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Abstract: The selection of clearance for vibration bearings of road rollers is an important link for the normal operation of vibration bearings. Many application units may enter into many misconceptions when selecting clearance for vibration bearings, and even affect product design. The article introduces the principles of selecting fit for vibration bearings and the method of calculating clearance.
Keywords: Vibration bearings; Gap; choice
0. Introduction
Vibration roller is an important field for the application of vibration bearings, and its main working device is inseparable from the key component of vibration bearings. Its correct selection is related to the success of vibration rollers. Therefore, it is very important for vibration rollers to demand the key technical parameter of vibration bearing clearance. Due to the special structure of the vibration chamber of the vibratory roller, cylindrical roller bearings are generally used in the selection of vibration bearings (considering factors such as load, speed, lubrication, temperature, etc.). Therefore, the selection and calculation of radial clearance for this type of cylindrical roller bearing are particularly important.
1. Factors affecting the clearance of vibration bearings
The factors that affect bearing clearance in practical applications mainly include the following aspects:
1) The reduction in radial clearance caused by fit: The reduction in radial clearance caused by the fit between the inner ring of the inner bearing and the shaft. The radial clearance decreases due to the fit between the outer ring of the bearing and the bearing.
2) The radial clearance decreases due to the temperature rise of the bearing during operation.
3) Reduced clearance caused by alternating loads.
4) The radial error caused by the coaxiality of machined holes is reduced.
2. Principles for selecting and matching vibration bearings
In terms of bearing fit, the fit between the inner ring of the bearing and the shaft adopts a base hole system. We know that the inner ring of a bearing rotates with the shaft. In order to prevent relative motion between them and wear of the joint surface, the fit between the two should have a certain degree of interference. However, since the inner ring is a thin-walled part and must be removed after a certain period of time, the fit interference should not be large. Therefore, the national standard for rolling bearings distributes the tolerance band of d below the zero line, At this point, when the inner ring of the bearing is matched with a general transitional fit shaft, not only can it ensure that there is not much interference, but there will also be no gap, which meets the requirements for the fit between the inner ring of the bearing and the shaft. At the same time, the shaft can be machined according to the standard deviation.
The outer ring of the bearing adopts a base shaft system. Usually, the fit between the two should not be too tight, therefore. The position of the outer diameter D tolerance zone of all precision bearings in the national standard is still distributed below the zero line according to the general reference axis, with an upper deviation of zero and a lower deviation of negative values.
Attention: In terms of the bearing capacity of the vibrating shaft (see Figure 1 for shaft capacity analysis), the outer ring of the bearing is subjected to cyclic load. In order to prevent slipping between the outer ring and the inner hole of the flange, a transitional fit should be selected for the bearing, and M7 is recommended. The inner ring of the bearing bears a local load, but considering the vibration effect, a looser transition fit should be selected.
3. Calculation of clearance of vibration bearings
3.1 Calculation of clearance of vibration bearings
The calculation formula for work clearance:
S=Sr- Δ Sp- Δ St. (1)
In the formula: S is the working clearance, which refers to the clearance of the bearing during normal temperature heating under operating conditions after installation; Δ Sp is the reduction in radial clearance caused by fitting; Δ St is the reduction in radial clearance caused by temperature rise; Sr is the internal radial clearance of the bearing, which is generally provided by the bearing manufacturer (taking NBI bearings as an example).
The reduction in radial clearance is caused by the expansion of the inner ring and the contraction of the outer ring during bearing installation (see Figure 2), and its calculation formula is
Δ Sp= Δ d+ Δ D.
In the formula: Δd is the expansion of the inner ring, μm; Δ D is the shrinkage of the outer ring, μm. The calculation formula for the expansion of the bearing inner ring is
Δd ≈ 0.9 × U × d/F ≈ 0.8 × U.
In the formula: d is the diameter of the bearing inner ring, mm; U is the theoretical interference fit with a tight fit, which refers to the difference in size deviation obtained by subtracting 1/3 of the actual size sum from the maximum physical deviation of each mating surface during interference fit; F is the diameter of the inner raceway, mm.
The calculation formula for the shrinkage of the outer ring of the bearing is
Δ D ≈ 0.7 × U × E/D ≈ 0.7 × U.
In the formula: E is the diameter of the outer ring raceway, mm; D is the diameter of the outer ring of the bearing, in millimeters.
Due to the large temperature difference between the inner and outer rings, the radial clearance changes significantly. The calculation formula is
Δ St= α× dm × 1000 (VIR - VAR).
In the formula: Δ St is the decrease in radial clearance caused by temperature rise, μm; α= 0.000 011 K-1; dm is the average diameter of the bearing, where dm=(d+D)/2 mm; VIR is the inner ring temperature, ℃; VAR is the outer ring temperature, ℃.
For high-speed running shafts, bearings with larger radial clearance should be selected to ensure sufficient thermal compensation between the bearing, shaft, and bearing seat. In this case, the clearance of bearings is much larger than that of ordinary bearings under continuous operation. When the vibrator has just started and has not yet reached the working temperature, the temperature of the inner and outer rings of the bearing is even higher than during stable operation. Taking NBI bearings as an example, NBI recommends reserving a radial working clearance of 40-140 μm.
According to equations (1) and (2)
S=Sr- Δ D- Δd- Δ St. (3)
When selecting the clearance of the vibrator, the coaxiality of the two bearing holes and the roundness of the shaft and holes should also be considered. Based on the selection of existing customers, the calculation of the clearance of the roller vibrator bearing is as follows: a certain roller vibration bearing is a cylindrical rolling bearing, with an inner ring of 85 mm and an outer ring of 180 mm. The outer ring adopts M7 fit and the inner ring adopts J6 fit. According to the Mechanical Design Manual and design drawings.
The reduction in radial clearance of the bearing inner ring is Δd ≈ 0.8 × U=0.8 × 19=15.2 μ m. The reduction in radial clearance of the outer ring of the bearing is Δ D ≈ 0.7 × U=0.7 × 18=12.6 μ m. Assuming a temperature difference of 10 ℃ between the inner and outer rings, the reduction in radial clearance caused by temperature rise is: Δ St= α× dm × 1000 (VIR-VAR)=0.000011 × (85+180)/2 × 1000 × 10=14.58 μm.
Taking NBI as an example, the bearing manufacturer recommends reserving a radial working clearance of 40-140 μm.
According to equation (1), Sr=S+ Δ Sp+ Δ St, S rmin=40+15.2+12.6+14.58=82.38 μ m. So S rmax=182.38 μm.
By comparing with Table 1 after calculation, it can be seen that the radial clearance of the vibration bearing can be selected in the range of C4 or C5.
3.2 Radial clearance of cylindrical roller bearings
The premise of verification calculation is to assume that the clearance group (i.e. CN C3, etc.) is used to calculate the working clearance S of the bearing. According to equation (3), the calculated Smin is less than 0, indicating that the vibrating bearing may actually operate in a negative clearance (interference) state, which will cause friction and heating between the inner and outer raceways of the bearing and the rolling element, leading to an increase in bearing temperature, causing severe heating of the bearing, resulting in bearing locking or tearing, and damaging the bearing. At this point, it is possible to switch to a larger clearance group. If the calculated Smin is greater than 0, the selected vibration bearing clearance group is safer.
4. Conclusion
The selection of clearance for vibration bearings of road rollers is an important issue that requires consideration of multiple factors in order to select bearings that meet product design requirements. The clearance of vibration bearings directly affects the key technical indicators of road rollers, such as load distribution, noise, vibration (stationarity), temperature rise, friction of bearings, and service life of vibration bearings. Excessive clearance often leads to a reduction in the load area inside the bearings, The contact stress of bearings increases, which shortens the service life of bearings. Excessive clearance can also reduce the operating accuracy of bearings, increase vibration and noise. If the clearance is too small, negative clearance (interference) may occur during actual operation, causing an increase in friction heat generation, an increase in bearing temperature rise, and thus making the effective clearance smaller or (interference greater), which in turn makes it easier to burn out the bearing.
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