CN106286740B - The rigidity that a kind of double nut gasket pre-tightens screw pair determines method - Google Patents
The rigidity that a kind of double nut gasket pre-tightens screw pair determines method Download PDFInfo
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- CN106286740B CN106286740B CN201610855581.6A CN201610855581A CN106286740B CN 106286740 B CN106286740 B CN 106286740B CN 201610855581 A CN201610855581 A CN 201610855581A CN 106286740 B CN106286740 B CN 106286740B
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16H—GEARING
- F16H25/00—Gearings comprising primarily only cams, cam-followers and screw-and-nut mechanisms
- F16H25/18—Gearings comprising primarily only cams, cam-followers and screw-and-nut mechanisms for conveying or interconverting oscillating or reciprocating motions
- F16H25/20—Screw mechanisms
- F16H25/22—Screw mechanisms with balls, rollers, or similar members between the co-operating parts; Elements essential to the use of such members
- F16H25/2204—Screw mechanisms with balls, rollers, or similar members between the co-operating parts; Elements essential to the use of such members with balls
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/17—Mechanical parametric or variational design
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Abstract
The present invention discloses a kind of rigidity of double nut gasket preload screw pair and determines method, includes the following steps：Step 1, the studied double nut gasket of structure pre-tighten screw pair axial rigidity and other respectively to the physical mappings relationship of rigidity；Step 2 determines that the double nut gasket pre-tightens the axial rigidity of screw pair according to product technology handbook, determines other respectively to rigidity respectively to the physical mappings relationship of rigidity with other based on its axial rigidity.The rigidity of the present invention determines that method considers axial rigidity with other respectively to rigidity simultaneously, and it is calculated by physical mappings relation pair rigidity numerical value, solution procedure avoids the introducing of many preferable assumed conditions and correction factor, and calculating is at low cost, and calculating process is simple.
Description
Technical field
The present invention relates to a kind of rigidity of screw pair to determine method, and more particularly to a kind of double nut gasket pre-tightens leading screw
The rigidity of pair of nut determines method.
Background technology
Screw pair is also referred to as ball guide screw nat, ball screw pair, can be by the rotary motion of machinery
Be converted into translational motion, due to it with relatively high rigidity, load disturbance sensibility is low, transmission efficiency, fever are small, resistance to
Abrasion, the advantages that service life is long, all the time, screw pair is widely used in various industrial equipments, precision instrument, essence
Close numerically-controlled machine tool etc..
To prevent ball in screw pair from sliding, the gap between the lead screw and screw nut is eliminated, the carrying for improving screw pair is firm
Degree, need to pre-tighten screw pair, wherein double nut gasket pre-tighten screw pair be common form therein it
One.
Rigidity Research around double nut gasket preload screw pair is always the emphasis of domestic and international correlative study.In recent years
Come, numerous domestic and foreign scholars solve the rigidity of screw pair, model and studied with mechanical property.Comprehensive existing correlation is ground
Study carefully, the rigidity that screw pair is pre-tightened to double nut gasket determines to be divided into three classes：The first kind：Based on product technology handbook,
It directly obtains double nut gasket and pre-tightens the rigidity of screw pair, and then its mechanical property is studied；Second class：Based on bullet
Property mechanical foundation and Hertzian contact theory, the rigidity that double nut gasket pre-tightens screw pair is calculated；Third class：Using phase
Mechanical property tests test equipment, the comprehensive mechanical property theory of testing are closed, test obtains its rigidity.
Due to often only providing its axial rigidity in screw pair product technology handbook, by first kind method without
Method obtain screw pair other respectively to rigidity.In the correlative study of the second class method, researcher increasingly focuses on
The calculating solution of its axial rigidity has ignored other respectively to Rigidity Calculation, and other of screw pair are respectively to rigidity equally to it
Performance, mechanical property have an important influence on, and solve the Hertzian contact theory used and are based on many preferable assumed conditions, real
Border situation is commonly present to be assumed not being inconsistent with ideal, computational accuracy will certainly be caused to reduce, and its many corrects of solution calculating introducing is
Number needs to table look-up, and calculating process complexity is cumbersome.Rigidity is tested by laboratory apparatus in third class method, operation is relatively multiple
Miscellaneous, time and expense cost are higher.
In addition, the document that applicant publishes《Dynamic Characteristic Study of Ball Screw
Feed Drive Systems Based on Multi flexible Body Model》(document is hereinafter referred to as text
The rigidity for pre-tightening screw pair in offering 1) only for 4 interference is solved, it is determined that 4 interference pre-tighten screw pair
Axial rigidity and other respectively to the physical mappings relationship of rigidity：
Axial rigidity k1：
In formula：Z is total rolling-operation ball number, can write z=iz1(i is the number of effective coils of ball-screw vice president；z1
For the rolling-operation ball number in individual pen, and(d0For the nominal diameter of ball-screw, dbIt is straight for single ball
Diameter),For the helix angle of leading screw, pressure angle when β is ball and raceway contact, kxIt is single ball along lead screw shaft axis
Axial rigidity, knFor directional stiffness of the single ball along its Contact normal direction.
Radial rigidity k2：
Torsion stiffness k4：
Bending stiffness k6：
In formula：L is ball-screw Contact Pair length.
Summary, it can be seen that at present double nut gasket pre-tighten screw pair rigidity numerical value determine method exist with
Lower problem：It pays close attention to its axial rigidity more and deficiency respectively is considered to rigidity to other；The basic theories of use, which calculates solution formula, to be existed
It is many preferable it is assumed that and introducing more correction factor needs and tabling look-up and cause calculating process complicated；And when using experiment test pair
Between and expense cost it is more demanding and complicated for operation.
Invention content
Goal of the invention：It is an object of the invention to be directed to problems of the prior art, a kind of double nut gasket is provided
The rigidity for pre-tightening screw pair determines method.
Technical solution：The rigidity that a kind of double nut gasket of the present invention pre-tightens screw pair determines method, including
Following steps：
Step 1, the studied double nut gasket of structure pre-tighten screw pair axial rigidity and other respectively to rigidity
Physical mappings relationship；
Step 2 determines that the double nut gasket pre-tightens the axial rigidity of screw pair according to product technology handbook, is based on
Its axial rigidity, respectively to the physical mappings relationship of rigidity, determines other respectively to rigidity with other.
In above-mentioned steps one, contact angular direction characterization is primarily based on, feed screw nut is pre-tightened to the double nut gasket studied
Pair carries out simplified characterization, simulates its simplified model under 4 interference firmly beforehand means；Then leading screw is pre-tightened according to 4 interference
Pair of nut rigidity mapping relations, determine studied double nut gasket pre-tighten screw pair axial rigidity and other respectively to firm
The physical mappings relationship of degree.
Specifically, step 1 includes the following steps：
Step 11, based on contact angular direction characterization, the letter that studied double nut gasket pre-tightens screw pair is first built
Change model one, then structure is in contact with it the opposite double nut gasket in angular direction and pre-tightens screw pair simplified model two；
Step 12, above-mentioned two simplified model is superimposed and synthesized, the screw pair simplified model after synthesis is equivalent to institute
The double nut gasket of research pre-tightens simplified model of the screw pair under 4 interference firmly beforehand means；
Step 13, screw pair rigidity mapping relations are pre-tightened according to 4 interference, determines the screw pair after synthesis
Axial rigidity and other respectively to the physical mappings relationship of rigidity；
Step 14, based on rigidity principle of stacking, determine that studied double nut gasket pre-tightens screw pair respectively to rigidity
With the screw pair after synthesis respectively to the proportionate relationship of rigidity, determine that studied double nut gasket is pre- according to the proportionate relationship
The axial rigidity of tight screw pair is with other respectively to the physical mappings relationship of rigidity.
In above-mentioned steps 13, the axial rigidity of the screw pair after synthesis is with other respectively to the physical mappings relationship of rigidity
It is represented by following characteristics equation：
In formula：k1 is total、k2 is total、k4 is total、k6 is totalThe axial rigidity of screw pair after respectively synthesizing, radial rigidity, torsion are firm
Degree, bending stiffness, d0For the nominal diameter of ball-screw,For the helix angle of leading screw, β is ball and pressure during raceway contact
Power angle, l be ball-screw Contact Pair length, ldFor gasket length, i is the number of effective coils of ball.
In above-mentioned steps 14, the double nut gasket screw pair studied is pre- in Changeable Lead firmly beforehand means and 4 interference
It is to the proportionate relationship of rigidity respectively under tight mode：
In formula：k1 point、k2 points、k4 points、k6 pointsThe double nut gasket respectively studied pre-tighten screw pair axial rigidity,
Radial rigidity, torsion stiffness and bending stiffness.
In above-mentioned steps 14, the axial rigidity of double nut gasket preload screw pair studied is with other respectively to rigidity
Physical mappings relationship represented by following characteristics equation：
Advantageous effect：Compared with prior art, it is an advantage of the current invention that the present invention is according to 4 Interference contact leading screw spiral shells
Female pair rigidity mapping relations, determine studied double nut gasket pre-tighten screw pair axial rigidity and other respectively to rigidity
Physical mappings relationship, then by product technology handbook determine double nut gasket pre-tighten screw pair axial rigidity, most
It is determined eventually respectively to rigidity numerical value, while considers axial rigidity with other respectively to rigidity, and it passes through physical mappings relation pair
Rigidity numerical value is calculated, and solution procedure avoids the introducing of many preferable assumed conditions and correction factor, calculates at low cost, meter
Calculation process is simple.
Description of the drawings
Fig. 1 is the structure diagram that double nut gasket pre-tightens screw pair；
Fig. 2 is the signal for the simplified model one that the double nut gasket based on contact angular direction characterization pre-tightens screw pair
Figure；
Fig. 3 pre-tightens screw pair simplification to contact the opposite double nut gasket in angular direction with the screw pair studied
The schematic diagram of model two；
Fig. 4 is the simplified model figure that Fig. 2 is superimposed the screw pair after being synthesized with simplified model obtained by Fig. 3；
Fig. 5 is works as ldDuring equal to 0, the screw pair after the synthesis becomes the simplification that 4 interference pre-tighten screw pair
Illustraton of model；
Fig. 6 is that the bending stiffness of the screw pair after synthesis solves schematic diagram.
Specific embodiment
Technical scheme of the present invention is described further below in conjunction with the accompanying drawings.
The rigidity that a kind of double nut gasket of the present invention pre-tightens screw pair determines method, includes the following steps：
Step 1, the studied double nut gasket of structure pre-tighten screw pair axial rigidity and other respectively to rigidity
Physical mappings relationship；
Specifically, being primarily based on contact angular direction characterization, pre-tightening screw pair to the double nut gasket studied carries out
Simplified characterization simulates its simplified model under 4 interference firmly beforehand means；Then 4 interference pre-tighten according to disclosed in document 1
Screw pair rigidity mapping relations determine that the axial rigidity of studied double nut gasket preload screw pair is each with other
To the physical mappings relationship of rigidity.
Step 2 determines that the double nut gasket pre-tightens the axial rigidity of screw pair according to product technology handbook, is based on
Its axial rigidity, respectively to the physical mappings relationship of rigidity, determines other respectively to rigidity with other.
By taking some double nut gasket pre-tightens screw pair as an example, such as Fig. 1, wherein, 1 is nut, and 2 be ball, and 3 be silk
Thick stick, 4 be gasket；Double nut gasket pre-tighten i.e. between two nuts 1 add in gasket 4, or so two nuts 1 strut, make a left side
The contact angular direction of right two nuts 1 and leading screw 4 on the contrary,
Step 1：Based on contact angular direction characterization, the letter that studied double nut gasket pre-tightens screw pair is first built
Change model one, then structure is in contact with it the opposite double nut gasket in angular direction and pre-tightens screw pair simplified model two；
In Fig. 1~Fig. 4, with " " and "/" symbolic indication or so contact angular direction of two nuts with lead screw shaft；It first passes through
This contact angular direction characterizing method, structure studies the simplified model one of double nut gasket preload screw pair, such as Fig. 2,
Wherein ldFor gasket length；It then proceedes to based on the contact angular direction characterizing method, structure connects with the screw pair studied
The opposite double nut gasket in feeler direction pre-tightens screw pair simplified model two, such as Fig. 3.
Step 12, above-mentioned two simplified model is superimposed and synthesized, the screw pair simplified model after synthesis is equivalent to institute
The double nut gasket of research pre-tightens simplified model of the screw pair under 4 interference firmly beforehand means；
Based on stacking method, the simplified model two of the simplified model one of Fig. 2 and Fig. 3 is synthesized, after being synthesized
Screw pair simplified model, such as Fig. 4, from fig. 4, it can be seen that during the screw pair simplified model after synthesis can be regarded as
Between have gasket length ld4 Interference contact screw pairs.
Step 13, screw pair rigidity mapping relations are pre-tightened according to 4 interference, determines the screw pair after synthesis
Axial rigidity and other respectively to the physical mappings relationship of rigidity；
Axial rigidity, radial rigidity, torsion stiffness, the bending stiffness of screw pair after definition synthesis are respectively k1 is total、
k2 is total、k4 is total、k6 is total.There is length l since the screw pair simplified model after synthesis can be regarded as centred4 interference pre-tighten
Screw pair, therefore 4 interference being referred in document 1 pre-tighten screw pair rigidity mapping relations, after synthesis
The axial rigidity of screw pair is respectively solved with other to the physical mappings relationship of rigidity.
If the total length of the screw pair after the synthesis or so nut and 4 interference pre-tighten screw pair total length
Identical i.e. l is identical, and containing identical ball number of turns etc., and unique difference is to have length among the screw pair after the synthesis
It spends for ldDistance, work as ldDuring equal to 0, then screw pair is identical with 4 interference preload screw pairs after the synthesis,
Such as Fig. 5.
Since screw pair axial rigidity and radial rigidity have been regarded as all working ball axial rigidity and radial direction just
The parallel connection of degree, therefore, ldAxial rigidity and radial rigidity are not interfered with, can be obtained：
Contain identical ball since screw pair or so nut after the synthesis and 4 interference pre-tighten screw pair
The number of turns, it is known that ldAlso torsion stiffness is not interfered with, therefore：
And due to length ldPresence, the rotate to it bending moment arm at center of screw pair is caused to change, because
This is needed to k6 is totalAgain it is solved.Fig. 6 solves schematic diagram for screw pair bending stiffness after synthesis, and in figure, 2 be ball,
3 be leading screw, and O is the bending center of rotation of guilde screw pair, it is assumed that around center O smaller bending corner occurs for ball screw assembly,
Δ γ, by document 1 it is found that being l apart from rotation center distancexA certain ball building ring, generation radial displacement be lxDuring Δ γ,
Its generate bending resistance torque be
By in all working number of turns ball generate total bending stiffness be
Due to having l among the screw pair after synthesisdGasket length, therefore, using formula (9) solve synthesis after
During the bending stiffness of screw pair, the l in formula (9)xIt should be：
Because
Formula (11) is substituted into formula (9) and composite type (5), can be obtained：
Step 14, based on rigidity principle of stacking, determine that studied double nut gasket pre-tightens screw pair respectively to rigidity
With the screw pair after synthesis respectively to the proportionate relationship of rigidity, determine that studied double nut gasket is pre- according to the proportionate relationship
The axial rigidity of tight screw pair is with other respectively to the physical mappings relationship of rigidity.
Since the screw pair after synthesis is to be pre-tightened screw pair by the double nut gasket studied and be in contact with it
The opposite double nut gasket in angular direction pre-tightens screw pair stack combinations and forms, and based on rigidity principle of stacking, can obtain and be studied
Double nut gasket pre-tighten screw pair respectively to rigidity with synthesis after screw pair respectively to the proportionate relationship of rigidity, ratio
Relationship such as the following table 1, where it is assumed that screw pair is respectively numerical value 1 to rigidity after synthesis, double nut gasket pre-tightens screw pair
Respectively to rigidity be synthesis after screw pair respectively to the 1/2 of rigidity.
Double nut gasket that table 1 is studied pre-tighten screw pair respectively to rigidity with synthesize after screw pair respectively to firm
The proportionate relationship of degree
Therefore, the axial rigidity k that double nut gasket pre-tightens screw pair can be obtained1 point, radial rigidity k2 points, torsion stiffness
k4 points, bending stiffness k6 pointsIt is to the proportionate relationship of rigidity respectively with the screw pair after synthesis：
Composite type (6) (7) (12) (13) can finally obtain, and the double nut gasket studied pre-tightens screw pair axial rigidity
k1 pointIt is to the physical mappings relationship of rigidity respectively with other：
Step 2：Inquiry product technology handbook determines that studied double nut gasket pre-tightens the axial rigidity of screw pair
k1 point=9.2 × 108N·m-1, the double nut gasket preload feed screw nut Contact Pair length l=0.105m, gasket length ld=
0.01m, ball and pressure angle β=45 ° during raceway contact, the helix angle of leading screwThe nominal diameter of ball-screw
d0=0.06m, the number of effective coils i=12 of ball substitute into above-mentioned parameter value in formula (14) (15) (16), further each to other
It is solved to rigidity, it is respectively k to finally obtain its radial rigidity, torsion stiffness, bending stiffness2 points=4.657 × 108N·m-1, k4 points=5.13 × 103Ngm/rad, k6 points=1.019 × 106Ngm/rad。
Claims (4)
1. the rigidity that a kind of double nut gasket pre-tightens screw pair determines method, which is characterized in that includes the following steps：
Step 1, the studied double nut gasket of structure pre-tighten screw pair axial rigidity and other respectively to the physics of rigidity
Mapping relations；
In this step, contact angular direction characterization is primarily based on, pre-tightening screw pair to the double nut gasket studied carries out letter
Change characterization, simulate its simplified model under 4 interference firmly beforehand means；Then it is firm to pre-tighten screw pair according to 4 interference
Spend mapping relations, determine studied double nut gasket pre-tighten screw pair axial rigidity and other respectively to the physics of rigidity
Mapping relations；It is as follows：
Step 11, based on contact angular direction characterization, the simplification mould that studied double nut gasket pre-tightens screw pair is first built
Then type one builds and is in contact with it the opposite double nut gasket preload screw pair simplified model two in angular direction；
Step 12, above-mentioned two simplified model is superimposed and synthesized, the screw pair simplified model after synthesis, which is equivalent to, to be studied
Double nut gasket pre-tighten simplified model of the screw pair under 4 interference firmly beforehand means；
Step 13, screw pair rigidity mapping relations are pre-tightened according to 4 interference, determines the axis of the screw pair after synthesis
To rigidity with other respectively to the physical mappings relationship of rigidity；
Step 14, based on rigidity principle of stacking, determine that studied double nut gasket pre-tightens screw pair respectively to rigidity with closing
Screw pair after determines that studied double nut gasket pre-tightens silk respectively to the proportionate relationship of rigidity according to the proportionate relationship
The axial rigidity of thick stick pair of nut is with other respectively to the physical mappings relationship of rigidity；
Step 2 determines that the double nut gasket pre-tightens the axial rigidity of screw pair, based on its axis according to product technology handbook
Determine other respectively to rigidity respectively to the physical mappings relationship of rigidity with other to rigidity.
2. the rigidity that double nut gasket according to claim 1 pre-tightens screw pair determines method, it is characterised in that：Step
In rapid 13, the axial rigidity of the screw pair after the synthesis is with other respectively to the physical mappings relationship of rigidity by following characteristics
Equation represents：
In formula：k1 is total、k2 is total、k4 is total、k6 is totalIt is the axial rigidity of screw pair, radial rigidity, torsion stiffness after respectively synthesizing, curved
Stiffness, d0For the nominal diameter of ball-screw,For the helix angle of leading screw, pressure angle when β is ball and raceway contact, l
For ball-screw Contact Pair length, ldFor gasket length, i is the number of effective coils of ball.
3. the rigidity that double nut gasket according to claim 2 pre-tightens screw pair determines method, which is characterized in that step
In rapid 14, the double nut gasket studied pre-tightens screw pair of the screw pair respectively after rigidity and synthesis respectively to rigidity
Proportionate relationship is：
In formula：k1 point、k2 points、k4 points、k6 pointsThe double nut gasket respectively studied has pre-tightened the axial rigidity of screw pair, radial direction just
Degree, torsion stiffness and bending stiffness.
4. the rigidity that double nut gasket according to claim 3 pre-tightens screw pair determines method, which is characterized in that step
In rapid 14, the axial rigidity of double nut gasket preload screw pair studied is with other respectively to the physical mappings relationship of rigidity
It is represented by following characteristics equation：
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| CN104048828B (en) * | 2014-06-27 | 2016-11-16 | 常州工学院 | The dynamic Stiffness laboratory table of a kind of high-speed ball screw pair and measuring method |
| CN105005673B (en) * | 2015-08-05 | 2018-04-13 | 天津大学 | A kind of complete machine Static stiffness adaptation design method towards lathe Top-Down Design |
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