CN104455315A - Gear with novel tooth profile curve - Google Patents

Abstract

The invention discloses a gear with a novel tooth profile curve. A tooth profile curve at the tooth top of the gear is in a convex shape. A tooth profile curve at the tooth root of the gear is in a concave shape. A meshed tooth pair of a gear pair is in convex-concave arc meshing. In a coordinate system O-xy with the gear center as an original point, through a gear parameter and tooth profile curve parameter equation, the tooth profile curve is obtained, the tooth profile curve is subjected to symmetry and rotation transformation, then the end face profile of the gear is obtained, and the gear pair formed by gears is in conjugation and in convex-concave arc meshing. The gear can be used in tooth profile design in large-load gear transmission, the bearing capacity of the gear is greatly increased compared with an involute, when a rack tool or hobbing is used for machining, machining tool design is simple, and only one tool needs to be machined. The gear is also used in design of a small-tooth-number gear pair with a small tooth number (z is smaller than or equal to 6), and accordingly the bearing capacity is improved.

Description

A kind of gear with tooth profile curve

Technical field

The present invention relates to a kind of design of tooth profile curved tooth cylindrical gear, belong to form of gear tooth design field.

Background technique

What the tooth curve of general gear all adopted is involute, this be due to involute have power transmission steadily, centre distance can divide and the easy advantage such as processing.But its deficiency is that the bearing capacity of gear pair is limited, the methods such as displacement, correction of the flank shape that propose in application improve its bearing capacity, but in some special transmission occasions, still can not meet the demands.

For the deficiency of the involute gear of above-mentioned proposition, people explore again and devise circular tooth gear and Novikov gears with double circular arc tooth profiles, and the engagement of double circular arc tooth wheel set is the engagement of convex-concave arc, and the synthetic curvature at point of contact place is little, and contact strength is high, improves the intensity of gear to a certain extent.But Novikov gears with double circular arc tooth profiles exist need to run and after could meet conjugation engagement, processing difficulties and to problems such as centre distance error sensitive.

Summary of the invention

For the problems referred to above, the object of the invention is to, overcome the deficiency of existing tooth curve, provide a kind of gear with tooth profile curve, the gear pair with tooth curve of the present invention is applicable to larger load or in the driving mechanism such as the gear number of teeth is less.

In order to solve the problems of the technologies described above, a kind of gear with tooth profile curve that the present invention proposes, the tip portion tooth curve of this gear is convex, the tooth curve of root portions is spill, the rodent population of gear pair is the engagement of convex-concave arc, in the system of coordinates O-xy taking Gear center as initial point, profile's factories equation is:

$\left\{\begin{array}{c}x\left(t\right)=t\sin (\mathrm{\α}+u)-\mathrm{\λ}\sin \left(\mathrm{\ωt}\right)\cos (\mathrm{\α}+u)+r\sin u-\mathrm{ru}\cos u\\ y\left(t\right)=t\cos (\mathrm{\α}+u)+\mathrm{\λ}\sin \left(\mathrm{\ωt}\right)\sin (\mathrm{\α}+u)+r\cos u+\mathrm{ru}\sin u\end{array}\right.(-\mathrm{\π}/\mathrm{\ω}\≤t\≤\mathrm{\π}/\mathrm{\ω})$

Wherein: α is pressure angle, $u=\frac{1}{r\sin \mathrm{\α}}(t+\frac{\mathrm{\λ\ω}[t\cos \mathrm{\α}+\mathrm{\λ}\sin \left(\mathrm{\ωt}\right)\sin \mathrm{\α}]\cos \mathrm{\ωt}}{\sin \mathrm{\α}-\mathrm{\λ\ω}\cos \mathrm{\α}\cos \mathrm{\ωt}}),\mathrm{\ω}=\frac{\mathrm{\π}\cos \mathrm{\α}}{h_a^{*}m},h_a^{*}$ For addendum coefficient, m is modulus, and r is pitch circle radius, and r=m (z+x), x are modification coefficient, and λ is derivative coefficient, λ ≠ 0, and this derivative coefficient is used for the convex-concave degree of tooth curve; Described tooth curve obtains the end profile of gear after symmetrical and rotation transformation, the mutual conjugation of gear pair that this gear is formed and engaging for convex-concave arc.

Compared with prior art, the invention has the beneficial effects as follows:

1. the gear pair with tooth curve of the present invention is that convex-concave arc meshed gears is secondary, improves the tooth face contact fatigue strength of gear, be suitable for use in the occasion of larger driven load compared with involute gear.

2. compared with involute gear, have the gear of tooth curve of the present invention, the sliding ratio of its gears meshing is little, and the flank of tooth not easily weares and teares, scuffing failure.

3. there are some characteristics of traditional Novikov gears with double circular arc tooth profiles, but it is insensitive to compare centre distance change compared with Double circular arc gear drive.

4. have the gear of tooth curve of the present invention, especially the bearing capacity of gear with little teeth number pair is significantly improved.

5., because the intermeshing representation with the tooth profile curve equation of the active and passive gear of tooth curve of the present invention is consistent, available one processes a pair mutually conjugate gear of energy rack cutter or gear hob.

6. in addition, involute is a kind of special circumstances of tooth curve of the present invention.

Accompanying drawing explanation

Fig. 1 is the tooth curve schematic diagram of gear of the present invention;

Fig. 2 is the gear pair schematic diagram with tooth curve of the present invention;

Fig. 3 is the secondary schematic diagram of gear with little teeth number with tooth curve of the present invention.

Embodiment

Below in conjunction with drawings and Examples, the present invention is described in detail, but not as any limitation of the invention.The present invention be utilize to tooth profile equation, not only need during design to choose ordinary gear parameter, such as: the number of teeth, modulus, pressure angle and modification coefficient etc., also need design to choose derivative coefficient lambda (λ=0 item for involute profile), the increasing of variable can be conducive to optimal design go out specified conditions under optimum gear pair.

As shown in Figure 1, a kind of gear with tooth profile curve of the present invention, the tip portion tooth curve of this gear is convex, the tooth curve of root portions is spill, the rodent population of gear pair is the engagement of convex-concave arc, the secondary flank profil of active and passive gears meshing has unified tooth curve representation, and in the system of coordinates O-xy taking Gear center as initial point, profile's factories equation is:

$\left\{\begin{array}{c}x\left(t\right)=t\sin (\mathrm{\α}+u)-\mathrm{\λ}\sin \left(\mathrm{\ωt}\right)\cos (\mathrm{\α}+u)+r\sin u-\mathrm{ru}\cos u\\ y\left(t\right)=t\cos (\mathrm{\α}+u)+\mathrm{\λ}\sin \left(\mathrm{\ωt}\right)\sin (\mathrm{\α}+u)+r\cos u+\mathrm{ru}\sin u\end{array}\right.(-\mathrm{\π}/\mathrm{\ω}\≤t\≤\mathrm{\π}/\mathrm{\ω})$

$u=\frac{1}{r\sin \mathrm{\α}}(t+\frac{\mathrm{\λ\ω}[t\cos \mathrm{\α}+\mathrm{\λ}\sin \left(\mathrm{\ωt}\right)\sin \mathrm{\α}]\cos \mathrm{\ωt}}{\sin \mathrm{\α}-\mathrm{\λ\ω}\cos \mathrm{\α}\cos \mathrm{\ωt}}),\mathrm{\ω}=\frac{\mathrm{\π}\cos \mathrm{\α}}{h_a^{*}m},$ R is pitch circle diameter, and x is modification coefficient, and λ is derivative coefficient, and λ ≠ 0, this derivative coefficient is used for the convex-concave degree of tooth curve.

Relevant parameters in embodiment 1 is:

Above-mentioned parameter is substituted into the tooth curve that profile's factories equation obtains as shown in Figure 1, this tooth curve obtains the end profile of the gear from tooth top to tooth root with convex-concave arc feature after symmetry and rotation transformation, with above-mentioned profile's factories equation can design can mutually conjugation and for convex-concave arc meshed gears secondary, as shown in Figure 2.

Adopt specific profile's factories equation in the present invention, and choose corresponding design parameter, the transverse tooth profile curve of design gear can obtain the gear with tooth profile curve, ben: to introduce derivative coefficient lambda in the present invention and mainly consider to strengthen Gear Contact fatigue strength, choose larger derivative coefficient lambda, Gear Contact fatigue strength can be strengthened further.

As shown in Figure 3, embodiment 2 is application examples of a gear with little teeth number, and this gear parameter is as follows: m=1.75, z ₁=3, z ₂=26, λ=0.18, small gear modification coefficient x ₁=0.8, gearwheel modification coefficient x ₂=-0.8, α=28 °, c ^*=0.25.With embodiment 1, finally obtaining can conjugation and engage for convex-concave arc and have the gear pair of gear with little teeth number mutually, and due to the characteristic of few, the large displacement of the gear with little teeth number number of teeth and topping, tooth curve only uses a part for tooth curve of the present invention.

The present invention has in the design of gears of tooth profile curve, first, utilizes above-mentioned parameter to adopt the tooth profile curve equation in the present invention to draw out tooth curve; Second half of gear-profile curve is drawn out again according to the symmetry properties of open top container ship condition and gear; Utilize the characteristic that the gear teeth are uniform on gear shaft, adopt transformation of coordinates to obtain the transverse tooth profile of gear.To the Fillet curve of gear, jointly determined by gear working method and cutter, what adopt in embodiment is the Fillet curve of cutter teeth the top of the horn angle envelope gained.

Although invention has been described by reference to the accompanying drawings above; but the present invention is not limited to above-mentioned embodiment; above-mentioned embodiment is only schematic; instead of it is restrictive; those of ordinary skill in the art is under enlightenment of the present invention; when not departing from present inventive concept, can also make a lot of distortion, these all belong within protection of the present invention.

Claims (1)

1. have a gear for tooth profile curve, the tip portion tooth curve of this gear is convex, and the tooth curve of root portions is spill, and the rodent population of gear pair is the engagement of convex-concave arc, it is characterized in that:

In the system of coordinates O-xy taking Gear center as initial point, profile's factories equation is:

$\left\{\begin{array}{c}x\left(t\right)=t\sin (\mathrm{\α}+u)-\mathrm{\λ}\sin \left(\mathrm{\ωt}\right)\cos (\mathrm{\α}+u)+r\sin u-\mathrm{ru}\cos u\\ y\left(t\right)=t\cos (\mathrm{\α}+u)+\mathrm{\λ}\sin \left(\mathrm{\ωt}\right)\sin (\mathrm{\α}+u)+r\cos u+\mathrm{ru}\sin u\end{array}\right.(-\mathrm{\π}/\mathrm{\ω}\≤t\≤\mathrm{\π}/\mathrm{\ω})$

Wherein: α is pressure angle, $u=\frac{1}{r\sin \mathrm{\α}}(t+\frac{\mathrm{\λ\ω}[t\cos \mathrm{\α}+\mathrm{\λ}\sin \left(\mathrm{\ωt}\right)\sin \mathrm{\α}]\cos \mathrm{\ωt}}{\sin \mathrm{\α}-\mathrm{\λ\ω}\cos \mathrm{\α}\cos \mathrm{\ωt}}),\mathrm{\ω}=\frac{\mathrm{\π}\cos \mathrm{\α}}{h_a^{*}m},h_a^{*}$ For addendum coefficient, m is modulus, and r is pitch circle radius, and r=m (z+x), x are modification coefficient, and λ is derivative coefficient, λ ≠ 0, and this derivative coefficient is used for the convex-concave degree of tooth curve; Described tooth curve obtains the end profile of gear after symmetrical and rotation transformation, the mutual conjugation of gear pair that this gear is formed and engaging for convex-concave arc.