JPS63271124A - Roughness estimating method for surface of rolling element of rolling bearing - Google Patents

Abstract

PURPOSE:To estimate simply, quickly, and also, with high accuracy and quantitatively roughness of the surface of a rolling element of a rolling bearing of an assembly state, by using an observation vibrating signal of one point on a still bearing ring. CONSTITUTION:An outer ring 10 of a hall bearing to be estimated 40 is held in a still state by applying thrust force thereto, and an inner ring 20 is rotated by a prescribed revolution speed. A vibration in an observation point 11 is detected by a vibration sensor 30, and its output is supplied to a digital audio recorder 63 through an amplifier 61 and a high-pass filter 62 and stored. A reproducing signal from this digital audio recorder 63 is inputted to a computer through a low-pass filter 64, a preamplifier 65 and an A/D converter 66, and the surface roughness of a ball of the ball bearing 40 is estimated.

Description

DETAILED DESCRIPTION OF THE INVENTION Field of the Invention The present invention relates to a method for estimating the degree of roughness of the surface of rolling elements of a rolling bearing based on observed vibration signals.

``Kuhoku Ai'' During the manufacturing process of rolling bearings, when cutting and polishing the inner and outer rings and rolling elements, the surfaces of the rolling elements may be scratched or polished insufficiently. Furthermore, even when a rolling bearing is incorporated into a product and is in operation, the surface roughness of the rolling elements may become large due to wear and the like. If a rolling bearing with such a rough rolling element surface is used, for example, in a video table food head or capstan bearing, it will cause a deterioration in image quality during recording and playback, and may also cause problems such as In rolling bearings, this can cause abnormal vibrations. Therefore, for rolling bearings used in this type of applications that require high processing accuracy, all products are inspected after assembly is completed.

As a method for this inspection, the vibration method that observes and analyzes vibrations that occur due to abnormalities such as damage has been widely used. For example, the peak, value, or peak value of the observed signal is A method for determining an abnormality from a time series change in a value divided by an effective value or an average value, and further,
A method has been proposed in which these values are normalized based on the rotational speed and shaft diameter of the rolling bearing, and based on this, the presence or absence of an abnormality is determined.

Problems to be Solved by the Invention However, these methods do not take into account the propagation behavior of vibration between the rolling element surface, which is the source of vibration, and the vibration observation point, and only the vibration signal at the observation point is used. This is to estimate abnormality. Therefore, although it is now possible to estimate the presence or absence of an abnormality, it has been difficult to accurately estimate the degree of roughness on the surface of the rolling element. As a result, pass/fail judges are required to have proficiency backed by many years of testing experience, and as a result, the amount of testing is limited by the number of skilled testers. There was a problem. In addition to this, as an inspection method performed before assembly of a rolling bearing, a method of directly scanning the surface roughness of the raceway surface using a stylus or an optical method is also in practical use.

However, this method cannot be applied to products in operation, and depending on the shape and dimensions of the rolling bearing, it is necessary to cut the parts into a scannable state, making it impossible to inspect all parts, and it takes a lot of time to make a determination. There are other problems.

Means for solving the problem Now, in order to study the behavior between the rolling element and the raceway surface when there is a scratch on the surface of the rotating rolling element, we will examine the location of the scratch on the rolling element on the inner and outer ring raceway surfaces. When the rolling element reaches , the rolling element rotates around one end of the scratch, and then the other end collides with the raceway surface, and this collision generates an impulse. However, it is known that the amplitude of the impulse generated by the lever is proportional to the width of the scratch to the 615th power.

(For example, art supplies, Takahashi “Research on ball bearing sound”, precision machinery 3
Vol. 0, No. 6, pp. 475-489, 1964), then
If the amplitude of this impulse is determined, the width of the scratches on the surface of the rolling element, that is, the degree of roughness of the surface of the rolling element, can be quantitatively determined. However, it is difficult to directly measure this impulse. Therefore, if we focus on the vibration at one point on the stationary raceway ring that can be observed now, this vibration is the natural vibration of the raceway ring or stationary raceway ring that rotates due to the impulse caused by the collision of scratches on the rolling elements. There is an excitation of
This is what has propagated to one point on the stationary orbital ring. Then, the seven actors that relate this impulse and vibration, namely the impulse response of the natural vibration of the bearing ring and the vibration propagation coefficient between the impulse generation position and the vibration observation point, must be determined in advance. The first aspect of the present invention, in which the magnitude of an impulse can be determined from a signal, was devised based on the foregoing. 1 on the other raceway held in the condition
The vibration in the radial direction is observed at a point, and then the measured equivalent driving impulse is calculated based on the observed vibration signal and the impulse response of the known natural frequency of the bearing ring, and each of the vibrations in the circumferential direction of the bearing ring is calculated. Based on the relational expression between the vibration propagation coefficient between the position and the vibration observation point and the estimated equivalent drive impulse estimated from the unknown impulse on the raceway surface of the rotating raceway caused by contact with scratches on the rolling element. The purpose is to calculate the unknown impulse and estimate the width of the flaw on the surface of the rolling element from the impulse. First, to simplify the explanation, we will assume a ball bearing with two balls as modeled in Figure 1, and assume that there is a flaw on the raceway surface rather than on the rolling elements. In Figure 0 explaining the relationship with the observed vibration signal, 10.20 are the inner and outer rings of the ball bearing, α and β are the balls interposed in the outer ring at an angle of π, The inner ring 20 is driven counterclockwise at an angle ω1 with respect to the outer ring 10 held stationary, so that the two balls α and β have an angular velocity ωb.
[=(ωT/2)(1-d/D)・eOsA, here d
: ball diameter, D: pitch diameter, γ: contact angle 1. Now, when the time is tl, balls α and β are inner ring 2
located at points a and b on the orbital surface of 0, and each point a
, Assuming that there are scratches @fc and fb at point b, each ball α and β rotates around one end of each corresponding scratch, collides with the other end, and generates an amplitude proportional to the width of the scratch to the 615th power. 5(a), 5(
b) respectively. The natural vibrations of the bearing ring are excited by each of these impulses, and the sum of these vibrations is transmitted onto the outer ring 10 and observed from one observation point 11 on the outer ring 10 as a vibration signal y(t+). Figure 2 (a) shows the above relationship using symbols, and time 1 =
1. The impulse generated at , which excites the natural vibration, can be expressed as
It is expressed as δ(t-b)-s(b)·δ(1-1,). The caterpillar h(t) is the impulse response of the natural vibration of the bearing ring 20, and W(θ(att, W(θ(βI t, )) is generated by hitting points a and b on the bearing ring 20, respectively. When the propagation coefficient indicates the weight of so-called vibration propagation when the natural vibration driven by an impulse is transmitted to the observation point 11 on the outer ring 10, the following relationship holds true for these openings.

y(t7)=W(θ(α,tI))h(t) Tree 5(a)
δ(t tI) + W (θ (β, shi)) h(t) * 5(b) δ(t-tz) Here, the book uses the trajectory to examine the above Figure 2 (a) representing convolution. The characteristics of the impulse response h(t) of the natural vibration of the ring 20 can be determined from the shape and material of the outer ring 10, and as a result, the impulses 5(a), δ(1-t, ), 5(b)・δ(1-1
Each natural frequency component driven by 0 has the same characteristics except for its amplitude. Therefore, as shown in FIG. 2(b), the observed vibration signal y(t) is arranged in the form of the convolution of the input zDl) that drives the natural vibration, that is, the equivalent drive impulse and the impulse response h(t).

y(t)=h(t) tree z(ti (2
) Furthermore, the estimated equivalent driving impulse estimated using the impulse and propagation coefficient of the model is as follows.

z(shi,)=W(θ(α, tr)) ・5(a)δ(t
-tI)+W(θ(βIt/)) ・5(b)δ(t-
b)=W(θ(αr b))・5(a) +W(θ(β, t/))・5(b) (3) Returning to Figure 1 again, from the state of (a) above, change the inner ring. 20 rotates further, and at the time, ball α reaches point b and ball β reaches point a. The dog relationship holds in the same way as above.

y(tz)=h(t)
(4) z(t,) = W(θ (β, t2)) s(
a) δ(t-b)+W(θ(αT t3)) s
(b) δ(t-tJ=W(θ(βtt2))S
(a) +W(θ(α, t,)) b(b) (5) Here, W(θ(β, t0), W(θ(α, shi)) are the times when the balls β and α are The natural vibration driven by the impulse generated by hitting points a and b on the raceway ring 20 causes the outer ring 1 to
This is a propagation coefficient indicating the weight transmitted to the observation point 11 on 0.

Among the terms in equations (2) to (5) above, ■ Propagation coefficient W (θ (α, b) ) * W (θ (β,
death)).

W(θ(α, t2)), W(θ(βytJt...) can be measured in advance.

■Angular velocity ωI of inner ring 20, revolution angular velocity ωb% of balls α and β
The positions of the balls a and β when t=0 can be determined in advance, and the respective revolution angular velocities of the balls and the raceway at each time are known.

■The impulse response M<t) of the natural vibration can be predicted in advance, and its inverse characteristic h(t) can be determined, and the second h
(t) is observed as a vibration signal y(tz), y(tz),...
By convolving with
z), ... are obtained.

Therefore, the only unknown terms are 5(a) and 5(b). Therefore, by solving equations (3) and (5) simultaneously, exact solutions to impulses 5(a) and 5(b) can be calculated. The width of the scratch can then be determined from 5(a) and 5(b). Note that if random noise is superimposed on the observed vibration signal y(t), it may be difficult to estimate with high accuracy using the exact solution method using equations (3) and (5). In such a case, the observation opportunity for each time when balls a and β come into contact with points a and b on the bearing ring 20, that is, the number of measurements, is increased, and each time t+ (i = 1 t 2 +...P) The accuracy can be improved by applying the least squares method to the relational expression. That is, in the model of FIG. 2(b), there are P times t+(i==i.

The estimated equivalent driving impulse zDi) of 2,...P) is as follows, z(tr)=:W(θ(αvti)) ・5(a)+W
(θ(β, 1+))・5(b)...(When i is an odd number) z(ti)=W(θ(βt ti))・5(a)+W
(θ(α, ti) )・5(b)...(when i is an even number) (6) This and the value 2(ti)( In other words, the inverse characteristic h(t
) is the square of the difference between impulse 5(a
), 5(a) by minimizing with respect to 5(b)
.

The most probable value of 5(b) is obtained.

The above has explained the principle using a ball bearing with two balls as an example to simplify the explanation, but in a rolling bearing in which a plurality of N rolling elements are arranged at equal intervals on the circumference, The above relationship also holds true in the same way. That is, in Fig. 3 (a), 10.20 are the outer and inner rings, respectively, and between the inner and outer rings there are N rolling elements 0°1,...li?・・N
-1 (the figure shows only the cross-sectional view of O and the 1st rolling element) is inserted at an equal angle of 2π/N, and the rolling element O at measurement start time 1 = 0 is relative to observation point 11. It has an initial angle of θ0 in the counterclockwise direction. And each rolling element 0, 1
．． N-1 is caused to revolve at an angular velocity ω0 as the inner ring 20 rotates (angular velocity ω).

5(x) indicates the amplitude of the impulse at position X on the raceway surface of the inner ring 20. 0:θ)
) is occurring. The above symbols represent that in the impulse generated at the position of X, that X is expressed as a function of the rolling element number, time, initial angle, etc. = Rolling elements 0, 1..., i・ for observation point 11 after nTs elapsed
... shows the positional relationship between N-1 and the inner ring 20, and these positions are all expressed as a function of time as follows. That is, now, the position of the i-th rolling element with respect to observation point 11 at time t is expressed as θ(i
, t: θ, ), it becomes θ(iyt:θo)=ω
llt+(2π/N) i+00, and if the position on the inner ring raceway surface that contacts the i-th rolling element at time t is x(i, t: θ0), then x(iyt: θo−)= (ω, -a+,)t+(2π/
N)i+〇0, and as in the case of the rolling bearing of the two rolling elements, the observed vibration signal y(t) at each time.
can be taken out, each position θ (ilt: θ6) and observation point 11
The vibration propagation coefficient W ((θ(i, t: θ, , ))) and the inverse characteristic 5(t) of the impulse response of the natural vibration are calculated in advance by measurement. Therefore, similarly to the above, the propagation coefficient W((θ(i, t:
θ, ))) can be determined, and the stiffness and observed vibration signal (B) and the inverse characteristic of the impulse response h(
t) to obtain the measured equivalent driving impulse z(t)
is determined, and the following relational expression holds.

z(t)=y(t) tree h(L)=z(t:θ)+Δz(
t:θ)・5((x(iyt:θ)) 2z(L): Actual equivalent drive impulse z(t:θo): Estimated equivalent drive impulse Δz(t:θ
o): Difference between the measured equivalent driving impulse and the estimated equivalent driving impulse (...): The remainder when ... is divided by 2π. Therefore, the square of the error between z(t) and z(t:θ,) is minimized. The most probable value of the impulse is determined from the conditions, and the width of the flaw is calculated based on it.

Although the observed vibration signal has been described above as an analog signal t), in actual calculations, it is more convenient to sample it every cycle Ts and process it using the digitized sampling signal y(n). The same is true in this case, and in equations (7) to (9) above, t=nTs(n
is 0°1, . . . integer), and the estimated equivalent drive impulse described by this is z(n:θ0), then it is expressed by the following equation.

z(n:θ0)=,ΣW((a+hnTs+(2π/N
) i + θo)) 2ru・5 (((ω or 1 ω) nTs + 2 to /N) i 10)) υG The above is a case where flaws are found at predetermined intervals on the circumferential surface of the orbit determined by the sampling period Ts. However, if flaws are to be found at certain intervals wider than this, the number of positions where flaws are to be found on the circumference 2π, that is, the number of calculation points, can be expressed as follows.

・s(([y4i, n:θo)])) (11) Here [... Tsukasa: The integer closest to the real number...
2 above [...remainder θ of dividing the bow by M, (11n:θ,):==ωbnTsM/2 yr+
(M/N) i ten. M/2π xJ (i, n: θ,) = (ωb-ωx)nTsM/2'
+(M/N)i+θM/2π In these cases, as in the case of the analog signal, the observed vibration signal y(n) has the inverse characteristic h of the impulse response of the natural vibration.
(n) to obtain the actual measured equivalent driving impulse z(n), which is combined with the above estimated equivalent driving impulse z(n
: θ, ), that is, uni, L: the data length of the interval that minimizes the error is the unknown impulse s(m) at the calculation point [If
l=0.1.2...By calculating the minimum limit θ)/cl s(m)=O(13) with respect to M-11 and solving the resulting linear simultaneous equations (normal equations) s(I+1) will be found.

Note that the impulse calculation described above may be performed in the following manner using vectors and matrices.

In other words, consider two vectors Z and S of M and L dimensions and one LXM matrix W as follows: Z = [z(0), z(1), -, 2(L -1)]
S = [5(0), 5(1)=...=, s(M 1)]
Here, , is the propagation coefficient multiplied by the impulse generated by the i-th ball in nTs, and W(([θ
(n, i: θ, )])).

By rewriting the above equation (12) using these vectors and matrices, the residual power becomes as follows, α(θ)=(Z-WS)(Z-WS) (14) Here, T is Represents the transpose of a matrix. From this and the above equation (13), the following normal equation is derived.

W”WS=W”Z (15)
In this case, the revolution angle at which a point on the inner ring raceway surface contacts the ball changes with time (ωI≠ω卜), and the propagation coefficient is a nonlinear function of the angle. Therefore, if the observation time is longer than the time required for a point on the inner ring raceway to come into contact with the rolling element at least once, the columns of W become linearly independent and the matrix W
There is an inverse matrix of 7W, and the least squares group S regarding scratches can be calculated using vectors and matrices as follows.

s=(wrw)wz (16) Here, we have specifically described the case where the outer ring is held still and the inner ring is rotated, but since the rotational speed of the inner ring is the relative speed between the raceway rings, here The explained principle holds true even when the outer ring and inner ring are reversed.

In order to facilitate understanding of the first invention, the principle has been explained assuming that there are scratches on the raceway itself rather than on the rolling elements. A detailed description of the present invention for estimating flaws will be given below.

In FIG. 4, as in FIG. 3, the angle that the 0th rolling element "O" makes with respect to the vibration observation point 111 at time [0], the angular velocity ωJ of the inner ring 20, and the rolling element "O'',
Let ω be the revolution angular velocity and rotation angular velocity of “1”, . Now, at time t, the angle that the i-th rolling element makes with the vibration observation point 11 is θ(i
, t: θ, ), it is expressed as (01+(2π/N)i 10 as shown in rj>. Among the i-th rolling elements in that state, the inner and outer rings 20 and , the contact points with the orbital surface are ω-1ωt4π, respectively.

Then, the sum of the vibrations excited by contact with both the inner and outer rings is transmitted to the vibration observation point 11. Therefore, the relational expression expressing the estimated drive impulse z (t: θ0) in this case is 5i ((ωat)) + ρ・51( (ωBt-zr))
It is expressed as follows using .

Here, S (...): Position on the surface of the first rolling element (...
): Surface roughness function ρ: Amplitude ratio of the two impulses excited by the collision between the inner and outer rings and the ball. However, in reality, it is difficult to obtain this amplitude ratio ρ, and it is difficult to distinguish between the two impulses. It is also difficult.

Therefore, for 0<x<π, the surface function 83×) defined as follows: i(×)=Sl(X)+ρ・5I((x+2π))
Introduce (18). Accordingly, the above equation (17) can be expressed as follows.

In one or more of the above processes, when there is a scratch on the raceway surface of the rotating raceway, the impulse caused by the collision of the rolling elements only with the raceway surface of the rotating raceway was taken into consideration, whereas the In estimating flaws, two positions separated by π on the rolling element are inside,
The two inseparable impulses that collide with the raceway surface of the outer ring at the same time and are generated as a result of the collision are treated as a sum, and other than that, except for defining this sum impulse as a surface function. The processing is exactly the same for both.

Therefore, in the same way as above, the actually measured equivalent drive impulse hole (1) is calculated by convolving the observed vibration signal y(t) with the inverse characteristic h(t) of the natural vibration, and this and the estimated equivalent drive impulse of equation (19) are calculated. By minimizing the square of the difference between z(t:θ,) and the unknown surface function sr(x), s<(x), which is a function of scratches on the rolling element, is calculated.

Furthermore, although the above is a case in which the observed vibration signal is an analog signal y(t), the observed vibration signal is converted into a digital sampling signal for each period Ts, similar to the case explained above assuming that there is a scratch on the rotating raceway surface. y(n), and flaws may be estimated for an appropriate number of points M between angles π on the surface of the rolling element. That is, the estimated equivalent drive impulse z(n:θ,) in this case is expressed as follows,
Same as above, minimum 2y! The surface function at the calculation point is calculated for each rolling element using the e method.

z(n:θ.)=, ΣW(([θJ(itn:θ,) Above, we have explained the case where N rolling elements of a rolling bearing always revolve at an equal interval of 2π/N, In the case of uneven spacing, that is, if there are variations in the period in which multiple rolling elements pass one point on the raceway surface, the above method will not give accurate results. If there is a period shift, it is necessary to reduce the sampling frequency.

In the second invention, the reduction is performed by power enveloping processing of the narrowband signal. That is, one bearing ring of a rolling bearing is rotated at a constant angular velocity, and radial vibration is observed at a point on the other bearing ring held stationary, and the period T of the vibration signal y(t) is
The inverse characteristic of the impulse response of the natural frequency of the rolling bearing is convolved with the sampling signal y(n> for every s) by the property b(n), and the resulting equivalent drive impulse ζ(,) is subjected to narrowband filtering. 3(n) near the natural vibration is extracted, and then the envelope signal 2-(n) formed by applying low-band filtering to the squared multiplier 1 zdn)l'' and the orbit are Each of the unknown impulses is calculated based on a relational expression between each position in the circumferential direction of the ring and the vibration propagation coefficient between the vibration observation points and the impulse on the trajectory based on the unknown flaws on the surface of the rolling element. The roughness of the rolling bearing ring raceway surface and rolling element surface of a rolling bearing is estimated from the impulse.

Hereinafter, in order to simplify the explanation of the @2 invention, the case where the roughness of the inner ring raceway surface instead of the rolling elements is estimated will be first explained as an example, similar to the explanation of the first invention.

Now, the estimated equivalent drive impulse z (n: θ.) of the equation (11) at time is expressed as follows.

Roots 2(n:θ,)=ΣW(([θJ(i, n:θ,)])
)+10・s(([x(i, n:θ,)])) gate・δ(nTs− also) (24) In this case, the i-th rolling element and the raceway surface contact each other at the time. The time difference Δ(i
, t, ), the above equation (20) is modified as follows.

z(n:θo)=ΣW(([θ, 7(i, n:θ,)]
)) r=o ”・5((Ex, I(i, n:θ,)])) Gate・δ(nTs−t, −Δ(i, t,)) (25) Next, the above estimation Band-narrowing filtering (center frequency a, bandwidth ±ΔF) is applied to the equivalent drive impulse.By the way, the impulse response h of this band-pass filter is
β(,) is the impulse response ht, (total Ts) of the low bandpass filter and the cosine wave C6S (2yr
FonT s).

hB(n)=hL(nT s) ・cas(2yr
F-nT 5) Therefore, the narrow bandpass signal ze(n) around the time can be expressed as follows.

zs(n)=ΣW (#i) ・5(xi)? 20・hL(nTs-tf-Δ(i,-) ・tbs 2 yr F, (nTs-to-Δ(i
, t, )) here W(θc=W(([θ(i, n:θ,)]))S(θ;
)=s(([x (i, n: 屹])) Next, the square multiplier of the narrow band pass signal z(n) is Iz[
1(n)I is formed, the envelope signal zL, which is the low frequency component of Iz,(n)l'', is passed through a low-pass filter.
(n) is taken out.

ZL(n)=ΣW(θ;) ・5(xi)・)LL(
nTs-1-Δ(i, t,))/2・465/2 yr
F, IΔ(i, ta)−Δ(Lt=Nt・h, 1n
Tsto-Δ(i,ta))・hJnTs-t,
−Δ(jwta)) (28) However, the sum of the second term is for the case i<j. In this envelope signal 2L(n), the influence of the period shift is
) and the constant of the second term (o
s/2πF,lΔ(i,t,)−8(j,to)l|2
seen in However, regarding (■) above, since the signal passed through the low frequency pass filter does not contain high frequency components,
It can be seen that the influence of phase rotation due to this periodic shift Δ(; 11a) can be ignored. In addition, when considering the above-mentioned (■), the center frequency Fe of the narrowband filter is high, and therefore the above-mentioned 2πFolΔ(it)−Δ(j,to)I
However, since the period deviation between the rolling elements is caused by slipping of the rolling elements, it is random and there is no correlation between Δ(i g tJ and Δ(jsts)).

As a result, 2πFOIΔ(!*ts) (j, t4)
l takes a random value between -1 and +1, and the second term, which is the sum of terms multiplied by this random value, is sufficiently smaller than the first term. Therefore, mu(n) is
Only the eliminated first term of Δ(i, t,) can be approximated as follows, and from this, the roughness function l
5(xi) l is calculated.

([θ
J (i+n Uni, h, CnT s-to): Low? Impulse response of J-band filter (at nTs near to) n: Sampling number t: Time i: Rolling element number of rolling bearing (o, i,...N-1) W(θi) Two rolling element number i Vibration propagation coefficient at angle θI' 5 (x9: surface roughness function at position Xλ of rolling element number i nTs −tl,) I, and after all, 1k(nT
s − t,) l ・W(([θj(Ln:θ=)])
) +/2, and its square value is used instead of the impulse. Therefore, according to this,
Instead of the propagation coefficient, it is sufficient to calculate its square value in advance,
This is easier to measure since it does not require information about the sign of the propagation coefficient. At the same time, random phase noise components are reduced in the processing process, so S
The above explanation takes the case of estimating the roughness of the inner ring raceway surface as an example.
29), the impulse s(([xcI(iyn:
Before the gate of θ,)])), a surface function sK(ωy
By substituting nTsN/π)), a relational expression for estimating the roughness of the surface of the rolling element is obtained. Also, here the outer ring is stationary,
The case where the inner ring is rotated has been described as an example, but since the rotational speed of the inner ring can be replaced by the relative speed between the raceways, the principle explained here applies when the outer ring is rotated and the inner ring is stationary. The same holds true.

dog m The present invention will be explained below based on Examples.

In FIG. 6 showing the vibration signal observation system, the type of ball bearing 40 to be estimated is JIS696, the outer ring 10 of this ball bearing is held stationary by applying a thrust force, and the inner ring is rotated at a constant rotation speed of 1800 rpm. So I rotated it. The observed vibration signal y(n) detects vibration at the observation point 11 by a vibration sensor 30, amplifies its electrical output by an amplifier 61, passes through a bypass filter 62, and passes the inner ring 20 included therein. The 1* component (30H) of the rotation was removed and it was temporarily stored in the digital audio record 62. It is then brought back from the test location to the signal processing location, and the output is then passed through a low bandpass filter 63.
, preamplifier 64 and then A-D converter 6
5, and sampling was performed at a period of Ts-30 μs.

Next, the inner ring angular velocity ωI that determines the contact position between the inner ring 20 and the balls 50 and the revolution angular velocity ωb of the balls 50 can be calculated from the rotation speed of the inner ring 20, the dimensions of each part of the ball bearing 40, and the contact angle, but here, the observation The vibration signal y(n) contains the angular velocity ω of the inner ring 20, the automatic angular velocity ωIF of the balls 30, and an angular frequency component that is a positive multiple of the orbital angular velocity of the balls 30 with considerable power (this is normal for the bearing). , occurs regardless of abnormality), we analyzed the frequency of the observed vibration signal y(n) and actually measured ωI, ω2, and ωshi. In addition, in determining the propagation coefficient W (θ) between each point on the raceway surface and the observation point 11, a ball bearing of the same type with a scratch at one place on the raceway surface of the outer ring 10 held stationary was used. , the angle θ of the scratch position with respect to the observation point 11 is sequentially changed and fixed, and for each fixed position, the weight with which the vibration generated by the contact between the scratch and the ball is transmitted to the observation point, that is, the propagation coefficient W (θ), is calculated. Although measured, good estimates of roughness can also be obtained using the propagation coefficients obtained in this way, as will be described later. Therefore, here, the position K (0, 1...M-1) of the flaw on the outer ring is sequentially changed over 16 points, and the square value of the propagation coefficient IW (
θ)1 was calculated as follows. First, the flaw position on the outer ring 10 is made to coincide with the point K=O, that is, the observation point 11, and a sampling signal y(n:K=0) is taken out. Next, it is subjected to narrow band pass filtering processing to extract the natural vibration component, and then, after squaring it,
An envelope signal of a squared signal is formed through a low band pass filter, and the power spectrum of the peak value of the envelope signal is calculated and determined.

Below, each scratch position = 1.2...(M-1)
(angle θ from observation point 11 is θ
= 2π/M), the peak value P(K) as above
are determined and normalized by the value of the =O point as described above to calculate the square value of the propagation coefficient at each point, that is, IW(θ)I =P(K)/P(K=O).

Then, by interpolating these 16 points of IW(θ)12,
The square values of the propagation coefficients for the four points were calculated. Figure 7 shows the results.

Further, the inverse characteristic of the impulse response of the natural frequency necessary for calculating the actually measured equivalent drive impulse z(n) → h(n) was estimated using a two-pulse model. Furthermore, this 2
The pulse model is a model in which vibrations caused by scratches are expressed by the sum of two natural vibrations driven by two impulses. This first impulse is excited when the scratches on the inner ring and the ball come into contact and the inner ring is struck, and at that time, this first impulse is reflected on the ball, and as a result, the ball hits the outer ring on the opposite side. When hitting , an impulse of $2 is excited. Therefore, the vibration signal of this model can be expressed as a linear combination of complex exponential functions driven by the two impulses.

Therefore, by applying the least squares method that minimizes the difference between the model signal and the measured vibration signal y(n) for various delays, the parameters of the vibration poles can be calculated, and from these parameters the impulse response of the natural vibration can be calculated. The inverse characteristic h(n) of is found. Next, in order to determine the position with roughness, the angular velocity ω1? Target 1 Along with b, it is necessary to determine the position of the first ball with respect to the observation point at the start of measurement, that is, the initial angle θ. We decided to find the most probable value of θ from the condition of minimizing Envelope signal ZL(n)
and the surface function (impulse) based on it was calculated. That is, the envelope signal 4(n) is the observed vibration signal y(
n), the inverse characteristic h of the impulse response of the natural vibration
(n) to obtain the actually measured equivalent driving impulse z(n:θ
0) is calculated, then narrow band filtering is performed using an FIR type filter (16 points) to extract only the component zdn) near the natural vibration, and then 2
The amplitude squared signal lz/n)|2 was subjected to moving averaging processing using a Hanning window (16 points) to remove high frequency components, and then sampling was performed at a low sampling frequency. After that, each of these points is substituted into the above equation (29), and each initial angle θ, (0≦
θ.

Square value Is(m)+L of the surface function at 2π/N)
(K, ::l:, m=o, 1.=63, abbreviation of the above I s (([x(i, n:θ)1)))
Finally, from among these, the initial angle θ that minimizes the power α(θ) shown in equation (12) above. The most probable value was calculated.

Figures 8(a) and 8(b) show the square value of the surface function 15(x) for the ball bearings described above, both normal and with a scratch on one of the balls.
This is the result of estimating l by forming an envelope signal, and (b)
From the results, it was estimated that there was one flaw on the surface of the 0th ball (as described above, in the estimation results, a surface function of the same size occurs even at a position shifted by π from the flaw position).

In addition, the results of comparing the surface functions calculated by the method of the present invention for 26 ball bearings (15 normal, 11 with scratches on the balls) classified by hearing tests by trained and experienced inspectors are as follows. As shown in Figure 11, if the threshold shown by the broken line is used, the identification rate is 10.
It was 0%.

The effects of the invention are as described above, and the present invention has the following advantages:
Using vibration signals observed at points, even non-experts can quantitatively estimate the roughness of the rolling element surface of an assembled rolling bearing easily, quickly, and with high accuracy, improving inspection accuracy. Inspection efficiency can be significantly increased without any loss.

[Brief explanation of drawings]

Fig. 1 is a model diagram of a hypothetical ball bearing with two balls for detailed explanation of the present invention, Fig. 2 is a model diagram showing the relationship between the impulse and observed vibration signal of the one in Fig. 1, and Fig. 3 Figure 4 is a model diagram showing the relationship between the inner ring rotation of a rolling element bearing with multiple rolling elements and the contact position change due to the revolution of the rolling elements. Figure 4 shows the relationship between the outer ring and the rolling elements of a rolling bearing with multiple rolling elements FIG. 5 is a model diagram showing the relationship between surface contact position changes; FIG. 5 is a model diagram showing a ball bearing with improper ball spacing; FIG. Figure 7 is a diagram showing an example of measured data of the propagation coefficient;
Figure 8 is a diagram showing an example of estimating flaws on the ball surface, and Figure @9 is a diagram showing the results of estimating flaws on the ball surfaces of 26 ball bearings according to the present invention.6 10: Outer ring 20: Inner ring

Claims (1)

[Claims] 1. While rotating a bearing ring of a rolling bearing at a constant angular velocity, radial vibration is observed at one point on the other bearing ring held stationary, and then the observed vibration signal and the The actual equivalent drive impulse calculated based on the impulse response of the known natural frequency of the bearing ring, the vibration propagation coefficient between each position in the circumferential direction of the bearing ring and the observation point of the vibration, and the rolling element The unknown impulse is calculated based on the relational expression between the unknown impulse on the raceway surface of the raceway ring caused by contact with the scratch and the estimated equivalent drive impulse estimated from the unknown impulse, and the width of the scratch on the surface of the rolling element is calculated from the impulse. Method 2 for estimating the roughness of the rolling element surface of a rolling bearing, the observed vibration signal is an analog signal y(t
), and the relational expression between the measured equivalent drive impulse and the estimated drive impulse is ￥￥￥(n)=y(n)*h(n)=z(n:θ) +Δ
z(n:θ_ο)z(n:θ_ο)=Σ_iW(([θ
(i, n: θ_ο)]_M))・s((ω_BnTsM
'/π_M')) Where n: Sampling number (t=nTs) z(n): Actual equivalent drive impulse z(n:θ): Estimated equivalent drive impulse h^-^1(n): Unique characteristic of the rolling bearing Inverse characteristic of impulse response of vibration frequency i: Ball number of rolling bearing (0, 1,...N-1) (・
): Remainder M when dividing ... by M: Number of propagation coefficient calculation points selected on the rotating raceway surface M': Points for flaw calculation selected between the angle π on the surface of the rolling element [ ]: Integer closest to real number W (([θd(i, n: θ_ο)): Propagation coefficient of vibration at the position of angle θ θ(i, n: θ_ο) = nTsMωb/2π+Mi/n
+Mθ/2π s'i ((ω_BnTsM'/π_M)): Surface roughness function at the rolling element position (ω_BnTsM'/π_M') ω_b: Revolutionary angular velocity of the rolling element ω_B: Rotation angular velocity of the rolling element θ_ο: Rolling element number 0 The method for estimating the surface roughness of a rolling element of a rolling bearing according to claim 1, wherein the revolution angle at t=0 of the rolling element is taken as the revolution angle at t=0. 3. While one bearing ring of a rolling bearing is rotated at a constant angular velocity, radial vibration is observed at a point on the other bearing ring held stationary, and the vibration signal y(t) is
The inverse characteristic of the impulse response of the natural frequency of the rolling bearing h^-^1(
n), the resulting equivalent drive impulse ￥￥￥￥(n) is subjected to narrow band filtering to extract the component z_■(n) near the natural vibration, and then it is
The envelope signal z_L(n) formed by applying low band pass filtering to the squared signal |z(n)|^2 and vibration propagation between each position in the circumferential direction of the raceway and the observation point of the drive. A rolling bearing in which each of the unknown impulses is calculated based on a relational expression between the coefficient and the impulse on the raceway ring based on the unknown flaw on the surface of the rolling element, and the width of the flaw on the surface of the rolling element is estimated from the impulse. A method for estimating the surface roughness of rolling elements.