modern mass production, people continue to explore new tooth profiles. The research shows that increasing the pressure angle of the gear can improve the bending fatigue strength of the dedendum. Commonly used involute helical cylindrical gears, due to the difference in load and meshing conditions between the working tooth surface and the non-working tooth surface, if the pressure angle on both sides of the gear is increased at the same time, the tooth top will become thinner and the teeth may be broken. The resistance increases, that is, the impact resistance of the gear teeth will decrease.

Utility model content

The technical problem to be solved by the utility model is to provide an involute helical gear which can not only improve the anti-fatigue strength of the tooth root, but basically not affect its anti-shock performance.

In order to solve the above technical problems, the utility model provides an involute helical gear, which is characterized in that: the tooth profile pressure angles on both sides of the teeth of the involute helical gear are not equal, and the tooth surface with a larger pressure angle The tooth surface with the smaller pressure angle is the non-engaging surface.

The formation of the tooth profile surface on the non-meshing side of the involute helical gear: draw the first base cylinder surface of the involute helical gear with the line segment r _bc as the radius, and there is a first occurrence surface Q that is tangent to the first base cylinder surface, The angle between the first line segment KK on the first occurrence surface Q and the axis of the first base cylinder is β _bc ≠0, when the first occurrence surface Q performs pure rolling without sliding along the first base cylinder surface, the first base cylinder The trajectory of a line segment KK is the right tooth surface of the involute helical gear (the non-meshing side tooth profile surface);

The formation of the tooth profile surface on the meshing side of the involute helical gear: take the line segment r _bd as the radius to make the second base cylindrical surface of the involute helical gear, where r _bc /r _bd = 1 ~ 1.36; and there is a second The occurrence surface P is tangent to the second base cylinder surface, the angle between the second line segment MM on the second occurrence surface P and the axis of the second base cylinder is β _bd ≠0, when the second occurrence surface P is along the second base cylinder When the surface is doing pure rolling without sliding, the track of the second line segment MM is the left tooth surface of the involute helical gear (meshing side tooth profile surface).

The utility model has positive effects: (1) the gear of the utility model is an involute helical gear which is shifted and the pressure angle of the tooth profile surface on both sides of the gear tooth is not equal. According to the generation characteristics of the gear tooth, the design idea of the involute helical cylindrical gear with different pressure angles on the tooth profile surface on both sides is given, and the calculation formula of the geometric parameters and dimensions of the gear is deduced in the case of displacement processing. The tooth profile pressure angles on both sides of the tooth profile are not equal. Compared with the prior art, it can be seen from Fig. 5 that the volume and weight of the gear can be reduced when the tooth profile adopts unequal pressure angles on both sides. Compared with conventional involute helical gears, the new involute helical gears have the advantages of large load capacity, small size, light weight, long service life and low noise. (2) The utility model proposes a method of using tooth profile curved surfaces with unequal pressure angles on both sides of the helical gear teeth and performing displacement processing. The characteristic of the involute helical gear of the present utility model is: by using base cylinders of different diameters, tooth profile surfaces with different pressure angles are generated on both sides of the involute helical gear; and the displacement is designed according to the work needs Gear geometry.

Description of drawings

Fig. 1 is the structural representation of the involute helical gear of the present utility model;

Fig. 2 is the tooth shape diagram of the involute helical gear in Fig. 1; reference numerals in the figure: 1--addendum circle, 2--dividing circle, 3--the first base cylindrical surface, 4-- Root circle, 5--second base cylindrical surface, 6--left tooth surface, 7--right tooth surface;

Fig. 3 is the generating schematic diagram of the meshing side tooth profile surface (that is, the left involute tooth profile) of the involute helical gear in Fig. 2;

Fig. 4 is a schematic diagram of generating the non-meshing side tooth profile surface (that is, the right involute tooth profile) of the involute helical gear in Fig. 2;

Fig. 5 is a schematic diagram comparing the tooth profile 8 of the involute helical gear in the prior art and the tooth profile 9 of the involute helical gear of the present invention.

Detailed ways

As shown in Figure 1-2, the tooth shape of the involute helical gear in this embodiment mainly includes the tooth top 1, the left tooth surface 6 formed by the second base cylinder 5, and the right tooth surface formed by the first base cylinder 3 7 and tooth root 4. When the gear is working, the left tooth surface 6 with a large pressure angle participates in meshing, and the right tooth surface 7 with a small pressure angle does not participate in meshing.

The formation of the tooth profile surface on the non-meshing side of the involute helical gear: draw the first base cylinder surface of the involute helical gear with the line segment r _bc as the radius, and there is a first occurrence surface Q that is tangent to the first base cylinder surface, The angle between the first line segment KK on the first occurrence surface Q and the axis of the first base cylinder is β _bc ≠0, when the first occurrence surface Q performs pure rolling without sliding along the first base cylinder surface, the first base cylinder The trajectory of a line segment KK is the right tooth surface 7 of the involute helical gear (the tooth profile surface on the non-meshing side);

The formation of the tooth profile surface on the meshing side of the involute helical gear: take the line segment r _bd as the radius to make the second base cylindrical surface of the involute helical gear, where r _bc /r _bd = 1 ~ 1.36; and there is a second The occurrence surface P is tangent to the second base cylinder surface, the angle between the second line segment MM on the second occurrence surface P and the axis of the second base cylinder is β _bd ≠0, when the second occurrence surface P is along the second base cylinder When the surface is doing pure rolling without sliding, the track of the second line segment MM is the left tooth surface 6 of the involute helical gear (meshing side tooth profile surface).

The number of teeth of the involute helical gear, the helix angle on the indexing cylinder, the modulus of the end face of the indexing circle, the modulus of the normal face of the indexing circle, the pressure angle of the end face of the indexing circle on the meshing side, the pressure angle of the end face of the indexing circle on the non-meshing side, The normal surface pressure angle of the index circle on the meshing side and the pressure angle on the normal surface of the index circle on the non-engaged side are: z, β, m _t , m _n , α _td , α _tc , α _nd , α _nc ;

The value of z meets the transmission ratio requirements and meets the principle of non-undercutting;

β=8～20°;

The value of m _n is selected according to "Gear Handbook" (Machinery Industry Press, 2004-2 2nd Edition, China Edition Library CIP Digital Kernel (2000) No. 09768) or customized according to needs;

m _t = m _n / cos β mm;

α _td = atan(tanα _nd /cosβ) degrees;

α _tc = atan(tanα _nc /cosβ) degrees;

α _nc = 20°;

α _nd satisfies: 45° > α _nd > α _nc > 14° on the premise of satisfying no undercutting and gear tooth impact resistance.

毫米，其中：d为渐开线斜齿轮的分度圆直径，

毫米。The radius of the second base cylindrical surface

mm, where: d is the pitch circle diameter of the involute helical gear,

mm.

The β _bd =atan(tanβ·cosα _td ) degree, and 0<β _bd <90°.

毫米。The radius of the first base cylindrical surface

mm.

The β _bc =atan(tanβ·cosα _tc ), and 0<β _bc <90°.

其中：The normal tooth top height coefficient of the meshing side tooth profile, the normal tooth top height coefficient of the non-meshing side tooth profile, the normal top clearance coefficient of the meshing side tooth profile, and the normal top clearance coefficient of the non-meshing side tooth profile are respectively for

in:

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; anc</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ;</span>$

${\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; nc</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0.25</span>}<span\; class="notranslate">\; ;</span>$

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; and</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 0.25</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; nd</span>}}<span\; class="notranslate">\; )</span>\frac{\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; tan</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; nc</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; the\; tan</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; nd</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 0.25</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; sec</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; nc</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; sec</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; nd</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; tan</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; nc</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; tan</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; nd</span>}}}<span\; class="notranslate">\; ;</span>$

${\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; nd</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; nd</span>}}<span\; class="notranslate">\; )</span>\frac{\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; tan</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; nc</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; the\; tan</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; nd</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 0.25</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; sec</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; nc</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; sec</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; nd</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; tan</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; nc</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; the\; tan</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; nd</span>}}}<span\; class="notranslate">\; .</span>$

The normal tooth thickness of the pitch circle and the end tooth thickness of the involute helical gear are s _n , s _t ;

but: ${\mathrm{the\; s}}_{\mathrm{no}}=\frac{\mathrm{\&pi;}{m}_{\mathrm{no}}}{2}+x_{\mathrm{no}}{m}_{\mathrm{no}}(\mathrm{the\; tan}{\mathrm{\&alpha;}}_{\mathrm{nd}}+\mathrm{the\; tan}{\mathrm{\&alpha;}}_{\mathrm{nc}})$ mm, ${\mathrm{the\; s}}_t=\frac{\mathrm{\&pi;}{m}_t}{2}+x_t{m}_t(\mathrm{the\; tan}{\mathrm{\&alpha;}}_{\mathrm{td}}+\mathrm{the\; tan}{\mathrm{\&alpha;}}_{\mathrm{tc}})$ mm.

x _n is the normal surface displacement coefficient of the involute helical gear, x _t is the end surface displacement coefficient of the involute helical gear, then x _t = x _n cosβ, and To prevent undercutting of the helical gear.

The diameter of the addendum circle of the involute helical gear is d _a ,

The diameter of the dedendum circle of the involute helical gear is d _f ,

Compared with the existing involute helical gears, the involute helical gears of the present invention can significantly improve the carrying capacity (research shows: use a large pressure angle as the meshing surface and a small pressure angle as the non-meshing surface Helical gears can improve their load-carrying capacity.), reduce volume, and reduce weight (the gears with different pressure angles between the meshing surface and the non-meshing surface are compared to the gears with the same pressure angle between the meshing surface and the non-meshing surface. narrower, the volume and weight will naturally become smaller), prolong the service life (the strength increases and the life prolongs), reduce vibration and noise (due to the gear transmission with different pressure angles between the meshing surface and the non-meshing surface, the vibration displacement and dynamic load are relatively small. The existing gear is small, so the vibration and noise during gear transmission are also reduced), the market prospect is broad, and it has huge social and economic benefits.

Apparently, the above-mentioned embodiments of the present utility model are only examples for clearly illustrating the present utility model, rather than limiting the implementation manner of the present utility model. For those of ordinary skill in the art, other changes or changes in different forms can be made on the basis of the above description. It is not necessary and impossible to exhaustively list all the implementation manners here. And these obvious changes or variations derived from the spirit of the present utility model are still within the protection scope of the present utility model.

Claims (10)

1. A kind of involute helical gear, it is characterized in that: the tooth profile pressure angle of the gear tooth both sides of this involute helical gear is unequal, and the tooth surface with bigger pressure angle is meshing surface, and the tooth surface with smaller pressure angle The tooth surface is a non-meshing surface. 2. The involute helical gear according to claim 1, characterized in that: the number of teeth of the involute helical gear, the helix angle on the indexing cylinder, the end face modulus of the indexing circle, and the normal surface modulus of the indexing circle , The end surface pressure angle of the indexing circle on the meshing side, the pressure angle on the end surface of the indexing circle on the non-engaging side, the pressure angle on the normal surface of the indexing circle on the meshing side, and the pressure angle on the normal surface of the indexing circle on the non-engaging side are: z, β, m _t , m _n , α _td , α _tc , α _nd , α _nc ; The value of z meets the transmission ratio requirements and meets the principle of non-undercutting; β=8～20°; The value of m _n is selected according to the "Gear Manual" or customized according to needs; m _t = m _n / cos β mm; α _td = atan(tanα _nd /cosβ) degrees; α _tc = atan(tanα _nc /cosβ) degrees; α _nc and α _nd satisfy: 45°>α _nd >α _nc >14°. 3. The involute helical gear according to claim 2, characterized in that: the radius of the second base cylindrical surface

mm, where: d is the pitch circle diameter of the involute helical gear, mm. 4 . The involute helical gear according to claim 3 , characterized in that: β _bd =atan(tanβ·cosα _td ) degrees, and 0<β _bd <90°. 5. The involute helical gear according to claim 4, characterized in that: the radius of the first base cylindrical surface mm. 6 . The involute helical gear according to claim 5 , characterized in that: β _bc =atan(tanβ·cosα _tc ) degrees, and 0<β _bc <90°. 7. The involute helical gear according to claim 6, characterized in that: the coefficient of the normal surface addendum height of the meshing side tooth profile, the normal tooth top height coefficient of the non-meshing side tooth profile, and the law of the meshing side tooth profile The surface head clearance coefficient and the normal surface head clearance coefficient of the non-meshing side tooth profile are respectively

in: ${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; anc</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; nc</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0.25</span>}<span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; and</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 0.25</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; nd</span>}}<span\; class="notranslate">\; )</span>\frac{\frac{{\mathrm{<span\; class="notranslate">\; \&pi;m</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; nc</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; nd</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 0.25</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; sec</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; nc</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; sec</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; nd</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; nc</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; nd</span>}}}<span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; nd</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; nd</span>}}<span\; class="notranslate">\; )</span>\frac{\frac{{\mathrm{<span\; class="notranslate">\; \&pi;m</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; nc</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; nd</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 0.25</span>}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; sec</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; nc</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; sec</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; nd</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; nc</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; tan</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; nd</span>}}}<span\; class="notranslate">\; .</span>$ 8. The involute helical gear according to claim 7, characterized in that: _{the pitch circle normal face tooth thickness and end face tooth thickness of the involute helical gear are sn and st respectively} ; but:

mm,

mm. 9. The involute helical gear according to claim 8, characterized in that: x _n is the normal surface displacement coefficient of the involute helical gear, x _t is the end surface displacement coefficient of the helical gear, then x _t =x _n cosβ, and ${\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; \&Greater\; Equal;</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; and</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; z</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; td</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&beta;</span>}}<span\; class="notranslate">\; .</span>$ 10. The involute helical gear according to claim 9, characterized in that: the diameter of the addendum circle of the helical gear is d _a ,

The diameter of the dedendum circle of the helical gear is d _f ,

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