Increasing Mandrel Life in a Cold Ring Rolling Process: An Application of DOE Principles to Reliability Analysis
Improving the life of machine equipment means a lot to process owners. With an increased life the number of breakdowns during the shift decreases and thus equipment effectiveness and efficiency increase. This is the operational side. On the other hand, you can accomplish shortened process lead times and hence satisfy your customer’s orders on time.
In the center of this study we have a "cold ring rolling" machine that is used to form the inner and the outer rings of ball bearings. The rings are rolled on cylindrical equipment called a "mandrel." After a certain number of rings have been rolled, the mandrel breaks down into two pieces.
Our aim is to increase the life of the mandrel by designing an experiment that includes the controllable process parameters and different materials used to produce the mandrel. Although increasing the life of the mandrel is in the core of this study, the cycle time of the process, which is another output, should not be increased. So the multiple response optimization method is used to solve the problem. Throughout the study, ReliaSoft's DOE++ and Weibull++ software are used to analyze life characteristics and to obtain the best factor combination.
Cold Ring Rolling Process
In the cold ring rolling process, the machine forms rolls inside and outside of the ring by a mandrel and forming roll. The work piece expands about 20% at the external diameter by form rolling. Sizing is done after form rolling and the work piece drops from the machine outlet.
The inner diameter of the preform ring determines the outer diameter of the mandrel. If the inner diameter of the preform is small, the outer diameter of the mandrel should also be small. The smaller the outer diameter of the mandrel, the shorter the life.
Holding the size of the preform rings constant, this article describes how a Design of Experiments (DOE) analysis was done to increase the life of the mandrel while keeping the cycle time to a reasonable level.
Life Data Analysis of Mandrels Before the Study
Prior to the study, we analyzed 24 complete data points using the Weibull++ software. The life distribution of mandrels with diameter Ø 15mm followed a 2-parameter Weibull distribution with a shape parameter (β) = 1.925 and scale parameter (η) = 972 cycles.
There are two responses for this DOE study. One is the life of the mandrel (cycles) and the other is the cycle time of the process (seconds/piece). At the end of this study, the life of the mandrel should be increased, but at the same time the process cycle time must not get longer. Therefore the DOE model must be solved for multiple responses.
Using the DOE++ software, a fractional factorial experiment was designed with the properties shown next.
Because running a full factorial experiment is expensive and time-consuming, we used a fractional factorial design in the study. The team also checked the curvature effect by using center points in the design. Table 2 summarizes the seven factors used.
Table 2: Seven factors in the fractional factorial design
Factor A is the hardness of the mandrel. Factor B is the pressure level of the rolling machine. Factor C is the feed rate of the rolling machine. Factor D is the condition of the rolling machine (where E502 is the old one and Y522 is the new one). Factor E is the length of the mandrel. Factor F is the flatness of the mandrel design. Factor G represents the two new materials used to produce the mandrel.
Carrying Out the Experiment
When the test was designed, the hardness factor was assumed to be controllable by the team, and therefore the recommended test design had 44 runs with 7 factors. However when the measurements were done, the hardness of the mandrels was not exactly at high or low levels. Since this factor was found to be not controllable, the team decided to treat the hardness column as a covariate during the analysis. This keeps the design "orthogonal" for the other 6 factors, and requires the assumption that the hardness covariate does not interact with other factors in the model. The results for all 44 runs were automatically imported to DOE++ using the File Import Wizard, as shown below. Then the data were analyzed as 6 factors with 1 covariate.
Reliability DOE vs. Classical DOE
The DOE++ software offers an analysis approach called Reliability DOE that has two basic advantages over classical DOE. First, suspended data can be incorporated into the model calculations along with complete data. Secondly, responses do not have to be distributed normally at any treatment level.
In this study, because one of the responses is the life of the mandrel, other distributions such as Weibull, exponential or lognormal are also possible. However, after considering the options, the team chose classical DOE for the following reasons:
Obtaining the DOE Model
In the first phase of analysis, the solution model was obtained with respect to the life response. By reducing the model terms according to the statistical significance (α=5%), the results obtained are shown next.
This model has an explanation power of the life response as R2adj=65.6% and σ=1123. The best combination that maximizes the life response is Machine Y522, Material 1, Speed=2, Pressure=4, Flatness=2 and Length=130. With this combination, the average life is predicted to be 10,358 pieces. However, this combination results in 13.5 seconds/piece cycle time, which is nearly two times the current cycle time. So this treatment is not an acceptable solution.
Then the runs were solved for the second response, which is cycle time. The results obtained are shown next.
The best combination that minimizes the cycle time response is Machine E502, Material 1, Speed=4, Pressure=4, Flatness=2 and Length=133. With this combination, the average cycle time is predicted to be 5.75 seconds/piece. However, this combination results in a life of 3,897 pieces per mandrel. This result for life is very low compared to other combinations.
(Note: Observant readers may notice from the table shown earlier that curvature was found to be significant in the analysis for the cycle time response. This was not a cause of concern for the purposes of this study because the primary objective was to improve the life of the mandrels and it was only necessary to control the cycle time at reasonable levels.)
When both of the single-response analyses were found to be inadequate, the team decided to perform a third analysis that considered both life and cycle time together. This analysis utilized the multiple response optimization features of DOE++, and the next figure shows a plot of the optimal solution.
The resulting combination that both optimizes life and cycle time is found to be Machine Y522, Material 2, Speed=2, Pressure=4, Flatness=2 and Length=130. With these factor levels, the mandrel has an average life of 9,069 pieces and cycle time of 8.7 seconds/piece.
We have made three confirmation runs in the best combination that maximizes life and minimizes cycle time. Table 3 gives the results. These results show that the best factor combination of the experiment is confirmed.
Table 3: Confirmation runs
This study is a good application of DOE principles to the reliability analysis of machine equipment. In order to improve the life characteristic of the mandrel, process parameters such as the speed of the machine or the material used to manufacture the mandrel are changed in a systematic manner and also noise factors such as the hardness of the material are taken into consideration. Optimization of the process parameters is done with respect to both life and cycle time responses. By the use of the multiple response optimization technique, the life of the mandrel was improved by nearly nine times while keeping the cycle time at reasonable levels.
 ReliaSoft. Experiment Design and Analysis Reference, Tucson, AZ: ReliaSoft Publishing, 2008.
 ReliaSoft. "Hands On: Reliability DOE with Covariates." Internet: http://www.weibull.com/hotwire/issue99/hottopics99.htm, May 2009.
 ReliaSoft. "Importing Data from Excel Files to DOE++." Internet: http://www.weibull.com/hotwire/issue107/hottopics107.htm, January 2010.
 S. R. Schmidt and R. G. Launsby. Understanding Industrial Designed Experiments, 4th ed. Colorado Springs, CO: Air Academy Press, 2005.
About the Author
Tayfun Kocabas is currently working as a consultant at S.P.A.C. Consulting, which he joined in 2007. He holds a B.S. in Industrial Engineering from Middle East Technical University and an M.B.A. in Business Administration from Dokuz Eylul University. He had worked in the automotive industry and the domestic appliance industry. His primary areas of interests are Reliability Engineering, Six Sigma applications, Design of Experiments and Accelerated Life Tests. He is a registered Certified Reliability Professional (CRP) by ReliaSoft and is currently serving as a representative and distribution partner for ReliaSoft in Turkey. For additional information, he can be reached at firstname.lastname@example.org.