CN101976292A - Method for acquiring natural frequency of vibration of gear - Google Patents
Method for acquiring natural frequency of vibration of gear Download PDFInfo
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- CN101976292A CN101976292A CN 201010530237 CN201010530237A CN101976292A CN 101976292 A CN101976292 A CN 101976292A CN 201010530237 CN201010530237 CN 201010530237 CN 201010530237 A CN201010530237 A CN 201010530237A CN 101976292 A CN101976292 A CN 101976292A
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Abstract
The invention discloses a method for acquiring natural frequency of vibration of a gear. The method comprises the following steps of: simplifying a gear teeth-free shaft section into a plane consisting of points which are connected in turn; generating a gear without gear teeth by rotating the gear teeth-free shaft section and generating a finite element model; simplifying the gear teeth into a finite element point unit and coupling to the gear without gear teeth; and finally calculating the natural frequency of the vibration of the gear through a finite element computational procedure. The method can realize the calculation of the natural frequency of the vibration of the gear on the premise of not performing three-dimensional geometric modeling on the gear. The data and the consumed time required for calculating the natural frequency of the vibration of the gear by the method are less than those required for calculating the natural frequency of the vibration of the gear by the conventional method under the condition that the same finite element calculating procedure is used; and the method can be applied to a spiral taper gear with complex geographic shape.
Description
Technical field
The present invention relates to a kind of method that obtains the gear vibration natural frequency, be particularly useful for the acquisition of the vibration natural frequency of the spiral bevel gear in aeromotor, the helicopter.
Background technology
Gear is the strength member of transmitting movement and power in the power machine, in the working gear process that rotating speed is higher, transmitted power is bigger vibration very big, need learn vibration natural frequency.At present, the method that existing gear obtains vibration natural frequency is to adopt finite element method, and the 3-D geometric model generation three-dimensional finite element unit by gear adopts finite element program to calculate the vibration natural frequency of gear.This method needs the 3-D geometric model of gear, and it is very big that whole gear is carried out the workload of 3 d geometric modeling.On the other hand, for the spiral bevel gear of widespread use in aeromotor, the helicopter, its gear teeth complex geometry still lacks a kind of method that can obtain the gear vibration natural frequency that does not need gear is carried out 3 d geometric modeling.
Summary of the invention
Technology of the present invention is dealt with problems: overcome the deficiencies in the prior art, a kind of method that obtains the gear vibration natural frequency is provided, this method can obtain the gear vibration natural frequency under the prerequisite of gear not being carried out 3 d geometric modeling, the data that need and the time of consumption should be lacked.
Technical scheme of the present invention is: a kind of method that obtains the gear vibration natural frequency, and performing step is as follows:
(1) the no gear teeth shaft section of gear is represented on the plane that constitutes with the point that connects successively; Described no gear teeth shaft section refers to the remaining shaft section in line deletion back with expression wheel addendum cone, toe, Heel in the gear shaft cross section;
(2) gather the data that calculating needs, comprising: exponent number is calculated in face, bearing type and the requirement at the XY coordinate of the point of the no gear teeth shaft section of expression gear, material properties, gear teeth quality, the number of teeth, bearing place; Described material properties comprises: elastic modulus, Poisson ratio and density; The computing method of described gear teeth quality are: gear teeth quality=gear teeth width * wheel tooth height * gear teeth thickness * density; Described bearing type comprises: ball bearing and axis of a cylinder hold;
(3) set up the finite element model of gear, specific implementation is:
(3.1) set up no gear teeth shaft section;
(3.2) no gear teeth shaft section is generated two-dimensional finite unit unit;
(3.3) will not have gear teeth shaft section and revolve three-sixth turn, generate the not gear of belt wheel tooth around Gear axis;
(3.4) gear to belt wheel tooth not generates the three-dimensional finite element unit;
(3.5) generate the finite element dot element of representing the gear teeth, the quality of finite element dot element equals gear teeth quality, and the number of finite element dot element equals the number of teeth, and all finite element dot elements are evenly distributed on the not gear outside of belt wheel tooth;
(3.6) the finite element dot element with all expression gear teeth is coupled on the gear of belt wheel tooth not; Described coupling specify each expression gear teeth of justice the finite element dot element and and the three-dimensional finite element unit of the gear of its nearest not belt wheel tooth between relative displacement be 0;
(3.7) face to the bearing place imposes restriction, and the method that imposes restriction is: if bearing is a ball bearing, the displacement of face on gear is radial and axial at definition bearing place is 0; Hold if bearing is an axis of a cylinder, the displacement that the face at definition bearing place directly makes progress at gear is 0;
(3.8), finish the finite element model of gear to the finite element model definition material properties of gear;
(4) to the finite element model of gear operation finite element program, to calculate exponent number serve as to finish the criterion calculated whether to reach requirement in the computation process; Described finite element program refers to be used in the common finite element software calculate the program of the vibration natural frequency of finite element model;
(5) from result of finite element, obtain the gear vibration natural frequency that exponent number is calculated in requirement.
The method of setting up no gear teeth shaft section in the described step (3.1) is: the point of the no gear teeth shaft section of gear is represented in generation according to the XY coordinate, will put successively with straight line to connect, and the plane that the definition straight line surrounds is no gear teeth shaft section.
The present invention's beneficial effect compared with prior art is: need carry out 3 d geometric modeling to gear at existing gear vibration calculation method for natural frequencies, and can't be applied to the problem of the spiral bevel gear of gear teeth complex geometry, a kind of Finite Element Method of calculating the gear vibration natural frequency is provided.Using the present invention does not need gear is carried out 3 d geometric modeling, but will there be the plane that gear teeth shaft section is reduced to the some formation that connects successively, the gear teeth are reduced to the finite element dot element, can effectively reduce and set up the data that the gear finite element model needs and the time of consumption.On the other hand, the present invention does not relate to the geometric configuration of the gear teeth, can be applied to the spiral bevel gear of gear teeth complex geometry.Therefore, the present invention is that a kind of energy obtain the gear vibration natural frequency within a short period of time, and the scope of application is wider than existing method.
Description of drawings
Fig. 1 is a method flow diagram of the present invention;
Fig. 2 is the shaft section of gear;
Fig. 3 is the plane that the point of connection successively constitutes;
Fig. 4 is no gear teeth shaft section;
Fig. 5 is the two-dimensional finite unit unit that no gear teeth shaft section is generated;
Fig. 6 is the gear of belt wheel tooth not;
Fig. 7 is the three-dimensional finite element unit that the gear to belt wheel tooth not generates.
Embodiment
Process flow diagram of the present invention as shown in Figure 1.Below in conjunction with accompanying drawing, be example with the process that obtains spiral bevel gear vibration natural frequency in certain model aeromotor, specify the inventive method, the shaft section of this gear is as shown in Figure 2.Among Fig. 2, dot-and-dash line is a Gear axis, and dotted line represents to take turns addendum cone, toe, Heel, and solid line represents not have gear teeth shaft section, and A represents that axis of a cylinder holds the face at place, and B represents the face at ball bearing place.
But protection scope of the present invention is not limited to following embodiment:
(1) the no gear teeth shaft section of gear is represented on the plane that constitutes with the point that connects successively;
The no gear teeth shaft section of gear is represented on the plane that constitutes with 20 points that connect successively, as shown in Figure 3.How many numbers of point determines that the axle ladder is many more according to no gear teeth shaft section axis ladder, and the number of point is many more.To the no gear teeth shaft section that solid line among Fig. 2 is represented, the number of point also can be more than 20 points, all can as 30,40,50 etc.
(2) gather the data that calculating needs, comprising: exponent number is calculated in face, bearing type and the requirement at the XY coordinate of the point of the no gear teeth shaft section of expression gear, material properties, gear teeth quality, the number of teeth, bearing place;
The XY coordinate of 20 points of the no gear teeth shaft section of expression gear is:
Point 1:0,17; Point 2:0,22.5; Point 3:45,22.5; Point 4:45,25; Point 5:63.8,25; Point 6:98.7,25; Point 7:98.7,28; Point 8:106.5,35.5; Point 9:106.5,45.9; Point 10:101.7,52.5; Point 11:101.7,61.2; Point 12:104.6,65.1; Point 13:121.8,53; Point 14:114.5,43.3; Point 15:114.5,21.1; Point 16:113,20.25; Point 17:98.7,20.25; Point 18:63.8,20.25; Point 19:63.8,17; Point 20:45,17;
Material properties is:
Elastic modulus 21000MPa, Poisson ratio 0.4, density 7.86e-9 ton/cubic millimeter;
Gear teeth quality is:
Gear teeth quality=gear teeth width * wheel tooth height * gear teeth thickness * density=21 * 7.5 * 5 * 7.86e-9=0.00000618975 ton;
The number of teeth is: 35;
The face at bearing place is: A face as shown in Figure 3 and B face;
Bearing type is: A represents that axis of a cylinder holds the face at place, and B represents the face at ball bearing place;
Requiring to calculate exponent number is: 20.
(3) set up the finite element model of gear:
1. set up no gear teeth shaft section;
Generate 20 points according to the XY coordinate of gathering in the step (2) in common finite element software, with straight line 20 points are connected successively, define the plane that 20 straight lines surround is no gear teeth shaft section, as shown in Figure 4.
2. no gear teeth shaft section is generated two-dimensional finite unit unit;
In common finite element software, as shown in Figure 4 no gear teeth shaft section is generated two-dimensional finite unit unit, as shown in Figure 5.
3. will not have gear teeth shaft section and revolve three-sixth turn, generate the not gear of belt wheel tooth around Gear axis;
In common finite element software, no gear teeth shaft section is as shown in Figure 4 revolved three-sixth turn around Gear axis, generate the not gear of belt wheel tooth, as shown in Figure 6.
4. the gear to belt wheel tooth not generates the three-dimensional finite element unit;
Gear to as shown in Figure 6 not belt wheel tooth in common finite element software generates the three-dimensional finite element unit, as shown in Figure 7.
5. generate the finite element dot element of the expression gear teeth, the quality of finite element dot element equals gear teeth quality, and the number of finite element dot element equals the number of teeth, and all finite element dot elements are evenly distributed on the not gear outside of belt wheel tooth;
In common finite element software, generate the finite element dot element of the expression gear teeth, the quality of finite element dot element equals 0.00000618975 ton, the number of finite element dot element equals 35, and all finite element dot elements are evenly distributed on the gear outside of not belt wheel tooth as shown in Figure 6.
6. the finite element dot element with all expression gear teeth is coupled on the gear of belt wheel tooth not;
In common finite element software finite element dot element of each expression gear teeth of definition and and the three-dimensional finite element unit of the gear of its nearest not belt wheel tooth between relative displacement be 0.
7. the face to the bearing place imposes restriction;
Therefore face to the bearing place in common finite element software imposes restriction: A as shown in Figure 6 represents that axis of a cylinder holds the face at place, and defining the displacement that the A face directly makes progress at gear is 0; B as shown in Figure 6 represents the face at ball bearing place, and therefore defining the displacement of B face on gear is radial and axial is 0.
8. to the finite element model definition material properties of gear, finish the finite element model of gear;
The material properties of the finite element model of definition gear in common finite element software, definition comprises that the elastic modulus of all finite element unit of two-dimensional finite unit unit, three-dimensional finite element unit, finite element dot element is 21000MPa, Poisson ratio is 0.4, density is 7.86e-9 ton/cubic millimeter, finishes the finite element model of gear.
(4) to the finite element model of gear operation finite element program, to calculate exponent number serve as to finish the criterion calculated whether to reach requirement in the computation process;
In common finite element software, select the finite element model of gear is carried out the finite element program that vibration natural frequency is found the solution; At first select derivation algorithm, in algorithms most in use such as piecemeal Lanezos method, subspace iteration method, "flop-out" method, select piecemeal Lanezos method; Defining the exponent number of finding the solution natural frequency again is 20 rank; Moving finite element program at last and the finite element model of gear is carried out vibration natural frequency find the solution, serves as to finish the criterion calculated whether to reach 20 rank vibration natural frequencies in the computation process.
(5) the gear vibration natural frequency on extraction 20 rank from result of finite element.
In common finite element software, read the result that the operation finite element program obtains, read the gear vibration natural frequency on 20 rank, for: 3485Hz, 3509Hz, 4323Hz, 4450Hz, 4484Hz, 5828Hz, 8043Hz, 8112Hz, 9345Hz, 9354Hz, 12974Hz, 13069Hz, 14271Hz, 14304Hz, 18110Hz, 18448Hz, 18623Hz, 19777Hz, 19807Hz, 21338Hz.
Shaft section gear is as shown in Figure 2 carried out the test of test vibration natural frequency, use the elastic force hammer that gear is carried out Hammering Test, by the frequency domain characteristic of acceleration transducer, data acquisition unit, charge amplifier seizure gear vibration, conversion obtains the gear vibration natural frequency.Owing to the limitation of test method, can't obtain all vibration natural frequencies of gear.Test records gear to be had to the vibration natural frequency in the 5000Hz scope at 100Hz: 3631Hz, 4387Hz, 4511Hz.
As can be seen, the 3631Hz that gear vibration natural frequency 3485Hz, 3509Hz that employing the present invention obtains and test record is approaching, the gear vibration natural frequency 4323Hz that adopts the present invention to obtain is approaching with the 4387Hz that test records, the 4511Hz that gear vibration natural frequency 4450Hz, 4484Hz that employing the present invention obtains and test record is approaching, and the result differs less than 3%, belongs in the acceptable scope of engineering problem.
In a word, the invention provides a kind of Finite Element Method of calculating the gear vibration natural frequency.Using under the same finite element program condition, application the present invention calculates the data of gear vibration natural frequency needs and the time of consumption should be less than existing method.And for the spiral bevel gear of gear teeth complex geometry, the present invention stands good.The present invention is applicable to the application of common engineering problem, and the approach of a new acquisition vibration natural frequency is provided for the gear in the engineering application especially spiral bevel gear.
Claims (2)
1. method that obtains the gear vibration natural frequency is characterized in that performing step is as follows:
(1) the no gear teeth shaft section of gear is represented on the plane that constitutes with the point that connects successively; Described no gear teeth shaft section refers to the remaining shaft section in line deletion back with expression wheel addendum cone, toe, Heel in the gear shaft cross section;
(2) gather the data that calculating needs, comprising: exponent number is calculated in face, bearing type and the requirement at the XY coordinate of the point of the no gear teeth shaft section of expression gear, material properties, gear teeth quality, the number of teeth, bearing place; Described material properties comprises: elastic modulus, Poisson ratio and density; The computing method of described gear teeth quality are: gear teeth quality=gear teeth width * wheel tooth height * gear teeth thickness * density; Described bearing type comprises: ball bearing and axis of a cylinder hold;
(3) set up the finite element model of gear, specific implementation is:
(3.1) set up no gear teeth shaft section;
(3.2) no gear teeth shaft section is generated two-dimensional finite unit unit;
(3.3) will not have gear teeth shaft section and revolve three-sixth turn, generate the not gear of belt wheel tooth around Gear axis;
(3.4) gear to belt wheel tooth not generates the three-dimensional finite element unit;
(3.5) generate the finite element dot element of representing the gear teeth, the quality of finite element dot element equals gear teeth quality, and the number of finite element dot element equals the number of teeth, and all finite element dot elements are evenly distributed on the not gear outside of belt wheel tooth;
(3.6) the finite element dot element with all expression gear teeth is coupled on the gear of belt wheel tooth not; Described coupling specify each expression gear teeth of justice the finite element dot element and and the three-dimensional finite element unit of the gear of its nearest not belt wheel tooth between relative displacement be 0;
(3.7) face to the bearing place imposes restriction, and the method that imposes restriction is: if bearing is a ball bearing, the displacement of face on gear is radial and axial at definition bearing place is 0; Hold if bearing is an axis of a cylinder, the displacement that the face at definition bearing place directly makes progress at gear is 0;
(3.8), finish the finite element model of gear to the finite element model definition material properties of gear;
(4) to the finite element model of gear operation finite element program, to calculate exponent number serve as to finish the criterion calculated whether to reach requirement in the computation process; Described finite element program refers to be used in the common finite element software calculate the program of the vibration natural frequency of finite element model;
(5) from result of finite element, obtain the gear vibration natural frequency that exponent number is calculated in requirement.
2. a kind of method that obtains the gear vibration natural frequency according to claim 1, it is characterized in that: the method for setting up no gear teeth shaft section in the described step (3.1) is: the point that generates the no gear teeth shaft section of expression gear according to the XY coordinate, to put connection successively with straight line, the plane that the definition straight line surrounds is no gear teeth shaft section.
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| CN2010105302372A CN101976292B (en) | 2010-11-03 | 2010-11-03 | Method for acquiring natural frequency of vibration of gear |
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| CN2010105302372A CN101976292B (en) | 2010-11-03 | 2010-11-03 | Method for acquiring natural frequency of vibration of gear |
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| CN101976292B CN101976292B (en) | 2012-06-27 |
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102968537A (en) * | 2012-11-30 | 2013-03-13 | 北京航空航天大学 | Method for analyzing torsional vibration inherent characteristic of planet gear transmission system |
| CN103234751A (en) * | 2013-04-23 | 2013-08-07 | 北京工业大学 | Vibration performance analysis method of cycloidal bevel gear under section gap function |
Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101482430A (en) * | 2008-02-04 | 2009-07-15 | 中信戴卡轮毂制造股份有限公司 | Method for measuring natural frequency of wheel |
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Patent Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101482430A (en) * | 2008-02-04 | 2009-07-15 | 中信戴卡轮毂制造股份有限公司 | Method for measuring natural frequency of wheel |
Non-Patent Citations (1)
| Title |
|---|
| 《华中科技大学学报（自然科学版）》 20051031 饶芳，王延忠等 复杂齿轮自动化及参数化有限元建模 第7-9页 1-2 第33卷, 第10期 2 * |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102968537A (en) * | 2012-11-30 | 2013-03-13 | 北京航空航天大学 | Method for analyzing torsional vibration inherent characteristic of planet gear transmission system |
| CN102968537B (en) * | 2012-11-30 | 2016-01-20 | 北京航空航天大学 | A kind of torsional vibration inherent characteristic of planet gear transmission system analytical approach |
| CN103234751A (en) * | 2013-04-23 | 2013-08-07 | 北京工业大学 | Vibration performance analysis method of cycloidal bevel gear under section gap function |
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