Sealing
Table 1 . Series of models used to fit and extrapolate at long-term prediction for compression set and compression stress relaxation . Properties Compression Set Compression Stress Relaxation
Power function model |
P ( t ) = A . t b |
NA |
Exponential model |
P ( t ) = Bexp (– kt α ) |
f ( t )
=
1
−Σ g i ( 1− exp ( −t / τ i )) i
|
P-T-t model P ( t ) = B 0 + B 1 · 1 / T + B 2 log ( t ) NA
Compression set The first to be studied was the compression set ( CS ) in accordance with ISO 815-1 . The test consisted of applying compression on the button and the O-ring ( cut to avoid tightness ) and to evaluate the elastic recovery of the rubber after disassembly ( Figure 1a and b ) at different temperatures and durations . Three samples are used to obtain an average and variance of measurement . The initial compression of 25 % is applied using standard spacers . The relation is given by :
CS = H 0 − H 1 . 100 H 0 − H 2
Here , H 0 is the initial value of thickness , H 1 the final value and H 2 the value of spacer .
Compression stress relaxation The second test apparatus ( Figure 2 ) was developed by Cetim to measure the continuous change of the sealing force relaxation F ( t , T ) with time and temperature , using a force sensor to determine the compression stress relaxation ( CSR ). Once
CS (%)
60
50
40
30
20
10
End-of-life criterion ( 50 %)
End-of-life criterion ( 30 %)
@ 200 ° C [ button ]
@ 150 ° C [ button ]
@ 200 ° C [ O-ring ]
@ 100 ° C [ button ]
CS
0,5
T 1
< T 2 < T 3 t 3
T 3
t 2
Log ( t )
T 1
< T 2 < T 3
( a ) |
( b ) |
( c ) |
Figure 4 . ( a ) and ( b ) and ( c ). |
|
|
again , the level of compression is 25 % on an SC-329 O-ring ( 50.17x5.33mm ). The initial force F 0 is determined and the normalised force values ( F / F 0
) are investigated with time .
Analysis methodology
The change of CS and CSR depends on the time , the ageing temperature , and the size of the sample . To analyse and compare the values obtained by the working group , and to estimate the lifetime performance of the rubber , several steps were performed on the data as shown in Figure 3 .
Modelling compression set and compression stress relaxation When you study the change of CS and CSR
|
0
0
|
200 |
400 |
600 |
800 |
1000 |
1200 |
8
0.0020
|
0.0022 |
0.0024 |
0.0026 |
0.0028 |
0.0030 |
Time ( hours ) |
1 / T ( K^-1 ) |
( a ) |
( b ) |
Figure 5 . ( a ) Evolution of compression set with time with 3 temperatures ( button and O-ring @ 200 ° C ) with |
power law model and ( b ) the determination of E a with 30 % end-of-life criterion . |
In ( t )
18
16
14
12
10
T 2
9535x-11 CS-criterion intersection values
t 1
T 1
CSR
1,0
0,5
T 3
T 2 t 3 t 2
T 1 t 1
Log ( t )
Ln ( t ) t 1
t 2
t 3
with time and temperature , it is possible to describe the value using different models to extrapolate for long-term prediction . A series of usual models is given in Table 1 for each property . For each configuration , a series of parameters are identified .
Arrhenius approach Based on the ISO 11346 ( Rubber , vulcanised or thermoplastic – estimation of lifetime and maximum temperature of use ), the Arrhenius approach could be applied to the empirical model proposed in Table 1 . This approach is used when thermooxidative ageing appears in the material . The first step is to fix an end-of-life criterion corresponding to a limit of change of the properties studied . Often , the value of 50 % is retained as end-life criterion as proposed in ISO 11346 . However , it is possible to select the value of this criterion in relation to an operational function , for example leakrate . Some authors evaluate the end-of-life criterion for CS at around 80-90 % for O-ring . The Arrhenius approach assumes that a chemical damage is induced by the reaction rate k defined by the equation following : k= Ae
−E a
RT
T 1
< T 2 < T 3
T 3
T 2
E a
RT
T 1
1 / T ( K -1 )
|
Relaxation index ( from CSR )
1.00 0.90 0.80 0.70 0.60 0.50
|
CSR-avg “@ 100 ° C ” CSR-avg “@ 150 ° C ” CSR-avg “@ 180 ° C ” f1-avg ( t ) -100 ° C f3-avg ( t ) -150 ° C f5-avg ( t ) -180 ° C criteria ( 50 %) |
In ( t )
16
15
14
13
12
|
4620x + 2.07 |
Here , A is the pre-exponential factor , E a the Arrhenius activation energy , R the gas constant ( 8.314 J / mol-K ) and T the absolute temperature . The activation energies are estimated from Figure 4a ( for CS ) Figure 4b for ( CSR ) transposed in Figure 4c . The slope of linear regression in ln ( t ) vs ( 1 / T ) allows calculation of E a
.
|
0.40 |
0.0020 |
0.0022 |
0.0024 |
0.0026 |
0.0028 |
0.0030 |
0.001 |
0.01 |
0.1
1
Time ( hours )
|
10 |
100 |
1000 |
10000 |
1 / T ( K^-1 ) |
|
|
( a ) |
|
|
|
|
( b ) |
Figure 6 . ( a ) Evolution of relaxation index ( CSR ) with time and ( b ) the determination of E a with 50 % endof-life |
criterion . |
Results and discussions Compression set A complete study of the member ’ s compression set test data was carried
52 Valve World August 2023 www . valve-world . net