Pneumatic technology is wildly used in industry due to its high speed, safety, and cleanness. Although the cylinder has a wide range of applications, the cylinder itself is not suitable for accurate control due to its poor stiffness, strong non-linearity, and the disadvantages of temperature and air pressure. The sealing performance of the cylinder is very important to the normal operation of the whole mechanism and its safety and reliability [1
]. The friction characteristics of the cylinder, especially the friction characteristics under different operating conditions, is one of the main factors that make it difficult to accurately control the cylinder. In recent years, the friction model of the cylinder has been developed and used to control the cylinder. However, friction models are also affected by the seal ring aging, which is directly related to the dynamic friction performance of the cylinder. So, it is of great significance to study the influence of hydrothermal aging on the dynamic friction model of rubber seals, which can lay the foundation for improving the performance and service life of the cylinder as well as the sustainable development of the economy.
Friction is a widespread and very complex phenomenon [2
], especially in soft material friction. A mathematical model has been widely developed to study the friction process based on a lot of friction tests [3
]. Friction force is not only related to surface roughness, but also to the lubrication state [5
]. The static friction coefficient is not a constant [6
], and it is higher than that of dynamic friction, which is related to the initial residence time and starting speed of rubber specimens in the friction surface [7
]. Friction characteristics of the cylinder are very important, which is related to the friction model [8
]. However, one of the most important causes of the complexity in pneumatic cylinder control is the friction force between piston and rubber seals, as friction force is highly nonlinear, which causes the well-known stick-slip phenomena. Several friction models have been developed. It is well-known that static friction models, such as the Karnopp model [10
], are incapable of correctly reproducing the phenomena. The friction force of cylinder dependence on the previously followed trajectory and on the time moving parts are previously still [11
]. The Dahl model [12
] is not directly applicable to pneumatic cylinders since it does not include the viscous phenomenon. The LuGre friction model represents a good trade-off between complexity and accuracy for fitting the friction properties of cylinders [13
]—a typical LuGre friction model is shown in Figure 1
Besides, the influence of parameters of the LuGre friction model on the pneumatic system was investigated for the gravity compensation cylinder [16
]. The LuGre friction model between rubber rollers and paper was also developed to study the effect of the viscous damping coefficient on the model [17
]. The LuGre model was used to describe the friction phenomenon for the friction compensation of rodless cylinders [18
]. Compared to the experimental results, it was found that the LuGre model cannot simulate the actual friction characteristics of the hydraulic actuator, so a modified LuGre model was proposed to simulate the actual dynamic characteristics of friction for hydraulic actuators with high accuracy [19
]. It was also found that the LuGre model could not fully characterize the friction characteristics of hydraulic cylinders; thus, an improved LuGre model was developed for correcting the viscous friction and dynamic characteristics of sliding oil film, which was better than the traditional model [20
As above, the LuGre model has been widely used in practical engineering applications. However, rubber seal aging has a great effect on the friction process of the cylinder under the service environment. So, the rubber seals of the cylinder are taken as the research object, then the rubber aging characteristic equation is established. Based on the LuGre model, the improved cylinder friction model is developed, which is of great significance to understand the friction characteristics change in the service process of the rubber seals. It lays the foundation for the safe service and accurate control of the cylinder under actual working conditions.
3. Experimental Setup
In order to find the relationship between the rubber friction force and the speed after aging, rubber aging and friction coefficient tests were carried out to obtain the experimental data for the cylinder friction model.
3.1. Friction Test
In friction tests, rubber is applied to a load of 5 kg, the lead screw is controlled to drive the bottom-feeding platform to move, and the friction force is tested under different feed speed conditions.
The friction test platform of the sealing material has been developed for observation of friction characteristics. It consists of a normal loading part, a horizontal feed part, a measurement control system, and a tooling fixture, etc. Figure 6
shows a schematic diagram of the friction test structure.
The normal loading part is loaded with weights, and the loading process is controlled by the air cylinder. The sealing rubber sample is fixed in the tooling fixture. The horizontal feed part is comprised of a servo drive motor and the sideway; the lateral friction force is obtained by the force sensor. The force and displacement are measured by the data acquisition card and real-time data acquisition. The developed test device is shown in Figure 7
, and each test was done three times. Besides, the accuracy of the force sensor is ±0.2 N.
3.2. Hydrothermal Aging Test
Based on ISO 188-2011, aging tests of rubber have been carried out in the homemade hydrothermal aging test chamber under the conditions of the compression state (compressing the test pieces to 80%, 90%, and uncompressed state of the original length), aging temperature (20° C, 40 °C, 60 °C, and 80 °C), and aging times (1 day, 2 days, 4 days, 8 days, 12 days, and 16 days).
4. Result and Discussion
4.1. Compression Ratio
The friction test has been carried out on the rubber specimens under different compression conditions, the predicted and measured friction force of the rubber specimens under different compression conditions, and the temperature of 60 °C are shown in Figure 8
. Figure 9
shows the Coulomb friction coefficient and the static friction coefficient after aging.
It can be seen that when the pre-compression increases, the friction coefficient decreases. In the uncompressed state, the static friction coefficient of the rubber sealing material is 0.835, and the coefficient of static friction reduces to 0.822 under the compression ratio of 80%.
shows the friction force under the compression of 80%, the temperature of 20 °C, 40 °C, 60 °C, and 80 °C. Then, the friction curve is fitted by the steady-state friction model. Besides, the Coulomb friction coefficient and static friction coefficient under different temperature and aging time are shown in Figure 11
When the aging temperature increases, the friction coefficient decreases. Here, the static friction coefficient is decreased from 0.935 to 0.855 when the temperature increases from 40 °C to 80 °C under the 2 days of aging. It is the same as the Coulomb friction coefficient. From Figure 11
, it can be seen that the variation ranges of the static friction coefficient are larger than the Coulomb friction coefficient, and the aging temperature is more likely to affect the friction coefficient.
4.3. Aging Time
shows the friction force of the rubber under the temperature of 60 °C, the compression of 80%, and the aging times of 1, 2, 4, 8, 12, and 16 days. Then, the friction curve is fitted to achieve the parameters of the steady-state friction model. Figure 13
shows the Coulomb friction coefficient and the static friction coefficient under different aging times.
Results indicate that the aging time has a great influence on the friction force of the rubber, especially in the first 4 days, which is similar to the rubber aging rate. In the first 4 days, the static friction coefficient decreases from 0.93513 to 0.75859, and the Coulomb friction coefficient decreases from 0.609 to 0.48429. From 4 to 16 days, there is no obvious change; here, the static friction coefficient decreases from 0.75859 to 0.70319, and the Coulomb friction coefficient decreases from 0.48429 to 0.44781.
4.4. Effect of Aging on Friction Model
Aging has a great effect on the mechanical properties of the rubber sealing ring, which leads to the changes in the friction coefficient. Figure 14
shows the relation curve between friction force and velocity of rubber after 16 days of aging under the temperature of 80 °C and the compression of 80%. It can be seen that the maximum friction value decreases from 49.4 N to 35.1 N after 16 days of aging under the temperature of 80 °C. Therefore, it is very important to study the effect of aging on friction model parameters.
The friction coefficient of rubber decreases with the aging time, and it can be found that the aging time has the same effect on the static friction coefficient and the Coulomb friction coefficient. Therefore, the relation curve of rubber friction coefficient and aging time is shown in Figure 13
Based on Equation (15), parameters of the Coulomb friction coefficient can be obtained by: a1 = 0.03307, b1 = 0.1324, c1 = 0.06621. Similarly, parameters of the static friction coefficient can be given by: a2 = 0.04448, b2 = 0.0804, c2 = 0.11159. By comparing the static friction coefficient and the Coulomb friction coefficient of the model with the test data, it can be found that the error of the fitting results is less than 5%.
Based on the predicted model, the Coulomb friction coefficient after 16 days of aging is 0.48082, and the static friction coefficient is 0.7. The cylinder friction model is shown in Figure 15
for fitting and comparison with experimental data. It can be seen that the model can fit the cylinder friction and velocity curves better.