The accelerometers are commonly applied to measure the vibrations in the fields of motion control and precision measurement, whose sensitivities are essentially important to their applications. The vibration calibration is utilized to determine their sensitivities before they are used or after a period of time. At present, the Nyquist sampling (NS), bandpass sampling (BPS), and mixer and low-pass filter sampling (MLPFS) based heterodyne laser interferometry are widely utilized to accomplish the vibration calibration. Compared with the NS method, the latter two methods can significantly reduce the sampling rate and extend the calibration frequency range. However, the BPS method has to adopt the complex algorithm and prior information so as to get its sampling rate, and the MLPFS method is inevitably influenced by an extra phase delay. In this article, a novel heterodyne laser interferometry is investigated to simultaneously determine the sensitivity magnitude and phase of the accelerometers with high accuracy in a wide frequency range. This method significantly eliminates the phase delay by introducing an appropriate symmetric differential demodulation strategy, which can improve the sensitivity phase calibration accuracy, especially at higher frequencies. The comparison experiments with the Earth's gravitation and monocular vision methods at low frequencies and the traditional MLPFS and NS methods confirm that the investigated method can calibrate the sensitivity magnitude and phase of accelerometers with the uncertainties of about 0.5% and 0.5° in the range from 0.1 Hz to 20 kHz.

The long-stroke shaker is essentially required for the calibration of low-frequency vibration transducers, whose performance parameters have significant impact on the calibration accuracy. The accurate measurement of these parameters is the prerequisite to establish a reliable vibration metrology and traceability system. Currently, an optical collimator or a reference accelerometer is applied to get the static parameter, the laser interferometry or triaxial sensor-based method is used to obtain the dynamic parameters. However, the former relies on an extra device which increases the complexity and cost of calibration system, and the latter is always difficult to accomplish the accurate and efficient measurement of these parameters. In this study, a binocular vision-based long-stroke shaker performance measurement method is investigated, which has ability to determine the static and dynamic parameters simultaneously during the calibration. This vision method obtains the shaker's bending by measuring the inclinations at the different positions of its guideway, and achieves the amplitude characteristic, distortion, repeatability as well as transverse ratio measurements by accurately acquiring the spatial displacements at different frequencies. Comparison experiments with the two commonly used inclination estimation methods, and the laser interferometry and sensor-based method demonstrate that the investigated method is able to get the satisfactory accuracies both for the static and dynamic parameters of long-stroke shaker in vibration calibration.

In this article, the low-frequency linear and angular vibration sensors have been gradually used in many applications of vibration monitoring because they can measure dynamic displacement and angle. These sensors must be calibrated before they are used and after they have been used for a period to ensure their measurement accuracy. Currently, the laser interferometry (LI) and sensor-based comparison method are commonly used to calibrate their sensitivities. However, the former suffers inevitably drawbacks in low-frequency range, while the latter usually has only a limited range, these undoubtedly limit their wide application. In this article, a new monocular vision-based multiparameter calibration method is investigated, which can determine the sensitivities of these sensors in a broad low-frequency range. The monocular vision method with improved line segment detector is applied to measure the linear and angular vibration excitations by extracting the motion feature edges with subpixel accuracy. This investigated method strongly promotes the perfection and unification of linear and angular vibration calibration. Many comparison experiments with the LI, the Earth's graviation method, and the circular grating-based method confirm that the investigated method gets the satisfactory accuracies in the linear and angular vibration calibration with an efficient, flexible, and low-cost system in the low-frequency range.

The low-frequency triaxial vibration sensors have been gradually applied in many engineering fields of vibration monitoring because they can measure the multidirection vibrations simultaneously. The accurate axial and transverse sensitivities, determined by the calibration method, are the prerequisite for ensuring their measurement accuracy. Currently, the laser interferometry (LI) which is based on a single component or a tricomponent linear shaker is usually applied to calibrate these sensitivities. However, the former has to require the multiple reinstallations of the sensor and the latter cannot avoid the motion coupling caused by the shaker, these inevitably increase the calibration uncertainty. In this article, we investigate a monocular vision (MV)-based two-component shaker calibration method, which determines the axial sensitivity based on the time-spatial synchronization and transverse sensitivity at the elliptical orbit excitation. The MV method is used to measure this excitation, and a plane sensitivity model is presented to describe these sensitivities. This investigated method can simultaneously reduce the uncertainties caused by the reinstallations and motion coupling to improve the calibration accuracy. Experimental results compared with the LI and Earth's gravitation method demonstrate that the investigated method obtains the satisfactory accuracies both in axial sensitivity magnitude and phase as well as transverse sensitivity magnitude and direction calibration.

Calibration is required to determine the frequency characteristics of vibration sensors to ensure their measurement accuracy in engineering applications. Thus, a monocular vision-based calibration method for low-frequency vibration sensors is investigated in this study. A sub-pixel edge detection method which based on Gaussian curve fitting is applied to extract the edges of motion sequence images in order to accurately measure the excitation acceleration of the sensors. Because the motion sequence images and the output signal of the sensors cannot be collected synchronously, it is very difficult to align the excitation acceleration signal obtained from the images and the output signal in the time domain. Although the misalignment only has a negligible effect on the magnitude frequency characteristic calibration, it dramatically decreases the calibration accuracy of the phase frequency characteristic, especially with the increasing of the frequency. A time-spatial synchronization technique is proposed to accurately calibrate the phase frequency characteristic by determining the phase of the excitation acceleration signal at a specific spatial position and that of the output signal at the corresponding time. Finally, both the magnitude and phase frequency characteristics are simultaneously calibrated by the investigated method with a flexible and low-cost vision system. The experimental results compared with laser interferometry show that the investigated method accomplishes the high-accuracy magnitude and phase frequency characteristics calibration in a broad low-frequency range. Its calibration accuracy is superior to that of laser interferometry when the frequency is less than 0.3 Hz, and is equivalent at other frequencies.