Static Force Research Articles

Mean temperature profiles in turbulent internal flows

We derive explicit formulas for the mean profiles of temperature (modeled as a passive scalar) in forced turbulent convection, as a function of the Reynolds and Prandtl numbers. The derivation leverages on the observed universality of the inner-layer thermal eddy diffusivity with respect to Reynolds and Prandtl number variations and across different flows, and on universality of the passive scalar defect in the core flow. Matching of the inner- and outer-layer expression yields a smooth compound mean temperature profile. We find excellent agreement of the analytical profile with data from direct numerical simulations of pipe and channel flows under various thermal forcing conditions, and over a wide range of Reynolds and Prandtl numbers.

Electronic Force Density Fields: Insights into Partial Bonds, Transition States, and Chemical Structure Evolution.

This paper presents the quantum-topological binding approach, in which the electrostatic and total static force density fields, Fes(r) and , together with the electron density gradient field ∇ρ(r), are simultaneously analyzed to elucidate the chemical structure of transition states and the nature of interatomic interactions for semibroken semiformed partial chemical bonds. The approach attributes the discrepancies between the force fields and Fes(r) to the nonclassical electron-electron interaction effects. The internuclear gap between the zero-flux boundaries of Fes(r) and ∇ρ(r) indicates the interatomic charge transfer phenomenon (ICT) that occurs upon the formation of a system from free atoms. Concomitantly, the mismatch of the zero-flux surfaces defined in and ∇ρ(r) can be interpreted as a phenomenon of the electron-transfer-induced quantum chemical response (QCR), which originates from the electron exchange correlation. Our study permits the assertion of parallels between partial bonds and noncovalent interactions, as both typically exhibit incomplete QCRs, indicating the partial electron sharing of the transferred density. The changes in atomic and pseudoatomic charges are employed to describe the evolution of the chemical structure upon the substitution reaction. It is observed that the acquired difference in the actual atomic electronegativity causes polarization upon the heterolytic breaking of virtually nonpolar bonds. It is further proposed that the proximity of closely related stationary states along the reaction path on a potential energy hypersurface implies their similarity in the manifestation of the ICT and sympathetic QCR. Furthermore, the involvement of an electron pair in a partial bond facilitates its delocalization through the attraction by the static forces and Fes(r) to a neighboring nucleus and through the smearing by the Pauli kinetic force FP(r).

Experimental investigation and fluid-structure interaction modelling of the casting of self-compacting concrete for CRTS III slab track in the curved segments

Ensuring the casting quality of self-compacting concrete (SCC) is crucial for the operational safety and durability of China railway track system (CRTS) III slab track. However, the mechanisms of key factors influencing flow behaviors of SCC and structural responses remain insufficiently understood, nor is the relationship between flow behaviors and structural responses during casting. In this study, fluid-structure interaction (FSI) models of SCC casting were developed and verified by full-scale physical tests, comprising slump flow, L-box flow and casting of SCC in an actual track at the field of Laixi-Rongcheng high-speed railway. Through in-depth analysis on the casting process of SCC in curved segments with a super elevation of 80 mm, the relationship between flow behaviors and structural responses was established. Furthermore, the influence mechanisms of key factors on flow behaviors and structural responses were investigated systematically. Results show that during gravity-fed SCC casting, its flow velocity diminishes, thus increasing the static pressure and the forces exerted on the slab by SCC. These vertical and lateral forces increase to 147.16 and 7.83 kN through three stages of development, acceleration and stabilization, resulting in commensurate structural responses. At the end of casting process, the central region of the slab exhibits maximum vertical deformation of 0.95 mm and tensile stress of 1.07 MPa. The tension rods at the side with lower elevation bear greater vertical and lateral forces than the ones at the side with higher elevation. The rise of funnel height from 1.05 to 1.35 m accelerates the casting process but increases the forces exerted by SCC by up to 26 % and augments the associated response of entire structures, whereas the funnel diameter shows little effect. Increasing yield stress of SCC from 9.3 to 49.3 Pa produces a more uniform flow morphology and thus higher static pressure and force by SCC in the middle region of the slab, impacting the structural responses by up to 15 %. The growth of plastic viscosity from 59 to 99 Pa⋅s significantly affects the volume rate and casting time by up to 66 % but has little effect on the flow morphology, fluid pressure and structural responses. In order to ensure high quality casting of SCC, five clamping beams are suggested with two beams positioned at either side of the slab and the other three evenly placed along the middle region of the slab.

The simplification and analytical verification of the static liquid bridge force model for particle adhesion in inferior seedling substrates

This study examines the adhesion mechanism in varying water contents of inferior seedling substrate blocks, focusing on the adhesion between particles‒particles and particles‒wall of the seedling tray. A simplified static liquid bridge force model based on the Young–Laplace equation is proposed. The correlation between the liquid bridge force and volume is derived and validated against existing experimental. The results indicate that the static liquid bridge force between particles decreases as the distance increases. A critical distance region is identified, where below this distance, a smaller liquid bridge volume results in a greater static liquid bridge force, and beyond this, the trend reverses, except when the solid–liquid contact angle is 50°. Additionally, the solid‒liquid contact angle has a minimal influence on the liquid bridge force between the particles and the inner sidewall of the seedling tray. This study also analyses the change in critical rupture distance during the transition of liquid bridges from pendulum to ring rope type, and this change increases with the liquid bridge volume.

Effects of Motor Learning on Corticospinal Tract Excitability During Motor Imagery.

We aimed to examine the effects of motor performance improvements produced by practice on corticospinal tract excitability during motor imagery (MI) of identical movements. Participants performed a motor task with no guidelines displayed on the monitor (performance test); the participants only imagined performing the task without performing the movement (MI test), and the participants performed the power output and then adjusted it (exercise). The output force conditions were 20, 40, and 60% of the maximum voluntary contraction, and the objective was for 21 participants to learn each output force condition. The outcome of the performance test was calculated as the difference between the actual motor output and the target. During the MI test, we applied a single transcranial magnetic stimulation during imagery, assessed the corticospinal tract excitability of the right first dorsal interosseous by motor-evoked potential (MEP) amplitude, and recorded the vividness of the MI in each trial. We evaluated performance and MI before practice (Pre-test), after 150 practice sessions (Post-test 1), and after another 150 practice sessions (Post-test 2). The MEP amplitude was significantly reduced at Post-test 2 compared to Pre-test. The vividness of the MI improved with practice. Corticospinal tract excitability during MI decreased as motor performance improved. Thus, actual motor practice was also reflected in the MI of the exercise. Performance improvement was accompanied by a decrease in redundant activity, enhancing the efficiency and appropriateness of the exercise.

Microbiology of human spaceflight: microbial responses to mechanical forces that impact health and habitat sustainability.

SUMMARYUnderstanding the dynamic adaptive plasticity of microorganisms has been advanced by studying their responses to extreme environments. Spaceflight research platforms provide a unique opportunity to study microbial characteristics in new extreme adaptational modes, including sustained exposure to reduced forces of gravity and associated low fluid shear force conditions. Under these conditions, unexpected microbial responses occur, including alterations in virulence, antibiotic and stress resistance, biofilm formation, metabolism, motility, and gene expression, which are not observed using conventional experimental approaches. Here, we review biological and physical mechanisms that regulate microbial responses to spaceflight and spaceflight analog environments from both the microbe and host-microbe perspective that are relevant to human health and habitat sustainability. We highlight instrumentation and technology used in spaceflight microbiology experiments, their limitations, and advances necessary to enable next-generation research. As spaceflight experiments are relatively rare, we discuss ground-based analogs that mimic aspects of microbial responses to reduced gravity in spaceflight, including those that reduce mechanical forces of fluid flow over cell surfaces which also simulate conditions encountered by microorganisms during their terrestrial lifecycles. As spaceflight mission durations increase with traditional astronauts and commercial space programs send civilian crews with underlying health conditions, microorganisms will continue to play increasingly critical roles in health and habitat sustainability, thus defining a new dimension of occupational health. The ability of microorganisms to adapt, survive, and evolve in the spaceflight environment is important for future human space endeavors and provides opportunities for innovative biological and technological advances to benefit life on Earth.

The sensitivity of agricultural biogas plants to changes in energy prices in Poland

In Poland, despite ambitious plans from 15 years ago, when it was assumed that by 2020, an agricultural biogas plant would be standard in every commune, the potential of agricultural biogas has not been used due to the lack of stable legal regulations and financing programmes for the construction of the plants. The situation has now changed due to new forms of support systems, which motivated the authors to compare two agricultural biogas plants operating in the certificate system and the support system in the form of feed-in premiums. Moreover, the authors pointed to differences in the number of agricultural biogas plants and their capacity by voivodeship due to changes in legal conditions in force in two periods: from 1 January 2011, to 30 June 2016, and from 1 July 2016, to 19 January 2024. Based on the research methods used ‒ including Earnings Before Interest, Taxes Depreciation and Amortisation, the Internal Rate of Return, risk matrix and data analysis in spatial terms ‒ it was indicated that: 1. agricultural biogas plants are characterised by very high sensitivity related to the probability of risk in the case of investment costs, substrate prices and changes in energy prices; 2. financial support is important at the stage of construction of a biogas plant, which largely makes it possible to shorten the payback period and thus increase the willingness of future investors to invest in biogas plants and 3. in the periods analysed, significant differences were noted in the spatial location of biogas plants due to trends towards lower-power biogas plants, which is probably dictated by the constant and predictable premium system in the new support system.

Design and Experimental Study of a Cleaning Device for Edible Sunflower Harvesting

Existing cleaning devices for edible sunflower have a low cleaning efficiency, high cleaning loss rate, and high impurity rate; therefore, a wind-sieve-type cleaning device for edible sunflower harvesting was designed. According to the characteristics of dislodged objects, a vibrating screen for the device was designed, and the dislodged edible sunflower objects in the device were used for a mechanical analysis of the force conditions to determine the displacement of the different edible sunflower objects dislodged by the action of airflow. Using FLUENT-DEM gas–solid coupling simulation technology, the velocity of the flow field, the velocity vector, and the trajectory of the dislodged objects inside the cleaning device were analyzed, and the law of motion applied to the airflow and the dislodged objects inside the device was clarified. According to the results of the coupled simulation analysis, the key factors affecting the operation of the cleaning device were wind speed, vibration frequency, and amplitude. Based on the key factors of wind speed, vibration frequency, and amplitude, an orthogonal rotary combination test was carried out with the loss rate and impurity rate of cleaned grains as the evaluation indexes, and the test parameters were optimized to obtain the optimal combination of operating parameters of the device, which were as follows: wind speed: 30 m·s−1; vibration frequency: 8.44 Hz; and amplitude: 41.35 mm. With this combination of parameters, the seed loss rate and impurity rate reached 3.47% and 6.17%, respectively. Based on the optimal combination of operating parameters, a validation test was performed, and the results of this test were compared with the results of the test bench using this combination of parameters. The results show that the relative errors of the loss rate and impurity rate between the bench test and the simulation test were 3.45% and 3.07%, respectively, which are less than 5%, proving the reliability of the simulation analysis and the reasonableness of the design of the test bench.

Convective flow of couple stress ternary nanoliquid flow through a permeable microchannel: irreversibility analysis

ABSTRACT Ternary hybrid nanoliquid is employed in various engineering and science applications including electronic heaters, pharmaceutical, nuclear safety, and solar energy production. Hence, the current study focused on the thermal and entropy analysis of water-based ternary couple stress hybrid nanoliquid and couple stress hybrid nanoliquid flow in an oblique channel. The significance of heat flux, porous media, buoyant force, magnetic field, and convective condition on the couple stress ternary liquid has been scrutinized. The governing partial differential equations are transferred into ordinary differential equations with the help of dimensionless terms. In the next step, the ordinary differential equations were solved by utilizing the RKF-45 numerical method. The outturn elucidated that the inflated Brinkman number greatly promotes the thermal field. The flow profile declines with enhanced permeability parameters. The outcome of the scrutiny of the couple stress parameter concludes that highly reinforced by ternary fluid than hybrid couple stress nanofluid.

Heat transfer augmentation in heat sink with fin-bars inserted in cooling channel

Adding obstacles and obstructing fluid flow in cooling channel to induce whirl velocity enhances thermal performance in heat sinks. An analysis is presented of conjugate heat transfer in a heat sink with transversely inserted bars in the flow channel. The numerical study seeks to maximise the dimensionless thermal conductance subject to constant total volume. The study contrasts a standard heat sink without a bar with cooling channel inserts with one, two, three, and 4 bars. To improve the surface area for heat transfer, the extended surfaces are placed longitudinally at various points in the cooling channel. A high-density heat flux is applied at the bottom wall of the heat sink and coolant with an inlet velocity vin between 4.26 and 7.26 m/s is pumped in a forced convective laminar condition to eliminate the heat. A computational fluid dynamic (CFD) code incorporated in Ansys fluent is used to solve the mathematical models. The numerical analysis indicates that the configuration featuring 3 bars inserted at the roof of the cooling channel exhibits the highest global thermal conductance, achieving a 53 % increase over other configurations. All configurations with 3 bars inserted up, down, left and right, maintain a constant pump power of 3.5 W across a Reynolds number range of 857–1461. Bars positioned at the roof of the cooling channel experience the lowest outlet and inner wall temperatures, whereas those at the floor exhibit the highest temperatures. The optimised design meets the highest porosity limit of 0.8.

Analytical Study of Barrier-free Door Closer Guide Rail System based on Slider-Crank Mechanism

Abstract One of the most important elements of barrier-free design is the door entrance system, particularly door closers. Door closers ensure that doors are easy to operate and do not pose any physical barriers to users. However, existing electro-mechanical door closers are relatively heavy, costly and have reliability issues in cases of power outages. Purely mechanical door closers, such as cam action with guide rail and rack-and-pinion with scissors arm, offer a more affordable option due to simpler design and fewer components used. Static forces and torque with geometrical constraints of the door closer guide rail system are considered in deriving the mathematical expressions of a door closer guide rail system using similar approaches as slider-crank mechanism. The formulation considers the effects of pinion torque of a door closer, installation inputs as design parameters, door angle and efficiency. The mathematical model and experimental results show close agreement. The contribution of this paper is that it demonstrates the underlying physics of the door closer guide rail system, thereby aiding in understanding the door behaviour. Additionally, the model can predict the behaviour of the system under different operating conditions, which can be useful for design and optimization purposes. More importantly, this model can be utilised to identify the most effective strategies in reducing opening forces on doors thereby providing design insights to barrier-free application in the future.

Force Analysis Using Self-Expandable Valve Fluoroscopic Imaging: a way Through Artificial Intelligence.

This study aimed to develop a force analysis model correlating fluoroscopic images of self-expandable valves with stress distribution. For this purpose, a nonmetallic measuring device designed to apply diverse forces at specific positions on a valve stent while simultaneously measuring force magnitude was manufactured, obtaining 465 sets of fluorescent films under different force conditions, resulting in 5580 images and their corresponding force tables. Using the XrayGLM, a mechanical analysis model based on valve fluorescence images was trained. The accuracy of the image force analysis using this model was approximately 70% (50-88.3%), with a relative accuracy of 93.3% (75-100%). This confirms that fluoroscopic images of transcatheter aortic valve replacement (TAVR) valve stents contain a wealth of mechanical information, and machine learning can be used to train models to recognize the relationship between stent images and force distribution, enhancing the understanding of TAVR complications.

Study on calculation method for dynamic load distribution of thread pair of planetary roller screw mechanism

To reveal the dynamic load distribution characteristics of planetary roller screw mechanism under the high-speed operating conditions, based on the spiral surface equation and deformation coordination relationship, a static contact force calculation method of the roller-screw and roller-nut thread at the contact point is proposed, and a formula for calculating the contact angle after bearing is derived. On this basis, further considering the inertial force generated by using high-speed operation, a dynamic load distribution model for planetary roller screw mechanism thread was established. By comparing with the finite element contact model of planetary roller screw mechansim, the error is below 5%, which verifies the correctness of the model established. Finally, the influence of the parameters such as screw speed, axial load, pitch, and tooth flank angle on the distribution of dynamic load was analyzed. The results show that the inertia force causes the roller to have a tendency to move closer to the nut and away from the screw resulting in a decrease in dynamic contact force on the roller screw side and an increase in dynamic contact force on the roller nut side. The degree of uneven distribution of dynamic load is positively correlated with the screw speed and pitch, and negatively correlated with the tooth side angle. The size of axial load has a significant impact on the distribution of dynamic load.

Design and Research of the Grasping Force Feedback Mechanism of Flexible Surgical Robots.

Robot-assisted microsurgery (RAMS) is gradually becoming the preferred method for some delicate surgical procedures. However, the lack of haptic feedback reduces the safety of the surgery. Surgeons are unable to feel the grasping force between surgical instruments and the patient's tissues, which can easily lead to grasping failure or tissue damage. This paper proposes a tendon-driven grasping force feedback mechanism, consisting of a follower hand and a leader hand, to address the lack of grasping force feedback in flexible surgical robots. Considering the friction in the tendon transmission process, a grasping force estimation model is established for the follower hand. The admittance control model is designed for force/position control of the leader hand. Through experimental validation, it has been confirmed that the grasping force sensing range of the follower hand is 0.5-5N, with a sensing accuracy of 0.3N. The leader hand is capable of providing feedback forces in the range of 0-5N, with a static force accuracy of 0.1N. The designed mechanism and control strategy can provide the grasping force feedback function. Future work will focus on improving force feedback performance. This research has no clinical trials.

Thermal convection of a liquid metal under an alternating magnetic field

The objective of this work is to measure the heat transfer of a liquid metal in a cylindrical cell under the conjugate effects of a temperature difference and a Lorentz force generated by an alternating current in a coil. The experimental results are compared to recent direct numerical simulations (DNS) (Guillou et al., 2022). 25 experiments are performed for a large range of frequency f, ac intensity amplitude I0 and temperature difference between the top and bottom walls ΔT0: 15≤f≤1000Hz, 2≤I0≤67 A and 6≤ΔT0≤11 K. In these experiments, the Hartmann number Ha, the shielding parameter Sω and Rayleigh number Ra vary in the following range: 6≤Ha≤200, 1≤Sω≤70, 2.3×106≤Ra≤4.1×106. The experiments with an ac magnetic field are compared with the Rayleigh–Bénard convection (RBC) experiments under the same thermal conditions. Three rings of thermocouples allow characterizing the fluid temperature distribution during the convection. The heat flux at the bottom and top walls are also measured. We observe a very good agreement between the experimental results and the DNS results. As previously shown by numerical simulations, a master curve of Nu/Peω vs. QJ/Qc allows predicting the evolution of the heat transfer under different conditions of temperature difference and Lorentz force. Here Nu and Peω are the Nusselt number and a Péclet number based on the Lorentz force, and QJ and Qc are the total power deposited by the Joule effect and the total conduction heat flux without motion, respectively. The experiments show that Nu/Peω∼(QJ/Qc)−2/5.

A Simplified Analytical Model for Strip Buckling in the Pressure-Assisted Milling Process.

A simplified column-buckling model is developed to understand the buckling mechanism of thin-walled strips restrained by uniform lateral pressure in the milling process. The strip is simplified as two rigid columns connected by a rotation spring, resting on a smooth surface, restrained by a uniform pressure and loaded by an axial force. Two loading cases are considered, i.e., the dead load and the follower load. Analytical solutions for the post-buckling responses of the two cases are derived based on the energy method. The minimum buckling force, Maxwell force and stability conditions for the two cases are established. It is demonstrated that the application of higher uniform pressure increases the minimum buckling force for the column and thus makes the column less likely to buckle. For the same pressure level, the dead load is found to be more effective than the follower load in suppressing the buckling of the system. The effect of initial geometric imperfection is also investigated, and the imperfection amplitude and critical restraining pressure that prevent buckling are found to be linearly related. The analytical results are validated by finite element simulations. This analytical model reveals the buckling mechanism of strips under lateral pressure restraint, which cannot be explained by the conventional bifurcation buckling theory, and provides a theoretical foundation for buckling-prevention strategies during the milling process of thin-walled strips, plates and shells commonly encountered in aerospace or automotive industries.

Effectiveness of 12-Week Core Stability Training on Postural Balance in Soccer Players With Groin Pain: A Single-Blind Randomized Controlled Pilot Study.

Core stability training (CST) is effective in improving postural balance, core endurance, and self-reported outcomes in different populations. This study aimed to investigate the effect of CST in soccer players with groin pain (GP). CST would improve postural balance performance, core endurance, and self-reported outcomes in soccer players with GP. Randomized controlled trial. Level 2. Soccer players with GP who met the selection criteria were assigned randomly to a CST (CSTG, n = 10) or a control (CG, n = 10) group. The CG undertook no additional physical activity program besides their usual training. The CSTG performed a 12-week CST comprising 76 ~75 min sessions. Static (force platform) and dynamic (Y-Balance test) postural balance, core endurance (McGill trunk endurance tests), and self-reported outcomes (Copenhagen Hip and Groin Outcome Score [HAGOS]) were assessed before and immediately after the 12-week CST. Significant improvements were seen in dynamic postural balance (P = 0.04 to <0.01), HAGOS scores (P = 0.02 to <0.01), and core endurance measures (P < 0.01) in the CSTG in posttest compared with pretest session and compared with CG. Static bipedal postural balance measures showed significant improvements (eyes open, P = 0.02; eyes closed, P < 0.01) in the CSTG in posttest compared with pretest session. However, no significant differences (P > 0.05) were observed between CSTG and CG after the training period. A 12-week CST improved static (foam surface) and dynamic postural balance, core endurance measures, and HAGOS scores. The beneficial effect of CST on improving postural balance, core endurance, and self-reported outcomes in soccer players with GP suggests that this training would be an important feature of rehabilitation programs for these players. Coaches and clinicians should prioritize CST training when designing rehabilitation programs.

Transient mode-III problem of the elastic matrix with a line inclusion

The method of pull-out test has been used to identify the mechanical performance of hybrid and fiber-reinforced composite materials. This paper investigates the elastic phase preceding the pull-out of a rigid line inclusion from the polymer matrix with fixed top and bottom surfaces. The mode-III problem is investigated such that the pull-out force is applied from the out-of-plane direction and it can be either transient or static. By applying the singular integral equation technique, the semi-analytical elastic field expressions are obtained. Under the static pull-out force, the stress intensity factor (SIF) near the inclusion tip shows a monotonic increase as the length and height of the matrix increase, whereas for the transient pull-out force, the SIF displays an initial increasing and followed by a decline. The maximum SIF is obtained for (1) the matrix length is 2 to 2.5 times of the inclusion length, and (2) the matrix height is 1 to 2 times of the inclusion length. Moreover, this paper provides a solution approach that incorporates the elasticity of the inclusion, showing that there is an optimal shear stiffness that minimizes the stress singularity of system. The conclusions of this study hold significance for the design and performance evaluation of fiber-reinforced composite materials.

Ideal performance assessment of non-recirculating anaerobic fluidized bed reactors treating low to high strength organic loads with low retention time

This study investigated the ideal performance of non-recirculating Anaerobic Fluidized Bed Reactors (AnFBRs) for treating organic wastewater of varying strengths under low Hydraulic Retention Time (HRT). Four 4.58 L AnFBRs were used to treat synthetic wastewater with an Organic Loading Rate (OLR) ranging from 4.50 to 40.11 gCOD/L-d, and HRT between 1.1 and 4.4 hours. The AnFBRs achieved high removal efficiencies ranging from 83 % to 96 % at steady state, except during the organic shock load, which reduced removal performance to 12 %. Shortened HRT conditions led to a decreasing trend in reactor pH due to an incomplete anaerobic cycle. The modified Stover-Kincannon model estimated the maximum substrate utilization rate of AnFBR's to be 196.08 gCOD/L-d, with a correlation coefficient of 0.98. Under shortended HRT, microbial diversity analysis identified predominant non-filamentous bacterial families, such as Streptococcaceae and Veillonellaceae, which collaborate during biofilm development in anaerobic environments. It was suggested that the porous media provided secure attachment sites for the biomass growth and biofilm formation under shock load and high shear force conditions. While these results offer valuable insights, further studies are needed to confirm these findings and enhance the understanding of the use porous media in non-recirculating AnFBRs.

Effectiveness of freezing temperatures on dormancy release of temperate woody species.

Spring phenological change of plants in response to global warming may affect many ecological processes and functions. Chilling temperature regulates budburst date by releasing dormancy. However, whether freezing temperature (<0°C) contributes to dormancy release is still debated. Our poor understanding of the role of chilling makes estimating shifts in budburst date difficult. A two-year chilling-forcing experiment was explicitly designed to test the effects of chilling temperatures on dormancy release of 9 temperate woody species in Beijing, China. A total of 1620 twigs were first exposed to a wide range of temperatures (-10 to 10 °C) with different durations and then moved to growth chambers. Based on budburst data in experimental conditions, we examined whether freezing temperatures are effective on dormancy release. We also developed a new framework for constructing chilling functions based on the curve between chilling duration and forcing requirement (FR) of budburst. The chilling function derived from this framework was not affected by experimental forcing conditions. We demonstrated that freezing temperatures down to -10°C were effective in dormancy release. The rate of dormancy release, indicated by the rate of decay in chilling duration-FR curve, did not differ significantly between chilling temperatures in most cases, although it exhibited a maximum value at 0 or 5°C. The chilling function-associated phenological models could simulate budburst date from independent experimental and observational data with a mean RMSE of 7.07 days. The effective freezing temperatures found here are contrary to the well-known assumption of <0°C temperature generally not contributing to accumulated chilling in many previous chilling functions. A chilling function assuming that temperature below an upper-temperature threshold has the same effects on dormancy release could be adopted to calculate chilling accumulation when using experiments to develop spring phenological models based on the chilling-forcing relationship.