1. A rolling bearing comprising a first race having a first raceway, a second race provided around the first race and having a second raceway, Z rolling bodies having a rolling surface and rollably disposed between the first raceway and the second raceway, and a retainer for holding the rolling bodies, such that under grease lubrication, the first race rotates at the frequency of f

### r (Hz) while the rolling bodies held in the retainer rotate at the frequency of f

### b (Hz) and revolve at the frequency of f

### c (Hz), wherein, when assumed that n, m, k and j are each a positive integer up to 100, respectively, that D

### a is the diameter of the rolling bodies, that dm is the pitch circle diameter of the rolling bodies, that is the contact angle between the rolling bodies and the first and second raceways and that vibration is generated at frequencies of mZf

### i, mZf

### i±f

### r, nZf

### c, 2kf

### b and 2kf

### b±f

### c due to the circumferential undulations of (mZ) waves and (mZ+1) waves existing on the surface of the first raceway, to the circumferential undulations of (nZ) waves and (nZ±1) waves existing on the surface of the second raceway and to the undulation of (2k) waves existing on the rolling surface of the respective rolling bodies, the formulas of (mZf

### j)≠jf

### r, (mZf

### i±f

### r)≠jf

### r, (nZf

### c)≠jf

### r, (2kf

### b)≠jf

### r and (2kf

### b±f

### c)≠jf

### r are satisfied for all of n, m, k and j with respect to the frequencies, where f

### i=f

### r−f

### c (Hz), nZf

### c=(1/2)nf

### r{1−(D

### a/d

### m)cos }Z, mZf

### i=(1/2)mf

### r{1+(D

### a/d

### m)cos }Z, and 2kf

### b=kf

### r{1−(D

### a/d

### m)

### 2cos

### 2 }d

### m/D

### a.

2. A rolling bearing comprising a first race having a first raceway, a second race provided around the first race and having a second raceway, Z rolling bodies having a rolling surface and rollably disposed between the first raceway and the second raceway, and a retainer for holding the rolling bodies, such that under grease lubrication, the first race rotates at the frequency of f

### r (Hz) while the rolling bodies held in the retainer rotate at the frequency of f

### b (Hz) and revolve at the frequency of f

### c (Hz), wherein, when assumed that n, m, k and j are each a positive integer up to 100, respectively, that D

### a is the diameter of the rolling bodies, that d

### m is the pitch circle diameter of the rolling bodies, that is the contact angle between the rolling bodies and the first and second raceways and that vibration is generated at frequencies of mZf

### i, mZf

### i±f

### r, nZf

### c, 2kf

### b and 2kf

### b±f

### c due to the circumferential undulations of (mZ) waves and (mZ±1) waves existing on the surface of the first raceway, to the circumferential undulations of (nZ) waves and (nZ±1) waves existing on the surface of the second raceway and to the undulation of (2k) waves existing on the rolling surface of the respective rolling bodies,

3. The rolling bearing of claim 2, wherein the formulas of nf

### c/mf

### i≧1.02, and nf

### c/mf

### i≦0.98 are satisfied, where nf

### c/mf

### i=(d

### m−D

### a)n/(d

### m+D

### a)m.

4. The rolling bearing of claim 2, wherein the natural frequency domain of the rotation system is in the range of F

### n±250 (Hz) where F

### n is the natural frequency which is determined by detecting an acceleration generated by impulse excitation of the rotation system by way of a hammer and processing the acceleration with FFT.

5. A rolling bearing comprising a first race having a first raceway, a second race provided around the first race and having a second raceway, Z rolling bodies having a rolling surface and rollably disposed between the first raceway and the second raceway, and a retainer for holding the rolling bodies, such that under grease lubrication, the first race rotates at the frequency of f

### r (Hz) while the rolling bodies held in the retainer rotate at the frequency of f

### b (Hz) and revolve at the frequency of f

### c (Hz), wherein, when assumed that n, m, k and j are each a positive integer up to 100, respectively, that D

### a is the diameter of the rolling bodies, that d

### m is the pitch circle diameter of the rolling bodies, that is the contact angle between the rolling bodies and the first and second raceways and that vibration is generated at frequencies of mZf

### i, mZf

### i±f

### r, nZf

### c, 2kf

### b and 2kf

### b±f

### c due to the circumferential undulations of (mZ) waves and (mZ±1) waves existing on the surface of the first raceway, to the circumferetial undulations of (nZ) waves and (nZ±1) waves existing on the surface of the second raceway and to the undulation of (2k) waves existing on the rolling surface of the respective rolling bodies, the formulas of (mZf

### i)≠jf

### r, (mZf

### i±f

### r)≠jf

### r, (nZf

### c)≠jf

### r, (2kf

### b)≠jf

### r and (2kf

### b±f

### c)≠jf

### r are satisfied for all of n, m, k and j with respect to the frequencies,

6. The rolling bearing of claim 5, wherein the formulas of nf

### c/mf

### i≦1.02, and nf

### c/mf

### i≦0.98 are satisfied, where nf

### c/mf

### i=(d

### m−D

### a)n/(d

### m+D

### a)m.

7. A method for design of the rolling bearing of claim 6 comprising the steps of:

8. The method of claim 7, where the diameter of the rolling bodies, the number of the rolling bodies and the pitch circle diameter of the rolling bodies are changed without changing the inner and outer diameters and the width of the ball bearing.

9. The rolling bearing of claim 5, wherein the natural frequency domain of the rotation system is in the range of F

### n±250 (Hz) where F

### n is the natural frequency which is determined by detecting an acceleration generated by impulse excitation of the rotation system by way of a hammer and processing the acceleration with FFT.