Frequency–Temperature Analysis of Thickness-Shear Vibrations of SC-Cut Quartz Crystal Plates with the First-Order Mindlin Plate Equations

Wu, Rongxing; Wang, Wenjun; Chen, Guijia; Du, Jianke; Ma, Tingfeng; Wang, Ji

doi:10.1007/s10338-021-00224-0

Cited by 6 publications

(5 citation statements)

References 32 publications

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“…Additionally, there is a phenomenon that the clock frequency drifts with temperature in any crystal. [24][25][26] Figure 8 takes the clock of the CNC system as an example, as well as the drive system. The phenomenon of temperature drift causes the inconsistent moment of sending position by the CNC system and receiving position by the drive system.…”

Section: Un-synchronization Caused By Temperaturementioning

confidence: 99%

“…R1 is the remainder term. In Equation (24), the second term of the arithmetic sequence sum formula is constant. As shown in Equation ( 26), the second constant term and the average of constant C1 are represented as the constant term C. Correspondingly, R is the mean of R1.…”

Section: Scope Of Compensational Interval In Embedded Systemmentioning

confidence: 99%

“…Additionally, there is a phenomenon that the clock frequency drifts with temperature in any crystal 24–26 . Figure 8 takes the clock of the CNC system as an example, as well as the drive system.…”

Section: Analysis Of Packet Loss Between Cnc and Reference Servomentioning

confidence: 99%

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Innovation of EtherCAT adaptive synchronization control in embedded CNC

Cao

Wang

Jia

et al. 2023

Int J Communication

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EtherCAT is a real-time Ethernet protocol and has been widely used in the field of motion control owing to its high speed (100 or 1000 Mbps), low processor occupancy, and good synchronization performance in slaves. However, the master-slave synchronization method is blank in the EtherCAT protocol. The study proposes a novel master-slave synchronization method that relies on the stable sync0 of reference slave by adjusting the trigger moment of master interpolation period to settle packet loss caused by EtherCAT master-slave un-synchronization, adaptively and dynamically. Furthermore, the proposed method improved EtherCAT to a whole new level, indicating that the EtherCAT master no longer depended on the real-time operating system (RTOS). In addition, a synchronization predictive compensation mechanism was adopted to eliminate the compensation lag defect of existing synchronization methods. Compared with conventional studies, the synchronization method improved compensation efficiency, settled inaccurate compensation with evaluation derived from different working frequencies, and eliminated accumulative error in clock. Finally, the proposed method added almost no computation and communication load and only required eight or 16 bytes to modify the EtherCAT frame coding in the interpolation period. Experiments were carried out on machine tools to demonstrate the advantage of the proposed method in improving the synchronization performance, with an average communication jitter of only 32-71 ns.

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Section: Un-synchronization Caused By Temperaturementioning

confidence: 99%

Section: Scope Of Compensational Interval In Embedded Systemmentioning

confidence: 99%

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Innovation of EtherCAT adaptive synchronization control in embedded CNC

Cao

Wang

Jia

et al. 2023

Int J Communication

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“…Nevertheless, the drawback of the direct delivery of power to the crystal is an increase in the thermal gradients. While the sensitivity of QCMs to temperature is well known and also the object of recent studies [ 13 , 14 , 15 ], thermal gradients are mostly neglected.…”

Section: Introductionmentioning

confidence: 99%

Characterization of Thermal Gradient Effects on a Quartz Crystal Microbalance

Magni

Scaccabarozzi

Palomba

et al. 2022

Sensors

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Quartz crystal microbalances are widely used sensors with applications for the detection of very-low-mass deposition in many different fields, from contamination monitoring in the high vacuum of deep space missions to the monitoring of biological activity or pollution using specifically designed active substrates. These sensors are very stable over time; nevertheless, their sensitivity to the temperature is well known, and different implementations have been devised to correct it, e.g., through compensation with a dual crystal. This paper deals with the effects of temperature on QCM but separates the case of uniform crystal temperature from the case of in-plane temperature gradients considering a QCM based on quartz crystals with deposited film resistors used as both RTDs and heaters. This configuration allows both an accurate temperature measurement and efficient thermal control, allowing the achievement of crystals temperatures in the order of 400 °C higher than the environment with a low power dissipation of the order of 1 W. The film resistors deposited around the electrodes allow directly measuring the average crystal temperature and directly delivering power to the crystal for thermal control. The localized delivery of the heat nevertheless also determines uncommon temperature fields on the crystal, and thus, an analysis of both the effects of temperature on the new microbalance was performed. The temperature gradient has strong effects on the frequency; therefore, along with the temperature, the thermal gradients have tobe compensated. The calibration of the QCM thermometers and the assessment of the achievable measurement accuracy were performed, as well as the determination of the frequency–temperature relationship. The comparison between frequency changes in the case of uniform temperature and those observed while using crystal heaters proved that temperature gradients have a strong effect on the crystal frequency. To identify the temperature field on the crystal surface of a QCM crystal, the gold coating of the deposited films was removed to achieve an emissivity acceptable for thermal imaging with an IR camera. Moreover, image processing for emissivity correction was developed. In order to correlate the temperature gradient with the frequency variation, a test campaign was performed to measure the frequency changes derived from different power levels delivered to the crystal heaters. From this test campaign and thermal analysis, the effect of the thermal gradient was assessed.

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“…Mindlin-Reissner plates accommodate shear deformation and have been widely used in structural analysis and design [1][2][3]. A typical numerical issue for such types of structures is shear locking, which is due to the mismatched interpolations between deflectional and rotational fields [1].…”

Section: Introductionmentioning

confidence: 99%

Coarse Mesh Superconvergence in Isogeometric Frequency Analysis of Mindlin–Reissner Plates with Reduced Integration and Quadratic Splines

Lin

Hou

et al. 2022

Acta Mech. Solida Sin.

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A frequency accuracy study is presented for the isogeometric free vibration analysis of Mindlin–Reissner plates using reduced integration and quadratic splines, which reveals an interesting coarse mesh superconvergence. Firstly, the frequency error estimates for isogeometric discretization of Mindlin–Reissner plates with quadratic splines are rationally derived, where the degeneration to Timoshenko beams is discussed as well. Subsequently, in accordance with these frequency error measures, the shear locking issue corresponding to the full integration isogeometric formulation is elaborated with respect to the frequency accuracy deterioration. On the other hand, the locking-free characteristic for the isogeometric formulation with uniform reduced integration is illustrated by its superior frequency accuracy. Meanwhile, it is found that a frequency superconvergence of sixth order accuracy arises for coarse meshes when the reduced integration is employed for the isogeometric free vibration analysis of shear deformable beams and plates, in comparison with the ultimate fourth order accuracy as the meshes are progressively refined. Furthermore, the mesh size threshold for the coarse mesh superconvergence is provided as well. The proposed theoretical results are consistently proved by numerical experiments.

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Frequency–Temperature Analysis of Thickness-Shear Vibrations of SC-Cut Quartz Crystal Plates with the First-Order Mindlin Plate Equations

Cited by 6 publications

References 32 publications

Innovation of EtherCAT adaptive synchronization control in embedded CNC

Innovation of EtherCAT adaptive synchronization control in embedded CNC

Characterization of Thermal Gradient Effects on a Quartz Crystal Microbalance

Coarse Mesh Superconvergence in Isogeometric Frequency Analysis of Mindlin–Reissner Plates with Reduced Integration and Quadratic Splines

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