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Fig.1 The roundness of the inner raceway of the inner ring groove of the inner ring of the bearing is an important quality index, which directly affects the working accuracy, stability and service life of the bearing. Grinding is usually the semi-finishing or finishing process of the inner ring channel, and it plays a decisive role in the roundness of the inner ring channel of the finished product. The roundness of the inner ring groove grinding depends on the accuracy and dynamics of the grinding process system. In addition to the characteristics, it is also closely related to the grinding process parameters. The former has been valued by many scholars and has undergone a lot of research, which has greatly improved the roundness of the inner ring groove. With the improvement of the precision of the grinding process system and the improvement of the dynamic characteristics, the grinding process parameters become the main factors affecting the roundness. Therefore, the influence of the grinding process parameters on the roundness is studied, and the rational choice of process parameters ensures the bearing channel. The roundness of grinding and the optimization of the process parameters for grinding the bearing channels are of great significance. Fig. 1 shows the error of the actual contour and the ideal contour of the groove cross-section of the inner ring of the grinding bearing. It can be expressed as the geometric error ∆Rw(F)=Rw(F)-Rw0 (1) where Rw(F) is actual Workpiece contour radius, Rw0 is the ideal workpiece contour radius. In the figure, O1 and O2 are the center of the geometry of the workpiece and the center of rotation of the measurement. The contour error ∆Rw(F) is a periodic function of F, which can be represented by the Fourier series ∆Rw(F)= x0 +∞Σi=1 xicos(iF+Fi) 2 (2) where: xi(i) =0,1,......) is the harmonic amplitude: F, Fi is the harmonic phase angle: x0/2 represents the processing size error, which is also the average value of the error function Rw(F). In formula (2), the first harmonic x1cos(F+F1) corresponds to the eccentric center of the inner ring channel and the eccentricity of the measurement center of rotation: the second to fifteenth harmonic xicos(iF+Fi) (2≤i≤15 ) corresponds to the roundness of the outer circle of the bearing channel. 2 Influencing factors of roundness analysis The bearing inner raceway usually adopts the variable feed speed cutting and grinding method. The grinding cycle can be divided into: rapid approach of the workpiece, coarse feed, fine feed and no feed grinding. Stages. The main factors affecting the roundness of the grinding bearing channel can be summarized as follows: (1) The precision of the process system in the grinding process, which depends on the precision of the grinding machine and the positioning principle, structural parameters and precision of the fixture: (2) Process system Dynamic characteristics, especially the balance of the grinding wheel: During dressing and grinding, the unbalance of the grinding wheel will cause forced vibration due to the difference in the relative position of the dresser and grinding wheel when dressing the grinding wheel and the relative position of the workpiece and the grinding wheel during grinding. , And the difference in the stiffness of the process system under these two different conditions makes the workpiece surface caused by vibration to be out of round: the grinding process parameters will affect the contact stiffness between the grinding wheel and the workpiece, the wear process of the grinding wheel, and the damping characteristics of the process system vibration. This affects the vibration characteristics of the grinding process and is ultimately reflected in the geometry (ie, roundness) and other surface qualities of the ground workpiece: (3) The original error of the workpiece caused by the elastic deformation of the process system: analysis of the grinding cycle workpiece It can be seen from the law of geometrical error variation that the error of the geometry of the workpiece after grinding mainly depends on the rigidity of the process system and the grinding process parameters. Original workpiece and wheel wear velocity error Δ. Considering the above factors, when the rigidity and dynamic characteristics of the process system are constant (especially the grinding wheel must be well-balanced), the roundness error of the grinding workpiece mainly depends on the grinding process parameters, so the roundness test data can be passed through. Stepwise regression modeling, selecting important parameters from multiple process parameters, and gradually introducing regression equations to establish an optimal regression equation for the relationship between grinding roundness and process parameters. 3 protocol test factor level table level factors Vw
(m/min) a1
(μm/r) a2
(μm/r) Sd
(mm/r) td
(mm) T
(mm3/mm) L2
(mm) 1 30 4 0.5 0.1 0.01 1T0 0.025 2 50.5 8 1 0.2 0.02 5T0 3 83 12 1.8 0.3 0.03 10T0 0.04 Note: T0 in the table is the grinding unit width of the single-piece grinding unit. This test T0 = 7.07mm3/ Mm. According to the analysis of the factors affecting the roundness of the workpiece, the performance of the grinding wheel and the grinding fluid, the wheel speed Vs, the stiffness and dynamic characteristics of the grinding wheel, and the grinding time are not changed. The factors are as stable as possible during the grinding test. The experimental factors selected in this study are: trimming of the lead Sd of the grinding wheel, dressing of the grinding wheel depth td per stroke, workpiece line speed Vw, grinding depth a1 per revolution of the coarse feed workpiece, and grinding depth a2 of fine feed workpiece per revolution, fine Feed stroke L2, the unit grinding width abraded metal volume T. All the process parameters except the fine feed stroke L2 take 2 levels, the rest are taken, the level, taking into account the interaction effects between the process parameters, according to the hybrid orthogonal table for testing. At the same time, in order to reflect the influence of different workpiece diameters caused by the change of the equivalent diameter of the grinding wheel on the roundness of the grinding, the 208, 308 and 306 bearings were respectively subjected to the grinding test, and the roundness of the ground workpiece was measured. Test factor levels are shown in the top right panel. Test conditions: (1) Machine tool is 3MZ1310: Automatic high-speed bearing inner ring groove grinder: (2) The workpiece positioning method is double circular motion support: (3) Grinding wheel is GB100ZR2A, diameter ds=560mm, speed ns=1600r/ Min: (4) The dressing tool is a single diamond dresser, light repair once: (5) polishing time 2.5s, common emulsion coolant: (6) roundness measuring instrument Taylor-HOBSON: (7) grinding workpiece 208, 306, 308 bearing outer ring groove, diameter dw = 48.1, 40, 51mm, material GCr15, hardness 60 ~ 65HRC. 4 Modeling Mathematical Modeling for Grinding Roundness and Process Parameters Assume that based on the previous analysis of the influencing factors of the roundness of roundness, considering the possible interaction between process parameters, it can be assumed that the mathematical model of roundness is R0 = KVwa1a1a2L2a3D4a4Twb1Sdb2ab23tdb4 
B1=p1+lnVwb1a1b2Tb3Sdb4a2b5Deb6 b2=p2+c1lna1+c2lnSd b3=p3+dlna1 b4=p4+f1lnSd+f2lntd (3) where R0 represents the roundness value and the rest are the process parameters and the pending constants. The equivalent diameter of the grinding wheel De=dsdw /(d3+dw). By taking the logarithm of both sides of equation (3) and performing variable substitution, it can be linearized as y=B0+B1x1+B2x2+...+B19x19 (4) The stepwise regression modeling of the circularity of the inner ring groove After the cutting test, the roundness data of the inner ring channel are measured, and the linearized response function formula (4) of equation (3) above is stepwisely regressed, ie, important factors are introduced to eliminate minor factors (Note: F-test threshold is taken as Fa = 0.4), until the step-by-step regression calculation is completed with neither the elimination nor the introduction of the variable. Set the value of each variable coefficient of equation (4) of the response function, and replace the linearized response function, then the mathematical model for the relationship between grinding process parameters and roundness can be obtained as R0=0.0623Vw0.442a13.262L20. 201De1.08Tb1Sdb2a2b3tdb4 B1=-0.335lna1-0.368lnSdb2=4.833+1.161lna1+2.178lnSdb3=-0.233lna1b4=-0.441lnSd (5) Standard deviation s=0.36, correlation coefficient g=0.94, F=26>Fa=0.4 From the established model's correlation coefficient and variance analysis F test value, we can see that the fitting effect is satisfactory and the model is feasible. 5 Results and Discussion 
(Note: a1=8μm/r, a2=1.5μm/r, Vw=50.5m/min, L2=0.03mm, De=45mm, T=58mm3/mm )
Figure 2 R0 changes with Sd and td 
(Note: Sd=0.15mm/r, td=0.02mm, Vw=50.5m/min, L2=0.03mm, De=45mm, T=58mm3/mm )
Figure 3 R0 changes with a1, a2 
(Note: Sd=0.15mm/r, td=0.02mm, a1=8μm/r, a2=1.5μm/r, De=45mm, L2=0.03mm )
Figure 4 R0 changes with Vw, T 
(Note: Sd=0.15mm/r, td=0.02mm, a1=8μm/r, a2=1.5μm/r, Vw=50.5m/min, T=58mm3/mm )
Fig. 5 Change of R0 with De and L2 Fig. 2 shows the relationship between the lead and depth of the dressing wheel and the roundness of grinding R0. In the figure, when Sd<0.16mm/r, the roundness of the grinding increases as the trimming lead Sd decreases: but when Sd>0.16mm/r, the roundness of the grinding follows the trimming lead. Increasing and increasing, at Sd=0.16mm/r, roundness reaches a minimum. As the dressing depth of the grinding wheel increases, the roundness of the grinding increases. Fig. 3 shows the relationship between the depth of rough feed and fine feed grinding and roundness of grinding. It can be seen from the figure that the increase in the depth of coarse feed and fine feed each causes the roundness of the grinding to decrease to different extents, wherein the grinding roundness decreases as the coarse feed grinding depth a1 increases. The small amplitude is related to the fine grinding depth a2. The larger the a2 is, the larger the roundness is. FIG. 4 shows the relationship between the workpiece linear velocity Vw and the unit grinding metal volume T and the roundness of grinding. The roundness of the grinding increases with the increase of the workpiece linear velocity, and the change of the unit metal removal volume has no significant influence on the roundness of the grinding. It shows that in the normal wear stage of the grinding wheel, the sharp state of the grinding wheel surface does not affect the roundness. FIG. 5 shows the relationship between the equivalent grinding wheel diameter De and the fine feed stroke L2 and the grinding roundness R0. Obviously, the fine feed stroke and the increase of the equivalent wheel diameter De increase the roundness of the grinding. This is consistent with the second point. The final point to be pointed out is that machine tool vibration caused by grinding wheel imbalance or other factors will seriously affect the roundness of the grinding workpiece. Maintaining a good working condition of the machine tool and a good balance of the grinding wheel are prerequisites for the application of the roundness mathematical model previously fitted. In addition, the hardness, structure and abrasive grain size of the grinding wheel and the type of abrasive, as well as the composition of the coolant, will have a certain influence on the roundness of the grinding.
The Influence of Process Parameters on Roundness of Grinding Inner Raceway of Bearings
1 Introduction