Flexometer predicts heat generation.

Internal heat generation is a result of energy absorbed by a rubber compound that is subjected to a cyclic deformation under load (refs. 1 and 2). The tire temperature reaches steady state after running for a certain period of time when the balance between heat generation and heat dissipation becomes equal. Heat dissipation, discussed in detail by Brownie (ref. 3) and Clark (ref. 4), is dependent on the thickness of the tire and the thermal conductivity of the rubber compound. Since rubber is a poor conductor, the steady state temperature can reach fairly high. Tire equilibrium temperature is affected by service conditions such as speed, load and surface texture of the pavement, as well as tire characteristics such as tire construction or material viscoelastic characteristics of each component.

Tire temperature has a marked effect on tire performance characteristics such as durability, tire wear resistance, handling and traction, as well as rolling resistance. Increase in tire temperature is the principal cause of rubber thermal degradation that leads to fatigue cracking or premature belt edge separation failure. Moreover, increase in temperature can also cause wire-to-rubber adhesion to deteriorate that can lead to severe belt separation. Tire temperature also has a strong influence on air permeability of the liner which plays an important role in tire durability. Elevated temperatures may also cause contained air to permeate more easily through the tire component which could provide more oxygen to the rubber compound and accelerate oxidative degradation or could cause inflation pressure loss which could result in a significant deflection of the tire. Change in tire temperature generally effects viscoelasticity of the rubber compound that can change rolling resistance, handling or traction performance. Temperature also affects the strength of rubber which will have significant effect on wear resistance as well as tread block tearing or chunking.

Usually, therefore, it is desirable to keep running temperature low enough to avoid any of the above mentioned tire failures. Running temperature often limits the speed and load at which a tire can operate, especially for heavy duty truck tires and off-the-road tires.

Heat generation is a result of energy loss of the rubber under cyclic deformation and therefore viscoelastic characteristics of the rubber compound should play a major role in temperature rise. The first part of this article will attempt to correlate material viscoelastic properties with tire temperature rise. However, since temperature rise is a balance between heat generation and heat dissipation, and heat dissipation is a heat transfer process which is not a function of viscoelasticity, temperature rise predicted solely from viscoelasticity may become artificial when the degree of heat dissipation is comparable to heat generation. A better way to circumvent such a situation is to directly observe the temperature rise itself by applying repeated deformation to a laboratory rubber specimen. The Goodrich Flexometer as well as the Firestone Flexometer are widely adopted in the tire industry over years as a laboratory tester to directly measure temperature rise. The second part of this article discusses some of the problems associated with the conventional Flexometer and introduced a new generation Flexometer that can better predict tire temperature.

Deformation index

When a tire is subjected to a cyclic strain, an energy loss occurs due to the deformation of the rubber components. The energy loss occurring during one periodic deformation cycle can be determined by equation 1 where [sigma] is stress and [epsilon] is strain.

(1) [Mathematical Expression Omitted]

Assuming that the periodic deformation cycle is sinusoidal, equation 1 may be rewritten as equation 2.

(2) Energy loss = [pi] [[sigma].sub.0][[epsilon].sub.0] sin[delta]

The relation between deformation amplitude and stress amplitude is given by equation 3 where [E.sup.*] is the complex modulus.

(3) [[sigma].sub.0] = [[epsilon].sub.0] [E.sup.*]

Therefore, when the deformation is a constant strain process, substitution of equation 3 into equation 2 to eliminate [[sigma].sub.0] gives equation 4 where E" is the loss modulus.

(4) [Mathematical Expression Omitted]

When the deformation is a constant stress process, substitution of equation 3 into equation 2 to eliminate [[epsilon].sub.0] gives equation 5.

(5) [Mathematical Expression Omitted]

Collins et al. (refs. 5 and 6) assumed that tire deformation is a linear addition of equation 4 and equation 5, and proposed equation 6 to predict the total tire energy loss where A, B and C are empirically determined constants.

(6) Energy loss = A E" + B(E"/[E.sup.*2]) + C

Futamura (refs. 7 and 8) simplified equation 6 by introducing the deformation index concept as is shown in equation 7 where "n" is called deformation index that ranges in any value between 0 and 2 and is an indication of the mode of deformation.

(7) Energy loss a E"/[([E.sup.*]).sup.n]

When n = 0, equation 7 reduces to equation 4 that represents a constant strain deformation. When n = 2, equation 7 reduces to equation 5 that represents a constant stress deformation and n = 1 represents constant energy deformation. Equation 7 is convenient since deformation index used in this equation is a singular parameter that describes whether the deformation is constant strain or constant stress depending on the value of "n". On the contrary, equation 6 required two constants, A and B, to describe the type of deformation which complicated the interpretation of the experimental results obtained. Futamura conducted a passenger tire test in an attempt to find a deformation index that best correlated the relationship between tire performance and tread viscoelasticity by regression analysis of equation 7. He found that the deformation index for wet traction is n = 0; a constant strain deformation process, while dry traction is n = 2; a constant stress deformation process. These completely opposite results are, however, self explanatory since wet traction is virtually a surface phenomena which is a constant strain deformation, while dry traction is more a function of total tread block deformation under compression which should be a constant stress deformation. Rolling resistance was generally around n = 1 except that inflation pressure and load significantly affected the deformation index.

Our previous work (ref. 9) proposed an even simpler formula than equation 7, but still used the deformation index concept as is shown in equation 8 where E' is the storage modulus.

(8) Energy loss [alpha] tan[delta]/[E'.sup.n-1]

This equation implies that energy loss is the ratio of loss tangent to storage modulus, and that the type of deformation only changes the storage modulus portion of the viscoelasticity. Equation 8 gives a better understanding of how physical properties will effect energy loss, namely, energy loss due to a constant strain deformation is proportional to storage modulus and energy loss due to a constant stress deformation is inversely proportional to storage modulus. Energy loss due to a constant energy deformation is independent of storage modulus, and merely a function of the loss tangent. In the previous work (ref. 9), the authors found that truck tire rolling resistance was closely approximated to a constant stress deformation. This result was somewhat different from Futamura's result on passenger tire rolling resistance, probably because of the much higher inflation pressure of truck tires. One will find that the results of equation 7 and equation 8 are practically equal as is shown in table 1. It should be noted that E' and E" are a function of temperature, rate of deformation and strain amplitude. Thus it is essential to test viscoelasticity under conditions as close as possible to the actual tire running conditions using time - temperature superposition.

[TABULAR DATA 1 OMITTED]

Another study by Sumner et al (ref. 10) demonstrated that belt edge separation is a constant stress deformation and side wall ozone cracking is a constant strain deformation. They also concluded that a pulse waveform better corresponded to tire results as compared to a sinusoidal waveform especially in a sidewalk deflection.

In the present work, the author attempted to empirically determine the deformation index for heat build up of truck tires.

Experimental results

Tire temperature

Five different tread compounds with a wide range of storage modulus and loss tangent were prepared using various carbon black and oil loading levels. Formulations and viscoelastic properties are shown in table 2. Some of the formulations were impractical from a tire performance standpoint (e.g. wear resistance) since the purpose of the test was purely to investigate the deformation index. A total of ten tube type 10.00R20 truck tires with a rib-lug pattern were built using the above tread compounds. One set of the tires was submitted to a rolling resistance test using a single axis drum, and the other set of tires was tested on an indoor wheel endurance test based on the step load FMVSS 119 procedure (speed of 65 km/hr, 0.75 MPa inflation pressure and ambient temperature 38[degrees]C). The temperature measurement was taken immediately after the tire was lifted from the drum and came to a stop. A thermocouple needle was inserted into the tire shoulder area above the belt edge region at the end of each step when the tire temperature reached steady state. Figure 1 shows the measured temperature at the first, second and third steps; 17.7kN, 22.8kN and 27.1kN load. The measured temperature was then plotted against energy loss calculated from equation 8 altering the value "n" from 0 to 2 in a 0.1 increment, and regression analysis was carried out on each "n" value. The best correlation was obtained at around n = 1.5 as was shown in figure 2. The highest correlation was observed for viscoelasticity at 60[degrees]C and 5% strain, although a fairly high correlation coefficient was found regardless of strain or temperature level. A multiple regression analysis would exhibit a similar result, but this study simply followed Futamura's procedure since it was straightforward and easier to find the correlation between different deformation patterns. Thus it was established from this study that heat generation in a truck tire is somewhat in-between a constant stress and a constant energy deformation.

[TABULAR DATA 2 OMITTED]

Figure 3 shows the correlation between temperature rise and energy loss calculated from equation 8 at n = 1.5.

Prediction of temperature rise using viscoelastic properties seemed to be successful with the five compounds employed in this study, when they had a fairly broad range of loss modulus and loss tangent. However, more deviation should be encountered in reality since compound variation would be narrower in normal practice. Moreover, viscoelastic properties would only predict energy loss that is the cause of heat generation, but would not predict heat transfer that is the cause of heat dissipation. In order to avoid any misleading results due to the heat generation and heat dissipation balance, a direct temperature rise measurement under repeated compression, as mentioned before using a flexometer would be more practical.

Flexometer

In a conventional flexometer, the sample is subjected to a cyclic compressive stress under constant static load and constant dynamic strain using a motor driven eccentric wheel. A typical sinusoidal constant strain cycle is shown in figure 4 where static strain increases and dynamic stress decreases with time. One of the problems associated with this instrument was that it could only be tested at a constant strain deformation. A new flexometer developed recently by Ueshima Seisakusho Co. Ltd., on the other hand, is capable of testing at either constant strain or constant stress deformation by the use of a servohydraulic drive system. A schematic diagram of the new flexometer is illustrated in figure 5. A typical sinusoidal constant stress cycle is shown in figure 6. Stress always stays in a constant sinusoidal repetition while both static and dynamic strain increases with time due to the compression set of the rubber specimen. The new flexometer has a frequency range of 1 to 50 Hz, maximum load 500N, peak to peak dynamic maximum stroke 6.5 mm, peak to peak dynamic maximum load 1,500N, and chamber temperature between room temperature and 150[degrees]C. The data obtained are recorded on a personal computer including time, temperature, stress, strain, as well as loss tangent and storage modulus as plotted in figure 7. The viscoelastic properties obtained from the new flexometer were similar to the normal viscoelasticity test results based on a sinusoidal compression and is handier to monitor than a conventional machine. Repeatability of the new flexometer test was found to be excellent because of the accuracy of the new system.

To reproduce the truck tire result, a laboratory test was first performed with the constant strain procedure using the conventional flexometer. Static load was set at 245N, chamber temperature at 40[degrees]C, frequency of loading was set to 30 Hz, and the dynamic strain level was set to 4.45 mm as designated in ASTM D263 (table 3). The correlation between the conventional flexometer and tire temperature rise turned out to be poor as shown in figure 8. This is of no surprise because the truck tire test concluded that the deformation was more of a constant stress than a constant strain deformation and suggested that laboratory tests should also be conducted at constant stress deformation. The conventional flexometer cannot be operated at such conditions. The tests were thus repeated with the new flexometer using a constant stress deformation. An insufficiently low dynamic force or an insufficiently low frequency did not create enough heat build up, while a more intensive dynamic load and frequency resulted in too high a temperature which led to blow out of the sample. The optimum static load was 196N and a 1.12 MPa dynamic force was applied at 10 Hz to duplicate actual truck tire deformation as denoted in table 3. A larger size specimen, 30 mm in diameter and 25 mm high, was used to simulate thick gauge of a truck tire tread block. The temperature was measured after 20 minutes when the temperature reached steady state using a sensor probe that was automatically inserted into the center of the sample. With this new procedure there is no error due to the temperature gradient as was the case with the conventional flexometer which only measured the platen surface temperature. The displacement of the specimen was similar to that of the conventional flexometer except that strain somewhat increased with time due to compression set of the specimen. The result was in excellent agreement with the tire temperature result and the correlation is shown in figure 9. Not only the tire temperature test but also the rolling resistance test results showed excellent correlation with the constant stress new Flexometer test. Thus it can be concluded that a constant stress motion is essential in predicting energy loss especially for truck tires.

[TABULAR DATA 3 OMITTED]

Summary

The goal of this study was to find a laboratory test procedure which would better predict heat generation in a truck tire. A deformation index study was carried out using a truck tire test that indicated truck tire heat generation was closer to a constant stress deformation than a constant strain deformation. Therefore, the conventional flexometer based on a constant strain deformation poorly predicted tire temperature while the new flexometer based on a constant stress deformation showed an excellent correlation. The new flexometer will also be useful to predict performance other than truck tire heat generation such as blow out in a racing tire, flat spot of a passenger tire, high speed endurance of a high performance passenger tire, or compression set of a off-the-road tire tread of which deformation is considered as constant stress.

[Figures 1 to 9 ILLUSTRATION OMITTED]

Acknowledgements

"Flexometer predicts heat generation" is based on a paper presented at the October, 1995 Rubber Division meeting.

"A straight-line braking test for truck tires" is based on a paper presented at the October, 1995 Rubber Division meeting.

"New technology polymer for tires" is based on a paper presented at IRC '95.

References

(1.) All. Medalia, Rubber Chem. and Technol., 64, 481 (1991).

(2.) J.D. Walter, F.S. Conant, Tire Science and Technology, 2, 235, (1974).

(3.) A.L. Browne, L.E. Wickliffe, Tire Science and Technology, 8, 37, (1980).

(4.) S.K Clark, Tire Science and Technology, 4, 181, (1976).

(5.) J.M. Collins, et al, Transactions of the Institution of the Rubber Industry, 40, 239, (1964).

(6.) J.M. Collins, et al, Rubber Chem. and Technol., 38, 400, (1965).

(7.) S. Futamura, Rubber Chem. Technol, 63, 315, (1990).

(8.) S. Futamura, the Tire Society Meeting, March 24-25, (1987).

(9.) H. Mouri, the 146th ACS Rubber Division Meeting, No. 56, (1994).

(10.) A.J.M. Sumner, S.A. Kelbch, V. Eisele, the 146th ACS Rubber Division Meeting, No. 18, (1994).