Correlation of wet traction with viscoelastic properties of passenger tread compounds.

Wet traction is one of the most debated tire performance characteristics. The tire's friction coefficient on wet road, as measured with a braking test, is a function of tread compound, tread design, tire characteristics, boundary conditions (temperature, road temperature, thickness of water), load supported by the tire, speed, surface of road and percentage of slip.

The friction coefficient ([Mu]) could be expressed as the sum of different contributions:

[Mu] = [[Mu].sub.adh.] + [[Mu].sub.def.] + [[Mu].sub.abr.] + [[Mu].sub.bdl.] where:

[[Mu].sub.adh.] = contribution of adhesion;

[[Mu].sub.def.] = contribution of deformation;

[[Mu].sub.abr.] = contribution of abrasion;

[[Mu].sub.bdl.] = contribution of boundary conditions (thickness of lubricant, kind of lubricant, environmental effects).

The contribution of abrasion and the contribution of boundary conditions are normally lower than the other two contributions.

Moore (ref. 1) developed an equation for the tread contribution:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Where: p = nominal pressure;

G' = elastic modulus;

tan [Delta] = loss factor;

[K.sub.1], [K.sub.2] = const.;

r [congruent] 0.2;

n [is less than or equal to] 1.

The first term on the right side of the equation is the hysteresis component and the second term is the adhesion component.

If we assume n = 1, according to Moore, the equation becomes:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Where: G" = tan [Delta][multiplied by]G' = loss modulus;

[K.sub.3], [K.sub.4] = const.;

tan [Delta]/G' = (G"/[G'.sup.2]) [congruent] J" is proportional to constant stress energy dissipation;

and G" is proportional to the constant strain energy dissipation. The effect of tread compound on the friction coefficient is thus related to the energy dissipation phenomenon induced by the stress-strain conditions in the tread itself.

[Mu] = a[multiplied by]G"+b [multiplied by]J" (3)

Where: J" = loss compliance

a,b = const.

The two terms are a function of experimental conditions. Futamura (ref. 2) suggested a new energy loss function in which the two terms were condensed in one using an exponent n:

[Mu] = K[multiplied by]G"/[(G*).sup.n] (4)

Where: K = const.

When n = 0, [Mu] is related to constant strain energy dissipation;

n = 2, [Mu] is related to constant stress energy dissipation.

Futamura calculated the values of n for wet traction, rolling resistance and dry traction and found:

n = 0 for wet traction;

n = 0.8 for rolling resistance;

n = 2 for dry traction.

Wet traction, therefore, is fundamentally a constant strain phenomenon.

Veith (ref. 3) studied surface roughness effects on the correlation between wet traction and viscoelastic properties. He found a change of energy dissipation from constant strain to constant stress with increasing surface roughness.

Viscoelastic properties of compounds are dependent on temperature and strain. This must be taken into account every time that the effects of compound properties on tire performances are analyzed.

Braking tests on two surfaces of different roughness were performed to study the effects of strain on correlation between wet grip and viscoelastic properties.

Experimental

Six compounds were evaluated for the tire braking test. Experimental compounds designed for this study were selected based on general requirements for a wide range of speed ratings.

Due to the large range of application, the 175/65 R14 H-rated tire was selected as a medium performance tire allowing a good characterization for the whole compound range. All tires were cured in the same mold, with the same curing cycle and with the same tread design. The selected compounds are listed in table 1.

                   Table 1 -- compounds selected

Compound        Application     Polymer(s),    Filler(s)
A               Low rolling     SSBR/ESBR      Carbon black/silica
                resistance
                S rated tires
B               S-T             ESBR/BR/NR     Carbon black
C (reference)   T-H             ESBR           Carbon black
D               H-V             ESBR           Carbon black
E               H-V             ESBR           Carbon black/silica
F               V-Z             ESBR/BR/NR     Carbon black/silica

Viscoelastic properties of compounds were measured using a Rheometrics RDA. Frequency of 1 Hz was selected for torsion sinusoidal deformation cycle on cylindrical specimen (radius = 5 mm, height = 6 mm).

Strain sweeps from 0.05% to 40% strain at four different temperatures, -10, 0, 10 and 23 [degrees] C, were performed using two sets of specimens.

The first series was directly taken from the tire and was cured in the tire mold with a non-isothermal production cycle. An example of strain sweep (0 [degrees] C) is shown in figure 1.

The second series was taken from the tread extrudate which was then cured in the laboratory mold under isothermal conditions with a temperature equal to the maximum reached in the tire mold for the time reaching the same total equivalent cure. All results are the average of five specimens.

The braking tests were carried out according to the ASTM method (ref. 4) measuring percentage of slip vs. friction coefficient from 0 to 40% and the slide value.

Tests were performed at constant speed of 96 Km/h and constant load of 3,924 N on two surfaces with different roughness and skid rating according to ASTM (ref.5), a medium roughness asphalt surface with a skid number of 45 (surface H), and granite with a skid number of 10 (surface L). Granite provides the lowest achievable friction coefficient. All tires were run in for 100 Km before testing. Tire inflation pressure was 220 KPa. Water volume rate per unit area was 60 [mm.sup.3][multiplied by]-[mm.sup.2][multiplied by][h.sup.-1].

The results of reference compound (C) were taken from an average of ten tires, the other results are taken from an average of three tires. On each tire ten braking tests were performed.

Results

Statistical analysis of braking data

The maximum friction coefficient is reached at different values of slip for the two different surfaces. In the data analysis, 10% and 100% slip were considered.

10% slip is not far from the peak for each compound tested on the rougher surface H. Even if 10% slip was not corresponding to [Mu] peak for surface L, this value was chosen to maintain constant slide speed, and to minimize elastohydrodynamic effect, as will be discussed later. 100% slip is the slide value.

The ASTM procedure inserts one reference tire every two experimental tires. This is done to control the daily changes in temperature, humidity and possible other environmental factors. The linear regression based on the reference tire is used to adjust the results of the experimental tires.

Statistical analysis was performed to control possible significant differences in die reference tire during the three test days. No variation in test results was observed during the three test days.

The coefficient of variance for this surface, defined as V.C. = 100 [multiplied by] (standard deviation/average), is very low. The maximum value is 4%.

The friction coefficients measured on surface L are very low compared to values measured on surface H. On this surface, slide values are closer to 10% slip value.

Data show a higher scattering and the coefficient of variation has a value near 7%.

As in the case of surface H, the statistical analysis of the reference tires on surface L has not shown any effect from testing time: all reference tires showed the same values for the three test days. Tables 2 and 3 show 10% and 100% slip values for surface H and L, respectively.

Table 2 -- friction coefficient at 10% and 100% slip for surface H

Compound        A       B       C       D       E       F
10% slip      0.820   0.857   0.866   0.873   0.880   0.889
100% slip     0.423   0.424   0.447   0.440   0.435   0.432

Table 3 -- friction coefficient at 10% and 100% slip for surface L

Compound       A       B       C       D        E        F
10% slip     0.111   0.152   0.139   0.1610   0.1750   0.156
100% slip    0.157   0.108   0.100   0.0903   0.0903   0.090

Correlation between viscoelastic properties and 10% slip data

The data analysis has been performed using the viscoelastic data obtained on the samples taken from the tire. Table 4 shows the maximum correlation coefficient ([R.sup.2]) with constant strain, constant stress and constant energy dissipation at three different temperatures (-10 [degrees] C, 0 [degrees] C and 10 [degrees] C) on the two surfaces. The [R.sup.2] values at temperatures higher than 10 [degrees] C are not reported, since they are definitely worse than those measured at 10 [degrees] C.

[TABULAR DATA NOT REPRODUCIBLE IN ASCII]

Regression is statistically significant at 95% confidence, if absolute value of R is higher than 0.811.

The best correlations are obtained at 0 [degrees] C and are consistent with a constant strain energy dissipation phenomenon. A contribution of constant stress energy dissipation is expected with increased roughness surfaces.

In figure 2, correlation coefficient of friction with G" on surface H is plotted versus the values of imposed strain in the viscoelastic test at three different temperatures (-10 [degrees] C, 0 [degrees] C and 10 [degrees] C).

The best correlation curve shows unexpectedly two peaks. The curve has two relative maximum points, one at very low strain and a second close to 10% of strain.

This behavior could be explained considering the viscoelastic properties. Medalia (ref. 6) described energy dissipation being a phenomenon due to disaggregation and reaggregation of the secondary network of filler agglomerates. According to this explanation, the two zones are both characterized by low contribution of secondary network: in the first case, strain is too low to have disaggregation of filler network, and in the second case, strain is too high to have reaggregation.

This explanation does not clarify what is the real strain of a tread element during the braking test. Figure 3 shows the best correlation for surface H with the predictive equation. The constant takes into account boundary conditions due to the depth of the water lamina and speed of the car.

Figure 4 shows [R.sup.2] versus strain for the correlation between friction coefficients at 10% slip measured on surface L and G" at three different temperatures. The shape of the best correlation curve is totally different. [R.sup.2] has a single maximum in the peak region of energy dissipation. On the smoothest surface the strain value for the best correlation is shifted towards lower values (2%).

The linear and quadratic regression between [Mu] and G" (0 [degrees] C, 2% strain, 1 Hz) are shown in figure 5. The best correlation is obtained with the quadratic regression. This could be due to the beginning of elastohydrodynamic effect which is the controlling factor of the compound behavior in slide, as will be discussed in the next paragraph. According to the description of Moore (ref. 1), for very smooth surfaces and high sliding speed, elastohydrodynamic effect becomes important and tends to eliminate the hysteresis effect and to build up a pressure profile which tends to separate the surfaces and decreases friction.

At 10% slip, it seems that the elastohydrodynamic effect is less effective for the softer compounds with lower modulus. Viscoelastic data at 0 [degrees] C at 2% and 10% strain are reported in table 5.

Table 5 -- viscoelastic parameters at 0 [degrees] C and 1 Hz at two different strains

  Compound          A      B       C      D       E       F
2%   G' Mpa      3.25   8.34    9.03   9.81    11.4    8.69
     G" Mpa     0.739   3.44    3.49   4.19    4.30    4.06
10%  G' Mpa      2.36   3.19     3.9   3.62    4.66    3.71
     G" Mpa     0.615   1.48    1.70   1.86    2.06    2.22

Correlation between viscoelastic properties and 100% slip (slide) data

Table 6 shows the best correlation coefficients [R.sup.2] obtainable for [Mu] 100% slip according to dissipation models at constant strain, constant stress or constant energy at four different temperatures (-10 [degrees] C , 0 [degrees] C, 10 [degrees] C and 23 [degrees] C). The viscoelastic data used are referring to samples taken from the tire.

[TABULAR DATA NOT REPRODUCIBLE IN ASCII]

For the rough surface (H) the best predictor is G" confirming a constant strain energy loss mechanism; the temperature and strain conditions are nevertheless different from the situation described for [Mu] prediction at 10% slip. The temperature and strain conditions change according to the modified operating condition of the compound in slide passing from 10% strain at 0 [degrees] C, to 40% strain at 10 [degrees] C (figure 6). This seems quite reasonable taking into account the very different operating conditions of the compound in the contact area. The tread compound is subject to higher deformation on the asperities of road surface H during sliding, and this explains the better correlation with G" measured at 40% strain. The increased level of temperature is probably due to the sum of two effects. The first is the increase in frequency of the deformation cycle which should lead to a decrease of the temperature according to WLF superposition principle, but it is also clear that the effective temperature of the sliding compound is significantly increased with respect to the compound moving on the surface at much lower sliding velocity. So the combination of increased frequency and temperature leads to an effective increase in temperature for best prediction at 10 [degrees] C, and from 0 [degrees] C to 10 [degrees] C moving from peak to slide conditions.

The case of surface L (granite) is very different from the previous one. Elastohydrodynamic effect becomes more important with increasing slip. In this case, better values of [Mu] are obtained for softer compounds, and so it is explained the negative slope of [Mu] with G".

Wet traction interpretation by viscoelastic measurements

According to the earlier observations, wet traction is a constant strain energy loss phenomenon except when sliding on smooth surface (granite). In figure 7 are shown the regions of interest of G" for better wet traction prediction in different operating conditions. It appears now quite reasonable to indicate the area of 10% strain for [Mu] peak on surface H, than the region of 0.1% strain.

Curing cycle effect on wet traction prediction

A satisfactory predictive method to predict wet traction as a function of viscoelastic properties of the tread compound must be based on data obtained with compounds mixed and cured under controlled conditions in the R&D laboratory. Only in this case the predictive model is useful in reducing the number of tire tests with a time and money savings.

The main differences between samples taken from the tire and samples prepared in the laboratory consist in the mixing and in the curing cycle (ref. 7).

All tire producers have a well established internal know-how which allows them to efficiently reproduce in the laboratory the mixing cycle used in the large scale production internal mixers. It is more difficult to simulate in the laboratory non-isothermal curing cycle. The results on this matter are still unsatisfactory.

Figure 8 shows the trend of [R.sup.2] with strain, where [R.sup.2] is the correlation coefficient between G" measured on samples taken from the tire and G" measured on samples cured with isothermal curing cycle and constant time. [R.sup.2] value decreases as strain increases. This confirms that the effect of the primary crosslink network on viscoelastic properties is important at high strain as stated by Payne (ref. 8) (and confirmed by Medalia). The consequence of this is a definite loss of the model predictive power with a dramatic decrease of the correlation coefficient.

In this study, the loss in predictivity might be acceptable. The wide range of the viscoelastic properties of the tread compounds is such to allow an appropriate ranking. However, in most of the cases, the compounders make only slight changes in the compound recipe to improve wet traction. In this case, the laboratory isothermal curing cycle used,could have misleading effects.

The tread compounds used have different t90 values, but all shorter than the curing cycle time. The compounds do not show cure reversion. A correction factor for G" has been defined as the ratio between t90 of the reference compound and t90 of the compounds themselves. So a modified G" is defined as:

[G".sub.i adj.] = G" [.sub.i][multiplied by][t90.sub.ref.]/t90 i where:

[G".sub.i adj.] = corrected value of G" of compound i;

[G".sub.i] = value of G" as measured of compound i;

t90 ref. = time to reach 90% of cure of reference compound C;

[t90.sub.i] = time to reach 90% of cure of compound i.

In table 7 are shown t90 [.sub.ref.]/t90i and [G".sub.adj.] at 0 [degrees] C, 1 HZ and 10% strain of tested compounds.

Table 7 -- t90 [.sub.ref.]/t90 and G" [.sub.adj.] (0 [degrees] C, 1 Hz, 10% strain) of tested compounds

Compound                    A      B     C      D      E      F
t90 [.sup.ref.]/[t90.sub.i]  0.648  0.961  1.00  0.921  0.982  1.285
G" [.sup.adj.] Mpa           0.408  1.320  1.74  2.060  1.960  2.590

This empirical correction permits to re-establish the model predictivity at the same level of the model obtained with viscoelastic properties measured on samples taken from the tire.

It is therefore clear that the problem of the isothermal curing cycle is, at this stage, only exploratory, and that it is necessary to perform more extensive work on this subject.

Innovative curing systems will probably require more sophisticated correction factors to maintain wet traction predictivity by viscoelastic properties.

Summary and conclusions

Good wet traction prediction is obtained by viscoelastic properties measurement at 0 [degrees] C. G" is the best predictor, varying the strain level according to road roughness and slip value. The two surfaces used in this study are relatively smooth to simulate the most critical conditions. It is expected that the energy loss at constant stress will give a contribution on rougher surfaces.

Slide values are well predicted by G" at higher strain and temperature only for surface H, for the smooth granite surface the elastohydrodynamic effects become important and tend to eliminate the hysteresis effect.

The effect of the curing cycle is critical for best prediction. The excellent wet traction correlation with G" for both surfaces was obtained with the viscoelastic properties measured on specimens taken from the tire treads. Laboratory isothermal curing causes a loss of the predictive power of the wet traction model which might cause wrong ranking of new experimental compounds. Additional work must be done on model compounds to investigate carefully the effect of the isothermal curing cycle to define appropriate "correctors" of G" based on the curing system and curing behavior of compounds.

References

[1.] D.F. Moore, "The Friction and lubrication of elastomers," Pergamon Press, 1972.

[2.] S. Futamura, Tire Science and Technology, 18, 1, 1990.

[3.] A.G. Veith paper no. 30 presented at Rubber Division Meeting, October, 17-20 1995.

[4.] ASTM F408-94, standard test method for tires for wet traction in straight-ahead braking, using a towed trailer.

[5.] ASTM E274-90, standard test method for skid resistance of paved surfaces using a full-scale tire.

[6.] A. Medalia, Rubber Chem. Tech., 51, 437 (1978).

[7.] A. Serra, A. Amaddeo and S.K. Mowdood "Effect of curing conditions on viscoelastic properties of tread compounds," Palermo (1994).

[8.] A.R. Payne, Rubber Plast. Age, Aug., 1961, p. 963.