CN109764104A - A Design Method of Incomplete Gear Transmission Mechanism with Variable Motion-to-stop Ratio - Google Patents

Abstract

Dynamic stop the design method than variable drive mechanism of non circular gear the invention discloses a kind of, comprising the following steps: S1, according to the modulus of the imagination of the driving wheel full all number of teeth and driven wheel calculates the full all numbers of teeth of imagination of driven wheel；S2, the registration that driving wheel and driven wheel are calculated according to driving wheel head tooth pressure angle and driven wheel tooth top pressure angle start to carry out step S3 if registration is greater than 1；Otherwise, the full all number of teeth values of imagination that S1 readjusts driving wheel are returned；S3, stop according to teeth section of corresponding center of circle angle each on driving wheel and with teeth section of corresponding move than determining center of circle angle value corresponding with described with teeth section adjacent active partial gear Locking arc；S4, with teeth section of number of driving wheel are equal with teeth section of number of driving wheel, and the difference of each with teeth section of number of teeth with teeth section of the number of teeth corresponding on driven wheel is 1 on driving wheel.The incomplete mechanism gear mechanism of the present invention program design is compact and design is easy.

Description

A Design Method of Incomplete Gear Transmission Mechanism with Variable Motion-to-stop Ratio

technical field

The invention relates to the technical field of transmission, in particular to a design method of an incomplete gear transmission mechanism with a variable start-stop ratio.

Background technique

In the process of various types of mechanical transmission, some components are usually required to achieve periodic motion and rest. The mechanism that can convert the continuous motion of the driving element into the regular motion and rest of the driven element is called an intermittent motion mechanism. Common intermittent mechanisms include ratchet mechanisms, sheave mechanisms and incomplete gear mechanisms. Among them, incomplete gear mechanisms are more flexible in design than ratchet and sheave mechanisms, and their motion-to-stop ratio is easier to control. Therefore, incomplete gear mechanisms It is the most commonly used intermittent motion mechanism. However, the power-to-stop ratio of the traditional incomplete gear mechanism is fixed, which limits its application range to a certain extent. In order to overcome this defect, many scholars advocate that the driving wheel or the driven wheel is divided into two parts, and then the two driving wheels or the two driven wheels are coaxially combined, and the relative position of the two driving wheels or the two driven wheels is changed. Makes the mechanism's dynamic-to-stop ratio variable. Although this method realizes the variable motion-to-stop ratio, the design structure is relatively complicated, and the mechanism volume is too large, which is not suitable for applications in small spaces. Based on this, it is of great significance to design an incomplete gear with a simple structure.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to provide a design method of an incomplete gear transmission mechanism with a variable moving-stop ratio with a compact and simple structure.

In order to solve the above technical problems, the technical solution adopted in the present invention is: a design method of an incomplete gear transmission mechanism with variable start-stop ratio, the incomplete gear transmission mechanism includes a driving wheel and a driven wheel, and the design method includes The following steps:

S1. Determination of the structural parameters of the driving wheel and the driven wheel: According to the imaginary full-circle teeth of the driving wheel and the modulus of the driven wheel, calculate the imaginary full-circle teeth of the driven wheel;

S2. Check the coincidence of the driving wheel and the driven wheel: Calculate the coincidence of the driving wheel and the driven wheel according to the pressure angle of the first tooth of the driving wheel and the pressure angle of the tip of the driven wheel. If the coincidence is greater than 1, proceed to step S3; otherwise , return to S1 to re-adjust the imaginary full-circle tooth value of the driving wheel until the coincidence degree is greater than 1, and then proceed to step S3;

S3. Determination of the central angle of the locking arc of the driving incomplete gear: according to the central angle corresponding to each toothed segment on the driving wheel and the moving-to-stop ratio corresponding to the toothed segment, determine the active non-stop adjacent to the toothed segment. The center angle value corresponding to the complete gear locking arc;

S4. The design of the number of teeth of the driven incomplete gear: the number of teeth of the driven wheel is equal to the number of teeth of the driving wheel, and the number of teeth of each segment on the driving wheel is the same as the number of teeth on the driven wheel. The difference in the number of teeth of the segment is 1.

Further, the step S1 specifically includes the following steps: selecting the module m of the driven wheel, the imaginary full-circle tooth number z' ₁ of the driving wheel, and calculating the tooth tip height coefficient h ^* _am of the driving wheel according to formula (1), so that 1- h ^* _am →min, thus obtaining the imaginary number of teeth of the driven wheel z' ₂ :

In the formula, h ^* _a1 is the standard addendum height coefficient, h ^* _a1 =1; the calculation formulas of δ and γ are shown in the following formula (2):

α ₀ is the pressure angle, α ₀ =20°, K is the number of teeth spanned by the locking arc of the driven wheel, which is a design variable parameter, and the K value should be selected to satisfy the condition of 1-h ^* _am →min. The value range of K value in the design process is usually between 1 and 5.

Further, in the step S2, the specific calculation process of the gear coincidence degree is as follows: First, the pressure angles α ₁ and α ₂ of the top tooth of the driving wheel and the tip circle of the driven wheel are calculated by formula (3) and formula (4), Substitute into formula (5) to obtain the coincidence degree ε _α :

In the formula, h ^* _a2 is the standard addendum coefficient of the driven gear, h ^* _a2 =1.

Further, in the step S3, according to the center angle β ₁ corresponding to the first segment with teeth, a first segment of locking arc is set between the first segment with teeth and the second segment with teeth, the The center angle of the first segment of the locking arc is According to _β1 and The satisfied relation (6) can be calculated

In the formula, k ₁ is the first group of power-to-stop ratio.

Further, the step S3 also includes calculating the central angle corresponding to the i-th locking arc according to the central angle corresponding to the i-th tooth segment and the i-th group of motion-to-stop ratios, where i is 2 to the active-stop ratio. Any natural number between the number of stops N per revolution of the wheel.

Further, in the step S4, the number of teeth of each toothed segment on the driven wheel is calculated according to formula (7), and the number of stops per revolution of the driven wheel is the same as that of the driving wheel, which is N times, and the number of teeth of each toothed segment of the driven wheel is as follows: Formula (7) calculates:

z ₂ =z ₁ -1 (7)

Further, the locking arc on the driving wheel and the locking arc on the driven wheel are in concave and convex matching and have the same radius of curvature.

Further, the step S1 also includes determining other structural parameters of the driving wheel and the driven wheel according to the imaginary number of full-circle teeth and the modulus, and the other structural parameters include the index circle radius, the tip circle radius, the root circle radius, the center. distance, driving wheel locking arc radius, engagement angle and engagement angle.

Further, the calculation formulas of the indexing circle radius, tip circle radius, root circle radius, center distance, driving wheel locking arc radius, engagement angle and engagement angle are as follows:

Index circle radius

Addendum radius

Root circle radius

Center distance

Driving wheel locking arc radius

bite angle

gnawed corners

in, _The value of z' is equal to the imaginary full _- circumferential tooth number z'1 of the driving wheel or the imaginary full-circumferential tooth number z'2 of the driven wheel.

The beneficial effects of the present invention are: the design method of the present invention realizes the variable dynamic-to-stop ratio by ingeniously designing the structure of the gear, and overcomes the inability to change the dynamic-to-stop ratio of traditional incomplete gears and the complex structure of multiple driving wheels or multiple driven wheels, which is difficult to achieve. The technical problem is that the solution of the present invention achieves the purpose of compact overall structure and simple design by realizing a plurality of moving-stop ratios on a pair of incomplete gear mechanisms; The intermittent transmission steering device has a simple and compact structure, and is easy to process and assemble. After calculating and setting the number of teeth on the full circumference of the two incomplete gears, the number of teeth in the meshing segment of the two gears and the arc length of the locking arc can be configured to realize the intermittent operation of different dynamic-to-stop ratios. It integrates multiple moving-stop ratios on a pair of incomplete gear mechanisms, and makes the entire mechanism compact and simple in design.

Description of drawings

1 is a schematic diagram of the design parameters of an incomplete gear transmission mechanism designed by an embodiment of the present invention;

FIG. 2 is a schematic diagram of the overall geometric dimensions of the incomplete gear transmission mechanism designed by the embodiment of the present invention.

Detailed ways

In order to describe in detail the technical content, achieved objects and effects of the present invention, the following descriptions are given with reference to the embodiments and the accompanying drawings.

The embodiment of the present invention is: a design method of an incomplete gear transmission mechanism with a variable start-stop ratio, as shown in FIG. 1 , the incomplete gear transmission mechanism includes a driving wheel and a driven wheel, and includes the following steps:

Step 1: Determine the number of teeth z' ₁ , z' ₂ in the full circumference of the two gears

First select the module m of the driving wheel and the driven wheel and the number of teeth z' ₁ in the full circumference of the driving wheel, and then substitute it into the following formula to obtain the driving wheel tooth tip height coefficient h ^* _am , so that 1-h ^* _am →min, so as to obtain The imaginary number of teeth z' ₂ of the driven wheel is obtained.

In the formula, h ^* _a1 is the standard addendum height coefficient, h ^* _a1 =1; α ₀ is the pressure angle, α ₀ =20°.

The calculation formulas of δ and γ are shown in the following formula (2):

,

K is the number of teeth spanned by the locking arc of the driven wheel.

Step 2: Check gear coincidence ε _α

In order to ensure the normal meshing of the two gears, the coincidence degree must be greater than 1. When calculating the coincidence degree, first calculate the pressure angles α ₁ and α ₂ of the top tooth of the driving wheel and the driven wheel by formula (3) and formula (4), and then substitute them into formula (5) to obtain the coincidence degree ε _α :

In the formula, h ^* _a2 is the standard addendum coefficient of the driven gear, h ^* _a2 =1.

Step 3: Determination of the central angle of the active incomplete gear locking arc

According to the actual motion requirements of the mechanism, determine the number of stops N per revolution of the driving wheel, and the number of teeth z _1a in the first segment, the center angle corresponding to it is β _{1 .} for ) constitute a set of motion-stop ratios k ₁ .

Design the dynamic-to-stop ratio according to the needs, and then configure the central angle corresponding to the locking arc on the active incomplete gear according to the determined dynamic-to-stop ratio, so as to determine the structure of the locking arc.

In the same way, set the number of teeth z _1b of the second segment with teeth (the angle between the center of the circle is β ₂ ), and the second segment of the locking arc (the angle between the center of the circle is β 2 ) ) constitutes the second group of motion-to-stop ratio k ₂ , and the calculation method is as in formula (6). If necessary, k ₃ , k ₄ . . . can also be appropriately configured.

Step 4: The driven incomplete gear has the number of teeth in the segment and the structural design of the locking arc on the driven gear:

The number of stops per revolution of the driven wheel is the same as N times of the driving wheel, and the number of teeth of each toothed segment of the driven wheel is calculated according to formula (7):

z ₂ =z ₁ -1 (7)

The locking arc on the driving wheel is a locking convex arc, and the locking arc on the driven wheel is a locking concave arc, and the locking convex arc and the locking concave arc have the same curvature radius.

Step 5: Determine other parameters of the two gears

Index circle radius

Addendum radius

Root circle radius

Center distance

Driving wheel locking arc radius

Engaging angle:

Nip out corners:

Specifically, the number of stops per revolution of the driving wheel and the driven wheel is N=2, the modulus m=1, and the number of full-circumferential teeth of the driving incomplete gear is 41.

First, according to equations (1) and (2), the number of full circumference teeth z' ₂ of the driven gear is obtained so that the addendum coefficient of the driving incomplete gear satisfies 1-h ^* _am →min: when z' ₂ =23, h ^* _am = 0.94, which meets the above requirements.

Then check the coincidence degree ε _α : According to formula (5), when the number of teeth of the driving wheel and the driven wheel are 41 and 23, respectively, ε _α =1.61, and ε _α >1 meets the design requirements.

Configure the drive-to-stop ratio of the drive wheel: According to the motion requirements of the mechanism, set the number of teeth of the first segment of the drive wheel to 9, the corresponding center angle of 77°, and the first drive-to-stop ratio of the drive wheel. Therefore, the center angle of the first segment of the locking arc is 55°. The number of teeth in the second segment of the driving wheel is 10, the corresponding center angle is 86°, and the center angle of the second segment locking arc is 142°, so

According to step 4, the driven incomplete gear is designed: from formula (7), it can be obtained that the number of teeth of the two segments of the driven gear is 8 and 9 respectively, the center angle of the two locking arcs is the same, and their radius of curvature is the same as that of the driving gear. The locking radius is the same.

Determine the geometric dimensions of the two incomplete gears according to step 5, as shown in Figure 2: the radii of the index circles of the two wheels are 20.5mm and 11.5mm respectively, the radii of the tip circles are 21.5mm and 12.5mm respectively, and the radii of the root circles are respectively 20.5mm and 11.5mm. It is 19.25mm and 10.25mm, the center distance is 32mm, the driving wheel locking arc radius is 19.88mm, the engagement angle is 0.190rad, and the engagement angle is 0.238rad.

The solution of the present invention can be used to solve the limitation of a single dynamic-to-stop ratio of a traditional incomplete gear mechanism. First, according to the design method of an incomplete gear, the number of full-circle teeth, the index circle diameter, the center distance, the locking arc radius, After the parameters such as the engagement angle and the engagement angle, the number of stops per revolution of the two incomplete gears, the number of teeth of the tooth segment, the angle between the center of the locking arc and other parameters are configured according to the actual dynamic-to-stop ratio requirements. This method can realize multiple The moving-stop ratio is integrated on a pair of incomplete gear mechanisms, and the overall structure of the mechanism is compact and the design is simple.

In the present invention, "the driven wheel has corresponding toothed segments" means that the driving wheel and the driven wheel are numbered in sequence, and the tooth value of the toothed segment on the driving wheel and the driven wheel in the same order differs by 1. The "first, second..." referred to in the present invention is not limited to the sequence, but is only a difference.

The above descriptions are only examples of the present invention, and are not intended to limit the scope of the present invention. Any equivalent transformations made by using the contents of the description and drawings of the present invention, or directly or indirectly applied in related technical fields, are similarly included in the within the scope of patent protection of the present invention.

Claims (8)

1. A design method of an incomplete gear transmission mechanism with a variable dynamic-stop ratio is characterized in that: the incomplete gear transmission mechanism comprises a driving wheel and a driven wheel, and the design method comprises the following steps:

s1, determining structural parameters of the driving wheel and the driven wheel: calculating the assumed full-circumference tooth number of the driven wheel according to the assumed full-circumference tooth number of the driving wheel and the modulus of the driven wheel;

s2, checking the contact ratio of the driving wheel and the driven wheel: calculating the contact ratio of the driving wheel and the driven wheel according to the head tooth pressure angle of the driving wheel and the tooth crest pressure angle of the driven wheel, and if the contact ratio is greater than 1, starting to perform step S3; otherwise, returning to S1 to readjust the virtual full-circle tooth number of the driving wheel until the contact ratio is greater than 1, and then proceeding to step S3;

s3, determining the locking arc central angle of the driving incomplete gear: determining a circle center included angle value corresponding to a locking arc of the driving incomplete gear adjacent to each toothed section according to a circle center included angle corresponding to each toothed section on the driving wheel and a dynamic-stop ratio corresponding to the toothed section;

s4, designing the tooth number of the driven incomplete gear with the tooth section: the number of the toothed sections of the driven wheel is equal to that of the toothed sections of the driving wheel, and the difference value between the number of teeth of each toothed section on the driving wheel and the number of teeth of the corresponding toothed section on the driven wheel is 1.

2. The method of designing a variable stop-ratio incomplete gear transmission as set forth in claim 1, wherein: the step S1 specifically includes the following steps: selecting the modulus m of the driven wheel and the supposed full-circle tooth number z 'of the driving wheel'₁Calculating the addendum height coefficient h of the driving wheel according to the formula (1)^* _amLet 1-h^* _am→ min, to derive the driven wheel virtual tooth number z'₂：

In the formula, h^* _a1Is a standard tooth crest height factor, h^* _a11 is ═ 1; the calculation formula of δ and γ is shown in the following formula (2):

α₀angle of pressure, α₀20 degrees, K is the number of teeth spanned by the locking arc of the driven wheel, the value is a design variable parameter, and the value of K is selected to satisfy 1-h^* _amCondition No. → min.

3. The dynamic stop of claim 2The design method of the incomplete gear transmission mechanism with variable ratio is characterized in that in the step S2, the specific calculation process of the gear contact ratio is as follows, firstly, the pressure angle α of the head tooth of the driving wheel and the addendum circle of the driven wheel is calculated through the formula (3) and the formula (4)₁And α₂Then substituted into the formula (5) to obtain the contact ratio epsilon_α：

In the formula, h^* _a2Is the standard tooth crest coefficient of the driven gear, h^* _a2＝1。

4. The method for designing an incomplete gear transmission mechanism with variable dynamic-stop ratio as claimed in claim 1, wherein in step S3, the included angle β is determined according to the circle center corresponding to the first toothed segment₁The first section is provided with a first section locking arc between the toothed section and the toothed section of the second section, and the included angle of the circle center of the first section locking arc isAccording to β₁Andthe satisfied relation (6) can be calculated

In the formula, k₁Is a first set of stop-and-go ratios.

5. The method of designing a variable stop-ratio incomplete gear transmission according to claim 4, characterized in that: step S3 further includes calculating a central angle corresponding to the locking arc of the ith segment according to the central angle corresponding to the toothed segment of the ith segment and the ith group of stop ratios, where i is any natural number from 2 to N times of stop per rotation of the driving wheel.

6. The design method of the incomplete gear transmission mechanism with variable dynamic stop ratio according to any one of claims 1 to 5, characterized in that: and the locking arc on the driving wheel is matched with the locking arc on the driven wheel in a concave-convex mode, and the curvature radius of the locking arc is equal to that of the locking arc on the driven wheel.

7. The design method of the incomplete gear transmission mechanism with variable dynamic stop ratio according to any one of claims 1 to 5, characterized in that: step S1 further includes determining other structural parameters of the driving wheel and the driven wheel according to the assumed full-circumference tooth number and the module, where the other structural parameters include a reference circle radius, a tooth top circle radius, a tooth root circle radius, a center distance, a driving wheel locking arc radius, a meshing angle, and a meshing angle.

8. The method of designing a variable stop-ratio incomplete gear transmission as set forth in claim 7, wherein: the calculation formulas of the reference circle radius, the addendum circle radius, the dedendum circle radius, the center distance, the driving wheel locking arc radius, the engagement angle and the engagement angle are as follows in sequence:

radius of reference circle

Radius of addendum circle

Root circle radius

Center distance

Radius of locking arc of driving wheel

Angle of engagement

Angle of engagement

Wherein,z ' and an imaginary full-circumference tooth number z ' of the drive wheel '₁Or imaginary full-cycle tooth number z 'of driven wheel'₂And the number of teeth spanned by the locking arc of the driven wheel is K, and the K is any natural number between 1 and 5.