CN109376439B - RV reducer acting force analysis method and device - Google Patents
RV reducer acting force analysis method and device Download PDFInfo
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Abstract
The invention relates to the field of mechanical design, and discloses a method and a device for analyzing acting force of an RV reducer. The acting force analysis method comprises the steps of determining the position and the direction of acting force on each transmission stage, establishing an acting force balance equation of each transmission stage, and solving the magnitude of each acting force on each transmission stage through the acting force balance equation of each transmission stage. Because stress analysis is carried out for each transmission stage, the force is calculated, and the influence factors of gravity are considered in the calculation process, the acting force analysis method can comprehensively analyze the acting force of the RV reducer, and is convenient for technicians to evaluate the rationality of the RV reducer, find out the key acting position of the RV reducer and the like. The design and production of the speed reducer are also conveniently guided by analysis results. The RV reducer acting force analysis device provided by the embodiment of the invention is used for realizing the acting force analysis method, so that the RV reducer acting force analysis device also has the same beneficial effects.
Description
Technical Field
The invention relates to the field of mechanical design, in particular to a method and a device for analyzing acting force of an RV reducer.
Background
The RV reducer consists of a front stage of a planetary gear reducer and a rear stage of a cycloidal pin gear reducer, has compact structure and large transmission ratio, and is one of the most commonly used reducers under certain conditions. The device has the advantages of small volume, strong impact resistance, large torque, high positioning precision, small vibration, large reduction ratio and the like, and is widely applied to the fields of industrial robots, machine tools, medical detection equipment, satellite receiving systems and the like. However, at present, the force analysis of the RV reducer is not comprehensive enough, so that the design and the performance of the RV reducer cannot be well and accurately evaluated, the design and the production of the RV reducer are difficult to guide by the existing analysis method, and the engineering design and the application of the RV reducer are greatly limited.
Disclosure of Invention
The invention aims to provide an acting force analysis method for an RV reducer, which can comprehensively analyze acting force of each transmission stage of the RV reducer, so that technicians can be helped to better design and performance of the RV reducer to make more accurate evaluation, and the analysis method is also convenient for guiding the design and production of the RV reducer.
Another object of the present invention is to provide an RV retarder force analysis apparatus for implementing the above analysis method.
Embodiments of the present invention are implemented as follows:
the utility model provides a RV reduction gear effort analysis method, is applied to the calculation analysis of the effort of each drive stage of RV reduction gear, RV reduction gear includes a plurality of drive stages of drive connection, RV reduction gear effort analysis method includes:
determining the position and direction of the acting force on each transmission stage;
establishing an acting force balance equation of each transmission stage;
solving the magnitude of each acting force on each transmission stage through an acting force balance equation of each transmission stage;
the acting force of each transmission stage comprises radial force, tangential force and gravity force applied to the transmission stage.
Further, establishing force balance equations of each transmission stage comprises establishing radial stress balance equations, tangential stress balance equations, vertical stress balance equations and torque balance equations of each transmission stage.
Further, the plurality of gear stages include a carrier, a crank shaft rotatably connected to the carrier, two cycloidal gears axially spaced in driving connection with the crank shaft, and a pin gear simultaneously engaged with the two cycloidal gears, the pin gear including a pin gear housing and pin teeth disposed circumferentially within the pin gear housing, the carrier being rotatably connected to the pin gear housing through an outer race large bearing, the step of establishing force balance equations for each gear stage further including establishing bending moment balance equations for the outer race large bearing, the crank shaft, and the carrier, respectively.
Further, the RV retarder effort analysis method further includes:
the absolute rotational speed of each gear stage of the RV reducer is calculated.
Further, the RV retarder effort analysis method further includes:
the torque of each gear stage of the RV reducer is calculated.
Further, the RV retarder effort analysis method further includes:
and screening out the key action positions of the RV reducer according to the magnitude of each acting force of each transmission stage.
The utility model provides a RV reduction gear effort analytical equipment, is applied to the calculation analysis of the effort of each transmission stage of RV reduction gear, RV reduction gear includes a plurality of transmission stages of transmission connection, RV reduction gear effort analytical equipment includes:
the analysis module is used for determining the position and the direction of acting force on each transmission stage;
the equation module is used for establishing an acting force balance equation of each transmission stage;
the acting force calculation module is used for solving the magnitude of each acting force on each transmission stage through an acting force balance equation of each transmission stage;
the acting force of each transmission stage comprises radial force, tangential force and gravity force applied to the transmission stage.
Further, the RV retarder force analysis apparatus further includes:
and the rotating speed calculating module is used for calculating the absolute rotating speed of each transmission stage of the RV reducer.
Further, the RV retarder force analysis apparatus further includes:
and the torque calculation module is used for calculating the torque of each transmission stage of the RV reducer.
Further, the RV retarder effort analysis method further includes:
and the screening module is used for screening out the key action positions of the RV reducer according to the magnitude of each acting force of each transmission stage.
The embodiment of the invention has the beneficial effects that:
the RV reducer acting force analysis method comprises the steps of determining the position and the direction of acting force on each transmission stage, establishing an acting force balance equation of each transmission stage, and solving the magnitude of each acting force on each transmission stage through the acting force balance equation of each transmission stage. The acting force of each transmission stage comprises radial force, tangential force and gravity force applied to the transmission stage. Because stress analysis is carried out for each transmission stage, the force is calculated, and the influence factors of gravity are considered in the calculation process, the acting force analysis method can comprehensively analyze the acting force of the RV reducer, and is convenient for technicians to evaluate the rationality of the RV reducer, find out the key acting position of the RV reducer and the like. The design and production of the speed reducer are guided through analysis results, such as adopting materials with higher strength and higher wear resistance in places with larger stress, or the design is adjusted so that the stress is not excessively concentrated.
The RV reducer acting force analysis device provided by the embodiment of the invention is used for realizing the acting force analysis method, so that the RV reducer acting force analysis device also has the same beneficial effects.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the embodiments will be briefly described below, it being understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and other related drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic diagram of an RV reducer in an embodiment of the present invention;
FIG. 2 is a flow chart of a force analysis method according to an embodiment of the invention;
FIG. 3 is a block diagram of a force analysis device according to an embodiment of the present invention;
FIG. 4 is a graph of input shaft force diagram in accordance with an embodiment of the present invention;
FIG. 5 is a diagram of a planet diagram according to an embodiment of the present invention;
FIGS. 6a and 6b are diagrams of two cycloidal gears, respectively, according to embodiments of the present invention;
FIGS. 7a and 7b are schematic diagrams illustrating the meshing of two cycloidal gears with a pin gear, respectively, in accordance with embodiments of the present invention;
FIG. 8 is a diagram of a pinwheel diagram in accordance with an embodiment of the present invention;
FIG. 9 is a diagram of a crankshaft in accordance with an embodiment of the present invention;
FIG. 10 is a graph of crankshaft torque loading in accordance with an embodiment of the present invention;
FIG. 11 is a simplified diagram illustrating a crankshaft bending analysis in accordance with an embodiment of the present invention;
FIG. 12 is a chart of a carrier diagram in accordance with an embodiment of the present invention;
FIG. 13 is a schematic view of a vertical force applied to a carrier in accordance with an embodiment of the present invention;
fig. 14 is a diagram showing a change in force of the cycloid gear 4A against the journal bearing 7Ai in the embodiment of the present invention;
fig. 15 is a diagram showing a change in force of the cycloid gear 4B against the journal bearing 7Bi according to the embodiment of the present invention;
FIG. 16 is a schematic view of the forces applied to the outer large bearings 9A,9B by the pinwheel in an embodiment of the present invention;
FIG. 17 is a graph showing the force of the supported bearing 8Ai of the crankshaft 3i in accordance with an embodiment of the present invention;
fig. 18 is a diagram showing the force variation of the supporting bearing 8Bi of the crank shaft 3i in the embodiment of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. The components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the invention, as presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Fig. 1 is a schematic diagram of an RV retarder in an embodiment of the present invention. Referring to fig. 1, the present embodiment provides a method for analyzing acting force of an RV reducer, which is applied to calculation and analysis of acting force of each transmission stage of the RV reducer, the RV reducer includes a plurality of transmission stages in transmission connection, the plurality of transmission stages include an input shaft 1, a planet carrier 6, a planet wheel 2 rotatably connected to the planet carrier 6 and meshed with the input shaft 1, a crankshaft 3 axially connected to the planet wheel 2 and rotatably connected to the planet carrier 6, two cycloid gears 4 in transmission connection with the crankshaft 3 at axial intervals, a pin gear 5 meshed with the two cycloid gears 4 at the same time, and an output shaft connected to one of the planet carrier 6 and the pin gear 5. In fig. 1 of the present embodiment, the pinwheel 5 is fixed, the output shaft is connected to the carrier 6 so as to rotate synchronously, and the crank shaft 3 is rotatably connected to the carrier 6 through the support bearing 8. It will be appreciated that in other embodiments the planet carrier 6 may be fixed, causing the pinwheel 5 to rotate, the output shaft being axially connected to the pinwheel 5 for synchronous rotation.
Referring to fig. 2, the method for analyzing the acting force of the RV retarder according to the embodiment of the present invention includes:
step S1, determining the position and the direction of acting force on each transmission stage;
step S2, establishing an acting force balance equation of each transmission stage;
and step S3, solving the magnitude of each acting force on each transmission stage through an acting force balance equation of each transmission stage.
The acting force of each transmission stage comprises radial force, tangential force and gravity which are applied to the transmission stage; the method comprises the steps of establishing an acting force balance equation of each transmission stage, wherein the acting force balance equation comprises a radial stress balance equation, a tangential stress balance equation, a vertical stress balance equation and a torque balance equation of each transmission stage. Since in this embodiment the pin wheel 5 comprises a pin housing and pins circumferentially arranged in the pin housing, the planet carrier 6 is in rotational connection with the pin housing via an outer ring large bearing 9, the step of establishing the force balance equation for each gear stage further comprises establishing a bending moment balance equation for the outer ring large bearing, the crank shaft and the planet carrier, respectively.
Further, the RV retarder effort analysis method further includes: absolute rotational speed and torque of each gear stage of the RV reducer are calculated. The absolute rotational speed, force magnitude and torque calculation method of each gear stage are described in detail below in conjunction with the accompanying drawings and formula deductions.
Table 1 shows the main codes, meanings and units of the examples of the present invention.
Table 1 major code
1. And calculating absolute rotation speed of each transmission stage.
In fig. 1, the input shaft 1 and the planetary gear 2 transmit load by gear engagement, the planetary gear 2 and the crank shaft 3 transmit load by spline, the crank shaft 3 and the cycloid gear 4 transmit load by the tumbler bearing 7, the crank shaft 3 and the carrier 6 transmit load by the support bearing 8, the carrier 6 and the pin gear 5 transmit load by the outer ring large bearing 9, and the cycloid gear 4 and the pin gear 5 transmit load by inner engagement. The deduction process of the absolute rotating speed calculation formula of each transmission stage is as follows.
The first-stage planetary gear ratio is:
the second cycloidal transmission ratio is:
wherein omega 1 For absolute rotational speed of the input shaft 1 (hereinafter referred to as absolute rotational speed) relative to the frame (usually fixed to the ground or the carrier), ω 2 For absolute rotational speed of planet wheel 2, ω 3 Omega is the absolute rotational speed of the crankshaft 3 4 For absolute rotation speed of cycloid wheel 4, ω 5 For absolute rotational speed of the pinwheel 5, ω 6 For the absolute rotational speed of the planet carrier 6, Z 1 For the number of teeth of the sun gear of the input shaft, Z 2 For the number of teeth of planet wheel, Z 4 For cycloidal gear number, Z 5 The number of teeth is the number of teeth (the number of teeth grooves of the needle gear shell).
The planet wheel is fixedly connected with the crank shaft through a spline, thus omega 2 ＝ω 3 。
As can be seen from the transmission characteristics, if the cycloid gear rotates, the crankshaft is driven to revolve, so that the planet carrier is driven to rotate, and omega 4 ＝ω 6 。
1) Needle gear shell is fixed, omega is when planet carrier outputs 5 =0, then
Simplifying and sorting to obtain the system transmission ratio in the state as follows:
at this time, the rotational speed of each main transmission member may be expressed as:
2) The carrier being fixed, the needle gear housing outputting, i.e. omega 6 =0, then
Simplifying the system transmission ratio in the state as follows:
at this time, the rotational speed of each main transmission member may be expressed as:
2. analysis and calculation of forces at each gear stage
The center Ob of the RV reducer is taken as the origin of coordinates, a Cartesian coordinate system is established, the X axis is positive to the right, the Y axis passes through the center of a planet wheel, the Y axis is positive upwards, the Z axis is vertical to the paper surface, and the Z axis is positive outwards, as shown in FIG. 4, and the deducing process and conclusion of the stress calculation formulas of each transmission stage are as follows.
(1) Input shaft stress analysis and calculation
The central wheel at one end of the input shaft 1 is meshed with n (n is larger than or equal to 2) planetary gears to transfer load (the number of the planetary gears 2 shown in fig. 5 is 3, the number of the planetary gears 2 can be adjusted according to actual needs), the planetary gears 2i (i=1, 2..n) averagely share the load of the input shaft, the included angle between adjacent planetary gears is 2 pi/n, and the tangential force of the planetary gears 2i acting on the input shaft 1 is F 2i-1t The radial force is F 2i-1r 。
In FIG. 4, the force and the moment are all in the X-Ob-Y plane, and the input shaft center Ob is subjected to force analysis to establish a balance equation:
torque balancing: t (T) 1 +F 2i-1t ·n·R 1 ＝0
Tangential stress balance:
radial stress balance:
from the initial position in FIG. 4, the prescribed rotation time is t(s), and the carrier rotation angle is θ 6 (rad), θ 6 ＝ω 6 T, the meshing point of the sun gear 1 with the planet gears 2i rotates with the revolution of the planet gears 2i, i.e. the rotation of the carrier 6.
Thus, when the central wheel at one end of the input shaft is engaged with n planets, the vector of the force applied by the ith planet 2i to the input shaft 1 can be expressed as:
wherein i=1, 2..n, R 1 For the pitch circle radius of the central wheel of the input shaft 1, α is the gear pressure angle.
(2) Planet wheel stress analysis and calculation
In fig. 5, the planetary gear 2i transfers the load with the sun gear of the input shaft 1 via involute gear engagement, the adjacent phase differences are 2 pi/n, and the planetary gear 2i transfers the load with the crank shaft 3i in spline connection. The planet wheel 2i is subjected to a force F exerted on it by the input shaft 1 1-2it 、F 1-2ir And a force F applied thereto by the crankshaft 3i 3i-2it 、F 3i-2ir Moment T 3i-2i The gravity of the planet wheel 2i is G2, the counter force for balancing the gravity of the planet wheel 2i on the crankshaft 3i is F3i-2ig, and the force and the moment are in the same plane.
Carrying out stress analysis on the center O2i of the planet wheel 2i, and establishing a balance equation:
torque balancing: t (T) 3i-2i +F 1-2it ·R 2 ＝0
Tangential stress balance: f (F) 1-2it +F 3i-2it ＝0
Radial stress balance: f (F) 1-2ir +F 3i-2ir ＝0
Vertical stress balance: f (F) 3i-2ig +G 2 ＝0
The acting force of the crankshaft 3i on the planetary gear 2i rotates with the revolution of the crankshaft 3i, that is, the rotation of the carrier 6, and thus the vector of the acting force of the planetary gear 2i on the crankshaft 3i can be expressed as:
the torque applied to the planet wheel 2i by the crankshaft 3i is:
(3) Cycloidal gear stress analysis and calculation
The two pieces of conjugated cycloidal gears 4 are cycloidal gear 4A and cycloidal gear 4B respectively, and cycloidal gear 4AThe gravity of both 4B and 4B is G4. The tangential force exerted by the rocking arm bearing 7Ai contacting the cycloid wheel 4A on the cycloid wheel 4A is F 7Ai-4At Another set of acting forces is F 7Ai-4Af The vertical acting force is F 7Ai-4Ag . The tangential force exerted by the rotating arm bearing 7Bi in contact with the cycloid gear 4B on the cycloid gear 4B is F 7Bi-4Bt Another set of acting forces is F 7Bi-4Bf The vertical acting force is F 7Bi-4Bg . The radial acting force of the pin teeth 5 on the cycloidal gear 4A is F 5-4Ar Tangential force is F 5-4At The radial acting force of the pin teeth 5 to the cycloidal gear 4B is F 5-4Br Tangential force is F 5-4Bt See fig. 6a and 6b.
In fig. 7a and 7B, in the case of an unmodified cycloid gear profile, the force of the pin wheel 5 on the cycloid wheel 4A is directed to its node PA and the force of the pin wheel 5 on the cycloid wheel 4B is directed to its node PB. Simplifying the needle tooth acting force to the nodes PA and PB to obtain resultant force F 5-4A 、F 5-4B The cycloidal gears 4A, 4B are arranged in a conjugated manner, the phases of which differ by pi, so F 5-4A 、F 5-4B Equal in size and opposite in direction as shown in fig. 6a and 6b.
In fig. 6a and 6b, the forces applied to the cycloid wheel 4A are all in the X-Ob-Y plane, and the force analysis is performed on the center O4A of the cycloid wheel 4A. The gravity of the cycloid wheel 4A is G4, and the vertical acting force applied to the cycloid wheel 4A by the rotating arm bearing 7Ai contacted with the cycloid wheel 4A is F 7Ai-4Ag ，F 7Ai-4Ag The O4A combined moment of the pair is 0, and the tangential acting force is F 7Ai-4At The resultant force of the needle teeth to the cycloidal gear is F 5-4A Force F 7Ai-4At And F 5-4A Balance the torque generated by point O4A, F 7Ai-4Af Another set of forces, applied to the cycloid wheel 4A for the tumbler bearing 7Ai, is the same as force F 5-4A Phase balance, establish the equilibrium equation:
torque balancing: f (F) 5-4At ·R a +F 7Ai-4At ·n·R 3 ＝0
Tangential stress balance:
resultant force F 5-4A Direction of receptionForce balance:
vertical stress balance:
wherein: alpha C Is F 5-4At And F 5-4A The included angle between the two is the pressure angle of the cycloid wheel, ra is the pitch radius of the cycloid wheel, a is the eccentric distance, rb is the pitch radius of the pin wheel, R3 is the distribution radius of the crank shaft, R 3 ＝R 1 +R 2 . For a 1-tooth difference mechanism, Z 5 ＝Z 4 +1。
In fig. 6a and 6B, the forces applied to the cycloid wheel 4B are all in the X-Ob-Y plane, and the force analysis is performed on the center O4B of the cycloid wheel 4B. The gravity of the cycloid wheel 4B is G4, and the vertical acting force applied to the cycloid wheel 4B by the rotating arm bearing 7Bi contacted with the cycloid wheel 4B is F 7Bi-4Ag ，F 7Bi-4Bg The O4B combined moment is 0, and the tangential acting force is F 7Bi-4Bt The resultant force of the needle teeth to the cycloidal gear is F 5-4B Force F 7Bi-4Bt And F 5-4B Balance the torque generated by point O4B, F 7Bi-4Bf Another set of forces, force F, applied to the cycloid wheel 4B for the rocker arm bearing 7Bi 5-4B Phase balance, establish the equilibrium equation:
torque balancing: f (F) 5-4Bt ·R a +F 7Bi-4Bt ·n·R 3 ＝0
Tangential stress balance:
resultant force F 5-4B The direction stress is balanced:
vertical stress balance:
and (3) finishing to obtain:
force F 7Ai-4Af Rotates with the rotation of the crankshaft 3i, force F 7Ai-4At The planetary carrier 6 rotates by rotating with the revolution of the crank shaft 3 i. Let the crank shaft 3i turn angle theta 3 (rad), θ 3 ＝ω 3 ·t。
Therefore, the force of the journal bearing 7Ai against the cycloid gear 4A can be expressed as:
the force of the arm bearing 7Bi against the cycloid gear 4B can be expressed as:
(4) Needle gear shell stress analysis and calculation
The pin wheel 5 is composed of a pin gear housing and pin teeth, and in fig. 8, the forces acting on the pin wheel 5 by the cycloidal gears 4A and 4B are respectively F 4A-5 、F 4B-5 The method comprises the steps of carrying out a first treatment on the surface of the The external acting force applied to the pinwheel is equivalent to Ob, the torque is T5, the vertical force is F5, and the bending moment is M5; the tangential force exerted by the outer ring big bearings 9A and 9B on the pin wheel 5 is F 9A-5t 、F 9B-5t The radial force is F 9A-5r 、F 9B-5r The vertical force is F 9A-5g 、F 9B-5g The method comprises the steps of carrying out a first treatment on the surface of the The pinwheel gravity is G5.
In fig. 8 (a), the pin wheel 5 is composed of a pin housing and pin teeth, and forces of the cycloid gears 4A and 4B to the pin wheel 5 are respectively F 4A-5 、F 4B-5 The method comprises the steps of carrying out a first treatment on the surface of the The external acting force applied to the pinwheel is equivalent to Ob, the torque is T5, the vertical force is F5, and the bending moment is M5; the tangential force exerted by the outer ring big bearings 9A and 9B on the pin wheel 5 is F 9A-5t 、F 9B-5t The radial force is F 9A-5r 、F 9B-5r The vertical force is F 9A-5g 、F 9B-5g The method comprises the steps of carrying out a first treatment on the surface of the Pin gear weightThe force is G5. The forces of the pinwheel 5 are not in the same plane, so the force analysis is performed on the center Ob of the pinwheel 5 in different planes. Establishing a balance equation in the X-Ob-Y plane:
torque balancing: t (T) 5 +(F 4A-5t +F 4B-5t )·R b ＝0
Tangential stress balance: (F) 4A-5t +F 4B-5t )+(F 9A-5t +F 9B-5t )＝0
Radial stress balance: (F) 4A-5r +F 4B-5r )+(F 9A-5r +F 9B-5r )＝0
In fig. 8 (B), in the Y-Ob-Z plane, bending moment balance analysis is performed on the centers O9A, O B of the outer ring large bearings 9A,9B, respectively, to establish a balance equation:
point O9A radial bending moment balance: f (F) 9B-5r ·2L 9 +F 4B-5r ·(L 4 +L 9 )+F 4A-5r ·(L 9 -L 4 )＝0
Point O9B radial bending moment balance: f (F) 9A-5r ·2L 9 +F 4A-5r ·(L 4 +L 9 )+F 4B-5r ·(L 9 -L 4 )＝0
Point Ob vertical bending moment balance: f (F) 9A-5g ·L 9 -F 9B-5g ·L 9 -M 5 ＝0
Vertical stress balance: f (F) 9A-5g +F 9B-5g +G 5 -F 5 ＝0
Radial stress balance: (F) 4A-5r +F 4B-5r )+(F 9A-5r +F 9B-5r )＝0
In fig. 8 (c), in the X-Ob-Z plane, bending moment balance analysis is performed on the centers O9A, O B of the outer ring large bearings 9A,9B, respectively, to establish a balance equation:
point O9A bending moment balance:
F 9B-5t ·2L 9 +F 4B-5t ·(L 4 +L 9 )+F 4A-5t ·(L 9 -L 4 )＝0
point O9B bending moment balance:
F 9A-5t ·2L 9 +F 4A-5t ·(L 4 +L 9 )+F 4B-5t ·(L 9 -L 4 )＝0
tangential stress balance:
(F 4A-5t +F 4B-5t )+(F 9A-5t +F 9B-5t )＝0
sorting to obtain a scalar type:
T 5 ＝2·F 4A-5t ·R b (the direction is the same as T1)
I.e.
At the same time
Force F 9A-5 Phase angle of (theta) 3 +α C ) Force F 9B-5 Phase angle of (theta) 3 +α C + pi), the force of the outer ring large bearings 9A,9B against the needle gear housing 5 can be expressed as:
(5) Crankshaft stress analysis and calculation
In fig. 9, point O2i on the crankshaft 3i is subjected to the force F of the planet wheel 2i 2i-3ir 、F 2i-3it 、F 2i-3ig The method comprises the steps of carrying out a first treatment on the surface of the Acting force F of supported bearing 8Ai at point O8Ai 8Ai-3ir 、F 8Ai-3it 、F 8Ai-3ig The method comprises the steps of carrying out a first treatment on the surface of the Acting force F of supported bearing 8Bi at point O8Bi 8Bi-3ir 、F 8Bi-3it 、F 8Bi-3ig The method comprises the steps of carrying out a first treatment on the surface of the The point O7Ai is acted on by the acting force F of the tumbler bearing 7Ai 7Ai-3if 、F 7Ai-3it 、F 7Ai-3ig The method comprises the steps of carrying out a first treatment on the surface of the The point O7Bi receives the acting force F of the rotating arm bearing 7Bi 7Bi-3if 、F 7Bi-33it 、F 7Ai-3ig The method comprises the steps of carrying out a first treatment on the surface of the Receiving torque T 3 ＝-T 2 。
The stress balance of the tumbler bearings 7Ai and 7Bi is as follows:
in fig. 10, in the X-O3i-Y plane, a torque balance equation is established for the crankshaft 3 i:
T 3 +F 7Ai-3if ·cos(α C )·a+F 7Bi-3if ·cos(α C )·a+F 7Ai-3it ·a+F 7Bi-3it ·a＝0
then
Therefore, the vector of the force of the pin wheel 5 against the cycloid wheels 4A, 4B can be expressed as:
will be
Substitution into T 5 ＝2·F 4A-5t ·R b (direction and T) 1 The same) to obtain the torque T of the needle gear shell 5 The method comprises the following steps:
will be
And->
Substitution of F derived from the foregoing 7Ai-4A 、F 7Bi-4B The vector of the force of the journal bearing 7Ai against the cycloid wheel 4A can be expressed as:
the vector of the force of the journal bearing 7Bi against the cycloid gear 4B can be expressed as:
the vector of the forces of the outer large bearings 9A,9B on the needle gear housing 5 can be expressed as:
in FIG. 11, the bending moment balance analysis is performed on points O8Ai, O8Bi on the crankshaft 3i in the Y-Ob-Z plane, force F 7Ai-3if 、F 7Bi-3if Rotates with the rotation of the crankshaft 3i, F 7Ai-3if Phase angle of (theta) 3 +α C )，F 7Bi-3if Phase angle of (theta) 3 +α C +π)，F 7Ai-3it 、F 7Bi-3it Rotates with the rotation of the planet carrier 6, the phase angle is
Let beta= (θ) 3 +α C -θ 6 ) Force F 7Ai-3if And F is equal to 7Ai-3it The dynamic included angle of (2) is->
Force F 7Bi-3if And F is equal to 7Bi-3it Can be expressed as +.>
F 7Ai-3ift 、F 7Bi-3ift Respectively F 7Ai-3if 、F 7Bi-3if Tangential component F of (2) 7Ai-3ifr 、F 7Bi-3ifr Respectively F 7Ai-3if 、F 7Bi-3if Is included in the radial component of (a).
Establishing vertical bending moment balance for the point O8 Ai:
F 8Bi-3ig ·2L 8 +F 2i-3ig ·(L 2 -L 8 )-F 7Ai-3ig ·(L 8 -L 7 )-F 7Bi-3ig ·(L 8 +L 7 )＝0
then there is
Establishing vertical bending moment balance for the point O8 Bi:
F 8Ai-3ig ·2L 8 -F 2i-3ig ·(L 2 +L 8 )-F 7Ai-3ig ·(L 8 +L 7 )-F 7Bi-3ig ·(L 8 -L 7 )＝0
then there is
Establishing tangential bending moment balance for the point O8 Ai:
F 2i-3it ·(L 2 -L 8 )-F 8Bi-3it ·2·L 8 -F 7Ai-3it ·(L 8 -L 7 )-F 7Bi-3it ·(L 8 +L 7 )-F 7Ai-3ift ·(L 8 -L 7 )
+F 7Bi-3ift ·(L 8 +L 7 )＝0
then there is
Establishing radial bending moment balance for the point O8 Ai:
F 2i-3ir ·(L 2 -L 8 )-F 8Bi-3ir ·2·L 8 -F 7Ai-3ifr ·(L 8 -L7)+F 7Bi-3ifr ·(L 8 +L 7 )＝0
then there is
Establishing tangential bending moment balance for the point O8 Bi:
F 2i-3it ·(L 8 +L 2 )-F 8Ai-3it ·2·L 8 +F 7Ai-3it ·(L 8 +L 7 )+F 7Bi-3it ·(L 8 -L 7 )+F 7Ai-3ift ·(L 8 +L 7 )
+F 7Bi-3ift ·(L 8 -L 7 )＝0
then there is
Establishing radial bending moment balance for the point O8 Bi:
F 2i-3ir (L 8 +L 2 )-F 8Ai-3ir ·2L 8 +F 7Ai-3ifr (L 8 +L 7 )+F 7Bi-3ifr (L 8 -L 7 )＝0
then there is
As a result of the fact that,
and F 8Ai-3ir 、F 8Ai-3it And rotates with the planet carrier 6.
Therefore, the force calculation formula of the support bearing 8Ai on the crankshaft 3i is:
similarly, the vector of the supporting bearing 8Bi acting on the crankshaft 3i can be expressed as:
(6) Planet carrier stress analysis and calculation
The planet carrier 6 is formed by fixedly connecting input and output flanges. In fig. 12, the force F of the support bearings 8Ai,8Bi on the carrier 6 8Ai-6 、F 8Bi-6 The acting force of the outer ring big bearings 9A and 9B on the planet carrier 6 is F 9A-6 、F 9B-6 . The weight of the planet carrier 6 is G6.
Establishing a vertical stress diagram of the planet carrier 6, as shown in fig. 13, wherein the gravity of the planet carrier 6 is G 6 Planet carrier supported bearing 8 Ai And 8 Bi Is F as the vertical force of (2) 8Ai-6g ，F 8Bi-6g The vertical force of the outer ring bearing 9A,9B is F 9A-6g ，F 9B-6g . Will F 8Ai-6g ，F 8Bi-6g To the point OM ON the central axis, ON is simplified, and the resultant force is F 8A-6g ，F 8B-6g 。
Point-to-point O 9A Establishing a vertical bending moment balance equation:
F 9B-6g ·2L 9 +F 8A-6g ·(L 8 -L 9 )-F 8B-6g ·(L 8 +L 9 )-G 6 ·L 9 ＝0
simplifying and obtaining
Point-to-point O 9B Establishing a vertical bending moment balance equation:
F 9A-6g ·2L 9 +F 8B-6g ·(L 8 -L 9 )-F 8A-6g ·(L 8 +L 9 )-G 6 ·L 9 ＝0
the vector of the forces of the outer large bearings 9A,9B on the needle gear housing 5 can be expressed as:
substituting the pin gear housing vertical force balance equation,
vertical stress balance: f (F) 9A-5g +F 9B-5g +G 5 -F 5 ＝0
Point Ob moment balance: f (F) 9A-5g ·L 9 -F 9B-5g ·L 9 -M 5 ＝0
The external forces exerted on the centre of gravity Ob of the needle gear housing are then:
the bending moment externally exerted on the pin housing center of gravity Ob is:
M 5 ＝nG 2 ·L 2 (anticlockwise)
In fig. 12, the carrier 6 is formed by fixedly connecting input and output flanges. The support bearing 8Ai is simultaneously subjected to the force F of the planet carrier 6-8Ai And the acting force F of the crankshaft 3i-8Ai The outer ring big bearing receives the acting force F of the planet carrier at the same time 6-9A Force F of the pinwheel 5-9A 。
The stress balance of the rotating arm bearing is as follows:
F 6-8Ai ＝-F 3i-8Ai
the stress balance of the outer ring large bearing is as follows:
F 6-9A ＝-F 5-9A
therefore, the vector calculation formula of the acting force of the outer ring large bearing 9A on the carrier 6 is:
F 9A-6 ＝-F 9A-5
the vector calculation formula of the acting force of the outer ring large bearing 9B on the planet carrier 6 is as follows:
F 9B-6 ＝-F 9B-5
similarly, the vector calculation formula of the acting force of the tumbler bearing 8Ai on the planet carrier 6 is as follows:
F 8Ai-6 ＝-F 8Ai-3i
the vector calculation formula of the acting force of the rotating arm bearing 8Bi on the planet carrier 6 is as follows:
F 8Bi-6 ＝-F 8Bi-3i
3. method for calculating torque of each transmission stage
Method for calculating torque of each transmission stage
The calculation formula of the planetary gear torque is as follows:
the crankshaft torque calculation formula is:
/>
the cycloidal gear torque calculation formula is: t (T) 4 ＝0
The pin gear housing torque calculation formula is:
the planet carrier torque calculation formula is:
4. on the basis of the absolute rotating speed, the acting force and the torque of each transmission stage, the acting force analysis method of the RV reducer further comprises the step of screening out the key acting position of the RV reducer according to the acting force of each transmission stage. Specifically, whether the gear stage is a key action position can be judged according to whether a certain acting force on each gear stage is larger than a preset value. The key action position can be the position with the greatest stress and most possibility of fatigue and damage, and the design and production of the speed reducer are concerned. For example, materials with higher strength and better wear resistance are adopted in places with higher bearing force. Or the design of the speed reducer is changed so that the acting force is not too concentrated.
The embodiment of the invention also provides an acting force analysis device of the RV reducer, which is used for realizing the acting force analysis method, and comprises the following steps:
the analysis module is used for determining the position and the direction of acting force on each transmission stage;
the equation module is used for establishing an acting force balance equation of each transmission stage;
the acting force calculation module is used for solving the magnitude of each acting force on each transmission stage through an acting force balance equation of each transmission stage;
the acting force of each transmission stage comprises radial force, tangential force and gravity force applied to the transmission stage.
Further, the RV reducer acting force analysis device further comprises a rotating speed calculation module for calculating the absolute rotating speed of each transmission stage of the RV reducer, a torque calculation module for calculating the torque of each transmission stage of the RV reducer and a screening module for screening out the key acting position of the RV reducer according to the acting force of each transmission stage.
The following is the result and analysis of the calculation for a specific RV retarder.
The pre-assigned variables are: parameter cycloidal wheel pressure angle alpha c =13.10°, involute gear pressure angle α=20°, output torque T 6 Output rotational speed ω=784n·mm 6 15 rpm, gear modulus m=1.75, center distance R 3 The planetary transmission eccentricity of cycloidal pin gear is a=1.5 mm, and the center distance L between the planetary gear and the pin gear is 42mm 2 33.4mm, distance L between cycloidal gear and pin gear center 4 ＝6mm，L 7 ＝L 4 Distance L between support bearing and center of needle wheel 8 Distance L between outer ring bearing and center of pinwheel =20mm 9 =19.25 mm, sun gear equivalent number of teeth Z 1 =12, planetary equivalent number of teeth Z 2 =36, pin gear tooth number Z 5 =40, cycloidal gear tooth number Z 4 =39, planet gravity G 2 =0.149777146×9.8n crankshaft gravity G 3 =0.15515951×9.8n, cycloidal gear gravity G 4 9.8n =0.65788422 x, needle gear case gravity G 5 =4.55055242×9.8n, carrier gravity G 6 =4.4850864×9.8n, number of planets n=3.
Torque and rotational speed analysis results:
TABLE 1 calculation results of the rotational speeds at each level (unit: rpm)
| ω 1 | ω 2 | ω 3 | ω 4 | ω 5 | ω 6 |
| 1815 | -585 | -585 | 15 | 0 | 15 |
TABLE 2 calculation results of the torques at each stage (unit: N.m)
| T 1 | T 2 | T 3 | T 4 | T 5 | T 5 |
| -6.4793 | -6.4793 | 6.4793 | 0 | -777.5207 | 784 |
Input shaft stress analysis results:
the input shaft 1 is mainly subjected to the acting force of the planet gears 2i, and the stress analysis result is shown in table 3.
Table 3 input shaft is subjected to the force (unit: N) of the planetary gear 2i
And (3) analyzing the stress of the planet wheel:
the planetary gear 2i receives the acting force of the crank shaft 3i and the input shaft 1 at the same time, wherein the acting force of the planetary gear 2i received by the input shaft 1 and the acting force of the input shaft 1 received by the planetary gear 2i are the reaction forces, and the forces are the same in magnitude and opposite in direction, and are shown in table 4.
The planet wheel 2i receives the forces of the crankshaft 3i in all directions simultaneously, the forces are shown in table 5, and the resultant forces are shown in table 6.
TABLE 4 Planet wheel 2i receives force (unit: N) from input shaft 1
TABLE 5 Planet wheel 2i receives the force (unit: N) of crankshaft 3i
TABLE 6 Planet wheel 2i receives the force-resultant force (unit: N) of crankshaft 3i
Cycloidal gear stress analysis results:
the cycloid gears 4A, 4B are mainly subjected to the force applied thereto by the pin gear 5 (see table 7) and the force applied thereto by the tumbler bearings 7Ai,7Bi (see tables 8, 9).
Table 7 cycloidal gear receives the force (unit: N) of the pin gear 5
Table 8 forces (unit: N) in directions of the rocking arm bearings 7Ai,7Bi are applied to the cycloid gears 4A, 4B
Table 9 forces acting on the cycloid gears 4A, 4B by the tumbler bearings 7Ai,7 Bi-resultant forces (unit: N)
Analysis of the data in table 9 shows that the force variation of the cycloid wheel 4A by the journal bearing 7A1,7A2,7A3 is shown in fig. 14, and the force variation of the journal bearing 7B1,7B2,7B3 of the cycloid wheel 4B is shown in fig. 15.
Needle gear housing stress analysis results:
the pin wheel 5 is mainly acted by the cycloidal gears 4A and 4B to respectively obtain the acting forces F on the pin wheel 5 4A-5 、F 4B-5 The method comprises the steps of carrying out a first treatment on the surface of the F applied to the pin wheel 5 by the outer ring large bearings 9A,9B 9A-5 ,F 9B-5 See table 10.
Wherein F is 4A-5 、F 4B-5 With cycloidal gear receiving force F of pin gear 5 5-4A ，F 5-4B The reaction forces are the same and opposite, and the details are shown in Table 7.
Table 10 the pinwheel 5 receives the forces (unit: N) of the bearings 9A,9B
Analysis of the data in table 10 shows that the pinwheel 5 is subject to the force changes of the outer large bearings 9a,9b, see fig. 16. As can be seen from the figure, F is not considered when the influence of gravity of the mechanism itself is taken into consideration 9A-5 ＝F 9B-5 = 2073.511728N, after taking into account gravity, F 9A-5 ，F 9B-5 And shows a periodic variation with crank angle.
Crankshaft force analysis results:
the point O2i on the crankshaft 3i is subjected to the force F of the planet wheel 2i 2i-3ir 、F 2i-3it 、F 2i-3ig And F is combined with 3i-2it ，F 3i-2ir ，F 3i-2ig The reaction forces are equal in magnitude and opposite in direction, and are shown in Table 3.
Point O 7Ai Is subjected to the acting force F of the tumbler bearing 7Ai 7Ai-3if 、F 7Ai-3it 、F 7Ai-3ig The method comprises the steps of carrying out a first treatment on the surface of the Point O 7Bi Acting force F of the rotating arm bearing 7Bi 7Bi-3if 、F 7Bi-3it 、F 7Ai-3ig The method comprises the steps of carrying out a first treatment on the surface of the The stress balance of the tumbler bearings 7Ai and 7Bi is as follows:
therefore: f (F) 7Ai-3if 、F 7Ai-3it 、F 7Ai-3ig ，F 7Bi-3if 、F 7Bi-3it 、F 7Ai-3ig The values are detailed in Table 8.
Acting force F of supported bearing 8Ai,8Bi at crank shaft 3i 8Ai-3i, F 8Bi-3i, See table 11 for details.
Table 11 the crankshaft 3i receives the force of the support bearings 8ai,8bi
Analysis of the data in table 10 shows that the force variation of the crankshaft 3i by the support bearing 8A1,8A2,8A3 is shown in fig. 17 and the force variation of the crankshaft 3i by the support bearing 8B1,8B2,8B3 is shown in fig. 18.
The analysis result of the planet carrier stress:
the planet carrier 6 is mainly acted by the acting force of the support bearing 8Ai,8Bi to the planet carrier 6
F 8Ai-6 、F 8Bi-6 The acting force of the outer ring big bearings 9A and 9B on the planet carrier 6 is F 9A-6 、F 9B-6 。
Wherein F is 8Ai-6 ＝-F 8Ai-3i ，F 8Bi-6 ＝-F 8Bi-3i The forces are equal and opposite, see Table 11.F (F) 9A-6 ＝-F 9A-5 ,F 9B-6 ＝-F 9B-5 The forces are equal and opposite, see Table 10 in detail.
The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (8)
1. The utility model provides a RV reduction gear effort analysis method, is applied to the calculation analysis of the effort of each transmission stage of RV reduction gear, RV reduction gear includes a plurality of transmission stages of transmission connection, characterized in that, RV reduction gear effort analysis method includes:
determining the position and direction of the acting force on each transmission stage;
establishing an acting force balance equation of each transmission stage;
solving the magnitude of each acting force on each transmission stage through an acting force balance equation of each transmission stage;
the acting force of each transmission stage comprises radial force, tangential force and gravity force which are applied to the transmission stage;
establishing an acting force balance equation of each transmission stage, including establishing a radial stress balance equation, a tangential stress balance equation, a vertical stress balance equation and a torque balance equation of each transmission stage;
the planetary gear transmission system comprises a plurality of transmission stages, a plurality of transmission stages and a plurality of transmission stages, wherein the transmission stages comprise a planetary carrier, n planetary gears rotatably connected to the planetary carrier, n crank shafts rotatably connected to the planetary carrier, two cycloidal gears in axial interval in transmission connection with the crank shafts and pin gears meshed with the two cycloidal gears simultaneously, the n crank shafts are in one-to-one correspondence with the n planetary gears and are coaxially connected, the pin gears comprise pin gear shells and pin teeth arranged in the pin gear shells along the circumferential direction, the planetary carrier is rotatably connected with the pin gear shells through outer ring big bearings, and the step of establishing force balance equations of the transmission stages comprises the steps of establishing bending moment balance equations for the outer ring big bearings, the crank shafts and the planetary carrier respectively;
the cycloidal gear is connected to the crank shaft through a tumbler bearing, and the force balance equation of the cycloidal gear includes:
wherein n is the number of planet gears, alpha C R is the pressure angle of the cycloidal gear a Is the pitch circle radius of the cycloid wheel, R 3 Distributing the radius of the circle for the crankshaft, G 4 F is the gravity of the cycloidal gear 5-4At 、F 5-4Bt Tangential forces of the pin teeth on the two cycloidal gears, F 5-4A 、F 5-4B Respectively the resultant force of the pin teeth to the two cycloidal gears, F 7Ai-4At 、F 7Bi-4Bt The two cycloidal gears are respectively subjected to tangential force from the ith rotating arm bearing, F 7Ai-4Ag 、F 7Bi-4Bg Two cycloidal gears are respectively subjected to vertical force from the ith rotating arm bearing, F 7Ai-4Af 、F 7Bi-4Bf The two cycloidal gears are respectively subjected to the force F from the ith rotating arm bearing 5-4A 、F 5-4B Opposite direction of the divisionForce relief;
the acting force of the ith rocking arm bearing on one of the cycloid gears is solved by the following steps:
the force of the ith rocking arm bearing on the other cycloid gear is solved by the following steps:
wherein θ 3 Theta is the rotation angle of the crank shaft 6 Is the rotation angle of the planet carrier.
2. The RV retarder effort analysis method of claim 1, further comprising:
and calculating the absolute rotation speed of each transmission stage of the RV reducer.
3. The RV retarder effort analysis method of claim 1, further comprising:
and calculating the torque of each transmission stage of the RV reducer.
4. The RV retarder effort analysis method according to any of claims 1-3, further comprising:
and screening out key action positions of the RV reducer according to the magnitude of each acting force of each transmission stage.
5. The utility model provides a RV reduction gear effort analytical equipment, is applied to the calculation analysis of the effort of each transmission stage of RV reduction gear, RV reduction gear includes a plurality of transmission stages of transmission connection, its characterized in that, RV reduction gear effort analytical equipment includes:
the analysis module is used for determining the position and the direction of acting force on each transmission stage;
the equation module is used for establishing an acting force balance equation of each transmission stage;
the acting force calculation module is used for solving the magnitude of each acting force on each transmission stage through an acting force balance equation of each transmission stage;
the acting force of each transmission stage comprises radial force, tangential force and gravity force which are applied to the transmission stage;
establishing an acting force balance equation of each transmission stage, including establishing a radial stress balance equation, a tangential stress balance equation, a vertical stress balance equation and a torque balance equation of each transmission stage;
the planetary gear transmission system comprises a plurality of transmission stages, a plurality of transmission stages and a plurality of transmission stages, wherein the transmission stages comprise a planetary carrier, n planetary gears rotatably connected to the planetary carrier, n crank shafts rotatably connected to the planetary carrier, two cycloidal gears in axial interval in transmission connection with the crank shafts and pin gears meshed with the two cycloidal gears simultaneously, the n crank shafts are in one-to-one correspondence with the n planetary gears and are coaxially connected, the pin gears comprise pin gear shells and pin teeth arranged in the pin gear shells along the circumferential direction, the planetary carrier is rotatably connected with the pin gear shells through outer ring big bearings, and the step of establishing force balance equations of the transmission stages comprises the steps of establishing bending moment balance equations for the outer ring big bearings, the crank shafts and the planetary carrier respectively;
the cycloidal gear is connected to the crank shaft through a tumbler bearing, and the force balance equation of the cycloidal gear includes:
wherein n is the number of planet gears, alpha C R is the pressure angle of the cycloidal gear a Is the pitch circle radius of the cycloid wheel, R 3 Distributing the radius of the circle for the crankshaft, G 4 F is the gravity of the cycloidal gear 5-4At 、F 5-4Bt Tangential forces of the pin teeth on the two cycloidal gears, F 5-4A 、F 5-4B Respectively the resultant force of the pin teeth to the two cycloidal gears, F 7Ai-4At 、F 7Bi-4Bt The two cycloidal gears are respectively subjected to tangential force from the ith rotating arm bearing, F 7Ai-4Ag 、F 7Bi-4Bg Two cycloidal gears are respectively subjected to vertical force from the ith rotating arm bearing, F 7Ai-4Af 、F 7Bi-4Bf The two cycloidal gears are respectively subjected to the force F from the ith rotating arm bearing 5-4A 、F 5-4B The opposite decomposition forces;
the acting force of the ith rocking arm bearing on one of the cycloid gears is solved by the following steps:
the force of the ith rocking arm bearing on the other cycloid gear is solved by the following steps:
wherein θ 3 Theta is the rotation angle of the crank shaft 6 Is the rotation angle of the planet carrier.
6. The RV retarder effort analysis device of claim 5, further comprising:
and the rotating speed calculating module is used for calculating the absolute rotating speed of each transmission stage of the RV reducer.
7. The RV retarder effort analysis device of claim 5, further comprising:
and the torque calculation module is used for calculating the torque of each transmission stage of the RV reducer.
8. The RV retarder force analysis device of any one of claims 5-7, wherein the RV retarder force analysis method further comprises:
and the screening module is used for screening out the key action positions of the RV reducer according to the magnitude of each acting force of each transmission stage.
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2007298458A (en) * | 2006-05-02 | 2007-11-15 | Ntn Corp | Dynamic analytical method for rolling bearing under planetary motion |
| CN104091007A (en) * | 2014-07-01 | 2014-10-08 | 重庆工商职业学院 | Small tooth difference planetary reducer dynamic simulation analysis method |
| CN108253115A (en) * | 2017-12-11 | 2018-07-06 | 广州市昊志机电股份有限公司 | A kind of method that the form of cycloidal gear tooth is obtained based on pinwheel tooth profiling quantity |
| CN108520159A (en) * | 2018-04-28 | 2018-09-11 | 济南大学 | A kind of computational methods of RV retarders transmission efficiency |
| CN108563831A (en) * | 2018-03-16 | 2018-09-21 | 浙江工业大学 | Optimization method for transmission precision of RV reducer |
-
2018
- 2018-10-30 CN CN201811280759.4A patent/CN109376439B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2007298458A (en) * | 2006-05-02 | 2007-11-15 | Ntn Corp | Dynamic analytical method for rolling bearing under planetary motion |
| CN104091007A (en) * | 2014-07-01 | 2014-10-08 | 重庆工商职业学院 | Small tooth difference planetary reducer dynamic simulation analysis method |
| CN108253115A (en) * | 2017-12-11 | 2018-07-06 | 广州市昊志机电股份有限公司 | A kind of method that the form of cycloidal gear tooth is obtained based on pinwheel tooth profiling quantity |
| CN108563831A (en) * | 2018-03-16 | 2018-09-21 | 浙江工业大学 | Optimization method for transmission precision of RV reducer |
| CN108520159A (en) * | 2018-04-28 | 2018-09-11 | 济南大学 | A kind of computational methods of RV retarders transmission efficiency |
Non-Patent Citations (2)
| Title |
|---|
| RV传动的效率及其受力分析;何卫东 等;《大连铁道学院学报》;19930331;第13卷(第1期);第73-78页 * |
| RV减速器静力学与动力学研究;陈川;《中国博士学位论文全文数据库工程科技Ⅱ辑》;20180915(第09期);正文第13-25页 * |
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