Torque Formula Research Articles

Research and analysis of rock breaking mechanical model of single-roller PDC compound bit

In order to improve wear resistance and rock breaking efficiency of single-roller bit, a new type of bit, single-roller PDC compound bit is designed. The mechanical model of interaction between PDC teeth and rock of single-roller PDC compound bit is established, and the theoretical calculation formula of resultant force and torque generated by interaction between PDC teeth and rock on cone and bit is obtained. The rock-breaking experiment on the single-roller PDC compound bit are carried out. The results show that with the increase of front inclination angle, the axial force and radial force of PDC teeth decrease greatly at first and then tend to be stable, while the tangential force of PDC teeth decreases at first and then increases slightly; the axial force, radial force and tangential force all increase with the increase of the cutting depth; the maximum values of the three forces all appear at the position of the combined effect of the maximum cutting depth and the minimum front inclination angle. The maximum value of moment [Formula: see text] and [Formula: see text] both appear at the minimum value of h C and δ, while the maximum value of moment [Formula: see text] appears at the minimum value of δ. In order to reduce the acting moment generated by PDC cutter on the roller, the PDC cutter at different position heights can be designed with different front inclination angles. The rock breaking experiment results show that compared with the common single-roller bit, the single-roller PDC compound bit has higher rock breaking efficiency and better development prospect. When drilling in hard limestone, the single-roller PDC compound bit is more energy-efficient under higher WOB.

A Recipe for Eccentricity and Inclination Damping for Partial-gap Opening Planets in 3D Disks

In a previous paper, we showed that, like the migration speed, the eccentricity damping efficiency is modulated linearly by the depth of the partial gap a planet carves in the disk surface density profile, resulting in less efficient e-damping compared to the prescription commonly used in population synthesis works. Here, we extend our analysis to 3D, refining our e-damping formula and studying how the inclination damping efficiency is also affected. We perform high-resolution 3D locally isothermal hydrodynamical simulations of planets with varying masses embedded in disks with varying aspect ratios and viscosities. We extract the gap profile and orbital damping timescales for fixed eccentricities and inclinations up to the disk scale height. The limit in gap depths below which vortices appear, in the low-viscosity case, happens roughly at the transition between classical type-I and type-II migration regimes. The orbital damping timescales can be described by two linear trends with a break around gap depths ∼80% and with slopes and intercepts depending on the eccentricity and inclination. These trends are understood on physical grounds and are reproduced by simple fitting formulas whose error is within the typical uncertainty of type-I torque formulas. Thus, our recipes for the gap depth and orbital damping efficiencies yield a simple description for planet–disk interactions to use in N-body codes in the case of partial-gap opening planets that is consistent with high-resolution 3D hydrosimulations. Finally, we show examples of how our novel orbital damping prescription can affect the outcome of population synthesis experiments.

Dynamical tides in binaries: Inconsistencies in the implementation of Zahn’s prescription

Binary evolution codes are essential tools to help in understanding the evolution of binary systems. They contain a great deal of physics, for example stellar evolution, stellar interactions, mass transfer, tides, orbital evolution. Since many of these processes are difficult to account for in detail, we often rely on prescriptions obtained in earlier studies. We highlight that the impact of the dynamical tides with radiative damping has been implemented inconsistently with respect to its original theoretical formulation in many studies. We derive a new analytical solution for the evolution toward synchronization in the case of circular orbits and propose turnkey equations for the case of eccentric orbits that can be used in population synthesis studies. We compare the strength of the tidal torque obtained with this new formula with respect to that obtained with the formula generally used in literature by studying how the evolution toward synchronization of main sequence stellar models is affected. We conclude that by using an incorrect formula for the tidal torque, as has been done in many binary codes, the strength of the dynamical tides with radiative damping is over- or underestimated depending on whether the star is close to or far from synchronization.

Unified Vector Torque Control for Reluctance Motor With Different Coil Pitch

This paper unifies the vector torque control of reluctance motor with different coil pitch in the classic vector model frameworks, including the typical switched reluctance motor (SRM), mutually coupled switched reluctance motor (MCSRM), synchronous reluctance motor (SynRM) and so on. Based on the proposed vector model, the instantaneous electromagnetic torque of the reluctance motor is decoupled into two components. The first partial torque is called as the Synchronous-Speed Reluctance Force (SSRF), generated by the interaction of the <i>d</i>-axis and <i>q</i>-axis currents. The second partial torque is the Double-Speed Reluctance Force (DSRF), generated by the interaction between the <i>dq</i>-plane current and the 0-axis current. The torque formula can reflect the torque generation and fluctuation reasons, and the proportion of the two torque components is related to the ratio of the varying components of the motor&#x0027;s self-inductance and mutual inductance. Different types of reluctance motors can be summarized in the unified vector model. The conclusion is that the SynRM only contains the SSRF torque while the typical SRM and MCSRM contain both the SSRF torque and DSRF torque. The proposed unified vector torque control method is verified by simulations and experiments of 12-slot 8-pole reluctance motors with different coil pitch.

Study of the Judder Characteristics of Friction Material for an Automobile Clutch and Test Verification

The friction judder characteristics during clutch engagement have a significant influence on the NVH of a driveline. In this research, the judder characteristics of automobile clutch friction materials and experimental verification are studied. First, considering the stick-slip phenomenon in the clutch engagement process, a detailed 9-degrees-of-freedom (DOF) model including the body, each cylinder of the engine, clutch and friction lining, torsional damper, transmission and other driveline parts is established, and the calculation formula of friction torque in the clutch engagement process is determined. Second, the influence of the friction gradient characteristics on the amplification or attenuation of the automobile friction judder is analyzed, and the corresponding stability analysis and the numerical simulation of different friction gradient values are carried out with MATLAB/Simulink software. Finally, judder bench test equipment and a corresponding damping test program are developed, and the relationship between the friction coefficient gradient characteristics and the system damping is analyzed. After a large number of tests, the evaluation basis of the test is determined. The research results show that the friction lining with negative gradient characteristics of the friction coefficient will have a judder signal. When the friction gradient value is less than −0.005 s/m, the judder signal of the measured clutch cannot be completely attenuated, and the judder phenomenon occurs. When the friction gradient is greater than − 0.005 s/m, the judder signal can be significantly suppressed and the system connection tends to be stable.

A recipe for orbital eccentricity damping in the type-I regime for low-viscosity 2D discs

Context. It is well known that partial and deep gap opening depends on a disc’s viscosity; however, damping formulas for orbital eccentricities have only been derived at high viscosities, ignoring partial gap opening. Aims. In this work, we aim to obtain a simple formula to model eccentricity damping of the type-I regime in low-viscosity discs, where even small planets of a few to a few tens of Earth masses may start opening partial gaps in the gas surface density around their orbit. Methods. We performed high-resolution, 2D, locally isothermal hydrodynamical simulations of planets with varying masses on fixed orbits in discs with varying aspect ratios and viscosities. We determined the torque and power felt by the planet to ultimately derive migration and eccentricity damping timescales. Results. We first find a lower limit to the gap depths below which vortices appear; this happens roughly at the transition between type-I and classical type-II migration regimes. For the simulations that remain stable, we obtain a fit to the observed gap depth in the limit of vanishing eccentricities that is similar to the one currently used in the literature but accurate down to α = 3.16 × 10−5. We then record the eccentricity damping efficiency as a function of the observed gap depth and the initial eccentricity. When the planet has opened a deep enough gap such that the surface density is less than ~80% of the unperturbed disc surface density, a clear linear trend is observed independently of the planet’s eccentricity; at shallower gaps, this linear trend is preserved at low eccentricities, while it deviates to more efficient damping when e is comparable to the disc’s scale height. Both trends can be understood on theoretical grounds and are reproduced by a simple fitting formula. Conclusions. Our combined fits for the gap depth and eccentricity damping efficiency yield a simple recipe to implement type-I eccentricity damping in N-body codes in the case of partial gap opening planets that is consistent with high-resolution 2D hydrodynamical simulations. The typical error of the final fit is of the order of a few percent, and at most ~20%, which is the error of type-I torque formulas widely used in the literature. This will allow a more self-consistent treatment of planet-disc interactions of the type-I regime for population synthesis models at low viscosities.

Development of a 1KVa fuel less generator using a Brushed Direct Current Motor

In this paper, the fuel less generator just as the name implies is a power generating system that doesn’t require any kind of fossil fuel for its operation. It is safe to say the fuel less generator is a zero-carbon energy system with two major categories; Dynamic Fuel less Generators and Static Fuel Less Generators. The constructed 1kVA Fuel less Generator comprised of a 240W Brushed Direct Current Motor, a 1kVA Alternator, Couplings, Flywheel, 12V 100AH Deep Cycle Battery, 12V 4A Charging Panel or Rectifying circuit (AC-to-DC), Automatic Voltage Regulator, Frame, and other accessories. The Brushed Direct Current Motor was directly coupled to the alternator with the flywheel in-between, also a digital thermometer was connected to the Brushed Direct Current Motor and alternator to monitor their temperature. A digital Direct Current Ammeter and Voltmeter were connected in series with the 12V 100AH Battery and across the Brushed Direct Current Motor terminals respectively to observe and obtain readings of the fuel-fewer generators. A digital energy meter with a current transformer was also connected between the power output of the alternator and the 5A single pole circuit breaker to obtain output parameters such as Voltage, Current, Frequency, Power Factor, and energy consumed. A handheld Digital Tachometer was used to obtain the speed of the fuel less generator during testing. Various tests such as the No-Load and Load Test, Temperature Test, and Speed Test were carried out during the performance evaluation using varying loads from the range of 0W to 800W. During the test, it was observed that the temperature of the Brushed Direct Current Motor increased drastically when a load of 300W was introduced into the system and the generator had its maximum efficiency of 88.71% at the same 300W load. The fuel less generator was operated with and without the flywheel which gave an output frequency of 40Hz and 25Hz respectively. The construction of fuel less generator with the ability to be in perpetual motion and continually generate electric energy is achievable provided the motor speed, torque, and cooling system are properly calculated. This research can be used to replace the conventional gasoline generators used in residential buildings and by Small and Medium Entrepreneurs (SMEs). The inclusion of a direct-coupled flywheel, power torque formula, and temperature monitor and control play an important role in the development of an efficient fuel less generator.

Deep-Investigated Analytical Modeling of a Surface Permanent Magnet Vernier Motor

Permanent magnet Vernier motors (PMVMs) possess the advantage of high torque density for high-performance applications. However, the low power factor challenge makes it unacceptable for direct-drive applications. A lack of accurate modeling method based on the motor sizing law, i.e., air-gap flux density, linear current density, and motor geometry parameters, raises difficulties for machine designers to further conduct research on the performance metrics. This article presents a deep investigation into the analytical modeling technique for surface PMVMs (SPMVMs). It can identify an accurate approach to obtain the performance metrics, including electromagnetic torque and power factor. The modeling technique is developed based on the conformal mapping method. By using this, both radial and tangential permeability functions can be calculated to obtain the motor magnetic loading accurately, considering the leakage flux. The slotting effect on both air-gap flux density and armature-winding function is analyzed to achieve a precise formula for torque and power factor computations. The new modeling technique is applied to integral-slot SPMVMs with different slot/pole combinations, gear ratios, slot openings, and magnet thickness to evaluate the impacts of motor parameters on high-power-factor and high-torque-density designs. Finally, an SPMVM with the characteristics of high torque density and power factor is fabricated to verify the analytical model at the power rating of 0.8 kW and the speed of 500 r/min. The experimental results show that the prototype exhibits a high power factor of 0.9 and high torque density 22.5 Nm/L.

A Simple Method to Calculate the Torque of Magnet-Rotating-Type Axial Magnetic Coupler Using a New Magnetic Equivalent Circuit Model

A magnet-rotating-type axial magnetic coupler (MAMC), namely, a novel axial magnetic coupler with rotatable monopole permanent magnets (PMs), is proposed. The speed of the MAMC can be adjusted by rotating the rotatable PMs mounted on the PM disk, or changing the axial air gap length between the PM disk and the conductor sheet (CS), or combining these methods. In order to analyze the torque performance, the magnetic circuit model of MAMC is established when the rotatable PMs are not parallel to the CS. Specifically, the influence of the induced eddy current is introduced into a new magnetic equivalent circuit (MEC) model. Combined with Kirchhoff’s law, the calculation formula of torque is derived. Moreover, according to Ampere’s law, the formula for calculating the induced eddy current is derived when the rotatable PMs after rotating are not parallel to the CS. Finally, the effectiveness of the proposed model is verified by the finite element method (FEM). The results obtained by the new MEC model proposed are consistent with those obtained by the FEM, and the formula derived is effective in the case of small rotational speed differences, small air gap lengths, and small thicknesses of the CS.

Mathematical model and experimental study of a magnet coupling with a stop

The paper presents an improved analytical model for axial-flux eddy-current couplings with permanent magnets. The design procedure is based on the torque formula derived from a two-dimensional approximation of the magnetic field distribution. The developed model takes into account the heating of the copper disk and magnets due to the high slip speed. Another advantage of the developed model is the reduction in computation time compared to 3-D finite element simulations. The model is validated experimentally. A correlation between the model and the experiment is obtained. The coupling torque is subject to reduction due to low manufacturing accuracy. The model is effective for engineering use at the design stage of magnet couplings, especially for cable drums of cranes.

On the free rotation of a polarized spinning-top as a test of the correct radiation reaction torque

The formula for dipole radiation reaction torque acting on a system of charges, and the Larmor-like formula for the angular momentum loss by this system, differ in the time derivative term which is the analogue of the Schott term in the energy loss problem. In the well-known textbooks this discrepancy is commonly avoided via neglect of the Schott term, and the Larmor-like formula is preferred. In the present paper both formulae are used to derive two different equations of motion of a polarized spinning-top. Both equations are integrable for the symmetric top and lead to quite different solutions. That one following from the Larmor-like formula is physically unplausible, in contrast to another one. This result is accorded with the reinterpretation of Larmor’s formula discussed recently in the pedagogical literature. It is appeared, besides, that the Schott term is of not only academic significance, but it may determine the behavior of polarized micro- and nanoparticles in nature or future experiments.

Characteristic Investigation and Torque Distribution Diagram-Based Computational Method for Continuously Variable Power-Split Transmission

The key parameter of power-split transmission is the planetary ratio. To obtain various planetary ratios in one transmission system, people use complex systems with multiple planetary gear trains, clutches, and brakes. Another solution is replacing the planetary gear train with a planetary traction drive. However, the participation of the planetary traction drive brings about creep and spin motion, which increase the difficulty of precise calculation. In this study, we investigate the relationships between torques and speeds. Then, we derive the torque and speed distribution formulas that consider the influence of spin torque and creep motion. This study is the first step to precisely calculate the emerging power-split transmission with the planetary traction drive. Based on a contact model and a proposed torque distribution diagram method, this study proposes a fast computational method for calculating the performance of the new continuously variable power-split transmission. The results show that the proposed torque distribution diagram-based computational method is feasible, and the planetary traction drive can be a competitive power-split device for power-split transmission.

Destruction Feature Extraction of Prefabricated Residential Building Components Based on BIM

In order to improve the damage feature extraction effect of prefabricated residential building components and improve the structural stability of prefabricated residential components, this paper applies BIM technology to the structural feature analysis of prefabricated residential components. Moreover, this paper adopts the simple superposition method and combines the first strength theory of material mechanics to derive the formula for calculating the cracking torque of prefabricated residential building components under compound torsion. In addition, based on the variable-angle space truss model, this paper uses a simple superposition method to derive the calculation formula for the ultimate torque of composite torsion of fabricated residential building components and applies it to the BIM fabricated residential model. Finally, this paper constructs an intelligent BIM prefabricated residential building construction damage characteristic monitoring system. Through experimental research, it can be seen that the intelligent BIM prefabricated residential building construction damage feature monitoring system proposed in this paper can monitor the damage characteristics of prefabricated residential building construction and can predict the evolution of subsequent building features.

Analysis and Revision of Torque Formula for Hydro-viscous Clutch

Hydro-viscous clutch is a speed-regulating device for heavy fans and water pumps. It has important engineering significance in the fields of soft-start for rotating machinery. More and more attention has been paid to its torque and control characteristics. This paper is focused on the torque formula for hydro-viscous clutch (HVC), assuming that multi-friction plates distribute ununiformly with different oil film thickness. A mathematical model of friction plates was constructed, then the distribution formula of the oil film thickness was obtained. A new expression was presented using a modified factor. Parameters such as pressure, viscous torque, and oil film thickness were obtained. The results show that each clearance of friction plates is not the same and the distribution of oil film thickness is influenced by pressing force, groove depth, angular ratio of groove/non-groove, and static friction force. To verify the proposed expression, relevant experiments were carried out on an HVC with multi-friction plates, and the experimental results indicate that the new expression is more accurate compared to the original one.

Hydrodynamic torque on a slender cylinder rotating perpendicularly to its symmetry axis

The torque experienced by a circular cylinder rotating steadily about an axis passing trough its centroid and perpendicular to its symmetry axis is computed over a wide range of Reynolds number and aspect ratios using fully resolved simulations. In the creeping-flow regime, numerical results are shown to match predictions of an improved slender-body approximation. In strongly inertial regimes, flow symmetries and boundary layer arguments are employed to derive scaling laws for the various contributions to the torque. We finally obtain an empirical formula for the total torque, valid throughout the parameter range explored in the simulations.

Analytical and Experimental Investigations of Novel Maglev Coupling Based on Opposed Halbach Array for a 2D Valve

In this paper, a novel maglev coupling based on the opposed Halbach array is proposed as the interface between the linear electro-mechanical converter and 2D valve body. This non-contact maglev coupling possesses several advantages over existing mechanical couplings such as zero friction and wear, low vibration and noise, and no lubrication, which is expected to greatly improve the control accuracy and life cycle of the 2D valve. A detailed analytical model of maglev coupling is established based on the electro-magnetic theory. Firstly, the permanent magnets of the Halbach array is decomposed into several types of basic elements to obtain their individual analytical expressions, which are then re-superimposed into the whole coupling to obtain the analytical formula of torque–displacement characteristics. In order to obtain maximum output torque of maglev coupling, a parametric analysis was performed using an analytical model and optimal pitch angle and shifted distance was explored and found. To verify the correctness of the analytical modelling and parametric analysis results, the torque–displacement characteristics were also studied through both the FEM simulation and experimental approach. The results of analytical modelling, FEM simulation and experiment were in a good agreement, which shows that the maximum magnetic torque can reach about 0.579 N·m when the external armature displacement is 1 mm. The research work provides an important reference for the future application of maglev coupling in a 2D valve.

Equivalence of three-dimensional acoustic radiation force and torque formulas based on angular spectrum and multipole expansion methods

Acoustic radiation force (ARF) or torque (ART) can be derived by integrating the time-averaged linear and angular radiation stress tensor (the flux of momentum tensor) over a far-field standard spherical surface including an arbitrarily shaped target. Following this idea, there are three sets of independent original derivation on the ARF ([Silva, J. Acoust. Soc. Am. 130, 3541–3544 (2011)] and [Baresh et al., J. Acoust. Soc. Am. 133, 25–36 (2013)] based on the multipole expansion method, and [Sapozhnikov and Bailey, J. Acoust. Soc. Am. 133, 661–676 (2013)] based on the angular spectrum method); and two independent work on the ART ([Silva et al., EPL 97, 54003 (2012)] based on the multipole expansion method and [Gong and Bandoin, J. Acoust. Soc. Am. (under review; 2020)] based on the angular spectrum method). In this work, we formally establish the equivalence between the expressions obtained by these two methods with the relation of beam shape coefficients at different elementary waves of the field for both the force and torque. The differences between the existing formulas in the literature are indicated and explained. The respective advantages of each form are discussed.

Torsion design of lightweight concrete beams without or with fibers: A comparative study and a refined cracking torque formula

Although a well established comprehension of the torsional design is a must for an accurate and economic design of concrete members, however, after 180 years of research very little is known about the torsion design of lightweight concrete (LWC) beams. Several projects are undergoing with the objective of improving design provisions, including but not limited to those for shear, torsion, and LWC, however, very limited studies have tackled either torsion design or combined torsion, shear and flexure design of LWC beams. This current study examines the current design of LWC beams under torsion. Selected torsion design provisions were reviewed and outlined. Findings from previous experimental testing of LWC beams under torsion were reviewed and outlined. An experimental database was compiled from previous works available in the literature, with a total of 90 beams tested under significant torsion. The cracking and ultimate torsion strength of all tested beams were calculated using selected design codes. The calculated cracking and ultimate torsion strength were compared to the experimentally observed ones. The effect of various parameters on the safety, accuracy, and consistency of the torsion design of LWC beams using various design codes was investigated. Cracking torque needed a revisit in order to account for LWC and using fibers in the concrete mix. A new formula for cracking torsional moments, which included the effect of all effective parameters was developed, validated, and proposed. The proposed formula was found to be remarkably better than existing design codes. More experimental testing for LWC beams under combined loading is needed in order to refine existing design codes and proposed formula.

Nonuniform Load Distribution between the Satellites of a Cycloid Gear

How may the load distribution among satellites in a cycloid gear be estimated? A mathematical model permits calculation of the nonuniformity of the load distribution. On that basis, the familiar formula for the maximum permissible torque at the gear cage may be refined. The nonuniformity of the load distribution is analyzed as a function of the gear’s linear dimensions.

The Design, Kinematics and Torque Analysis of the Self-Bending Soft Contraction Actuator

This article presents the development of a self-bending contraction actuator (SBCA) through the analysis of its structure, kinematics, and torque formulas, and then explores its applications. The proposed actuator has been fabricated by two methods to prove the efficiency of the human body inspiration, which represents the covering of human bones by soft tissues to protect the bone and give the soft texture. The SBCA provides bending behaviour along with a high force-to-weight ratio. As with the simple pneumatic muscle actuator (PMA), the SBCA is soft and easy to implement. Both the kinematics and the torque formula presented for the SBCA are scalable and can be used with different actuator sizes. The bending actuator has been tested under an air pressure of up to 500 kPa, and the behaviour of its bending angle, parameters, dimensions, and the bending torques have been illustrated. On the other hand, the experiments showed the efficient performances of the actuator and validate the proposed kinematics. Therefore, the actuator can be used in many different applications, such as soft grippers and continuum arms.