Among various nanometer-level displacement measurement methods, grating interferometry-based linear encoders are widely used due to their high robustness, relatively low cost, and compactness. One trend of grating encoders is multi-axis measurement capability for simultaneous precision positioning and small order error motion measurement. However, due to both lack of suitable hardware data processing platform and of a real-time displacement calculation system, meeting the requirements of real-time data processing while maintaining the nanometer order resolutions on all these axes is a challenge. To solve above-mentioned problem, in this paper we introduce a design and experimental validation of a field programmable gate array (FPGA)-cored real-time data processing platform for grating encoders. This platform includes the following functions. First, a front-end photodetector and I/V conversion analog circuit are used to realize basic analog signal filtering, while an eight-channel parallel, 16-bit precision, 200 kSPS maximum acquisition rate Analog-to-digital (ADC) is used to obtain digital signals that are easy to process. Then, an FPGA-based digital signal processing platform is implemented, which can calculate the displacement values corresponding to the phase subdivision signals in parallel and in real time at high speed. Finally, the displacement result is transferred by USB2.0 to the PC in real time through an Universal Asynchronous Receiver/Transmitter (UART) serial port to form a complete real-time displacement calculation system. The experimental results show that the system achieves real-time data processing and displacement result display while meeting the high accuracy of traditional offline data solution methods, which demonstrates the industrial potential and practicality of our absolute two-dimensional grating scale displacement measurement system.
Cantilever-type rotating bending fatigue tests were conducted under a very high cycle fatigue regime using conventionally manufactured Ti-6Al-4V specimens having drilled artificial defects with different sizes. The relationship between fatigue limit and defect size was defined as a fatigue limit design curve considering the transition from the fracture-mechanics dominating area to the fatigue-limit dominating area. A conventional Murakami’s equation was applicable as a design curve of additively manufactured Ti-6Al-4V with defects at 107 cycles. However, conventional equation gave un-conservative predictions for the fatigue limit at 108 cycles. Therefore, two kinds of modified Murakami’s equation were proposed as fatigue limit design curves for the very high cycle fatigue regime. Simple parallel shift of Murakami’s equation gave a conservative fatigue limit, whilst better result was obtained by changing the slope of Murakami’s equation. The proposed design curve was valid for the defect sizes ranging from 10 to 500 μm.
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