WO2020238075A1 - Double-arc gapped meshing small-tooth-difference planetary transmission device - Google Patents

Double-arc gapped meshing small-tooth-difference planetary transmission device Download PDF

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WO2020238075A1
WO2020238075A1 PCT/CN2019/119448 CN2019119448W WO2020238075A1 WO 2020238075 A1 WO2020238075 A1 WO 2020238075A1 CN 2019119448 W CN2019119448 W CN 2019119448W WO 2020238075 A1 WO2020238075 A1 WO 2020238075A1
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Prior art keywords
gear
tooth
arc
meshing
tooth profile
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PCT/CN2019/119448
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French (fr)
Chinese (zh)
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李伟达
李轩
杨杰
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苏州博安捷机器人科技有限公司
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Publication of WO2020238075A1 publication Critical patent/WO2020238075A1/en

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    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16HGEARING
    • F16H1/00Toothed gearings for conveying rotary motion
    • F16H1/28Toothed gearings for conveying rotary motion with gears having orbital motion
    • F16H1/32Toothed gearings for conveying rotary motion with gears having orbital motion in which the central axis of the gearing lies inside the periphery of an orbital gear
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16HGEARING
    • F16H55/00Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
    • F16H55/02Toothed members; Worms
    • F16H55/08Profiling
    • F16H55/0826Novikov-Wildhaber profile
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16HGEARING
    • F16H55/00Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
    • F16H55/02Toothed members; Worms
    • F16H55/08Profiling
    • F16H55/088Profiling with corrections on tip or foot of the teeth, e.g. addendum relief for better approach contact
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16HGEARING
    • F16H57/00General details of gearing
    • F16H57/04Features relating to lubrication or cooling or heating
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16HGEARING
    • F16H1/00Toothed gearings for conveying rotary motion
    • F16H1/28Toothed gearings for conveying rotary motion with gears having orbital motion
    • F16H1/32Toothed gearings for conveying rotary motion with gears having orbital motion in which the central axis of the gearing lies inside the periphery of an orbital gear
    • F16H2001/323Toothed gearings for conveying rotary motion with gears having orbital motion in which the central axis of the gearing lies inside the periphery of an orbital gear comprising eccentric crankshafts driving or driven by a gearing

Definitions

  • the invention relates to the technical field of gear transmissions, in particular to a planetary transmission device with double circular arcs with clearance meshing and less tooth difference
  • the existing implementation schemes include cycloidal pin wheel few tooth difference planetary transmission, involute few tooth difference planetary transmission and so on.
  • the tooth profiles of the conjugate gears of the existing planetary transmission with small tooth difference are complex curves such as involutes and involutes, cycloids and arcs, resulting in relatively complicated manufacturing and difficult to ensure accuracy, especially the processing of cycloids. Generally, it needs to be carried out on special machine tools. The processing cost is high, and it is difficult to match the design curve with the processed curve. This high-precision modification method was once controlled by foreign companies.
  • the technical problem to be solved by the present invention is to provide a planetary transmission device with double-arc gap meshing and small tooth difference, which solves the problems of high-precision machining of complex curves and tooth profile modification, and maintains a good precision operation effect.
  • the present invention provides a double-arc gap meshing planetary transmission device with small tooth difference, comprising a box body and an eccentric shaft arranged in the box body, a first eccentric part and a second eccentric shaft of the eccentric shaft
  • Two external gears are respectively provided on the parts
  • internal gears are provided on the inner wall of the box corresponding to the external gears
  • the internal gears mesh with the external gears.
  • a plurality of driving pins are also provided between the two external gears. Both ends of the driving pin are connected with the two end plates to form a planet carrier structure and output power.
  • the tooth profile of the internal gear and the external gear are both arcs, and there is an initial meshing gap between the internal gear and the external gear.
  • both the internal gear and the external gear have gear teeth with arc-shaped tooth profiles.
  • the tooth profile of the internal gear is obtained by an inner roller needle arranged on the tooth portion, the inner roller is provided with a containing groove on the corresponding tooth portion, and the outer gear has an arc-shaped tooth profile. Gear teeth.
  • the tooth profile of the external gear is obtained by an outer roller needle arranged on the tooth portion, the outer roller is provided with a containing groove on the corresponding tooth portion, and the inner gear has a circular arc tooth profile.
  • Gear teeth are obtained by an outer roller needle arranged on the tooth portion, the outer roller is provided with a containing groove on the corresponding tooth portion, and the inner gear has a circular arc tooth profile. Gear teeth.
  • the tooth profile of the internal gear is obtained by an inner roller needle arranged on the tooth part, the inner roller is provided with a containing groove on the corresponding tooth part, and the tooth profile of the external gear is set by The outer roller needle on the tooth is obtained, and the outer roller is provided with a containing groove on the corresponding tooth.
  • box body is also provided with a needle roller limit retaining ring.
  • a method for forming a double-arc gap meshing gear pair includes the following steps:
  • Step 1) Determine the number of teeth of the external gear z 1 , the number of teeth of the internal gear z 2 and the arc radius of the external gear tooth profile r o according to the structural size and transmission ratio of the transmission device, and preliminarily determine the eccentricity e and the index circle radius of the external gear R o Range and initial value;
  • is the arc angle variable
  • Step 2 According to the relative motion law of the internal gear and the external gear, use the arc of the external gear tooth profile to envelop the conjugate tooth profile curve of the internal gear to determine the internal gear conjugate tooth profile equation f(x 2 ,y 2 ) And the meshing equation ⁇ , the conjugate tooth profile equation is obtained as follows:
  • Step 3 Calculate the meshing limit function ⁇ t of the internal gear tooth profile and solve the meshing limit value ⁇ t simultaneously with the meshing equation.
  • the equations can be as follows:
  • Step 4) Fit the function in the range of [- ⁇ t , ⁇ t ] Solve to obtain the single-tooth arc profile radius r i and the center coordinates (x c , y c ) of the internal gear;
  • (x 2j ,y 2j ) is the coordinate value of the conjugate tooth profile of the internal gear, and n is the number of data points;
  • Step 6) Determine the size of the fitting gap and the initial meshing gap limit value c 0. If 0 ⁇ c i ⁇ c 0 , then the set of design parameters meets the design requirements, determine the design parameters R i and r i , and end the design process, and vice versa , You need to change the optimized parameters eccentricity e, external gear indexing circle radius Ro , and recalculate until the design requirements are met.
  • the double-arc tooth profile meshing can avoid the processing of complex curves, and the arc processing is less difficult; the processing technology is simple and the precision is high, and it has better processing economic precision.
  • the backlash meshing gear pair is equivalently obtained by the conjugate meshing tooth profile, and the meshing running state is good; at the same time, the number of meshing teeth is large, the meshing range is large, and the bearing capacity is high; the error equalization effect is obvious, which can reduce the transmission error and improve the transmission accuracy .
  • This method first calculates the arc tooth profile of the external gear, and derives the meshing conjugate tooth profile, arc tooth profile, tooth profile radius, and circle parameters of the internal gear according to the arc tooth profile of the external gear.
  • the transmission device does not need to be modified later, and the gap can be ensured and effectively controlled during design.
  • the transmission device adopts a simple support structure to withstand large external axial force and radial force, and can achieve coaxial dual output; it adopts oil seal for complete sealing, ensuring good lubrication conditions.
  • Figure 1 is a schematic diagram of the overall structure of the present invention.
  • Figure 2 is an exploded schematic diagram of part of the structure of the present invention
  • Figure 3 is a schematic diagram of the gear pair meshing of the present invention.
  • Figure 4 is a schematic diagram of the head gap in Figure 3 of the present invention.
  • Figure 5 is a schematic diagram of the bottom gap in Figure 3 of the present invention.
  • Figure 6 is a schematic diagram of the side gap in Figure 3 of the present invention.
  • Fig. 7 is a schematic diagram of equivalent conjugate meshing of the gear pair in Fig. 3 of the present invention.
  • Figure 8 is a schematic diagram of the integral gear tooth structure of the present invention.
  • Figure 9 is a schematic diagram of the head gap in Figure 8 of the present invention.
  • Figure 10 is a schematic diagram of the bottom gap in Figure 8 of the present invention.
  • Figure 11 is a schematic diagram of the side gap in Figure 8 of the present invention.
  • Figure 12 is a schematic structural view of the present invention with an inner needle roller
  • Figure 13 is a schematic diagram of the head gap in Figure 12 of the present invention.
  • Figure 14 is a schematic diagram of the bottom gap in Figure 12 of the present invention.
  • Figure 15 is a schematic diagram of the side gap in Figure 12 of the present invention.
  • Figure 16 is a schematic view of the structure of the present invention with external needle rollers
  • Figure 17 is a schematic diagram of the head gap in Figure 16 of the present invention.
  • Figure 18 is a schematic diagram of the bottom gap in Figure 16 of the present invention.
  • Figure 19 is a schematic diagram of the side gap in Figure 16 of the present invention.
  • Fig. 20 is a flow chart of the formation of the double-arc gapped meshing gear pair of the present invention.
  • an embodiment of the double-arc gap meshing planetary transmission device with small tooth difference of the present invention includes a box body, an eccentric shaft 1 arranged in the box body, and a first eccentric portion 2 of the eccentric shaft
  • Two external gears 4 are respectively provided on the second eccentric part 3 and an internal gear 6 is provided on the inner wall of the box corresponding to the external gear.
  • the internal gear meshes with the external gear, and a plurality of drives are also provided between the two external gears.
  • Pin 7, the two ends of a plurality of driving pins are connected with two end disks 9 to form a planet carrier structure and output power; the end disks are fixed by an oil seal 10 and a bearing 11 to ensure output stability.
  • the matching relationship is shown in Fig. 1.
  • the number of end discs can be two, which are respectively arranged on both ends of the eccentric shaft in the axial direction to form a bidirectional output effect.
  • the eccentric shaft drives the outer gear to eccentrically rotate, and the outer gear meshes with the inner gear, and forms the effect of rotating output with less tooth difference.
  • the tooth profile of the internal gear teeth and the tooth profile of the external gear teeth are all circular arcs.
  • the circular arc design is adopted, that is, there is no problem of complex curve modification.
  • the circular arc is easy to prepare, and the preparation accuracy is high. After forming, the arc does not need to be modified by the arc curve, so the preparation difficulty is greatly reduced.
  • the initial meshing gap can be generated after the arc structure is assembled, and the gap is stable and controllable; and the double arc design After meshing, the number of meshing teeth can be increased. With reference to the conjugate meshing effect shown in FIG.
  • the meshing range is large, the load-bearing capacity is greatly improved, and the transmission error can be reduced and the transmission accuracy can be improved.
  • the tooth grooves between adjacent gear teeth do not participate in meshing (that is, the tooth grooves between adjacent tooth profiles).
  • the tooth profile of the internal gear mentioned above is obtained by the inner needle 41 arranged on the tooth
  • the tooth profile of the external gear is obtained by the outer needle 61 arranged on the tooth.
  • the outer surface of the needle is It is a circular arc structure.
  • a needle roller limit retaining ring 12 is also provided in the box. The needle roller limit retaining ring restricts the matching position of the inner needle and the outer needle to prevent the movement of the needle.
  • the needle roller preparation technology is mature and the cost is low; the inner gear and the two outer gears are slotted to accommodate the above inner and outer needles, which is also very convenient, that is, the outer needle Containment grooves are provided on the corresponding teeth and can be formed by conventional processing methods, with high processing accuracy and low difficulty.
  • both the inner needle roller and the outer needle roller can perform self-rotating motion. Therefore, while the outer gear drives the outer needle roller to rotate, the outer needle roller can also mesh with the inner needle roller to generate self-rotating motion, thereby reducing the time of meshing rotation.
  • the friction of the teeth reduces the meshing loss and improves the output capacity.
  • both the internal gear and the external gear have teeth with arc-shaped tooth profiles, between the internal gear and its corresponding gear teeth, and between the external gear and its corresponding gear teeth They are all integrally formed structures with stable structure, low preparation cost and low preparation difficulty.
  • the tooth profile of the internal gear is obtained by the inner roller needle arranged on the tooth portion.
  • the outer surface of the needle roller is the arc structure, and the inner roller corresponds to the tooth A containing groove is provided on the part to install and accommodate the inner needle roller.
  • the outer gear has gear teeth with an arc-shaped tooth profile.
  • the outer gear and the gear teeth are integrally formed. The preparation cost is low, the preparation difficulty is small, and the inner needle roller effectively reduces the meshing Rotation loss.
  • the tooth profile of the external gear is obtained by the outer roller needle arranged on the tooth part.
  • the outer surface of the needle roller is the arc structure, and the outer roller corresponds to the tooth A containment groove is provided on the part for mounting and accommodating the outer needle roller.
  • the inner gear has gear teeth with an arc-shaped tooth profile.
  • the inner gear and the gear teeth are integrally formed. The preparation cost is low, the preparation difficulty is small, and the outer needle roller effectively reduces the meshing Rotation loss.
  • the present application also provides a method for forming a double-arc gap meshing gear pair, which includes the following steps:
  • Step 1) Determine the number of teeth of the external gear z 1 , the number of teeth of the internal gear z 2 and the arc radius of the external gear tooth profile r o according to the structural size and transmission ratio of the transmission device, and preliminarily determine the eccentricity e and the index circle radius of the external gear R o Range and initial value;
  • is the arc angle variable
  • Step 2 According to the relative motion law of the internal gear and the external gear, use the arc of the external gear tooth profile to envelop the conjugate tooth profile curve of the internal gear to determine the internal gear conjugate tooth profile equation f(x 2 ,y 2 ) And the meshing equation ⁇ , the conjugate tooth profile equation is obtained as follows:
  • Step 3 Calculate the meshing limit function ⁇ t of the tooth profile of the internal gear and solve the meshing limit value ⁇ t together with the meshing equation.
  • the equations can be as follows:
  • Step 4) Fit the function in the range of [- ⁇ t , ⁇ t ] Solve to obtain the single-tooth arc tooth profile radius r i and the center coordinates (x c , y c ) of the internal gear;
  • (x 2j ,y 2j ) is the coordinate value of the conjugate tooth profile of the internal gear, and n is the number of data points;
  • Step 6) Determine the size of the fitting gap and the initial meshing gap limit value c 0. If 0 ⁇ c i ⁇ c 0 , then the set of design parameters meets the design requirements, determine the design parameters R i and r i , and end the design process, and vice versa , You need to change the optimized parameters eccentricity e, external gear indexing circle radius Ro , and recalculate until the design requirements are met.
  • the modification provides a meshing gap to form a lubricating oil film and improve the lubrication conditions. After the modification, the number of meshing teeth will be reduced; the arc-shaped internal gear and external gear formed by the above method can Used directly, the gap value can exist, and because it is not a complex curve during processing, the processing accuracy is high, and it can be used directly within the designed gap value without modification.
  • the new double needle roller meshing gear with clearance is designed to replace the complex
  • the curved gear pair fundamentally solves the problems of high-precision machining of mixed curves and tooth profile modification. Reduce the manufacturing difficulty and processing cost, and at the same time ensure that in the presence of the meshing gap, the number of meshing teeth is large, the overlap is large, and the high load-bearing capacity is maintained.

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  • General Engineering & Computer Science (AREA)
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Abstract

Provided is a double-arc gapped meshing small-tooth-difference planetary transmission device, comprising: a box body and an eccentric shaft (1) arranged in the box body, wherein a first eccentric part (2) and a second eccentric part (3) of the eccentric shaft are respectively provided with two outer gears (4); and an inner gear (6) is arranged on the inner wall of the box body corresponding to the outer gear, the inner gear being meshed with the outer gears in a matched mode, a plurality of driving pins (7) being further arranged between the two outer gears, two ends of each driving pin being connected and matched with two end discs (9) to form a planetary carrier structure and output power, the tooth profile of the inner gear and the tooth profile of each outer gear being both arcs, and an initial meshing gap existing between the inner gear and each outer gear. Thus, the problems of complex curve high-precision machining and tooth profile modification are solved, and a good precision operation effect is maintained.

Description

一种双圆弧有隙啮合少齿差行星传动装置Planetary transmission device with double circular arcs with clearance meshing and small tooth difference 技术领域Technical field
本发明涉及齿轮传动技术领域,具体涉及一种双圆弧有隙啮合少齿差行星传动装置The invention relates to the technical field of gear transmissions, in particular to a planetary transmission device with double circular arcs with clearance meshing and less tooth difference
背景技术Background technique
少齿差行星传动由于具有传动比大、结构紧凑、承载能力大和传动效率高等优点,已经在冶金、矿山和化工等动力传动领域得到广泛应用。该传动由于啮合齿数多,误差均化效应明显,近年来在机器人、航空航天和数控机床等精密传动领域也越来越受到广泛关注。Due to the advantages of large transmission ratio, compact structure, large carrying capacity and high transmission efficiency, planetary transmission with small tooth difference has been widely used in power transmission fields such as metallurgy, mining and chemical industry. Due to the large number of meshing teeth, this transmission has obvious error averaging effect. In recent years, it has received more and more attention in precision transmission fields such as robots, aerospace and CNC machine tools.
现有的实现方案有摆线针轮少齿差行星传动、渐开线少齿差行星传动等。The existing implementation schemes include cycloidal pin wheel few tooth difference planetary transmission, involute few tooth difference planetary transmission and so on.
现有少齿差行星传动其共轭齿轮的齿廓分别为渐开线与渐开线、摆线与圆弧等复杂曲线,导致加工制造相对复杂且精度不易保证,特别是摆线轮的加工一般需要在专用的机床设备上进行,加工成本高,并且设计曲线与加工后的曲线很难匹配一致,这种高精度的修形方式一度被国外企业掌控。The tooth profiles of the conjugate gears of the existing planetary transmission with small tooth difference are complex curves such as involutes and involutes, cycloids and arcs, resulting in relatively complicated manufacturing and difficult to ensure accuracy, especially the processing of cycloids. Generally, it needs to be carried out on special machine tools. The processing cost is high, and it is difficult to match the design curve with the processed curve. This high-precision modification method was once controlled by foreign companies.
发明内容Summary of the invention
本发明要解决的技术问题是提供一种双圆弧有隙啮合少齿差行星传动装置,解决了复杂曲线高精度加工以及齿廓修形问题,并保持良好的精密运行效果。The technical problem to be solved by the present invention is to provide a planetary transmission device with double-arc gap meshing and small tooth difference, which solves the problems of high-precision machining of complex curves and tooth profile modification, and maintains a good precision operation effect.
为了解决上述技术问题,本发明提供了一种双圆弧有隙啮合少齿差行星传动装置,包括箱体以及设置在箱体内的偏心轴,所述偏心轴的第一偏心部和第 二偏心部上分别设置有两个外齿轮,所述外齿轮对应的箱体内壁上设置有内齿轮,所述内齿轮与外齿轮配合啮合,两个外齿轮之间还设置有多个驱动销,多个驱动销两端与两个端盘连接配合形成行星架结构并输出动力,所述内齿轮的齿廓、外齿轮的齿廓均为圆弧,所述内齿轮与外齿轮存在初始啮合间隙。In order to solve the above technical problems, the present invention provides a double-arc gap meshing planetary transmission device with small tooth difference, comprising a box body and an eccentric shaft arranged in the box body, a first eccentric part and a second eccentric shaft of the eccentric shaft Two external gears are respectively provided on the parts, internal gears are provided on the inner wall of the box corresponding to the external gears, and the internal gears mesh with the external gears. A plurality of driving pins are also provided between the two external gears. Both ends of the driving pin are connected with the two end plates to form a planet carrier structure and output power. The tooth profile of the internal gear and the external gear are both arcs, and there is an initial meshing gap between the internal gear and the external gear.
进一步的,所述内齿轮与外齿轮均具有圆弧状齿廓的轮齿。Further, both the internal gear and the external gear have gear teeth with arc-shaped tooth profiles.
进一步的,所述内齿轮的轮齿齿廓由设置在齿部上的内滚针获得,所述内滚针对应的齿部上设置有包容槽,所述外齿轮具有圆弧状齿廓的轮齿。Further, the tooth profile of the internal gear is obtained by an inner roller needle arranged on the tooth portion, the inner roller is provided with a containing groove on the corresponding tooth portion, and the outer gear has an arc-shaped tooth profile. Gear teeth.
进一步的,所述外齿轮的轮齿齿廓由设置在齿部上的外滚针获得,所述外滚针对应的齿部上设置有包容槽,所述内齿轮具有圆弧状齿廓的轮齿。Further, the tooth profile of the external gear is obtained by an outer roller needle arranged on the tooth portion, the outer roller is provided with a containing groove on the corresponding tooth portion, and the inner gear has a circular arc tooth profile. Gear teeth.
进一步的,所述内齿轮的轮齿齿廓由设置在齿部上的内滚针获得,所述内滚针对应的齿部上设置有包容槽,所述外齿轮的轮齿齿廓由设置在齿部上的外滚针获得,所述外滚针对应的齿部上设置有包容槽。Further, the tooth profile of the internal gear is obtained by an inner roller needle arranged on the tooth part, the inner roller is provided with a containing groove on the corresponding tooth part, and the tooth profile of the external gear is set by The outer roller needle on the tooth is obtained, and the outer roller is provided with a containing groove on the corresponding tooth.
进一步的,所述箱体内还设置有滚针限位挡圈。Further, the box body is also provided with a needle roller limit retaining ring.
一种双圆弧有隙啮合齿轮副形成方法,包括以下步骤:A method for forming a double-arc gap meshing gear pair includes the following steps:
步骤1)根据传动装置结构尺寸、传动比,确定外齿轮齿数z 1、内齿轮齿数z 2以及外齿轮齿廓的圆弧半径r o,初步确定偏心距e、外齿轮分度圆半径R o范围及初始值; Step 1) Determine the number of teeth of the external gear z 1 , the number of teeth of the internal gear z 2 and the arc radius of the external gear tooth profile r o according to the structural size and transmission ratio of the transmission device, and preliminarily determine the eccentricity e and the index circle radius of the external gear R o Range and initial value;
外齿轮圆弧齿廓方程为:The arc tooth profile equation of the external gear is:
Figure PCTCN2019119448-appb-000001
Figure PCTCN2019119448-appb-000001
其中,θ为圆弧角变量;Among them, θ is the arc angle variable;
步骤2)根据内齿轮和外齿轮相对运动规律,应用外齿轮齿廓的圆弧包络出与其共轭的内齿轮齿廓曲线,确定内齿轮共轭齿廓方程f(x 2,y 2)及啮合方程Φ,得到共轭齿廓组方程如下: Step 2) According to the relative motion law of the internal gear and the external gear, use the arc of the external gear tooth profile to envelop the conjugate tooth profile curve of the internal gear to determine the internal gear conjugate tooth profile equation f(x 2 ,y 2 ) And the meshing equation Φ, the conjugate tooth profile equation is obtained as follows:
Figure PCTCN2019119448-appb-000002
Figure PCTCN2019119448-appb-000002
其中,
Figure PCTCN2019119448-appb-000003
分别为内外齿轮转角,λ=ez 1/R o
among them,
Figure PCTCN2019119448-appb-000003
They are the rotation angles of internal and external gears, λ = ez 1 /R o ;
步骤3)计算内齿轮齿廓啮合界限函数Φ t并与啮合方程联立求解啮合界限值θ t,可方程组如下: Step 3) Calculate the meshing limit function Φ t of the internal gear tooth profile and solve the meshing limit value θ t simultaneously with the meshing equation. The equations can be as follows:
Figure PCTCN2019119448-appb-000004
Figure PCTCN2019119448-appb-000004
求解可得,啮合界限值
Figure PCTCN2019119448-appb-000005
The solution is available, the meshing limit value
Figure PCTCN2019119448-appb-000005
步骤4)在[-θ tt]范围内对拟合函数
Figure PCTCN2019119448-appb-000006
求解,得到内齿轮单齿圆弧齿廓半径r i及圆心坐标(x c,y c);
Step 4) Fit the function in the range of [-θ tt ]
Figure PCTCN2019119448-appb-000006
Solve to obtain the single-tooth arc profile radius r i and the center coordinates (x c , y c ) of the internal gear;
其中,(x 2j,y 2j)为内齿轮共轭齿廓坐标值,n为数据点个数; Among them, (x 2j ,y 2j ) is the coordinate value of the conjugate tooth profile of the internal gear, and n is the number of data points;
步骤5)计算拟合间隙
Figure PCTCN2019119448-appb-000007
Step 5) Calculate the fitting gap
Figure PCTCN2019119448-appb-000007
步骤6)判断拟合间隙与初始啮合间隙限定值c 0的大小,如0<c i≤c 0,则该组设计参数满足设计要求,确定设计参数R i、r i,结束设计过程,反之,则需要改变优化参数偏心距e、外齿轮分度圆半径R o,重新计算直到满足设计要求 为止。 Step 6) Determine the size of the fitting gap and the initial meshing gap limit value c 0. If 0 <c i ≤ c 0 , then the set of design parameters meets the design requirements, determine the design parameters R i and r i , and end the design process, and vice versa , You need to change the optimized parameters eccentricity e, external gear indexing circle radius Ro , and recalculate until the design requirements are met.
本发明的有益效果:The beneficial effects of the present invention:
1、采用双圆弧齿廓啮合,能够避免复杂曲线的加工,圆弧加工难度低;加工工艺简单且精度高,具有较好的加工经济精度。1. The double-arc tooth profile meshing can avoid the processing of complex curves, and the arc processing is less difficult; the processing technology is simple and the precision is high, and it has better processing economic precision.
2、其有隙啮合齿轮副由共轭啮合齿廓等效获得,啮合运行状态良好;同时啮合齿数多且啮合范围大,承载能力高;误差均化效应明显,能够降低传动误差,提高传动精度。2. The backlash meshing gear pair is equivalently obtained by the conjugate meshing tooth profile, and the meshing running state is good; at the same time, the number of meshing teeth is large, the meshing range is large, and the bearing capacity is high; the error equalization effect is obvious, which can reduce the transmission error and improve the transmission accuracy .
3、本方法采用先计算外齿轮圆弧齿廓,根据外齿轮圆弧齿廓推导得出内齿轮的啮合共轭齿廓、圆弧齿廓、齿廓半径及圆形等参数,使得制备后的传动装置无需后期修形,在设计时即可保证间隙的存在并有效控制。3. This method first calculates the arc tooth profile of the external gear, and derives the meshing conjugate tooth profile, arc tooth profile, tooth profile radius, and circle parameters of the internal gear according to the arc tooth profile of the external gear. The transmission device does not need to be modified later, and the gap can be ensured and effectively controlled during design.
4、本传动装置采用简支支撑结构可以承受较大外加轴向力与径向力,可实现同轴双输出;采用油封进行完全密封,保证了良好的润滑条件。4. The transmission device adopts a simple support structure to withstand large external axial force and radial force, and can achieve coaxial dual output; it adopts oil seal for complete sealing, ensuring good lubrication conditions.
附图说明Description of the drawings
图1是本发明的整体结构示意图;Figure 1 is a schematic diagram of the overall structure of the present invention;
图2是本发明部分结构爆炸示意图;Figure 2 is an exploded schematic diagram of part of the structure of the present invention;
图3是本发明齿轮副啮合示意图;Figure 3 is a schematic diagram of the gear pair meshing of the present invention;
图4是本发明图3中顶隙示意图;Figure 4 is a schematic diagram of the head gap in Figure 3 of the present invention;
图5是本发明图3中底隙示意图;Figure 5 is a schematic diagram of the bottom gap in Figure 3 of the present invention;
图6是本发明图3中侧隙示意图;Figure 6 is a schematic diagram of the side gap in Figure 3 of the present invention;
图7是本发明图3中齿轮副的等效共轭啮合示意图;Fig. 7 is a schematic diagram of equivalent conjugate meshing of the gear pair in Fig. 3 of the present invention;
图8是本发明一体轮齿结构示意图;Figure 8 is a schematic diagram of the integral gear tooth structure of the present invention;
图9是本发明图8中顶隙示意图;Figure 9 is a schematic diagram of the head gap in Figure 8 of the present invention;
图10是本发明图8中底隙示意图;Figure 10 is a schematic diagram of the bottom gap in Figure 8 of the present invention;
图11是本发明图8中侧隙示意图;Figure 11 is a schematic diagram of the side gap in Figure 8 of the present invention;
图12是本发明具有内滚针的结构示意图;Figure 12 is a schematic structural view of the present invention with an inner needle roller;
图13是本发明图12中顶隙示意图;Figure 13 is a schematic diagram of the head gap in Figure 12 of the present invention;
图14是本发明图12中底隙示意图;Figure 14 is a schematic diagram of the bottom gap in Figure 12 of the present invention;
图15是本发明图12中侧隙示意图;Figure 15 is a schematic diagram of the side gap in Figure 12 of the present invention;
图16是本发明具有外滚针的结构示意图;Figure 16 is a schematic view of the structure of the present invention with external needle rollers;
图17是本发明图16中顶隙示意图;Figure 17 is a schematic diagram of the head gap in Figure 16 of the present invention;
图18是本发明图16中底隙示意图;Figure 18 is a schematic diagram of the bottom gap in Figure 16 of the present invention;
图19是本发明图16中侧隙示意图;Figure 19 is a schematic diagram of the side gap in Figure 16 of the present invention;
图20是本发明双圆弧有隙啮合齿轮副形成流程图。Fig. 20 is a flow chart of the formation of the double-arc gapped meshing gear pair of the present invention.
具体实施方式Detailed ways
下面结合附图和具体实施例对本发明作进一步说明,以使本领域的技术人员可以更好地理解本发明并能予以实施,但所举实施例不作为对本发明的限定。The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention, but the cited embodiments are not intended to limit the present invention.
参照图1至图3所示,本发明的双圆弧有隙啮合少齿差行星传动装置的一实施例,包括箱体以及设置在箱体内的偏心轴1,偏心轴的第一偏心部2和第二偏心部3上分别设置有两个外齿轮4,外齿轮对应的箱体内壁上设置有内齿轮6,内齿轮与外齿轮配合啮合,两个外齿轮之间还设置有多个驱动销7,多个驱动销两端与两个端盘9连接配合形成行星架结构并输出动力;端盘通过油封10和轴承11固定,保证输出稳定性,匹配关系参见图1所示。Referring to Figures 1 to 3, an embodiment of the double-arc gap meshing planetary transmission device with small tooth difference of the present invention includes a box body, an eccentric shaft 1 arranged in the box body, and a first eccentric portion 2 of the eccentric shaft Two external gears 4 are respectively provided on the second eccentric part 3 and an internal gear 6 is provided on the inner wall of the box corresponding to the external gear. The internal gear meshes with the external gear, and a plurality of drives are also provided between the two external gears. Pin 7, the two ends of a plurality of driving pins are connected with two end disks 9 to form a planet carrier structure and output power; the end disks are fixed by an oil seal 10 and a bearing 11 to ensure output stability. The matching relationship is shown in Fig. 1.
端盘可以为2,分别设置在偏心轴轴向两端上,形成双向输出效果。The number of end discs can be two, which are respectively arranged on both ends of the eccentric shaft in the axial direction to form a bidirectional output effect.
偏心轴带动外齿轮偏心转动,外齿轮与内齿轮啮合,并形成少齿差转动输出的效果。将内齿轮轮齿的齿廓、外齿轮轮齿的齿廓均为圆弧,采用圆弧设计,即不存在复杂曲线修形的问题,圆弧是容易制备的,并且制备精度高,通过设计成形后,圆弧不需要进行弧形曲线修形,因此制备难度大大降低,参照图4至图6所示,圆弧结构装配后可产生初始啮合间隙,间隙稳定可控;并且双圆弧设计在啮合后能够提高啮合齿数,参照图7所示的共轭啮效果,啮合范围大,承载能力大大提高,并且还能够降低传动误差,提高传动精度。该结构设计中,相邻轮齿之间的齿槽是不参与啮合的(即相邻齿廓之间的齿槽)。The eccentric shaft drives the outer gear to eccentrically rotate, and the outer gear meshes with the inner gear, and forms the effect of rotating output with less tooth difference. The tooth profile of the internal gear teeth and the tooth profile of the external gear teeth are all circular arcs. The circular arc design is adopted, that is, there is no problem of complex curve modification. The circular arc is easy to prepare, and the preparation accuracy is high. After forming, the arc does not need to be modified by the arc curve, so the preparation difficulty is greatly reduced. As shown in Figures 4 to 6, the initial meshing gap can be generated after the arc structure is assembled, and the gap is stable and controllable; and the double arc design After meshing, the number of meshing teeth can be increased. With reference to the conjugate meshing effect shown in FIG. 7, the meshing range is large, the load-bearing capacity is greatly improved, and the transmission error can be reduced and the transmission accuracy can be improved. In this structural design, the tooth grooves between adjacent gear teeth do not participate in meshing (that is, the tooth grooves between adjacent tooth profiles).
具体的,上述的内齿轮的轮齿齿廓由设置在齿部上的内滚针41获得,外齿轮的轮齿齿廓由设置在齿部上的外滚针61获得,滚针外表面即为圆弧结构。进一步的,箱体内还设置有滚针限位挡圈12。滚针限位挡圈限制内滚针和外滚针的配合位置,防止脱出移动等。采用双滚针的结构时,滚针制备技术成熟,并且成本低;内齿轮、两个外齿轮均采用开槽的方式容置上述的内滚针和外滚针也极为便捷,即外滚针和内对应的齿部上均开设包容槽,采用常规的加工方式即可成型,加工精度高,难度低。并且在啮合运行过程中,内滚针和外滚针均可以进行自转运动,因此在外齿轮带动外滚针周转的同时,外滚针还能够与内滚针啮合产生自转运动,从而减少啮合转动时齿部的摩擦力,减少啮合损耗,提高输出能力。Specifically, the tooth profile of the internal gear mentioned above is obtained by the inner needle 41 arranged on the tooth, and the tooth profile of the external gear is obtained by the outer needle 61 arranged on the tooth. The outer surface of the needle is It is a circular arc structure. Further, a needle roller limit retaining ring 12 is also provided in the box. The needle roller limit retaining ring restricts the matching position of the inner needle and the outer needle to prevent the movement of the needle. When the double needle roller structure is adopted, the needle roller preparation technology is mature and the cost is low; the inner gear and the two outer gears are slotted to accommodate the above inner and outer needles, which is also very convenient, that is, the outer needle Containment grooves are provided on the corresponding teeth and can be formed by conventional processing methods, with high processing accuracy and low difficulty. And in the process of meshing operation, both the inner needle roller and the outer needle roller can perform self-rotating motion. Therefore, while the outer gear drives the outer needle roller to rotate, the outer needle roller can also mesh with the inner needle roller to generate self-rotating motion, thereby reducing the time of meshing rotation. The friction of the teeth reduces the meshing loss and improves the output capacity.
在一实施例中,参照图8至图11所示,内齿轮与外齿轮均具有圆弧状齿廓的轮齿,内齿轮与其对应的轮齿之间以及外齿轮与其对应的轮齿之间均为一体成型结构,结构稳定,制备成本低,制备难度小。In one embodiment, referring to Figures 8 to 11, both the internal gear and the external gear have teeth with arc-shaped tooth profiles, between the internal gear and its corresponding gear teeth, and between the external gear and its corresponding gear teeth They are all integrally formed structures with stable structure, low preparation cost and low preparation difficulty.
在一实施例中,参照图12至图15所示,内齿轮的轮齿齿廓由设置在齿部上的内滚针获得,滚针外表面即为圆弧结构,内滚针对应的齿部上设置有包容槽,以安装容置内滚针,外齿轮具有圆弧状齿廓的轮齿,外齿轮和轮齿一体成型,制备成本低,制备难度小,并且内滚针有效降低啮合转动损耗。In one embodiment, referring to Figures 12 to 15, the tooth profile of the internal gear is obtained by the inner roller needle arranged on the tooth portion. The outer surface of the needle roller is the arc structure, and the inner roller corresponds to the tooth A containing groove is provided on the part to install and accommodate the inner needle roller. The outer gear has gear teeth with an arc-shaped tooth profile. The outer gear and the gear teeth are integrally formed. The preparation cost is low, the preparation difficulty is small, and the inner needle roller effectively reduces the meshing Rotation loss.
在一实施例中,参照图16至图19所示,外齿轮的轮齿齿廓由设置在齿部上的外滚针获得,滚针外表面即为圆弧结构,外滚针对应的齿部上设置有包容槽,以安装容置外滚针,内齿轮具有圆弧状齿廓的轮齿,内齿轮和轮齿一体成型,制备成本低,制备难度小,并且外滚针有效降低啮合转动损耗。In one embodiment, referring to Figures 16 to 19, the tooth profile of the external gear is obtained by the outer roller needle arranged on the tooth part. The outer surface of the needle roller is the arc structure, and the outer roller corresponds to the tooth A containment groove is provided on the part for mounting and accommodating the outer needle roller. The inner gear has gear teeth with an arc-shaped tooth profile. The inner gear and the gear teeth are integrally formed. The preparation cost is low, the preparation difficulty is small, and the outer needle roller effectively reduces the meshing Rotation loss.
参照图20所示,本申请还提供一种双圆弧有隙啮合齿轮副形成方法,包括以下步骤:Referring to FIG. 20, the present application also provides a method for forming a double-arc gap meshing gear pair, which includes the following steps:
步骤1)根据传动装置结构尺寸、传动比,确定外齿轮齿数z 1、内齿轮齿数z 2以及外齿轮齿廓的圆弧半径r o,初步确定偏心距e、外齿轮分度圆半径R o范围及初始值; Step 1) Determine the number of teeth of the external gear z 1 , the number of teeth of the internal gear z 2 and the arc radius of the external gear tooth profile r o according to the structural size and transmission ratio of the transmission device, and preliminarily determine the eccentricity e and the index circle radius of the external gear R o Range and initial value;
先将外齿轮圆弧齿廓确定,参照下述的方程:First determine the arc tooth profile of the external gear, referring to the following equation:
Figure PCTCN2019119448-appb-000008
Figure PCTCN2019119448-appb-000008
其中,θ为圆弧角变量;Among them, θ is the arc angle variable;
步骤2)根据内齿轮和外齿轮相对运动规律,应用外齿轮齿廓的圆弧包络出与其共轭的内齿轮齿廓曲线,确定内齿轮共轭齿廓方程f(x 2,y 2)及啮合方程Φ,得到共轭齿廓组方程如下: Step 2) According to the relative motion law of the internal gear and the external gear, use the arc of the external gear tooth profile to envelop the conjugate tooth profile curve of the internal gear to determine the internal gear conjugate tooth profile equation f(x 2 ,y 2 ) And the meshing equation Φ, the conjugate tooth profile equation is obtained as follows:
Figure PCTCN2019119448-appb-000009
Figure PCTCN2019119448-appb-000009
其中,
Figure PCTCN2019119448-appb-000010
分别为内外齿轮转角,λ=ez 1/R o
among them,
Figure PCTCN2019119448-appb-000010
They are the rotation angles of internal and external gears, λ = ez 1 /R o ;
步骤3)计算内齿轮齿廓啮合界限函数Φ t并与啮合方程联立求解啮合界限 值θ t,可方程组如下: Step 3) Calculate the meshing limit function Φ t of the tooth profile of the internal gear and solve the meshing limit value θ t together with the meshing equation. The equations can be as follows:
Figure PCTCN2019119448-appb-000011
Figure PCTCN2019119448-appb-000011
求解可得,啮合界限值
Figure PCTCN2019119448-appb-000012
The solution is available, the meshing limit value
Figure PCTCN2019119448-appb-000012
步骤4)在[-θ tt]范围内对拟合函数
Figure PCTCN2019119448-appb-000013
求解,得到内齿轮单齿圆弧齿廓半径r i及圆心坐标(x c,y c);
Step 4) Fit the function in the range of [-θ tt ]
Figure PCTCN2019119448-appb-000013
Solve to obtain the single-tooth arc tooth profile radius r i and the center coordinates (x c , y c ) of the internal gear;
其中,(x 2j,y 2j)为内齿轮共轭齿廓坐标值,n为数据点个数; Among them, (x 2j ,y 2j ) is the coordinate value of the conjugate tooth profile of the internal gear, and n is the number of data points;
步骤5)计算拟合间隙
Figure PCTCN2019119448-appb-000014
Step 5) Calculate the fitting gap
Figure PCTCN2019119448-appb-000014
步骤6)判断拟合间隙与初始啮合间隙限定值c 0的大小,如0<c i≤c 0,则该组设计参数满足设计要求,确定设计参数R i、r i,结束设计过程,反之,则需要改变优化参数偏心距e、外齿轮分度圆半径R o,重新计算直到满足设计要求为止。 Step 6) Determine the size of the fitting gap and the initial meshing gap limit value c 0. If 0 <c i ≤ c 0 , then the set of design parameters meets the design requirements, determine the design parameters R i and r i , and end the design process, and vice versa , You need to change the optimized parameters eccentricity e, external gear indexing circle radius Ro , and recalculate until the design requirements are met.
由于复杂曲线为少齿差传动多齿啮合的特点,理论上全部齿对接触,一半齿轮参与力矩转递,重合度大,导致在实际应用过程中需要对共轭齿廓进行修形,以防止由于加工、装配误差导致齿廓干涉,修形提供啮合间隙以形成润滑油膜,改善润滑条件,而在修形后,会降低啮合齿数;采用上述方式进行成型的圆弧形内齿轮和外齿轮能够直接配合使用,间隙值以存在,并且加工时由于不是复杂曲线,因此加工精度高,在设计的间隙值内能够直接使用,无需修形,因此该设计的新型双滚针有隙啮合齿轮替代复杂曲线构成的齿轮副,从根本上接解决杂曲线高精度加工以及齿廓修形问题。降低制造难度及加工成本,同时保证在啮合间隙存在形况下,同时啮合齿数多,重合度大,保持较高的承载能 力。Since the complex curve is the characteristic of multi-tooth meshing with small tooth difference transmission, theoretically all teeth are in contact, half of the gears participate in torque transmission, and the coincidence degree is large, which leads to the need to modify the conjugate tooth profile in the actual application process to prevent The tooth profile interference is caused by machining and assembly errors. The modification provides a meshing gap to form a lubricating oil film and improve the lubrication conditions. After the modification, the number of meshing teeth will be reduced; the arc-shaped internal gear and external gear formed by the above method can Used directly, the gap value can exist, and because it is not a complex curve during processing, the processing accuracy is high, and it can be used directly within the designed gap value without modification. Therefore, the new double needle roller meshing gear with clearance is designed to replace the complex The curved gear pair fundamentally solves the problems of high-precision machining of mixed curves and tooth profile modification. Reduce the manufacturing difficulty and processing cost, and at the same time ensure that in the presence of the meshing gap, the number of meshing teeth is large, the overlap is large, and the high load-bearing capacity is maintained.
以上实施例仅是为充分说明本发明而所举的较佳的实施例,本发明的保护范围不限于此。本技术领域的技术人员在本发明基础上所作的等同替代或变换,均在本发明的保护范围之内。本发明的保护范围以权利要求书为准。The above embodiments are only preferred embodiments for fully explaining the present invention, and the protection scope of the present invention is not limited thereto. The equivalent substitutions or changes made by those skilled in the art on the basis of the present invention are all within the protection scope of the present invention. The protection scope of the present invention is subject to the claims.

Claims (7)

  1. 一种双圆弧有隙啮合少齿差行星传动装置,包括箱体以及设置在箱体内的偏心轴,所述偏心轴的第一偏心部和第二偏心部上分别设置有两个外齿轮,所述外齿轮对应的箱体内壁上设置有内齿轮,所述内齿轮与外齿轮配合啮合,其特征在于,两个外齿轮之间还设置有多个驱动销,多个驱动销两端与两个端盘连接配合形成行星架结构并输出动力,所述内齿轮的齿廓、外齿轮的齿廓均为圆弧,所述内齿轮与外齿轮存在初始啮合间隙。A planetary transmission device with double-arc meshing and small tooth difference, comprising a box body and an eccentric shaft arranged in the box body. The first eccentric part and the second eccentric part of the eccentric shaft are respectively provided with two external gears, An internal gear is provided on the inner wall of the box corresponding to the external gear, and the internal gear meshes with the external gear. The feature is that a plurality of driving pins are also provided between the two external gears, and the two ends of the driving pins are connected with The two end discs are connected and cooperated to form a planet carrier structure and output power. The tooth profile of the internal gear and the external gear are both arcs, and there is an initial meshing gap between the internal gear and the external gear.
  2. 如权利要求1所述的双圆弧有隙啮合少齿差行星传动装置,其特征在于,所述内齿轮与外齿轮均具有圆弧状齿廓的轮齿。The double-arc backlash meshing planetary transmission device with less tooth difference according to claim 1, wherein the internal gear and the external gear both have gear teeth with arc-shaped tooth profiles.
  3. 如权利要求1所述的双圆弧有隙啮合少齿差行星传动装置,其特征在于,所述内齿轮的轮齿齿廓由设置在齿部上的内滚针获得,所述内滚针对应的齿部上设置有包容槽,所述外齿轮具有圆弧状齿廓的轮齿。The double-arc backlash meshing planetary transmission device with a small tooth difference according to claim 1, wherein the tooth profile of the internal gear is obtained by an internal roller needle arranged on the tooth portion, and the internal roller is directed against The corresponding tooth part is provided with a containing groove, and the external gear has teeth with a circular arc tooth profile.
  4. 如权利要求1所述的双圆弧有隙啮合少齿差行星传动装置,其特征在于,所述外齿轮的轮齿齿廓由设置在齿部上的外滚针获得,所述外滚针对应的齿部上设置有包容槽,所述内齿轮具有圆弧状齿廓的轮齿。The double-arc backlash meshing planetary transmission device with a small tooth difference according to claim 1, wherein the tooth profile of the external gear is obtained by an external needle arranged on the tooth, and the external roller is directed against The corresponding tooth portion is provided with a containing groove, and the internal gear has gear teeth with a circular arc tooth profile.
  5. 如权利要求1所述的双圆弧有隙啮合少齿差行星传动装置,其特征在于,所述内齿轮的轮齿齿廓由设置在齿部上的内滚针获得,所述内滚针对应的齿部上设置有包容槽,所述外齿轮的轮齿齿廓由设置在齿部上的外滚针获得,所述外滚针对应的齿部上设置有包容槽。The double-arc backlash meshing planetary transmission device with a small tooth difference according to claim 1, wherein the tooth profile of the internal gear is obtained by an internal roller needle arranged on the tooth portion, and the internal roller is directed against The corresponding tooth portion is provided with a containing groove, the tooth profile of the external gear is obtained by an outer roller needle provided on the tooth portion, and the corresponding tooth portion is provided with a containing groove.
  6. 如权利要求3-5任意一项所述的双圆弧有隙啮合少齿差行星传动装置,其特征在于,所述箱体内还设置有滚针限位挡圈。The double-arc gapped meshing planetary transmission device with a small tooth difference according to any one of claims 3 to 5, wherein a needle roller limit retaining ring is also provided in the box body.
  7. 一种双圆弧有隙啮合齿轮副形成方法,其特征在于,包括以下步骤:A method for forming a double-arc gap meshing gear pair is characterized in that it comprises the following steps:
    步骤1)根据传动装置结构尺寸、传动比,确定外齿轮齿数z 1、内齿轮齿 数z 2以及外齿轮齿廓的圆弧半径r o,初步确定偏心距e、外齿轮分度圆半径R o范围及初始值; Step 1) Determine the number of teeth of the external gear z 1 , the number of teeth of the internal gear z 2 and the arc radius of the external gear tooth profile r o according to the structural size and transmission ratio of the transmission device, and preliminarily determine the eccentricity e and the index circle radius of the external gear R o Range and initial value;
    外齿轮圆弧齿廓方程为:The arc tooth profile equation of the external gear is:
    Figure PCTCN2019119448-appb-100001
    Figure PCTCN2019119448-appb-100001
    其中,θ为圆弧角变量;Among them, θ is the arc angle variable;
    步骤2)根据内齿轮和外齿轮相对运动规律,应用外齿轮齿廓的圆弧包络出与其共轭的内齿轮齿廓曲线,确定内齿轮共轭齿廓方程f(x 2,y 2)及啮合方程Φ,得到共轭齿廓组方程如下: Step 2) According to the relative motion law of the internal gear and the external gear, use the arc of the external gear tooth profile to envelop the conjugate tooth profile curve of the internal gear to determine the internal gear conjugate tooth profile equation f(x 2 ,y 2 ) And the meshing equation Φ, the conjugate tooth profile equation is obtained as follows:
    Figure PCTCN2019119448-appb-100002
    Figure PCTCN2019119448-appb-100002
    其中,
    Figure PCTCN2019119448-appb-100003
    分别为内外齿轮转角,λ=ez 1/R o
    among them,
    Figure PCTCN2019119448-appb-100003
    They are the rotation angles of internal and external gears, λ = ez 1 /R o ;
    步骤3)计算内齿轮齿廓啮合界限函数Φ t并与啮合方程联立求解啮合界限值θ t,可方程组如下: Step 3) Calculate the meshing limit function Φ t of the tooth profile of the internal gear and solve the meshing limit value θ t together with the meshing equation. The equations can be as follows:
    Figure PCTCN2019119448-appb-100004
    Figure PCTCN2019119448-appb-100004
    求解可得,啮合界限值
    Figure PCTCN2019119448-appb-100005
    The solution is available, the meshing limit value
    Figure PCTCN2019119448-appb-100005
    步骤4)在[-θ tt]范围内对拟合函数
    Figure PCTCN2019119448-appb-100006
    求解,得到内齿轮单齿圆弧齿廓半径r i及圆心坐标(x c,y c);
    Step 4) Fit the function in the range of [-θ tt ]
    Figure PCTCN2019119448-appb-100006
    Solve to obtain the single-tooth arc tooth profile radius r i and the center coordinates (x c , y c ) of the internal gear;
    其中,(x 2j,y 2j)为内齿轮共轭齿廓坐标值,n为数据点个数; Among them, (x 2j ,y 2j ) is the coordinate value of the conjugate tooth profile of the internal gear, and n is the number of data points;
    步骤5)计算拟合间隙
    Figure PCTCN2019119448-appb-100007
    Step 5) Calculate the fitting gap
    Figure PCTCN2019119448-appb-100007
    步骤6)判断拟合间隙与初始啮合间隙限定值c 0的大小,如0<c i≤c 0,则该组设计参数满足设计要求,确定设计参数R i、r i,结束设计过程,反之,则需要改变优化参数偏心距e、外齿轮分度圆半径R o,重新计算直到满足设计要求为止。 Step 6) Determine the size of the fitting gap and the initial meshing gap limit value c 0 , such as 0 <c i ≤ c 0 , then the set of design parameters meet the design requirements, determine the design parameters R i and r i , and end the design process, and vice versa , You need to change the optimized parameters eccentricity e, external gear indexing circle radius Ro , and recalculate until the design requirements are met.
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