RU2019761C1 - Helical gearing - Google Patents

Abstract

FIELD: mechanical engineering. SUBSTANCE: helical gearing has helical gear-wheels. Each toothing is provided with ring slots width of which is equal to integer number of axial steps. The ring slots are arranged on the toothings uniformly. Minimum number of slots is defined by a relationship proposed. EFFECT: enhanced longevity. 5 dwg

Description

 The invention relates to mechanical engineering and can be used in gear mechanisms for various purposes to reduce their vibration.

 Known helical transmission containing gears, the width of the rims of which is a multiple of the axial pitch.

 However, by choosing the width of the gear wheel, which is a multiple of the axial step, the reduction of the vibration level of the transmission is achieved by eliminating only one disturbing factor - variable stiffness in the engagement phase. Moreover, in some cases, this choice does not lead to a decrease in the level of transmission vibration.

 Closest to the proposed application by technical nature is a cylindrical gear containing helical gears with ring slots, the width of the gear rims of which is an integer number of axial steps and the distance to the slots from the ends of the gears of the same name is selected depending on the width of the wheels.

 The disadvantage of this gear transmission is that the reduction of vibration caused by various disturbing factors is possible only at the gear frequency.

 The aim of the invention is to reduce the level of vibration of the helical gear at the same time at all harmonics of the tooth frequency.

cos K

Zωt +

(i - 1)

= 0 ,
K=1, 2, 3..., где n - количество кольцевых прорезей,
К - номер гармоники зубцовой частоты, на которой желательно снизить уровень вибрации передачи,
i - номер участка зубчатого венца, отсчитываемого от торца колеса со стороны входа зубьев в зацепление;
ε_β- коэффициент осевого перекрытия.This goal is achieved in that in a helical gear transmission containing gears with ring slots, the width of the gears of which is an integer number of axial steps and the distance to the slots from the same ends of the gears is selected depending on the width of the wheels, the gears of the wheels are divided by ring slots into equal parts, the minimum number of slots is selected from the ratio

cos K

Zωt +

(i - 1)

= 0,
K = 1, 2, 3 ..., where n is the number of ring slots,
K is the harmonic number of the tooth frequency, at which it is desirable to reduce the vibration level of the transmission,
i is the number of the part of the ring gear, measured from the end of the wheel from the input side of the teeth into engagement;
ε _β is the axial overlap coefficient.

 A comparative analysis of the inventive helical gear with the prototype shows that the gear in question is distinguished by the presence of ring slots on the rim of each gear wheel, dividing these crowns into equal parts, while the minimum number of slots is determined by calculation using the dependence proposed in the claims.

 Thus, the claimed transmission meets the criterion of "Novelty."

 When comparing the proposed solution with other technical solutions in the art, it was not possible to identify in these solutions the features that distinguish the claimed solution from the prototype, which allows us to conclude that the criterion of "significant differences".

 The dependence for determining the minimum number of ring slots on the gears is obtained from the following considerations.

.It is known that an involute helical wheel with a width B can be imagined in the form of a set of wheels of infinite small width dB, rotated in the plane of rotation one relative to the other by an infinitesimal angle d _α . This explains the order of the location of the contact lines on the field of engagement of the pair of helical gears shown in Fig. 1 (The value of the angle of rotation of the wheel d _α depending on the angle of inclination of the tooth β _o on the main cylinder of radius r and width dB is expressed as
d _α =

.

Thus, in each section with a width of dB, the contact lines are out of phase relative to the neighboring section by the value of d _α (Fig. 4).

) относительно первого участка (фаза контактных линий которого принята за ноль и отнесена к началу входа очередной пары зубьев в зацепление) определяется как
α_i =

(i - 1).If the ring gear of the wheel is divided into equal sections by ring slots, (end sections of FIG. 5e), then the phase shift of the contact lines for such a gear transmission in these sections can be defined as α = 2πε _β / n + 1. Moreover, the phase shift of the contact lines of any selected i-th section α _i i = (

) relative to the first section (the phase of the contact lines of which is taken to be zero and assigned to the beginning of the entry of the next pair of teeth into engagement) is defined as
α _i =

(i - 1).

Thus, it can be argued that the ring gear is composed of n toothed sections (wheels), each of which is rotated relative to the other by an angle α _i .

Having connected the phase φ _{i of the} disturbing force of the form F _i cos (Z ωt + φ _i ), where Z is the number of teeth of the wheel, ω is the revolution frequency, with the phase d _i characterizing the position of the contact lines on the engagement field for the ith section of the wheel under consideration, distinguished by annular slots, it can be argued that the phase shift between the disturbing forces acting on the ith sections clearly corresponds to the phase shift between the contact lines of these sections.

(i - 1). (1)
Для компенсации возмущающих сил, возникающих в каждой части зубчатого колеса, образованной кольцевыми прорезями, необходимо чтобы их фазовые соотношения удовлетворяли условию:

F_icosK(Z ω t + φ_i) = 0. (2)
Условие (2) должно выполняться независимо от физической природы возникновения возмущающих сил (переменная жесткость по углу поворота колеса, ударный вход зубьев в зацепление и т.д.). В силу того, что зубчатое колесо (ведомое и ведущее) разделено прорезями на равные участки, т.е. на равные по ширине пары зубчатых "независимых" передач, можно утверждать, что все F_i равны между собой по амплитуде, а поэтому условие (2) перепишем в виде
F

cosK(Z ω t + φ_i) = 0. (3)
Или в силу однозначного соответствия между φ_i и α_i условие (2) запишем как:
F

cosK(Z ω t + α_i) = 0. (4)
Окончательно выражение (4) с учетом (1) имеет вид

cos K

Zωt +

(i - 1)

= 0 . (5)
Механизм компенсации возмущающих сил можно пояснить иным способом.However, the obtained expression for the phase shift α _{i is} valid only for the first harmonic of the tooth frequency, because the axial (end) step of the wheel corresponds to the period with the gear frequency, i.e. 2 π. For any Kth harmonic, the phase relations will have the form
α _i = K

(i - 1). (1)
To compensate for the disturbing forces arising in each part of the gear formed by annular slots, it is necessary that their phase relations satisfy the condition:

F _i cosK (Z ω t + φ _i ) = 0. (2)
Condition (2) must be satisfied regardless of the physical nature of the occurrence of disturbing forces (variable stiffness in the angle of rotation of the wheel, impact input of the teeth into gearing, etc.) Due to the fact that the gear wheel (driven and driving) is divided by cuts into equal sections, i.e. equal to the width of the pair of gears of "independent" gears, it can be argued that all F _i are equal in amplitude, and therefore we rewrite condition (2) in the form
F

cosK (Z ω t + φ _i ) = 0. (3)
Or, due to the unambiguous correspondence between φ _i and α _i, condition (2) can be written as:
F

cosK (Z ω t + α _i ) = 0. (4)
Finally, expression (4), taking into account (1), has the form

cos K

Zωt +

(i - 1)

= 0. (5)
The mechanism of compensation of disturbing forces can be explained in another way.

If we take two identical pairs of gears for an example of a width of _1.2 = 1.5 P _x operating in phase, then the engagement fields for each of them will be identical (Figs. 1 and 2). After the rotation of the second pair of gears relative to the first by an angle corresponding to the gear ¹⁸⁰ by the frequency, the contact line on the second field will take the position shown in Figure 2 by dotted lines.

The common field of engagement (figure 3) can be obtained by connecting the wheels of two pairs of gears in question. Figure 3 shows that the thus obtained field of engagement corresponds to the field of the gear transmission with wheels of width B = B ₁ + B ₂ obtained using an annular slot. Therefore, it can be argued that the assembled pair consists of two pairs of wheels deployed one relative to the other respectively 180 ^° , i.e. working in antiphase with a perturbation at the gear frequency.

 Similar reasoning can be given for other combinations of different numbers of slots, taking into account harmonics of the tooth frequency.

In FIG. Figures 1 and 2 show the engagement fields of two identical pairs of helical gears with ε _β = 1.5, Fig. 3 shows the gear engagement field formed by the rigid connection of two pairs of wheels, Fig. 4 shows a portion of the gear engagement field with a width of dB, Fig. 5 - a pair of helical cylindrical wheels with annular slots.

cos K

Zωt +

(i - 1)

= 0 ,
K = 1, 2, 3..., где n - число кольцевых прорезей,
К - номер гармоники зубцовой частоты, на которой необходимо снизить уровень вибрации,
i - номер участка зубчатого венца, отсчитываемого от торца со стороны входа зубьев в зацепление,
ε_β- коэффициент осевого перекрытия.The transmission contains helical involute wheels 1, 2 with annular slots 3 on each of the gears, the width B _{w of} which is equal to an integer number of axial steps. Slots 3 divide the ring gears of wheels 1, 2 into equal parts 4. The minimum number of slots required for this is selected from the ratio

cos K

Zωt +

(i - 1)

= 0,
K = 1, 2, 3 ..., where n is the number of ring slots,
K is the harmonic number of the tooth frequency at which it is necessary to reduce the level of vibration,
i is the number of the portion of the ring gear, counted from the end from the input side of the teeth into engagement,
ε _β is the axial overlap coefficient.

To reduce the vibration of the transmission, for example, at the 2nd and 3rd harmonics, the dependence in the expanded form gives
at = 1
cos2Z ω t + cos2Z ω t + cos3Z ω t -
- cos3Z ω t = 2cos2Z ω t
at = 2
cos2Z ω t + cos2Z ω t + cos2Z ω t +
+ cos3Z ω t + cos3Z ω t + cos3Z ω t =
= 3 (cos2Z ω t + cos3Z ω t);
at = 3
cos2Z ω t - cos2Z ω t + cos2Z ω t -
- cos2Z ω t + cos3Z ω t - sin3Z ω t -
- cos3Z ω t + sin3Z ω t = 0.

 Consequently, the minimum number of slots, providing compensation for disturbing forces at the 2nd and 3rd harmonics, is three. Slots divide the ring gears into four equal parts.

 With the rotation of the gears, the contact lines 3 begin to move along the field of engagement, and when the wheel is rotated through an angle of 2 π / Z, they again occupy the initial position. Therefore, the process is periodically repeated with a gear frequency.

 With a certain selection, due to the ring slots of the phase relationships between the disturbing forces, mutual compensation of these forces is carried out regardless of the sources of their occurrence, because the field of engagement of the areas identified by the slots are identical in all parameters and differ only in the phase shift between the contact lines.

Claims (1)

Scythe-free cylindrical gears containing gears with ring slots, the width of the gears of which is equal to an integer number of axial steps, characterized in that, in order to reduce the vibration level of the gear at the gear frequency, the gears of the wheels are divided by ring cuts into equal parts, and the minimum number of cuts selected from the ratio

cos K

Z

t

+

- 1)

= 0,
where n is the number of slots;
k is the number of the tooth frequency at which it is necessary to reduce the level of vibration;
i is the number of the part of the ring gear, measured from its end from the input side of the teeth in engagement;
ε _β is the axial overlap coefficient;
Z is the number of teeth of the wheel;
ω is the reverse frequency.

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