Most machines and instruments constantly require elastomeric materials like rubber for the purposes of shock absorption, noise attenuation, and sealing. The material properties and accurate lifetime prediction of rubber are closely related to the quality of machines, especially their durability and reliability. The properties of rubberlike elastomers are influenced by ambient conditions, such as temperature, environment, and mechanical load. Moreover, the initial properties of rubber gaskets must be sustained under working conditions to satisfy their required function. Because of its technical merits, as well as its low cost, the highly accelerated life test (HALT) is used by many researchers to predict the longterm lifetime of rubber materials. Methyl vinyl silicone rubber (VMQ) has recently been adopted to improve the lifetime of automobile radiator gaskets. A fourparameter method of determining the recovery ability of the gaskets was recently published, and two revised methods of obtaining the recovery were proposed for polyacrylate (ACM) rubber. The recovery rate curves for VMQ were acquired using the successive zooming genetic algorithm (SZGA). The gasket lifetime for the target recovery (60%) of a compressed gasket was computed somewhat differently depending on the selected regression model.
Most machines and instruments constantly require elastomeric materials like rubber for the purposes of shock absorption, noise attenuation, and sealing [
In this study, we predict the lifetime of a VMQ radiator gasket recently developed by a local company using the method proposed in 2014 [
The HALT is a test methodology that accelerates the degradation of material properties using several specimens, and it has been used by many researchers during the material development stage and design process. This test is also commonly applied to rubber materials for gaskets and dampers and facilitates the identification and resolution of weaknesses in new product designs. The methodology diminishes the probability of inservice failures; that is, it increases product quality by virtue of reliability and decreases the development cost and time [
In this method of lifetime prediction, the Arrhenius model [
According to most references investigating a lifetime evaluation adopting the linear Arrhenius equation [
With accurate lifetime predictions at high temperatures, the linear Arrhenius model in the
The successive zooming genetic algorithm (SZGA) method is used to achieve a smart reduction of the search space around the candidate optimum point [
Flowchart and schematics of SZGA.
Methods of mathematically predicting the quantitative lifetime are introduced in this section. To obtain an Arrhenius plot of the longterm lifetime, we first needed to fit the recovery rate curve for a given temperature to obtain the lifetime corresponding to a recovery rate of 60%. Two methods of fitting curves for the ACM were adopted here for the VMQ [
An Arrhenius equation presents the kinetic rate
For a single ratelimited thermally activated process, an Arrhenius plot gives a straight line as a function of the activation energy and temperature as
Equation (
The lifetimes for higher temperatures are plotted in Arrhenius form, and the longterm lifetimes may be predicted by linearly extrapolating the given data in the semilog plane of
Arrhenius plot used to predict lifetime.
Fourparameter (
When the time is greater than the reference time
Recovery rate curve using fourparameter method 1.
In fourparameter (
Recovery rate curve using fourparameter method 2.
Before the HALT test of the VMQ, a rubber material property test was performed by the Korea Testing and Research Institute (KTR) and the Korea Polymer Testing & Research Institute (KOPTRI) according to ASTM standards. The test results are given in Table
Material properties of VMQ.
Material properties  Exp. value  Test standard 

Basic properties  
Hardness (IRHD)  70  ASTM D412 
Tensile strength (MPa)  7.8  
Ultimate elongation (%)  150  
Heat resistance  
Change in hardness (%)  0  ASTM D573 
Change in tensile strength (%)  −19.9  
Change in elongation (%)  −7.6  
Compression set (%)  9.2  ASTM D395, method B; 22 h, 150°C, plied 
Compression set (%)  33.6  ASTM D395, method B; 1000 h, 150°C, plied 
Fluid resistance  
Change in hardness (IRHD)  −5  ASTM D471, ASTM oil number 1; 70 h, 150°C 
Change in tensile strength (%)  −10.1  
Change in elongation (%)  −3.3  
Change in volume (%)  3.4  
Fluid resistance  
Change in hardness (IRHD)  −10  ASTM D471, ASTM oil number 3; 70 h, 150°C 
Change in volume (%)  17.5  
Low temp. brittleness  No cracking  ASTM D2137, method A; −55°C, 3 min 
The ability of a rubber to return to its original thickness after prolonged compression is measured by a compression set test at high and low temperatures. The compression set tests in this study were carried out under a compression rate of 30% with VMQ silicon rubber gaskets. For the lifetime prediction at a high temperature, the compression set test was performed with components that were heataged in an oven at temperatures of 150, 180, and 200°C for periods ranging from 20 to 500 h, and a cold resistance test was performed at a temperature of –70°C for periods ranging from 48 to 120 h. The dimensions of the specimen (diameter = 29 mm and thickness = 12.5 mm) and the compression set were determined according to ISO 8151 (Figure
Jig for measuring the compression set.
Table
Results of the compression set test with a compression rate of 30% at (a) high temperatures and (b) a low temperature.
Temp. (°C)  Time (h)  CS (%)  Recov. (%)  Temp. (°C)  Time (h)  CS (%)  Recov. (%)  Temp. (°C)  Time (h)  CS (%)  Recov. (%) 

150  22  9.20  90.80  180  48  10.33  89.67  200  20  10.67  89.33 
1000  33.60  66.40  96  25.67  74.33  30  18.33  81.67  
120  31.00  69.00  40  19.67  80.33  
196  32.67  67.33  50  30.00  70.00  
240  34.33  65.67  200  83.00  17.00  
300  86.00  14.00  
400  92.00  8.00  
500  97.00  3.00 
Temp. (°C)  Time (h)  CS (%)  Recov. (%) 

−70  48  1.93  98.07 
72  2.73  97.27  
96  3.34  96.66  
120  3.78  96.22 
Representative automobile companies require the compression set rates of engine head rubber gaskets to be less than 40%. In other applications, the lifetimes of a gasket are defined as the time until its recovery rate is 60%. Both heat and cold resistance tests were performed. Experimental data at each temperature were obtained from the compression set test, and the recovery rate curves were fit using the SZGA method to find the optimal parameters of the smallest MSE between the bestfit function and the experimental data. Subsequently, the lifetime of the recovery rate at 60% was obtained from the bestfit recovery rate curve using a bisection method to solve the nonlinear equation. Finally, a linear regression model was fit by superimposing the recovery rate curve on the Arrhenius plot to obtain the longterm lifetime at the working temperature.
The lifetime evaluations have been made on the two differently regressed curves of methods 1 and 2.
The recovery rate curves were acquired using fourparameter methods 1 and 2. The SZGA method was used to optimize the four parameters, and the recovery rate curves of the two methods were fit using these four parameters. The recovery rate curves were compared with the experimental data. The results showed that the recovery rate curves could be fit properly using the four parameters. Figures
Recovery rate curves using fourparameter method 1 with a compression rate of 30% at temperatures of (a) 150°C, (b) 180°C, and (c) 200°C.
Recovery rate curves using fourparameter method 2 with a compression rate of 30% at temperatures of (a) 150°C, (b) 180°C, and (c) 200°C.
The MSE [
MSEs of the fourparameter methods at a compression rate of 30%.
Method  MSE  Total MSE  

150°C  180°C  200°C  
Fourparameter method 1  0  10.432  3.998  14.430 
Fourparameter method 2  0  6.712  3.988  10.700 
One can see that fourparameter method 2 yields a smaller MSE than method 1 for a compression rate of 30%.
Compression set rates less than 40% are required by major automobile companies. The precise lifetime corresponding to a recovery rate of 60% can be determined using the bisection method from the fourparameter equations. The method with the minimum MSE is the best choice to obtain the lifetime with a 60% recovery rate. The lifetime data acquired from each recovery rate curve were plotted using linear regression, and a linear equation was derived using the Origin Pro system (Figure
Arrhenius plots for fourparameter methods (a) 1 and (b) 2.
Under operating conditions of 30 mph (mile/hour) at 100°C, the lifetime mileage values of the rubber gasket predicted by fourparameter methods 1 and 2 are 6,836,220 and 7,805,780 mi, respectively, as shown in Table
Lifetime mileage determined using the Arrhenius equation.
Compression rate 30%  

Fourparameter method 1  Fourparameter method 2  



Temperature (°C)  Lifetime mileage (10^{3}miles)  Temperature (°C)  Lifetime mileage (10^{3} miles) 
80  57,911  80  69,453 
100  6,836  100  7,805 
120  1,003  120  1,095 
140  177  140  186 
160  36  160  37 
180  9  180  9 
A closer look at the experimental data at a low temperature (Table
Lifetimes from the fitted line.
Recovery rate (%) = 


Time (h) 

Compressed set (%)  Recovery rate (%) 
2,579  7.8552  10  90 
30,384  10.3217  15  85 
357,960  12.7882  20  80 
4,217,197  15.2547  25  75 
49,683,641  17.7212  30  70 
Recovery rate curve at low temperature (–70°C).
A compression set test was carried out on developed VMQ gaskets at a compression rate of 30%. The SZGA method was applied to determine the optimal four parameters for the two fourparameter methods used in this study and calculate the recovery rate curves. The MSEs of the regression functions from different models and the experimental data were compared. By comparing the results of both methods, it was determined that either method can be used to accurately predict gasket lifetime because they showed only small differences in their results. We obtained the target lifetime for a recovery rate of 60% (80% for –70°C) through the fitted recovery rate curve using the bisection method at each temperature.
Referring to the data points of the 60% (80% for –70°C) recovery found from the recovery rate curves, a linear Arrhenius plot in the
The results are summarized as follows.
A procedure using fourparameter methods 1 and 2 to predict the longterm lifetimes of rubber gaskets was suggested.
Using fourparameter methods 1 and 2, the quantitative lifetime of a rubber gasket could be accurately predicted at any given temperature.
The lifetime mileage of VMQ was predicted to be 6,836,220 and 7,805,780 mi using fourparameter methods 1 and 2, respectively, at a working temperature of 100°C.
The lifetime of the VMQ rubber is 41 years at an ambient temperature of –70°C based on the standard recovery rate of 80%.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This study was carried out under the Small and Medium Business Technology Development Program supported by the Small and Medium Business Administration of the Republic of Korea. The authors are partially supported by the BK21 Plus Project of the Korea Research Foundation.