【菜鸟成长记】20岁后，我在机械的每一天

黑森林的鹿

【20160411】Fundamental law of gearing

% ?( Y2 B+ N9 w0 c' QFundamental law of gearing：the angular velocity ratio between the gears of a gearset remains constant throughout the mesh.
+ @, i4 M; Y  f% ?齿廓啮合基本定律：啮合过程中两齿轮的角速度之比保持不变。
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P: instant center.
P点为速度瞬心。
Velocity ratio:

5 U; C# w7 U- o; N: z* G- C8 tConstant velocity ratio：point P should be fixed.
9 A6 f4 I  Y2 A( T7 l! ^- }& Y速度比恒定的意义：P点固定。
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の小南灬

看看，加油

zqphho999

也想进步。

黑森林的鹿

【20160412】Involute Tooth Profile

An involute shape is constructed by unwinding a taut wire from a base circle with diameter db.
" e2 E) h3 j! c渐开线由直径为db的基圆上解开一条拉线形成。

“Taut wire” is always tangent to base circle and normal to involute.
“拉线”总与基圆相切，垂直于渐开线。
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The center of curvature of the involute is always at the point of tangency of the “taut wire” with the base circle.
9 v9 a. ^" K3 _- S; V曲率中心总在基圆与拉线切点处。
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Any portion of tooth profile inside the base circle is not an involute.
7 z# ]9 \) @6 O" W; r  R0 ^* k基圆以内无渐开线。
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* V0 H  Z8 c/ M6 a" m* AInvolute profile provide the constant velocity ratio.
渐开线能保证速度比恒定。
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黑森林的鹿

の小南灬 发表于 2016-4-11 21:18
看看，加油

5 y! p, i3 o% I: }0 ~' P恩呐~
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黑森林的鹿

zqphho999 发表于 2016-4-12 19:50
也想进步。

; k5 Y. a! ~3 L  V' \+ U: S共同进步！
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黑森林的鹿

【20160413】Standard Gears
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3 R2 V+ r8 ^8 x% ]. `7 e" k2 lAny two involute gears with the same diametral pitch and pressure angle will mate.
' |( \" Q: j2 X4 V$ w& C9 Z# c径节和压力角相同的渐开线齿轮可以配合。
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Gear teeth have been standardized based on the diametral pitch and pressure. Standard pressure angles are

齿轮的齿以径节和压力为基准进行标准化。标准压力角如图。
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The standardized values of diametral pitch：
标准径节值如下表：
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The manufacturers must follow a standard convention to form the details of the gear tooth profile. The AGMA is the primary organization that oversees this standardization scheme.
齿轮齿廓的加工必须遵循一定规则，美国齿轮制造协会首先制定相关规定。

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黑森林的鹿

【20160414】Relationships of Gears in Mesh
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8 B6 \0 c2 c# I% ^3 f8 XCenter Distance

/ ^! m1 N" M" F8 W3 ?; KPinion-the smaller gear  小齿轮
Bull gear or gear -the larger gear  大齿轮

1 m' }) C1 a4 q  k  ?: |% Y( _! aContact ratio( mp ): the average number of teeth that are in contact at any instant.
& j; O" V$ E- p7 f/ N8 I# v重合度：任意时刻相互接触的齿数。
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where
Z -The length of the contact path( length of straight line）
0 z( r2 ?% N! Q, X% xpb-The base pitch, which is defined as the distance between corresponding points of adjacent teeth, measured on the base circle( length of arc )
啮合度=接触长度（直线长度）/节距（弧线长度）


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An involute shape is constructed by unwinding a taut wire from a base circle.
+ }9 n& E# A  u% H7 E% ]% r& U渐开线的形成方式决定了直线段KN与弧线段AN的长度相等。


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1 v/ _: U) i! `3 a1 [6 s" KInpractice, contact ratios should be greater than 1.2.
实际应用中，重合度应大于1.2。
  Q* O. Y" ^" i( DA contact ratio of 1.2 indicates that one pair of teeth is always in contact and a second pair of teeth is incontact 20 percent of the time.
重合度为1.2意味着，一对齿总是接触，第二对齿有20%的时间接触。

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黑森林的鹿

【20160415】Interference
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5 d# r6 w5 I+ i7 [: T3 M* Kdedendum circle > base circle
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7 D! d: {! Y5 c: |% ^dedendum circle < base circle

Gear teeth have involute profiles between the base circle and the addendum circle. When a gear with few teeth and small pressure angles is constructed, the dedendum circle is considerably smaller than the base circle of the involute. Therefore, the tooth between the base circle and the dedendum is not an involute.
基圆与齿顶高间的齿具有渐开线齿廓。当齿轮的齿数过少并且压力角很小时，齿根高远小于形成渐开线的基圆。因此，基圆与齿根高间的齿不是渐开线齿轮。

0 s! w; n* z* x$ \! i6 GInterference：If the mating gear tooth were to contact the non-involute portion of the tooth, the fundamental condition for constant velocity ratio would be violated.
6 k) \# R4 c7 c  l8 N' {7 k干涉：配合的齿轮在非渐开线处接触时，常速定理不满足。
drastic noise, vibration, and wear 不利：噪音，速度突变，磨损

To avoid interference，the maximum number of gear teeth is given as

) m: S5 k  U6 B! {/ y% y为避免干涉，最大齿数应满足如上公式。
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