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Prediction of rolling resistance factor (RRF) for conveyor belt cover compounds with a rebound resilience tester.

Energy consumption reduction is a national goal for many reasons, from economic and national security to improving air quality and decreasing the greenhouse effect. An increase in the price of energy is affecting consumers and businesses, and also contributing to increases in the Consumer Price Index in the last few years.

There has been significant technical progress in the transport of bulk materials in the last few years. Conveyors have always moved materials over uneven terrain, through mountain tunnels and around horizontal curves; but today, the next step to improved conveyor efficiency is the reduction of power required to operate these high performance systems. Just as some tires provide lower rolling resistance, depending on their construction and compounds, a conveyor belt can also be designed to provide lower resistance as it rolls over the supporting idlers.

The factor energy efficiency (ref. 1) will gain significance in the future as a criterion for the acquisition, and therefore as a target value in the phase of development of technical systems, as well as in the bulk materials handling technique. This tendency will be determined on the one hand due to increasing energy costs, which will focus more on the life cycle costs of machines and systems when decisions of investment are made. On the other hand, the general climate debate encourages ecological thinking in the context of sustainable economic activities. The ecological action, i.e., the economical handling of resources such as electric current, which will also become more attractive financially in the future, as shown above, offers two advantages from the entrepreneur's point of view: The ecological necessity is now also economically reasonable.

The belt conveyor system also has ecological advantages, as shown in a case study by Zamorano (ref. 2), which provides a comparison between a dumper and a belt conveyor system with regard to the carbon dioxide emissions for two different conveyor lines.

Rubber is a viscoelastic material, and it has viscous as well as elastic phases. Under deformation of rubber, energy input is involved, part of which is returned when the rubber returns to its original shape. That part of energy, which is not returned as mechanical energy, is dissipated in the form of heat in the rubber (ref. 3).

Many rubber products are used for applications in which they undergo rapid cyclic deformations at a certain range of frequency, e.g., tire sidewalls, or tread and engine mounts, which serve the purpose of isolating engine vibration from a chassis or building. The dynamic mechanical properties are strongly dependent on temperature, frequency, the presence of fillers and the extent of deformation (refs. 3 and 4).

A variety of analytical and computational methods exists for calculating the indentation rolling resistance of conveyor belts. These include both one- and two-dimensional analytical approaches (refs. 5-9), and two-dimensional finite element methods (refs. 10-12). One-dimensional Winker Foundation models provide a simple and direct way to analyze the rubber deformation. Jonkers (ref. 13) focuses on the energy dissipation rate of the cover material in a steady deformation cycle, whereas Lodewijks (ref. 14) and others determine the power of the stress distribution at the idler/backing interface. Direct indentation rolling resistance measurement is practically limited to a small set of operating conditions compared to the wide range of loads on a belt conveyor or the operating environment for a particular application.

Analytical and computational methods rely on the measurement of the dynamic mechanical properties of the bottom cover compounds. These properties are typically measured using dynamic mechanical analysis (DMA) equipment. DMA machines rely on time-temperature transformations to simulate high frequency cyclic tests, where low frequency, low temperature data are shifted along the frequency axis to simulate higher frequency tests at the temperature being analyzed. The measured rubber properties are then used in the theoretical models based on the frequency of indentation and operating temperature.

A lower tan delta value is expected to provide lower rolling losses on a field conveyor, and therefore less horsepower consumed. Tan delta results can be gathered from tension, compression or shear methods. The tan delta component of energy loss is a valuable tool for correlating rolling resistance of rubber compounds (ref. 15).

A wide variety of experimental techniques for measuring dynamic mechanical properties of rubber compounds has been developed in research laboratories for specific investigations (refs. 16-40).

In a rebound resilience tester, deformation is an indentation due to a single impact. The ratio of energy returned to the energy applied is termed the resilience. When deformation is an indentation due to a single impact, this ratio is termed the rebound resilience. The value of rebound resilience for a given material is not a fixed quantity, but varies with temperature, strain distribution, strain rate, strain energy and strain history (ref. 41).

In a dynamic mechanical analyzer (DMA1000+), dynamic properties are measured using a strip specimen between -20[degrees]C to +70[degrees]C at 2% dynamic strain and 10 Hz frequency in tension mode. The properties that can be measured in a dynamic mechanical analyzer (ref. 42) are as follows:

* Elastic or storage modulus, E', is the real part of the complex modulus, E*. It represents the rigidity of an elastic material (elastic component) and is proportional to the maximum energy stored during a load cycle.

* Viscous or loss modulus, E", is the imaginary part of the complex modulus, E*. It represents the viscous component and is proportional to the energy dissipated during a load cycle.

* Loss factor, tan [delta], is the ratio of the loss modulus, E", over the storage modulus, E'.

* Rolling resistance factor, RRF, is calculated as:

RRF (measured by DMA) = (E")/[(E').sup.4/3] (A)

Experimental

Nine compounds having different rubber blends and carbon blacks (a major contributing element to viscoelastic properties) are mixed in a 1.5 liter laboratory internal mixer and are given in table 1. The mixing is done following the power integrator method of mixing. The discharged compounds from the internal mixer are sheeted out using a laboratory two-roll mill.

The green compounds are cured in an electrically heated laboratory hydraulic curing press. The curing condition maintained for determination of rebound resilience is at 150[degrees]C for tc90 + 5 minutes and at 150[degrees]C for tc90 + 2 minutes for dynamic mechanical properties.

The dynamic mechanical properties are measured using a viscoanalyzer (Metravib DMA 1000+) following ASTM D 5992, and rebound resilience is measured using a rebound resilience tester following ISO 4662.

The rolling resistance factor is predicted by using linear regression analysis and [R.sup.2] coefficient of regression (ref. 43) with the help of equation B:

Y = m * X + C (B)

Where, X is measured rebound resilience; Y is predicted rolling resistance factor using rebound; m is slope of the trend line; and C is intercept.

Results and discussion

Rebound resilience at 25[degrees]C is measured by a rebound resilience tester, and rolling resistance factor (RRF) is measured by a DMA1000+. The predicted, measured and percent variations are summarized in table 2.

The percent variations of measured and predicted rolling resistance factor values are calculated using equation C:

Percent variation = [(Predicted value--measured value)/measured value] x 100 (C)

We have also calculated the correlation coefficient between rebound resilience and RRF with a dynamic mechanical analyzer. The coefficient of correlation value is found to be 99%.

Linear regression used for prediction of rolling resistance factor and its coefficient of regression are mentioned in figure 1.

Conclusion

Rolling resistance factor (RRF) values measured by both pieces of equipment show excellent correlation (coefficient of correlation = 99%). The rolling resistance factor prediction by rebound shows less than 10% variation as compared to the value measured by the DMA1000+. The dynamic mechanical analyzer (DMA) is a very costly tester as compared to the rebound resilience tester, and it is very difficult for small-scale rubber producers to measure dynamic mechanical properties with a DMA tester. Therefore, the above experiment will assist in predicting the viscoelastic properties measured by DMA by simply measuring through a comparatively much less expensive tester, the rebound resilience tester.

by S.L. Agrawal, B.B. Sharma and Virendra Rathod, Reliance Industries Ltd., India

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Caption: Figure 1--linear regression analysis
Table 1--formulations used

Ingredients           RRF1     RRF2      RRF3      RRF4     RRF5

Natural rubber        0.00    60.00     40.00      0.00    70.00
PBR, Cisamer 01       0.00    40.00     10.00      0.00    30.00
Sty lamer SBR1502     0.00     0.00     50.00    100.00     0.00
Stylamer SBR1783    137.50     0.00      0.00      0.00     0.00
Carbon black         68.80    70.00     50.00     50.00    24.00
Ppt. silica           0.00    10.00     13.00      0.00    18.00
Aromatic oil          0.00    16.00     18.00      0.00     2.00
Zinc oxide            3.00     4.00      4.00      3.00     4.00
Stearic acid          1.00     2.00      2.00      1.00     2.00
Antidegradants        2.00     3.00      2.00      2.00     2.00
Accelerator            1.4      1.0       1.0       1.0      1.0
Soluble sulfur        1.75     1.90      2.00      1.75     2.00

Ingredients           RRF6     RRF7      RRF8      RRF9

Natural rubber       40.00    50.00      0.00     20.00
PBR, Cisamer 01      60.00    50.00    100.00     80.00
Sty lamer SBR1502     0.00     0.00      0.00      0.00
Stylamer SBR1783      0.00     0.00      0.00      0.00
Carbon black         33.00    30.00     60.00     39.00
Ppt. silica          12.00    14.00      0.00      8.00
Aromatic oil          2.00     2.00     15.00      2.00
Zinc oxide            4.00     4.00      3.00      4.00
Stearic acid          2.00     2.00      2.00      2.00
Antidegradants        2.00     2.00      2.00      2.00
Accelerator            2.0      1.0       0.9       2.0
Soluble sulfur        2.00     2.00      1.50      1.00

Table 2--prediction of rolling resistance factor (RRF)
by rebound value

Sample                  Rebound at    E' measured    E" measured
identification    25[degrees]C (%)         by DMA         by DMA
                                            (MPa)          (MPa)

RRF1                          37.6          13.01           5.72
RRF2                          41.3          15.99           6.10
RRF3                          42.2          11.67           4.12
RRF4                          49.8          15.25           4.27
RRF5                          56.8           7.10           1.16
RRF6                          58.7           8.27           1.31
RRF7                          58.9           8.70           1.48
RRF8                          59.3           8.98           1.48
RRF9                          61.0          10.11           1.62
Correlation
coefficient                                             (-) 0.99

Sample            RRF measured    RRF predicted            %
identification          by DMA       by Rebound    variation

RRF1                     0.187            0.175         -6.4
RRF2                     0.151            0.158          4.6
RRF3                     0.156            0.154         -1.3
RRF4                     0.113            0.119          5.3
RRF5                     0.085            0.087          2.4
RRF6                     0.078            0.078          0.0
RRF7                     0.083            0.077         -7.2
RRF8                     0.079            0.076         -3.8
RRF9                     0.074            0.068         -8.1
Correlation
coefficient
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Author:Agrawal, S.L.; Sharma, B.B.; Rathod, Virendra
Publication:Rubber World
Geographic Code:9INDI
Date:Jan 1, 2018
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