CN102022426A - Method for improving running performance of rolling bearing - Google Patents

Abstract

The invention discloses a method for improving running performance of a rolling bearing. The method comprises the following steps of: (1) primarily selecting basic parameters of the rolling bearing: determining the number of rolling bodies and the ripple number of a roller way; and (2) analyzing integral stress and integral vibration effect of the rolling bearing, and then selecting the bearing according to the specific requirement of an application situation: defining a phase tuning factor ko = mod (loNw/Nr), wherein in the formula, ko is the phase tuning factor, lo is harmonic order number of excitation frequency, Nr is the number of the rolling bodies, and Nw is the ripple number of the roller way. When the ripple number of the roller way is relatively prime with the number of the rolling bodies, if the phase tuning factor ko is equal to 2, 3, 4...Nr-2, the system is in a stress balance state; and when the maximum common factor of the ripple number of the roller way and the number of the rolling bodies is 2, 3, 4...Nr-2, if the ko is equal to Q, Q+1...Qr-Q, the system is to be in a stress balance state. The method can realize reasonable matching the basic parameters of the bearing, further realizes vibration absorption and noise reduction, and improves the running precision.

Description

Improve the method for rolling bearing runnability

Technical field

The present invention relates to a kind of method that reduces vibration and noise, be specifically related to a kind of method that reduces bearing vibration and noise.

Background technique

As far back as nineteen fifty, China just begins to build bearing industry, through semicentennial development, has formed the production and the technical system of comparison system, becomes the world Production of bearing big country of rank after Japan, the U.S. and Germany.

But, to compare with industrially developed country, still there is very big gap in the bearing industry of China.As far back as nineteen fifty-three, Europe is with regard to vibration and noise problem (Yang Xiaowei, external noise-free bearing technical development, bearing, 2002 (4): 31-34) of the rolling bearing that begins one's study.Japan has researched and developed quiet and super-silent bearing, and the bear vibration level of China is usually than more than the high 10dB of japanese product.And, abroad begin one's study already and use " not reproducible beating " this meticulous running accuracy index, and China is still blank in the research aspect this.

In the index of various measurement bearing qualities, vibration noise is a key technical index.For example in the computer hard drive system, the non-repeatability vibration that is produced by rolling bearing is one of major obstacle that limits its performance boost.As everyone knows, the surface characteristics that the bearing manufacture process forms is one of principal element that causes vibration noise, and correspondingly, the waviness of bearing and rolling element number just become two important basic parameters of decision vibration noise characteristic.Forefathers have studied vibration force and the vibration frequency problem that comes from waviness.Document (Yhland, E.M., 1967, Waviness Measurement-An Instrument for QualityControl in Rolling Bearing Industry, Proe.IMechE, 182, Part 3K, pp.438-445) reported the ripple number variation produced axially and the radial vibration frequency.Document (Takayuki Miyagawa, Fujisawa-shi, etc.Rolling bearing, US Patent 2003/0198415A1) has provided relation between ripple number and the vibration frequency, and is as described in Table 1.

Table 1 ripple number and vibration frequency relation (Hz)

In the table: the n-positive integer; Z-rolling element number; f _i-inner ring rotational frequency; f _e-retainer rotational frequency; f _b-rolling element rotation frequency; f _b=f _i-f _e

Document (Wardle, F.P., and Poon, S.Y., 1983, Rolling Bearing Noise, Cause and Cure, Chart.Mech Engineering, July/Aug, pp.36-40) studied the relation of rolling element number and ripple number, thought when rolling element number and ripple number are complementary, will produce serious vibration.Document (Wardle, F.P., 1988, Vibration Forces Producedby Waviness of the Rolling Srufaces of Thrust Loaded Ball Bearing, Part1:Theory, Proe.IMechE, 202, No.C5, pp.305-312) and (Wardle, F.P., 1988, Vibration Forces Produced by Waviness of theRolling Srufaces of Thrust Loaded Ball Bearing, Part2:Experimental Validation, Proe.IMechE, 202, No.C5 pp.313-319) has also studied the relation of ripple number and excitation force.Should be noted that, although document (Yhland, E.M., 1967, Waviness Measurement-An Instrument for Quality Control in Rolling BearingIndustry, Proe.IMechE, 182, Part 3K is pp.438-445) with (Takayuki Miyagawa, Fujisawa-shi, etc.Rolling bearing, US Patent 2003/0198415A1) has studied relation between ripple number and the vibration frequency, but does not provide the relation between parameters such as ripple number and rolling element number and vibration mode and the noise characteristic.Document (Wardle, F.P., andPoon, S.Y., 1983, Rolling Bearing Noise, Cause and Cure, Chart.Mech Engineering, July/Aug, pp.36-40, Wardle, F.P., 1988, Vibration Forces Produced by Waviness of the Rolling Srufaces ofThrust Loaded Ball Bearing, Part1:Theory, Proe.IMechE, 202, No.C5, pp.305-312, Wardle, F.P., 1988, Vibration Forces Produced by Waviness of the Rolling Srufaces of Thrust Loaded BallBearing, Part2:Experimental Validation, Proe.IMechE, 202, No.C5, pp.313-319) studied the rolling element number, relation between ripple number and the excitation force, but can't explain the vibration characteristics of rolling bearing well.In addition, document (G.H.Jang, S.W.Jeong, Nonlinear Excitation Model of Ball Bearing Waviness in a Rigid RotorSupported by Two or More Ball Bearings Considering Five Degrees of Freedom, Transactions ofthe ASME, 2002,124 (1): 82-90) also proposed a non-linear five degree of freedom model, and the adopted numerical Method Research vibration problem of bearing arrangement, especially the side frequency phenomenon that causes by non-linear factor.Document (Shoji Noguchi, KyosukeOno, Reduction of NRRO in Ball Bearings for HDD Spindle Motors, Precision Engineering, 2004,28:409-418) studied the influence that inside and outside raceway, rolling element error and rolling element number are beated to non-repeatability, obtained many useful conclusions, also analyzed the rolling element radial symmetric and distributed the influence of bearing performance.

In sum, because rolling bearing is not simple and mechanical parts in general sense, it is a kind of engineering goods that enrich technical connotation that comprised.How mate rationally, easily aspect ripple number and the rolling element number, still have following technical barrier:

(1) existing document has only provided the relation between bearing ripple number or rolling element number and the vibration frequency, do not provide the relation between the stressed of above-mentioned parameter and bearing and the vibration noise characteristic, thereby, can't use the design of the low vibration of existing theoretical direction noise-free bearing; (2) because the application difference of rolling bearing, therefore, be difficult for providing the ripple number with general directive significance and the selection principle of rolling element number, therefore, prior art is still rule of thumb carried out auxiliary judgment to the coupling of two parameters.

Summary of the invention

The objective of the invention is to overcome the deficiencies in the prior art, a kind of method of improving the rolling bearing runnability that realizes vibration and noise reducing and help to improve running accuracy is provided.

A kind of method of improving the rolling bearing runnability of the present invention, it may further comprise the steps:

(1) basic parameter of primary election rolling bearing: comprise and determine rolling element number and raceway ripple number, described rolling element number is not less than 7, and described raceway ripple number is not less than 2, and described rolling element number and described ripple number can combination in any;

(2) according to the whole stressed and body vibration effect of following step analysis rolling bearing, choose bearing according to the specific requirement of application then: definition phase place tuning factor k _o=mod (l _oN _w/ N _r), k in the formula _oBe phase place tuning factor, l _oBe the harmonic order of energizing frequency, N _rBe rolling element number, N _wBe raceway ripple number, when raceway ripple number is any positive integer times of rolling element number, if described phase place tuning factor k _o=0, will evoke torsional vibration; When raceway ripple number and rolling element number are relatively prime, if described phase place tuning factor k _o=1 or N _r-1, will evoke translational vibration, if described phase place tuning factor k _o=0, will evoke torsional vibration, if described phase place tuning factor k _o=2,3,4 ..., N _r-2, then system is in the stress balance state; When the greatest common factor (G.C.F.) of raceway ripple number and rolling element number is 2,3,4 ..., N _r-2 o'clock, if described phase place tuning factor k _o=0, will evoke torsional vibration, if k _o=Q, Q+1 ... N _r-Q, system will be in the stress balance state, and Q is the greatest common factor (G.C.F.) of raceway ripple number and rolling element number in the formula.

Adopt the beneficial effect of the inventive method to be: can be implemented in the design phase estimates the vibration and the noise characteristic of rolling bearing, perhaps instructs the dynamic characteristic optimal design of bearing in view of the above.In addition, the different vibrational modes of bearing centre member will influence its noise and running accuracy, therefore, can adopt this method to realize the rational Match of bearing basic parameter, and then realize vibration and noise reducing and improve running accuracy.

Description of drawings

Accompanying drawing is the structure and the stressed schematic representation of rolling bearing.

Embodiment

Below in conjunction with specific embodiment and with reference to accompanying drawing, the present invention is described further:

A kind of method of improving the rolling bearing runnability of the present invention, it may further comprise the steps: the basic parameter of (1) primary election rolling bearing: comprise and determine rolling element number and raceway ripple number, described rolling element number is not less than 7, described raceway ripple number is not less than 2, and described rolling element number and described ripple number can combination in any; (2) according to the whole stressed and body vibration effect of following step analysis rolling bearing, choose bearing according to the specific requirement of application then: definition phase place tuning factor k _o=mod (l _oN _w/ N _r), k in the formula _oBe phase place tuning factor, l _oBe the harmonic order of energizing frequency, N _rBe rolling element number, N _wBe raceway ripple number, when raceway ripple number is any positive integer times of rolling element number, if described phase place tuning factor k _o=0, will evoke torsional vibration; When raceway ripple number and rolling element number are relatively prime, if described phase place tuning factor k _o=1 or N _r-1, will evoke translational vibration, if described phase place tuning factor k _o=0, will evoke torsional vibration, if described phase place tuning factor k _o=2,3,4 ..., N _r-2, then system is in the stress balance state; When the greatest common factor (G.C.F.) of raceway ripple number and rolling element number is 2,3,4 ..., N _r-2 o'clock, if described phase place tuning factor k _o=0, will evoke torsional vibration, if k _o=Q, Q+1 ... N _r-Q, system will be in the stress balance state, and Q is the greatest common factor (G.C.F.) of raceway ripple number and rolling element number in the formula.

Preferred described rolling element number is selected from 7,8,9,10,11,12,13,14, in 15,16,17,18,19 or 20 one, described raceway ripple number is selected from 2,3,4, in 5,6,7,8,9,10,11 or 12 one, and described rolling element number and described raceway ripple number are relatively prime.

Below in conjunction with accompanying drawing is example with the rolling bearing, the relation between the dynamics of announcement ripple number and rolling element number and bearing.In the accompanying drawing

With

Be respectively the tangential and radial component of i rolling element and outer ring contact force, ψ _OiIt is the mechanical location angle of i rolling element and x axle forward.

Suppose N _wBe ripple number, ω ₀Be the retainer rotating speed, then the energizing frequency of Mechanical Contact power

ω _t＝N _wω ₀ (1)

Suppose that first rolling element is positioned at x axle forward, its mechanical location angle is zero, if the rolling element number is N _r, then i (i=1,2 ..., the Nr) angle of individual rolling element and x axle forward

ψ _oi＝2π(i-1)/N _r (2)

When retainer rotates a circle, will finish an Energizing cycle, so the phase difference between the rolling element is

α _r＝2πN _w/N _r (3)

The initial phase of supposing first rolling element that is positioned at x axle forward is zero, and then the phase place that can get i rolling element by formula (2) and formula (3) is

φ _oi＝N _wψ _oi (4)

Then the outer ring along the x direction make a concerted effort be

$F_{\mathrm{ox}}=\underset{i=1}{\overset{N_r}{\mathrm{\Σ}}}(F_{\mathrm{ot}}^i\sin {\mathrm{\ψ}}_{\mathrm{oi}}+F_{\mathrm{or}}^i\cos {\mathrm{\ψ}}_{\mathrm{oi}})---\left(5\right)$

The tangential force and the radial force of i position are decomposed into fourier series, can get

$F_{\mathrm{ot}}^i=\underset{l_o=0}{\overset{\∞}{\mathrm{\Σ}}}\left\{a_i^{l_o}\sin \right[l_o({\mathrm{\ω}}_{t}t+{\mathrm{\φ}}_{\mathrm{oi}})]+b_i^{l_o}\cos [l_o({\mathrm{\ω}}_{t}t+{\mathrm{\φ}}_{\mathrm{oi}})\left]\right\}---\left(6\right)$

$F_{\mathrm{or}}^i=\underset{l_o=0}{\overset{\∞}{\mathrm{\Σ}}}\left\{c_i^{l_o}\sin \right[l_o({\mathrm{\ω}}_{t}t+{\mathrm{\φ}}_{\mathrm{oi}})]+d_i^{l_o}\cos [l_o({\mathrm{\ω}}_{t}t+{\mathrm{\φ}}_{\mathrm{oi}})\left]\right\}---\left(7\right)$

In the formula

With

Be respectively l _oThe fourier coefficient of order harmonics power.The l that can make a concerted effort by formula (5), formula (6) and formula (7) _oThe order harmonics coefficient is

$F_{\mathrm{ox}}^{l_o}=\underset{i=1}{\overset{N_r}{\mathrm{\Σ}}}\left(a_i^{l_o}\sin \right[l_o({\mathrm{\ω}}_{t}t+{\mathrm{\φ}}_{\mathrm{oi}})]\sin {\mathrm{\ψ}}_{\mathrm{oi}}+b_i^{l_o}\cos [l_o({\mathrm{\ω}}_{t}t+{\mathrm{\φ}}_{\mathrm{oi}})]\sin {\mathrm{\ψ}}_{\mathrm{oi}}$ (8)

$+c_i^{l_o}\sin \left[l_o({\mathrm{\ω}}_{t}t+{\mathrm{\φ}}_{\mathrm{oi}})\right]\cos {\mathrm{\ψ}}_{\mathrm{oi}}+d_i^{l_o}\cos \left[l_o({\mathrm{\ω}}_{t}t+{\mathrm{\φ}}_{\mathrm{oi}})\right]\cos {\mathrm{\ψ}}_{\mathrm{oi}})$

Defining factor k _o

k _o＝mod(l _oN _w/N _r) (9)

Mod in the formula (a/b) is the remainder of round numbers a and b.

According to the computation performance of trigonometric function, by formula (8) and formula (9) as can be known, if k _o=1, then

$F_{\mathrm{ox}}^{l_o}=\frac{N_r^2}{2}[(a^{l_o}+d^{l_o})\cos l_o{\mathrm{\ω}}_{t}t+(c^{l_o}-b^{l_o})\sin l_o{\mathrm{\ω}}_{t}t]---\left(10\right)$

If k _o=N _r-1, then

$F_{\mathrm{ox}}^{l_o}=\frac{N_r^2}{2}[({-a}^{l_o}+d^{l_o})\cos l_o{\mathrm{\ω}}_{t}t+(c^{l_o}+b^{l_o})\sin l_o{\mathrm{\ω}}_{t}t]---\left(11\right)$

If k _o≠ 1 or Nr-1, then

$F_{\mathrm{ox}}^{l_o}=0---\left(12\right)$

If the equivalent redius of known outer ring is R _o, the resultant moment of force that then acts on the outer ring is

$T_o=R_o\underset{i=1}{\overset{N_r}{\mathrm{\Σ}}}{F}_{\mathrm{ot}}^i---\left(13\right)$

By formula (2), formula (4), formula (6) and formula (13), the l of resultant moment of force _gOrder harmonics is

$T_o^{l_o}=R_o\underset{i=1}{\overset{N_r}{\mathrm{\Σ}}}\left(\right[a_i^{l_o}\cos \frac{2\mathrm{\π}(i-1)k_o}{N_r}-b_i^{l_o}\sin \frac{2\mathrm{\π}(i-1)k_o}{N_r}]\sin l_o{\mathrm{\ω}}_{t}t$ (14)

$+[a_i^{l_o}\sin \frac{2\mathrm{\π}(i-1)k_o}{N_r}+b_i^{l_o}\sin \frac{2\mathrm{\π}(i-1)k_o}{N_r}]\cos l_o{\mathrm{\ω}}_{t}t)$

If k _o≠ 0, then

$T_o^{l_o}=0---\left(15\right)$

If k _o=0, then

$T_o^{l_o}=R_o{N}_r{a}^{l_o}\sin l_o{\mathrm{\ω}}_{t}t---\left(16\right)$

In fact, ripple number and rolling element number can be odd number or even number, suppose

Q＝GCD(N _w，N _r) (17)

GCD in the formula (a, b) greatest common factor (G.C.F.) for getting a and b.

Can get by formula (9) and formula (17)

k ₀＝mod[l _oQN′ _w/(QN′ _r)] (18)

N ' in the formula _wAnd N ' _rRelatively prime.Can get according to formula (18)

k _o＝Qmod(l _oN′ _w/N′ _r) (19)

Defined variable

k′ _o＝mod(l _oN′ _w/N′ _r) (20)

Therefore

k′ _o∈[1，N′ _r-1] (21)

According to formula (19) and formula (21)

k _o＝Qk′ _o∈[Q，Q(N′ _r-1)] (22)

With

QN′ _r＝N _r (23)

Can get according to formula (21) and formula (23):

k _o∈[Q，N _r-Q] (24)

Formula (24) is ripple number and the common factor of rolling element number and the relation between its remainder of rolling bearing.

Mapping relations between the dynamic characteristic of table 2 ripple number and rolling element number and bearing

As shown in Table 2,, will evoke the torsional vibration of central component, therefore, can curb, promptly only evoke torsional vibration by the transverse vibration of this parameter selection mode with central component if the ripple number can be divided exactly by the rolling element number.According to the sound principle of shaking, compare with torsional vibration, the easier supporting structure that reaches of transverse vibration, and then give off noise, therefore if consider from the noise reduction angle, the parameter scheme that the present invention recommends the ripple number to be divided exactly by the rolling element number.And, if greater than 1, then there is not transverse vibration in the common factor of ripple number and rolling element number this moment, be very beneficial for noise reduction.Be without loss of generality, suppose that the ripple number is 2～12, the rolling element number is 7～20, harmonic order l _o=1～5, can get the vibration characteristics of bearing according to table 2 at each order harmonics place, as described in Table 3.

In addition, according to table 2 as can be known, adopt the inventive method to can also be used to improving the precision of rolling bearing.If the bearing application is to located lateral precision sensitivity, then can select to suppress the parameter selection mode of translational motion, for example make the ripple number be divided exactly, or the common factor that makes the two then can suppress the central component translational motion error that is caused by waviness this moment greater than 1 by the rolling element number.In like manner,, then can make ripple number and rolling element number relatively prime, guaranteeing the suppressing circumferential movement error, and then improve circumferential Location accuracy if the application is to circumferential Location accuracy sensitivity.In order to prove the beneficial effect of the method for the invention, now provide document (Shoji Noguchi, Kyosuke Ono, Reduction of NRRO in Ball Bearings for HDD Spindle Motors, Precision Engineering, 2004, the 28:409-418) result's (table 4) in.By table 2 and table 4 as can be known, the method for the invention possesses the effect that improves the rolling bearing running accuracy.

Mapping relations between table 3 ripple number and rolling element number and the bearing vibration characteristic

Annotate: N _w---the ripple number; N _r---the rolling element number; l _o---harmonic order; R---torsional vibration; T---translational vibration; B---stress balance.

Mapping relations (nm) between table 4 rolling bearing ripple number and rolling element number and maximum non-repeatability are beated

Annotate: digital " 0 " represents that numerical value is less than 1nm in the table.

Although the objective for implementation of described method is described rolling bearing, according to structure and stressed symmetry properties as can be known, described method possesses versatility, can be used to analyze and solve the vibration noise and the running accuracy problem of other types of bearings.

Claims (2)

1. method of improving the rolling bearing runnability is characterized in that it may further comprise the steps:

(1) basic parameter of primary election rolling bearing: comprise and determine rolling element number and raceway ripple number, described rolling element number is not less than 7, and described raceway ripple number is not less than 2, and described rolling element number and described ripple number can combination in any;

(2) according to the whole stressed and body vibration effect of following step analysis rolling bearing, choose bearing according to the specific requirement of application then: definition phase place tuning factor k _o=mod (l _oN _w/ N _r), k in the formula _oBe phase place tuning factor, l _oBe the harmonic order of energizing frequency, N _rBe rolling element number, N _wBe raceway ripple number, when raceway ripple number is any positive integer times of rolling element number, if described phase place tuning factor k _o=0, will evoke torsional vibration; When raceway ripple number and rolling element number are relatively prime, if described phase place tuning factor k _o=1 or N _r-1, will evoke translational vibration, if described phase place tuning factor k _o=0, will evoke torsional vibration, if described phase place tuning factor k _o=2,3,4 ..., N _r-2, then system is in the stress balance state; When the greatest common factor (G.C.F.) of raceway ripple number and rolling element number is 2,3,4 ..., N _r-2 o'clock, if described phase place tuning factor k _o=0, will evoke torsional vibration, if k _o=Q, Q+1 ... N _r-Q, system will be in the stress balance state, and Q is the greatest common factor (G.C.F.) of raceway ripple number and rolling element number in the formula.

2. the method that is used to reduce the bearing vibration noise and improves running accuracy according to claim 1, it is characterized in that: described rolling element number is selected from 7,8,9,10,11,12,13,14,15,16,17,18, in 19 or 20 one, described raceway ripple number is selected from 2,3,4,5,6,7,8, in 9,10,11 or 12 one, and described rolling element number and described raceway ripple number are relatively prime.

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