#### 1.What is the basic law of tooth profile engagement and what is the basic law of tooth profile engagement with fixed transmission ratio? What is the function of the basic law of tooth profile engagement?

Answer: for a pair of gear meshing transmission, the tooth profile contacts at any point, and the transmission ratio is equal to the inverse ratio of the two line segments divided by the common normal line of the contact point of the two wheel connecting centerlines. This law is called the basic law of tooth profile meshing. If the common normal line of all tooth profile contact points is connected with the center line at the fixed point, it is the basic law of tooth profile engagement with constant transmission ratio. Function: the requirement of tooth profile curve is put forward by whether the transmission ratio is constant.

#### 2.What is node, pitch line and pitch circle? The track of node on gear is round. Why gear?

Answer: the intersection point of the common normal line and the connecting center line of the tooth profile contact point is called the node, the track of the node on the gear during the meshing process of a pair of tooth profiles is called the pitch line, and the pitch line which is circular is called the pitch circle. The gear with pitch circle is circular gear, otherwise it is non-circular gear.

#### 3.What is conjugate tooth gallery?

Answer: a pair of tooth profiles satisfying the basic law of tooth profile engagement is called conjugate tooth profile.

#### 4.How is the involute formed? What is the nature of it?

Answer: the occurrence line rolls purely on the base circle. The track of any point of the occurrence line is called involute. Nature:

1) The length of the straight line where the line is rolled is equal to the length of the arc on the base circle.

2) The normal of any point of the involute must be tangent to the base circle.

3) The smaller the radius of curvature of the point close to the base circle on the involute is, the larger the radius is, the straighter the involute is.

4) The distance in the normal direction of two involutes on the same base circle is equal.

5) The shape of the involute depends on the size of the base circle. The smaller the base circle is, the larger the curvature of the involute is, the larger the base circle is, the smaller the curvature is, the infinite base circle is, and the involute becomes a straight line.

6) There is no involute in the base circle.

#### 5.Please write the polar equation of involute.

Answer: rk = Rb / cos α K θ k = inv α k = TG α K – α K

#### 6.What is the reason why the involute tooth profile satisfies the basic law of tooth profile engagement?

Answer: 1) in the involute property, the normal of any point of the involute must be tangent to the base circle

2) There is only one common tangent line on the same side of two circles, and the common normal line of the contact point of the involute of the tooth profile of two wheels must be tangent to two base circles, so there is only one node, that is, i12 = ω 1 / ω 2 = o2p / o1p = R2 ′ / R1 ′ = Rb2 / RB1 = constant

#### 7.What is the engagement line?

Answer: the locus of the contact point of the two tooth profiles.

#### 8.What are the characteristics of involute profile engagement and why?

Answer: 1) the transmission ratio is constant, because i12 = ω 1 / ω 2 = R2 ′ / R1 ′, because there is only one common tangent line on the same side of the two base circles, and it is the common normal line and meshing line of the contact point of the two tooth profiles, so there is only one intersection point with the connecting center line. Therefore, the transmission ratio is constant. NrpoJac3v1

2) The center distance is separable, < that is, the transmission ratio is invariable after the center distance is separated) the rotation ratio is invariable, because i12 = ω 1 / ω 2 = Rb2 / Rb1, the transmission ratio has been determined after a pair of gears are processed, which is independent of the center distance.

3) The direction of the positive pressure between the tooth profiles is the same, because the direction of the positive pressure between the tooth profiles is along the common normal line of the contact point, which is the internal common tangent line on the same side of the two base circles, and there is only one, so the direction of the positive pressure between the tooth profiles is the same.

4) Engagement angle α

It varies with the center distance because a cos α = a ′ cos α ‘.

5) Four in one,

(1) . the engagement line is the internal common tangent line on the same side of two base circles,

(2) Is the common normal of the tooth profile contact point,

(3) The locus of the contact point is the engagement line,

(4) It is the positive pressure line between tooth profiles and the sum of curvature radius of contact points.