# Study of the Lifetime Testing of Spherical Rubber Isolators
## 2 Vibration Test Method  
This paper mainly studies the nonlinear mechanical characteristics and fatigue lifetime of a thin-walled hollow spherical rubber isolator. Figure 1 illustrates the external structure and geometric dimensions of the rubber isolator. The nonlinear dynamic characteristics of rubber isolators are obtained through harmonic and random vibration testing and analysis. Figure 2a illustrates the fundamental principle of the vibration system. Figure 2b shows the photo of the vibration system. The experimental system was mainly composed of a data acquisition instrument, a power amplifier, a computer, a digital vibration table, and acceleration sensors. The vibration table (ES-3-150, Dongling Co., Ltd., Suzhou, China) has a frequency range of [5; 4000] Hz. The maximum load of the vibration table (vertical direction) reaches 120 kg. The sensitivity of the acceleration sensors (PCB Piezotronic, 352a24) is 100 mV/g. The measurement error scope of the sensors is assured to be within \(\pm\)5% in the frequency range of [1; 8000] Hz. In the experiment, the excitation signal was amplified by the power amplifier to prompt the moving parts of the shaker to vibrate. Meanwhile, the excitation feedback signal was used to ensure the stability of the input signal frequency and amplitude in real time. After the dual-channel vibration signal  
Figure 1: Schematic diagram of the rubber isolator’s structure. connected to the tooling was processed by the data acquisition instrument, the experimental data were transmitted to the computer. The system structure is presented in Figure 3a. The system structure was mainly composed of a vibration table, casing, a rubber isolator, a mass, and accelerometers. Figure 3b shows the installation method of the rubber isolator and the location diagram of the acceleration sensor. A3 is the accelerometer for the control signal, and A1 and A2 are the output accelerometers. In this experiment, the linear bearing and the guide shaft were used to suppress the vibration mode of the isolator in other directions. Meanwhile, two accelerometers were positioned symmetrically along 180\({}^{\circ}\) at the bottom of the mass block with acceleration levels averaged to minimize the potential tilting. The vibration experiment adopted the average control method. The control signal was a single channel. The test signal was a dual channel. The nonlinear characteristics of rubber isolators under harmonic and random vibrations were tested. For harmonic vibrations, experiments were carried out by changing the acceleration excitation levels. The experimental load was 50 g, and the acceleration level of the input excitation was dense with small values and loose with large values, i.e., [0.3; 0.35; 0.4; 0.45; 0.5; 0.55; 0.6; 0.65; 0.7; 0.8; 0.9; 1.0; 1.1; 1.2; 1.3] g. The resonance peak was typically in the range of [30; 250] Hz under the excitation levels in the study. Because this paper mainly studies the dynamic characteristics at the resonance peak, this frequency band at room temperature was selected for the experiment. The sweep rate evolved slowly enough (0.5 Oct/min), and the response could be estimated as stable at the resonance peak. For random vibrations, the dynamic characteristics of the rubber isolator were tested by constantly increasing the excitation level. Random experiments were conducted with a constant power spectral density of [0.01; 0.05; 0.10; 0.20; 0.30] (ms\({}^{-2}\))\({}^{2}\)/Hz over a frequency  
Figure 3: **(a)** Photo of the experimental setup; **(b)** schematic diagram of the rubber isolator structure. Figure 2: **(a)** Schematic diagram of the experimental equipment system; **(b)** photo of the vibration system. range of [30; 250] Hz. The frequency response function (FRF) plots the ratio of the output acceleration over the input acceleration, i.e., ((A1 + A2)/A3). At present, accelerated lifetime testing is a vital approach for the evaluation of fatigue lifetime [12].