Jon Shelley
Doug Hogge
June 15, 2001
Stress Concentration Factors For
Snap-Ring Grooves In Tension
Introduction:
When designing shafts for various applications it is important to understand the stresses that the shaft will experience during the life of the shaft. Many charts have been developed that characterize the stress concentration factors for different cross sections. However, information about stress concentration factors for snap ring grooves have not been made available. For our project we will use Ansys to obtain data about the stress concentration factors related to snap ring grooves. For this design study, we had to ensure that our model was robust enough to handle the variation in our outer diameter, inner diameter, groove radius, groove depth, groove width, and the mesh applied to the model.
To achieve our objective from the constraints listed above we used a macro file (see Appendix A) using the Application Protocol Language (API) in Ansys to generate the different models that we wanted to analyze quickly and efficiently. This macro file also generated an output file that contained the maximum stress in the snap ring groove. Next, we used isight to run the macro file with the input parameters for the desired models. The rest of this paper will discuss the type of model the macro file generates and the results we obtained using this method.
Theory:
Stress concentration factors are used to represent the changes in stress as the cross section of the part changes. These factors allow the designer to better understand the stresses that must be accounted for if the design is to function properly. The stress concentration factor is defined as
Where max is the maximum stress in the groove, and nom is the nominal stress.
nom is defined as
Where P is the load and Areduced is the cross sectional area of the groove.
P for a constant surface load on a round bar is defined as
Where od is the outer diameter of the round shaft.
Areduced for a round shaft can be defined as
Where id is the outer diameter of the shaft minus two times the groove depth. Substituting these equations back into the first Kt equation we get
This is the equation that we used to calculate our Kt factor.
Model:
Due to symmetry of the shaft and the groove we decided to model this as an axisolid. We used the plane 82 element defined in Ansys. Symmetric boundary conditions in the Y direction were applied at the center of the groove to minimize the size of the problem. A surface load of 10000 lbs/in^2 was applied to the top surface. This type of loading was used in order to avoid stresses at the top edge of the model caused by point loads thus allowing us to reduce the size of our model. An area around the groove was created which could be meshed with smaller elements to better model the stresses in the snap ring groove. Below is the model we created in Ansys to analyze the stresses in the snap ring grooves along with the smaller area around the groove with the smaller mesh.
Results:
The table below shows the needed input variables that were used to obtain our results. The macro file reads the values from a text file and then calculated the results.
Outside Diameter / 1” – 4” (13 Values)Ratio of Outside Diameter to Inside Diameter / 1.02 – 1.1 (9 Values)
Fillet Radius / 0.005” – 0.15” (4 Values)
Gap of Groove / 0.2”
Height of Modeled Section / 2”
Modulus of Elasticity / 30e6 psi
Axial Load / 10,000 psi
Table 1: Axial Stress Contour
The nodes nearest the groove where selected and then plotted as shown in figure 2 below. This allowed a better visual representation of the stresses near the groove. The stress contour plot show that the axial stress is highest where the fillet starts which is what we would expect. The stresses ranged from 20,000 psi to 90,000 psi for the different dimensions shown in table 1. (Appendix B shows a graph with the results for each individual run.)
Figure 2: Axial Stress Contour
The displacement plot, Figure 3, shows only the elements nearest the groove. The tensile force that is applied causes the shaft to shrink radialy as well as displace in the vertical direction. This figure also shows that the boundary conditions were applied correctly since there is no displacement upward in the elements along the bottom edge.
Figure 3: Displacement Showing Deformed and Undeformed Shape
From the results the stress concentration factor was calculated for each run. Figure 4 shows a chart of stress concentration factors for a radius of 0.005”. The figure shows that Kt increases as the ratio of outside diameter to inside diameter increases. Three more charts were created for radius of 0.007”, 0.01”, and 0.015”. (These are shown in Appendix C.)
Figure 4: Stress Concentration Factor for R=0.005"
In order to test the praticality of the generated kt charts we used values for snap rings from the Smalley Steel Ring Company. The Kt was found on the charts for the specific dimensions and then the stress was calculated. Our analysis model was also run for the dimensions and the results are shown below in table 2. The error ranged from 0.05% to 4.1% showing that the charts could produce fairly accurate results.
ratio / od / r / Chart Kt / Calculated Stress / Ansys Kt / Ansys Stress / Error1.0504 / 1 / 0.005 / 3.3 / 36,412 / 3.322 / 36,650 / -0.653
1.0549 / 1.5 / 0.005 / 4.1 / 45,621 / 3.995 / 44,458 / 2.549
1.0627 / 2 / 0.005 / 4.8 / 54,208 / 4.693 / 52,996 / 2.236
1.0495 / 2.5 / 0.005 / 4.9 / 53,975 / 4.781 / 52,668 / 2.421
1.0409 / 3 / 0.005 / 4.8 / 52,011 / 4.842 / 52,471 / -0.884
1.0410 / 3.5 / 0.005 / 5.1 / 55,273 / 5.182 / 56,167 / -1.617
1.0357 / 4 / 0.005 / 5.2 / 55,783 / 5.228 / 56,079 / -0.532
1.0504 / 1 / 0.01 / 2.7 / 29,791 / 2.590 / 28,572 / 4.091
1.0549 / 1.5 / 0.01 / 3.21 / 35,718 / 3.212 / 35,738 / -0.056
1.0627 / 2 / 0.01 / 3.9 / 44,044 / 3.745 / 42,297 / 3.966
1.0495 / 2.5 / 0.01 / 3.8 / 41,858 / 3.817 / 42,044 / -0.443
1.0409 / 3 / 0.01 / 3.95 / 42,801 / 3.866 / 41,891 / 2.126
1.0410 / 3.5 / 0.01 / 4.05 / 43,893 / 4.128 / 44,734 / -1.917
1.0357 / 4 / 0.01 / 4 / 42,910 / 4.164 / 44,667 / -4.096
Table 2: Calculated and Analysis Results of Actual Snap Ring Data
Conclusion:
We were able to model the stresses in the snap ring groove and calculate the stress concentration factors. By checking our results and creating a finer mesh around the snap ring groove we felt confident with the results. From the charts that we generated we were able to take Kt values from them and compare them with the results we obtain from Ansys. The error between our calculations and the Ansys results were less then five percent.
Future Work: (For the academically curious)
Compare the charts that we generated with actual test data.
Generate charts for bending and torsion.