Response of elastomeric bushings to combined compression/shear loadings.
Elastomeric bushings for military tracked vehicles are molded onto steel pins, which are then inserted into the track shoe. The percent compression of the bushing is approximately 35% to 40% (ref. 6). In actual use, the track bushing experiences a complex combination of compression and torsion. The torsion is the result of the track passing over the drive sprocket. Compression on one side of the bushing is the result of track tension, which is applied to the track string to keep it on the vehicle. This static tension is reported to be in the range of 11,000 N during operation. During track movement, dynamic tension is also present and may result in forces as high as 200,000 N on the track assembly (ref. 7). These high stresses cause the bushings to show extreme heat build-up, with temperatures up to 150[degrees]C seen in actual use (ref. 6). Failure of the bushing occurs on the compressed side of the bushing, with cracks beginning on the inside surface of the pin, eventually resulting in failure of the material in this region. Tests for monitoring the failure behavior of bushing compounds have been developed (refs. 8 and 6) that simulate the most severe conditions experienced by the bushings. In these tests, the bushing is subjected to a fixed torsional angle of [+ or -] 15[degrees] and a radial load of 12.4 MPa.
Simula et al (ref. 9) investigated the effects of initial compression of the service life of bushings. The results from both laboratory and field tests suggested that reduced initial compression improved bushing endurance. Considerable information exists to model the stress-strain behavior of bushings (refs. 10-12), including methods to predict the sinusoidal behavior (ref. 13), however, there has been little information on the hysteresis behavior of bushing compounds.
Failure as the result of heat build-up or thermal runaway can lead to the blowout of both tank track pads and solid tires (refs. 14-16). Heat build-up behavior is often predicted using the properties measured by dynamic mechanical analysis (shear storage modulus, G', shear loss modulus, G", and tan delta) (ref. 17). These data are usually generated at low strains, under simple loadings such as tension or shear. Since heat build-up is an important contributor to bushing failure, it was of interest to determine the effect of more complex loadings on the dynamic properties of elastomeric materials. Under a fixed sinusoidal deformation, the energy dissipated per cycle is equal to [pi][([[gamma].sup.0]).sup.2] G"([omega]) where [[gamma].sup.0] is the strain amplitude (ref. 18). Heat build-up can be predicted under this type of operating condition if the strain amplitude, dynamic and thermal properties of the material are known.
Relatively limited testing has been performed on the material behavior under the effects of combined loading. Porter and Meinicke (ref. 19) studied the effect of compression and shear for bonded rubber blocks. They found that when the data were corrected for change in area due to bulging, differences in shear strain due to thickness changes and change in shear loads due to stored force from compression, the shear stress strain behavior was unaffected by compression. The dynamic behavior of rubber under the effects of this type of combined loading was not studied. Kar and Bhowmick (ref. 20) investigated the effect of constrained extension on the hysteresis behavior of elastomeric compounds. Their results showed higher hysteresis loss under constrained deformation when compared to pure shear and uniaxial deformations. The focus of this research was the response of elastomeric bushings when subjected to combined compression and shear loadings. Results from these experiments can be used to predict the performance of bushings under severe service requirements.
Five elastomeric compounds with three different base polymers were used for this study. Three of the compounds were based on epoxidized natural rubber, one utilized natural rubber, while the final compound incorporated hydrogenated nitrile rubber. Table 1 shows the general formulations for these materials. All five compounds contain carbon black, with filler shown as a component of the masterbatch for the NR compounds. Only the HNBR formulation used a peroxide crosslinking agent, all the others used sulfur.
In order to simulate the operating environment of a tank bushing, a specialized fixture was designed to apply a compressive force while the material was undergoing shear displacement. It consisted of a stationary platen and a movable platen attached to a pressure cylinder. The device was designed to be mounted in a conventional testing machine with the compressive force applied horizontally and the shear displacement to be applied vertically. Two rubber pads and a metal plate were sandwiched between the platens. Cylindrical elastomer samples, 15.2 mm thick and 25.4 mm in diameter, were cut from molded rubber blocks using a cutting die for testing. The surfaces in contact with the samples were grit blasted with #80 mesh media to replicate surfaces observed in commercial bushing designs. The central metal plate was connected to the load cell on the testing machine. Compressive force was generated using an 82.55 mm diameter pneumatic cylinder pressurized with compressed dry nitrogen, which was adjusted using the pressure regulator on the nitrogen tank. An amplified pressure transducer was used to monitor the pressure and thus compression force on the samples. A rectilinear potentiometer was affixed to the apparatus to monitor the position of the plates to determine thickness of the compressed sample during testing.
Dynamic tests were performed using a servo-hydraulic with an amplitude of 6.35 mm and a frequency of 2 Hz was applied to the specimens. To minimize the thermal effects on the material being tested, 100 cycles were run at each level of compressive force, followed by a 10 minute rest period before the next compression level. Compression force was increased from 775 to 7,540 N in 750 N increments. All tests were performed at an ambient temperature of 25[degrees]C.
A data acquisition system was used to collect all testing data. Force and displacement data were collected from the testing machine at a rate of 80 samples per second. The compressed thickness of the samples during the testing was recorded using the rectilinear potentiometer. Calculation of hysteresis values was performed using a script program developed specifically for this task, integrating the loop area using the trapezoidal rule with the 40 data points defining every cycle tested.
Static compression tests were performed using the test fixture in a universal testing machine. The true areas were measured using pressure indicating films. Before testing, the films were inserted between the platen and the rubber pad, and a compressive load was applied. The film was removed and a new set of film was inserted for the next load level. The actual load area of the compressed sample was determined by measuring the loaded area of the test specimen using image analysis software.
Results and discussion
Figure 1 shows representative hysteresis loops in fixed shear displacement as a function of an order of magnitude increase in compressive force. This figure plots measured shear force versus deforming displacement. The data show hysteresis increasing with compressive load, as indicated by the enhanced areas of the curves. Nonlinearity of the viscoelastic response is observed in the nonuniformity of the resultant ellipses. Changes in the axis of rotation are believed to be related to geometric nonlinearities in the sample, which will be corrected in subsequent discussions, specifically, changes in applied shear strain and loaded area.
[FIGURE 1 OMITTED]
In tensile compression applications, the static load results in a lateral expansion or bulge on the material, changing the effective loaded area of the specimen. This deflection causes the strain level to change, since, in our test conditions, the amplitude of the applied displacement was maintained at a constant value. The actual shear strain on the specimen was calculated by using the displacement amplitude (6.35 mm) divided the actual thickness of the compressed sample as measured by the potentiometer. To convert the forces into stress values, the actual area of the sample must be determined. Actual areas measured from the pressure sensitive film at different compressive strains (applied statically) are shown in figure 2. As expected, load area increases with compressive strain. These measured areas were used to calculate the true stresses on the specimens.
[FIGURE 2 OMITTED]
Since the pressure sensitive paper obtained the actual loaded areas of the bulged sample, it was of interest to compare these results with various calculation methods. The most simplistic method is to assume that the rubber is on a frictionless surface and free to expand. For most applications, this is not realistic behavior. The bushing in actual service is not bonded to the outer surface, but is held in place under the effects of compression and friction. In our testing apparatus, the specimen is held in place without the aid of any adhesive.
Prior work comparing the frictionless surface approach to the actual measured areas indicated that a frictionless surface approach is not applicable (ref. 21). Porter and Meinecke (ref. 19) describe a method to calculate the areas based on lateral expansion of the specimen for bonded rubber blocks. Figure 3 shows a comparison of the areas calculated using their approach to the results from the pressure sensitive film. At high compressive forces, the results differ from the theoretical calculations. In order to approximate the highly compressed region, a second approach was formulated. We assume that the volume of the rubber cylinder remains constant and that the outer surfaces of the bulge area can be described by a semi-circle. Figure 4 illustrates classic compression of a bonded rubber block. For the uncompressed cylinder, the volume is:
(1) V = [pi][R.sup.2]t
where R is the radius of the uncompressed cylinder and t is the uncompressed thickness of the cylinder. When the block has been compressed, the volume of the cylinder is:
(2) V = [pi][r.sup.2]t'+2[pi]r(1/8[pi][t'.sup.2])
where r is the new radius of the compressed sample and t' is the thickness. Assuming constant volume, equation 1 must be equal to equation 2. This reduces to:
(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
then r = R. Equation 3 can be used to calculate the loaded area of the sample. From figure 3 we see that this new model provides a better representation of the effective areas at high strains, however, the model by Porter and Meinecke is superior at low strains.
[FIGURES 3-4 OMITTED]
The actual areas were used to calculate the compressive and shear stresses. The shear stress, [tau], in simple shear is defined as the reaction force, F, divided by the area, A. The shear strain, [gamma], is defined as the displacement, d, divided by the sample thickness. Figure 5 shows typical hysteresis behavior in terms of actual shear stress and strain as a function of applied compressive stress. These curves should be compared with those in figure 1 to highlight the correction imposed by using true compressed area.
[FIGURE 5 OMITTED]
Figure 6 shows the average energy loss (average of 100 cycles) per second by the sample for all the materials as a function of applied compressive force. These data have not been corrected to reflect the true stress and strain on the specimen, but can be used to compare heat generation behavior for different materials. The data for HNBR-12 are shown only for the lower values of compressive force as the material failed prematurely. Both figures 5 and 6 show that as the compressive stress increases, the area of the hysteresis loop correspondingly increases. This is not unexpected, as the deflection of the sample will cause the strain level to change (increase), since in the test conditions, the amplitude of the applied displacement was maintained at a constant value. Figure 7 compares the hysteresis loss for all the materials corrected to reflect the true stress and strain on the materials. Based on the equation given in the introduction for a sinusoidal strain cycle, we anticipate that the hysteresis should be a linear function of the shear strain squared, if compression did not affect the material behavior. When the data are replotted as a function of corrected shear strain squared (figure 8), the hysteresis is a nearly linear function of the shear strain squared, indicating a single value of dynamic loss can be used to predict the hysteresis, provided the conditions are scaled to reflect the actual loads and strains applied to the sample. Comparing the different materials, we note that three of the epoxidized natural rubber compounds show lower hysteresis loss than the natural rubber compound.
[FIGURES 6-8 OMITTED]
In determining the hysteresis behavior of these materials, it is important to understand the effect of material behavior on the resulting energy input to the system. For a fixed strain cycle, a stiffer material will perform poorly because the loads that are developed will be much higher than for a softer material (ref. 14). On the other hand, in a fixed stress cycle, a stiffer material may perform better because the deflections will be reduced compared to a softer material. In the case of a fixed load coupled with a fixed displacement mode, the situation is more complex. The stiffer material will deflect less, resulting in a reduced shear strain value. As a result, an extremely soft sample may not perform as well as might be anticipated. Figure 9 compares the dynamic shear stiffness, H*, of the materials. As the behavior was highly nonlinear, a dynamic stiffness value was determined by taking the slope of the line between the maximum and minimum shear stress and strain data points. As evidenced by these plots, the natural rubber compound shows an increase in dynamic shear stiffness at higher compressive strains, possibly the result of strain crystallization. This increased dynamic shear stiffness could explain the higher hysteresis values found for the NR formulation. In actual application, the stiffer NR compound would deflect less under the applied compressive loading, resulting in a lower applied strain value, and has been reported to perform well in field tests (ref. 22).
[FIGURE 9 OMITTED]
Elastomeric military tracked vehicles are subjected to severe service requirements and premature failures. Heat build-up is often a major contributor to part failure. A test fixture has been developed to study the response of elastomeric bushings to combined compression/shear loadings. To analyze the material behavior, the data were corrected for change in shear strain as a result of thickness changes due to compression force. They were also corrected for change in loaded area due to bulging of the sample due to compression. When the data were plotted as a function of shear strain squared, the hysteresis was found to be a linear function of the shear strain squared, indicating a single value of dynamic loss can be used to predict the hysteresis behavior, provided the conditions are scaled to reflect the actual loads and strains applied to the sample. The epoxidized NR compounds showed lower hysteresis loss than the NR compounds. A model to predict the area changes due to bulging at high compressive strains was demonstrated. When coupled with failure properties, the results of this type of testing can be used to predict the failure behavior of elastomeric bushing compounds.
Table 1--rubber formulations HNBR- ENR- ENR- ENR- NR-37 12 6 7 8 Epoxidized NR 100.00 100.00 100.00 HNBR 100.00 NR masterbatch 160.00 Zinc oxide 2.00 5.00 5.00 5.00 4.50 Stearic acid 2.00 2.00 2.00 Calcium stearate 5.00 5.00 5.00 Activator 2.60 Carbon black 50.00 30.00 45.00 35.00 Antioxidants 0.50 3.50 3.50 3.50 1.00 Accelerator 1.70 Sulfur 3.00 3.00 3.00 2.00 Peroxide 3.25
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R.P. Kezar, Z. Tao, K.J. Patenaude, J.L. Mead and R.G. Stacer, University of Massachusetts Lowell and G. Rodriguez, U.S. Army Research Laboratory
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