WO2004020875A1

WO2004020875A1 - Gears with the minimum number of teeth and high contact ratio

Info

Publication number: WO2004020875A1
Application number: PCT/CN2002/000598
Authority: WO
Inventors: Jiangming Huo; Hong Zheng
Original assignee: Zhuhai Biscuits & Food Co., Ltd.
Priority date: 2002-08-28
Filing date: 2002-08-28
Publication date: 2004-03-11
Also published as: AU2002330423A1

Abstract

With inventions and design on drive gears, It has been a desire to obtain a gear with high contact ratio, low number of teeth, small relative curvature and lower sliding velocity. Those characteristics above make the gear be smaller, lighter, quieter and more reliable. Compared with the standard involute spur gear, the minimum number of teeth being (7) and (33) when the contact ratio being required by (1) and (2) respectively, the present involute spur gear achieves the minimum number of teeth of (4) and (22) respectively.

Description

Gear with small number of teeth and large coincidence

The invention relates to gears, in particular to a tooth profile curve of a gear that strictly meets the plane conjugate meshing conditions, and a standard spur gear with a minimum coincidence degree of 1 and a minimum tooth count of 2 and a minimum coincidence degree of 2 minimum using this tooth profile design Standard spur gear method with 22 teeth.

technical background

Earlier mathematical analysis has determined that there are two curve shapes that can be used for gears, both of which belong to the family curve of the outer convolution line. One type is called epicycloid, and it is defined as the motion trajectory line left by a certain point on the moving circle when a moving circle is purely rolled around a fixed circle. The other is called involute, which is defined as the motion trace line left by one end of a straight line segment when a straight line segment rolls purely around a fixed circle. The French scholar Phillipe De La Hire discussed the family curve of the entire outer cycloid line in 1694, and concluded that the involute curve is the best of the family curve of the outer cycloid line. However, the involute was not used in the following 150 years. It was not until 1898 that the involute tooth profile was truly universally applied.

In 1907, the British Humphris published a paper to put forward the idea of arc tooth gear. In 1926, Wildhaber, Switzerland, obtained the patent for the circular arc toothed helical gear. In 1955, Novikov of the former Soviet Union completed a practical study, and the arc tooth profile began to enter industrial applications. It is important to note that this so-called arc tooth profile is not actually a conjugate tooth profile, because arcs cannot meet the conjugate conditions. The conjugate condition requires that the two conjugate teeth have a constant angular rate ratio and are always equal to the number of teeth ratio. The circular tooth gear can only rely on the curved surface generated by the continuous spiral movement of the circular tooth shape in the axial direction to achieve conjugate transmission in the axial direction.

In 1972, Saari first invented a conjugate tooth profile whose relative curvature is close to a constant value, which is the largest near the nodes and decreases to both sides. The invention of the tooth profile obtained US patent number 3631736. Subsequent to this type of tooth-shaped inventions are mainly representative of the US patent No. 4899609 of Nagata in 1986, US patent No. 4640149 of Drago in 1987 and US patent No. 5271289 of 1993 of Baxter. One common feature of these conjugate tooth patents whose relative curvature is close to a constant value and whose maximum value is close to the nodes and decreases to both sides is that there are no closed analytic expressions, that is, they are not mathematical curves. The cycloid family curve is also a strict mathematical curve, and the relative curvature of the invention also meets the maximum value near the nodes and decreases to both sides. On the other hand, large coincidence, small number of teeth, and small relative curvature are the goals pursued by gear power transmission, because it can be smaller, lighter, quieter and more reliable. In theory, the minimum number of teeth of a standard involute spur gear is not less than 7, and the minimum number of teeth with a coincidence of 2 is not less than 33. However, the minimum number of teeth of the standard spur gear of the present invention can be as small as 4, and the minimum number of teeth of the coincidence degree 2 can be as small as 22. Gears with very few teeth have special application requirements. For example, gear pumps pursue the use of small-tooth gears. The pursuit of fewer teeth is better.

Brief Description of the Drawings

Figure 1 is used to determine the coordinate system of the gear tooth profile parameter equation and the geometric meaning of the parameters of the present invention. Fig. 2 is a design example of a gear with five teeth according to the present invention.

The technical description is shown in Figure 1. The value of the rotation angle 8 of the pinion 1 about its rotation center Oi is Γ = 0 represents the initial position where the meshing point K coincides with the node P, and t> 0 indicates that the pinion 1 rotates counterclockwise. t <0 represents a clockwise rotation angle value, represents the number of teeth of the pinion 1, and Σ _n represents the minimum number of designed teeth. The value of the rotation angle 10 of the large gear 2 about its rotation center O ₂ is ^ ^, where the number of teeth of the large gear 2 is represented. As shown in FIG. 1, the trajectory 3 of the meshing point κ is called a meshing line, and the line PK from the node P to the entanglement point κ is defined as the meshing line diameter. The angle 3 between it and the line passing through the node P and perpendicular to the centerline is defined as the angle of the spray line diameter. It is also referred to as "pressure angle" below. It is also called the pressure angle. connection is defined coincident engagement point κ κ contact point of the radial toothed, identified hereinafter _^,;. ,, said it from the gear tooth point dead center point ^ ₁ intersects the pitch circle 1 5 The included angle 9 of the connecting line O is defined as the tooth-shaped spreading angle, and „,. Is used in the following. ,, 0) indicates that the polar coordinate parameter equation of the tooth shape of the pinion 1 is expressed as follows:

mz cos (" ₀ )-

^ pinioiv ^ '―

2 osia ρΰήοη

( 1 )

("(J) ^-a )-CCpinionif] ~ ^t -where

]

z _n cosla. 0

(2)

The connecting line O ₂ T of the large gear is defined as the tooth-shaped radial diameter, which is represented by r _geai t) in the following, and the angle 12 between the connecting line 0 _{2 and the} body ₂ is defined as the large gear tooth-shaped spreading angle, which is expressed in the following, Then the polar coordinate parameter equation of the gear tooth shape of the large gear 2 is expressed as follows:

ear (cos (a ₀ )-a ₂ t ² ) -a (t) + t

a _gear (0 = (4)

Is the modulus, ". Is the nodal pressure angle, a ₂ is the tooth profile coefficient. When a ₂ ≥ 0.2, the constant curvature is close to constant, and the value near the node is the largest and decreases to both sides, and the conclusion does not change with the change of S ₀ and z _min and does not change with the number of teeth greater than _in . The tooth profile of the present invention has an infinite number of minimum design teeth, that is, there are gears with any small number of teeth. However, there is a difference and connection between the minimum number of designed teeth and the minimum number of developed teeth. When the minimum design tooth number can take any natural number, it is said that there are infinitely many minimum design tooth numbers for the tooth shape. At this time, the minimum design tooth number is the basic design parameter of the tooth shape. When the tooth shape is smaller than the minimum design tooth number, there must be a minimum formed tooth number, that is, undercutting occurs when the tooth shape is smaller than the minimum formed tooth number. If there is a unique minimum number of teeth for a tooth profile, it must also be equal to the minimum number of teeth. Since the tooth shape of the present invention has an infinite number of minimum design teeth, it has become a design parameter, and the true minimum number of non-root-cut teeth is actually the minimum number of developed teeth. The tooth profile of the present invention is formed by using a rack. Therefore, the basic rack design of the tooth profile determines the gear corresponding to the tooth profile. Helical gears, bevel gears, and curved bevel gears can all be generated using the rack spreading method. The relative curvature of the present invention is close to constant, the relative radius of curvature is large at the nodes and small on both sides of the tooth tip and the tooth root. The quality of the contact stress of this type of tooth shape is completely determined by the relative curvature at the nodes. In order to improve the tooth contact stress characteristics, the relative curvature radius at the joint must be as large as possible, so the design based on the relative curvature of the joint It is a design based on the tooth contact stress characteristics. It is easy to see that increasing the joint pressure angle can reduce the relative curvature of the joint. Next consider the tooth shape design parameter as flr. = 20 ^Q , z _Min = 17, and A _a = l. Obviously, this is also the basic design parameter of the standard involute gear. This example can compare the advantages and disadvantages between the tooth profile of the present invention and the involute tooth profile.

Table 1

Table 1 shows that the relative curvature of the nodes of the present invention is the same as the involute and the maximum relative slip rate is less than half of the involute. Except for the degree of coincidence which is slightly smaller than the involute, all other indicators are more than the involute. Open line is superior.

Increasing the degree of coincidence is beneficial to the gear's increased contact and bending strength, and to improve the smoothness and manufacturing accuracy of the transmission. In particular, the minimum degree of coincidence is

The design of 2 has very practical significance. The minimum design tooth number, minimum coincidence degree, top height coefficient, top clearance coefficient and other four basic gear parameters can be used to determine the node pressure angle. Tables 2 and 3 are several design examples.

Table 2

Figure 2 is a design example of a standard high-tooth spur gear with a minimum design tooth number of 5, a nodal pressure angle of 15 degrees, a tooth profile coefficient of 0.28, and a modulus of 10. 23 is a tooth root transition curve.

Claims

Claim

1. A gear pair consisting of a pair of meshing spur gears. The tooth profile of this pair of gears meets the conjugate condition with each other. The tooth profile is precisely defined by the following mathematical parameter equation:

Where is the modulus, α. Is the nodal pressure angle, ^ is the number of two gear teeth, is the tooth shape coefficient, and z _min is the minimum design tooth number. The tooth profile coefficient a is non-zero and non-negative. ₂ = 0 will degenerate into an involute tooth profile.

2. The gear according to claim 1, when the tooth profile coefficient is> 0.2, the relative curvature constant satisfies the maximum value near the node and decreases to both sides.

3. The gear according to claim 1, wherein a standard spur gear with a minimum coincidence of 1 and a minimum number of teeth of 4 and a standard spur gear with a minimum coincidence of 2 and a minimum number of 22 are designed.

4. Various structural gears cut using the cutting principle of forming method include cylindrical spur gears, cylindrical helical gears, conical spur gears, conical helical gears, curved bevel gears (arc bevel gears or quasi-hyperbolic bevel gears), etc. Their tooth profile satisfies Equation 1

5. The cutting tool of the forming method according to claim 4, which includes a gear type insert cutter and a milling cutter (including a disc type and a finger type), and their knife-shaped contours satisfy Formula 1.

6. Use the direct machining principle (including various CNC machining methods, EDM, laser) and various special machining principles (various chemical and physical based) to process forming tools that meet the requirements of 5.

7, using the direct method of processing principles (including various types of numerical control processing methods, electric sparks, lasers) and various special processing principles (various chemical and physical based) for processing various structural gears including cylindrical spur gears, cylindrical helical gears, cones Gears such as spur gears, conical helical gears, curved bevel gears (arc bevel gears or quasi-hyperbolic bevel gears), and their tooth profile meet the formula 1.