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

A: 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. This law is called the basic law of tooth profile meshing. If the common normal of all tooth profile contact points intersects the center line at the fixed point, it is the basic law of tooth profile meshing with constant transmission ratio. The function is to ask for the tooth profile curve with the constant transmission ratio.

2. What are nodes, nodal lines and nodal circles? What is a gear if the locus of the node on the gear is circular?

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

3. What is conjugate tooth profile?

Answer: a pair of tooth profiles that satisfy the basic law of tooth profile meshing are called conjugate profiles.

4. How do involutes form? What's the nature?

Answer: the generating line is pure rolling on the base circle, and the locus of any point on the generating line is called involute.

nature:

(1) The length of the line rolled by the generating line is equal to the length of the arc on the base circle.

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

(3) The closer the involute is to the base circle, the smaller the radius of curvature is, and vice versa.

(4) The distance between the normal directions of two involutes on the same base circle is equal.

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

(6) There is no involute in the base circle.

5. Please write the involute polar equation.

A: rk = Rb / cos α K θ k = inv α k = TG α K - α K

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

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

(2) There is only one common tangent on the same side of the two circles, and the common normal line of the contact point of the involute of the two gears must be tangent to the 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 meshing line?

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

8. What are the characteristics of involute tooth profile meshing and why?

Answer: (1) the transmission ratio is constant, because i12 = ω 1 / ω 2 = R2 ′ / R1 ′, because there is only one common tangent 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 central line. Therefore, the transmission ratio is constant.

(2) Because i12 = ω 1 / ω 2 = Rb2 / Rb1, the transmission ratio of a pair of gears has been determined after machining, and has nothing to do with the center distance.

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

(4) The engagement angle α varies with the center distance because a cos α = a ′ cos α′.

(5) Four lines in one: ① the meshing line is the inner common tangent on the same side of the two base circles; ② is the common normal line of the contact point of the tooth profile; ③ the locus of the contact point is the meshing line; ④ is the action line of the positive pressure between the tooth profiles, and is the sum of the curvature radius of the contact point.

9. What are modulus and dividing circle?

Answer: the circle where M = P / π is the modulus and m and α are the standard values is called the dividing circle.

10. What are the girth, tooth thickness and alveolar width?

Answer: the arc length between two adjacent teeth on the same side of a circle is called the circumference. The arc length occupied by tooth thickness is called tooth thickness, and the arc length occupied by alveolar is called alveolar width.

11. What is a standard gear?

A: m, α, h * a, c * are the standard values, and S = e = P / 2.

12. What are the characteristics of the rack?

Answer: (1) the circumference of each straight line parallel to the tooth top line is equal, and its modulus and pressure angle are standard values.

(2) Parallel to the top line of teeth, the straight line with the width equal to the tooth thickness is called the center line, which is the reference line for determining the rack size.

13. What are the theoretical meshing line, actual meshing line and tooth profile working section?

Answer: theoretical meshing line: the inner common tangent on the same side of two base circles is theoretically the locus of the meshing point of tooth profile, and the two tangent points are the meshing limit points.

Actual meshing line: the line segment between the intersection point of the top circle of two teeth and the theoretical meshing line.

Working section of tooth profile: the part of gear transmission in which the tooth profile participates in meshing.

14. What are the correct Meshing Conditions and continuous meshing transmission conditions of involute spur gears?

Answer: correct engagement condition: M1 = M2 = m α 1 = α 2 = α

The condition of continuous engagement: ε α = b1b2 / Pb ≥ 1

15. What is the essential meaning of coincidence degree? What does coincidence degree have to do with it?

Answer: the size of coincidence degree represents the logarithm of meshing on the meshing line of a pair of gears in the process of transmission. The size of coincidence degree is an important index of bearing capacity and stability of gear. The size of coincidence degree has nothing to do with m, and increases with the increase of Z1 and Z2. The larger α′, the smaller ε α, α′ changes with the center distance, the larger a, the larger α′, and the smaller ε α.

16. What is the standard installation center distance of standard gear. What are the features of standard installation?

Answer: the center distance of standard gear installed according to no backlash is called the standard installation center distance of standard gear, and the center distance of standard gear installed according to standard top clearance is also called standard installation center distance.

For standard installation, a = a ', r = R', a = R1 + R2

17. What is the non-standard installation center distance? What are the features of non-standard installation?

Answer: a pair of meshing transmission gear, pitch circle and graduation circle do not coincide with the installation is called non-standard installation, and the center distance is called non-standard installation center distance.

Characteristic R ≠ R ′, a ≠ a ′, a ′ = R1 ′ + R ′ 2 = (R1 + R2) cos α / cos α′, that is, a ≠ a α′≠ α R1 ′≠ R2 C ′≠ C

There is tooth side clearance, which produces impact, the coincidence degree decreases and the stability is poor.

18. What are the characteristics of gear rack meshing transmission?

Answer: (1) the position of the meshing line does not change with the change of the relative position between the gear and the rack. It is always a fixed straight line cut to the base circle and perpendicular to the straight tooth profile of the rack.

(2) R = R ′ α′ = α = rack profile angle

19. What are the characteristics of machining standard gear with standard rack cutter?

Answer: the dividing circle of the wheel blank is tangent to the center line of the rack cutter, and pure rolling. The number of teeth of the gear to be processed is ensured by the moving speed of the cutter and the angular speed of the wheel blank rotation, and the V cutter = R ω blank.

20. What is undercutting phenomenon of involute tooth profile? What is the reason?

Answer: the phenomenon of undercutting is called undercutting when the finished involute profile is cut off by generating method.

Cause: the intersection point between the tooth top line and the meshing line of the cutter exceeds the meshing limit point of the gear to be cut. The reason why the tooth top line of the cutter exceeds the meshing limit point is that the number of teeth of the gear to be processed is too small, the pressure angle is too small, and the coefficient of addendum height is too large.

21. How to determine the minimum number of teeth without undercutting?

A: it is determined by Zmin = 2H * A / sin2 α.

22. What is modified gear?

Answer: indexing circle tooth thickness is not equal to the width of the tooth and the tooth top height is not the standard value of the gear is called modified gear. In machining, the center line of the rack cutter is not tangent to the graduation circle of the gear to be processed, and such a gear is called a modified gear.

23. What are the displacement, the coefficient and the minimum coefficient of displacement?

A: displacement: the vertical distance that the center line of the tool is shifted from the position of machining standard gear.

Modification coefficient: the coefficient required to express the displacement with standard modulus.

Minimum modification coefficient: the minimum value of modification coefficient required for undercutting of involute gears.

xmin = h*a （Zmin - Z）/ Zmin

24. Compared with the standard gear with the same number of teeth, which size of the modified gear has changed, which size remains unchanged, and why?

Answer: the number of teeth, modulus, pressure angle, dividing circle, base circle, pitch circle and whole tooth height remain unchanged, while the top circle, root circle, graduation circle, tooth thickness and width of tooth slot have changed.

Reason: when the standard gear cutter is used to process the modified gear, the processing method remains unchanged, that is, the correct meshing condition remains unchanged, so the modulus of the dividing circle and the pressure angle remain unchanged. Therefore, it can be seen from the formula that the dividing circle and the base circle remain unchanged, and then the calculation of the tooth root height, the tooth top height, the tooth root circle and the tooth term circle are calculated. When machining the modified gear, if the center line of the standard cutter moves outward from the dividing circle, the tooth root height becomes smaller, and the tooth root circle becomes larger; if the whole tooth height is constant, the tooth top height increases and the tooth top circle becomes larger, because the tool moves outward at the cutter tooth at the gear graduation circle When the thickness becomes smaller, that is to say, the tooth space becomes smaller, and because the pitch of the indexing circle remains unchanged, the tooth thickness becomes thicker.

25. How is the tooth profile of helical involute surface formed?

Answer: when the involute generating surface is pure rolling on the base cylinder, there is a line on the generating surface which forms an angle of β B with the generatrix of the base circle, and its trajectory forms the involute spiral surface of helical gear teeth.

26. Is the helix angle of each coaxial cylindrical surface where the helical gear tooth profile is located is the same? Why?

Answer: the helix angle is different, because the helix angle β I is determined by the lead L and the diameter Di of the cylinder. The lead is the same, but the diameter of each circle is different, so the helix angle is different. The relationship is: TG β I = L / π di

27. What are the meshing characteristics of helical gears?

Answer: (1) the tooth profiles of the two wheels start to contact from the point, and the contact line changes from short to long, and then becomes shorter, until the point contact, and then disengages. Unlike the spur gear transmission, it suddenly contacts along the whole tooth width and suddenly disengages from engagement, but gradually enters into the meshing and gradually disengages from the meshing. This kind of impact is small, the noise is small, and the transmission is stable.

(2) Large coincidence degree ε = ε α + ε β

28. Which face is the standard parameter surface of helical gear and which is the standard involute? Explain why.

A: the normal surface is the standard parameter surface.

Theoretically, the end face is a standard involute, because the formation of involute is the pure rolling of the surface on the base cylinder, and the track of the oblique line on the generating surface is an involute.

In processing, the normal surface is the standard involute, because the helical gear tooth profile is processed with the standard cutter for processing spur gear, and the cutting direction is along the tangent line of the helix, and the cutter face is on its normal surface. Therefore, the normal surface is the standard involute.

29. What is the relationship between the geometric parameters of helical gear end face and normal surface, and why the end face parameter is needed?

Answer: Mn = MT cos β, TG α n = TG α t cos β B, h * at = h * ancos β, c * t = C * ancos β, because the geometric dimensions are DT, DBT, DAT, DFT, Pt, PBT.

30. What are the correct Meshing Conditions and continuous transmission conditions for a pair of helical gears?

Answer: correct meshing condition: Mn1 = Mn2 = m α N1 = α N2 = α

External meshing β 1 = - β 2 internal meshing β 1 = β 2

Continuous transmission condition: ε = ε α + ε β ≥ 1

31. What is the equivalent gear and equivalent number of teeth of a helical gear? What is the purpose of the equivalent number of teeth?

Answer: the spur gear equivalent to the normal surface of helical gear is called the equivalent gear of helical gear. The number of teeth in an equivalent gear is called the equivalent number of teeth. The equivalent number of teeth is an important basis for selecting the tooth profile of the cutting tool in gear machining by profiling method, and the equivalent tooth number is the main basis for gear strength design.

32. What are the characteristics of worm gear and worm mechanism?

Answer: (1) transfer the motion and power between spatial staggered axes, namely spatial mechanism.

(2) In theory, the tooth profile contact is point contact, but the worm gear is added by the hob of the worm gear meshing with the worm gear, which is actually a space curve contact.

(3) The transmission ratio of worm and worm gear is calculated by the number of worm heads (lines).

(4) The diameter of dividing circle of worm is not the number of head multiplied by modulus, but the characteristic coefficient multiplied by modulus, that is, D1 = QM

(5) The center distance of worm gear and worm is also calculated by characteristic coefficient.

a＝ m（q＋Z2）/2

(6) It can obtain large transmission ratio and self-locking when worm gear is active.

33. Which surface is the standard parameter surface of worm gear and worm; what are the conditions for correct meshing?

Answer: (1) it is the main section, that is, the section parallel to the end face of the worm gear and passing through the axis of the worm is called the main section.

(2) The correct meshing condition is: MA1 = MT2 = m α A1 = α T2 = α β 1 + β 2 = 900, the rotation direction is the same

34. Why is the characteristic coefficient Q of worm determined as the standard value?

Answer: (1) it is conducive to the standardization of worm and reduces the number of worm.

(2) The number of worm hobs for machining worm gear is reduced.

35. How to determine the steering direction of worm gear meshing transmission?

Answer: first of all, determine the direction of rotation of worm or worm gear: erect the axis of worm gear or worm, the height on the right side of helix is right rotation, and the height on the left side is left rotation. Then determine the direction of rotation: the right hand rule is used for right rotation. The active worm is right-handed. Use four fingers of the right hand to hold the worm along the worm's direction of rotation. The direction of the thumb is opposite to the direction of the node speed of the worm gear to determine the turning direction of the worm gear.

36. What are the characteristics of straight bevel gear mechanism?

Answer: (1) transfer the motion and power between two intersecting axes.

(2) The gear is distributed on the cone and shrinks from the big end to the small end.

(3) The large end face is the standard parameter surface.

(4) The tooth profile curve is spherical involute.

37. What is the correct meshing condition of straight bevel gear?

Answer: M1 = M2 = m, α 1 = α 2 = α R1 = R2 (R is cone distance)

38. What is the back cone, equivalent gear and equivalent number of teeth of a bevel gear?

Answer: the cone which is tangent to the dividing circle on the spherical surface of the bevel gear is called the back cone of the bevel gear. The sector formed by the projection and expansion of the parallel conical generatrix on the large end surface of the bevel gear is called the sector gear. The spur gear which is equivalent to the large end surface of bevel gear is called the equivalent gear of bevel gear, and the number of teeth is called the equivalent number of teeth.

39. What is the purpose of equivalent gear and equivalent number of teeth?

Answer: a pair of equivalent gears of bevel gears are used to study the meshing principle of bevel gears, such as coincidence degree and correct meshing conditions. A single equivalent gear is used to calculate the minimum number of teeth not undercut and to select the tool number and calculate the bending strength of bevel gears when machining bevel gears with profiling method.