Checking the Soviets: The Life of the Bearings

The last of our series on “Checking the Soviets” will deal with the roller bearings for the S-834. Roller bearings, be they spherical or cylindrical, are an important part of vibratory pile driving equipment, although for Vulcan’s machines cylindrical bearings were the rule.

The bearings (#4 in the diagram above) were GOST 5721-57 3614 bearings. Specifications for this type are hard to come by; however, bearings tend to be a standardized (if very precision) product. The nearest equivalent is the “22314” series, which are made by a variety of manufacturers. In all cases the inner race I.D. is 70 mm, the outer race O.D. is 150 mm, and the thickness of the bearing is 51 mm. We will compare our own results with those of the Soviets given at the end of Soviet S-834 Impact-Vibration Hammer: Calculations, Part II.

According to Juvinall and Marshek (1991), the equation for roller bearing life is given by the following:

$L={\it L_R}\,\left ({\frac {C}{{\it F_r}}}\right )^{10/3}$ (1)

where

L = bearing life in number of cycles, or more accurately the life at which one would expect a certain percentage of the bearings to still be in operation. Generally that percentage is 90%, based on L_R
L_R = design life of bearing (typically 1,000,000 cycles, but can be different)
C = Rated load, units of force. Plain C is the dynamic rating; the static rating is C₀ (usually lower)
F_r = load on the bearing in units of force

Bearings are a dynamically loaded and moving component where the load on the components is constantly changing. Bearings are thus designed for a certain life; if the load is increased, the life of the bearing will go down. Manufacturers have applied different factors to Equation (1) but we’ll stick with the original formulation for this analysis.

With rotating machinery, the bearing load is usually applied once per revolution. For a constant speed rotation, the hours of use can be computed by the equation

$h={\frac {1}{60}}\,{\it L_R}\,\left ({\frac {C}{{\it F_r}}}\right )^{10/3}{{\it RPM}}^{-1}$ (2)

where

h = hours of life for rated operation
RPM = rotational speed of bearings

In the case of an impact-vibration hammer, the hammer does not make impact with every rotation. The Soviets assumed that it did, which is a conservative assumption; we will do the same.

According to the SKF literature, for this bearing C = 400 kN = 400,000 N (these values have edged up since Vulcan manufactured vibratory hammers in the 1980’s and 1990’s.) In our post Checking the Soviets: Determining the Bending of the Shaft, the CFRAME program computed the reactions. The total reaction is the Euclidean sum of the impact and dynamic force reactions, thus Fr = (64,750² + 12,260²)^1/2 = 65,900 N. Substituting these L_R = 1,000,000 cycles and RPM = 950 into Equation (2) yields h = 7,156 hours.

This is considerably longer than the Soviets computed. To try to figure out what happened, we first noted that for them C = 330,000 kg_f, which is considerably larger than SKF’s value. They also curiously apply a factor of safety of 1.5, which is generally not necessary for a life calculation such as this. So let’s say that C = 220,000 kg_f. Using their reaction force of 6070 kg_f, there are two ways of using Equation (2) to obtain a life approximately equal to theirs of 160 hours:

Holding C constant and reducing the design life estimate requires that the value of C is based on a L_R = 60 cycle life for the bearing.
Changing C for a more conventional L_R = 1,000,000 cycles would result in a value of C = 17,700 kg_f, which is a little less than half of SKF’s value.

I am inclined to go with the latter, based on experience with Soviet civilian production. It’s worth noting that FAG’s figure for this bearing in the 1990’s was 75,000 lb, and the backfigured design load for this is a little over 39,000 lb, or a little more than half of FAG’s load.

This is the last in this series. I trust you have found it beneficial and intersting.