In engineering,all movable expanse revolving objects manifest gyroscopic effects.These effects are created by the action of the outer load on the revolving items whose rotating mass originates eight inertial torques a...In engineering,all movable expanse revolving objects manifest gyroscopic effects.These effects are created by the action of the outer load on the revolving items whose rotating mass originates eight inertial torques about two axes.Two torques of centrifugal forces,one torque of the Coriolis force originated by the rotating distributed mass,and the torque of the change in the angular momentum of the center mass act about each axis.The inertial torques activate rotations of the gyroscope by the determined correlation.Inertial torques depend on their geometry and orientation at the spatial coordinate system.The known analytical model for the rotation of the revolving disc about axes contains a mechanical error.This error was obtained by the incorrect integration of the centrifugal inertial torque.The corrected inertial torque yields the accurate expression for the interacted rotations of the revolving disc about axes.展开更多
This study proposes a new nonlinear tracking control method with safe angular velocity constraints for a cushion robot. A fuzzy path planning algorithm is investigated and a realtime desired motion path of obstacle av...This study proposes a new nonlinear tracking control method with safe angular velocity constraints for a cushion robot. A fuzzy path planning algorithm is investigated and a realtime desired motion path of obstacle avoidance is obtained. The angular velocity is constrained by the controller, so the planned path guarantees the safety of users. According to Lyapunov theory, the controller is designed to maintain stability in terms of solutions of linear matrix inequalities and the controller's performance with safe angular velocity constraints is derived.The simulation and experiment results confirm the effectiveness of the proposed method and verify that the angular velocity of the cushion robot provided safe motion with obstacle avoidance.展开更多
The performance of any inertially stabilized platform （ISP） is strongly related to the bandwidth and accuracy of the angular velocity signals. This paper discusses the development of an optimal state estimator for s...The performance of any inertially stabilized platform （ISP） is strongly related to the bandwidth and accuracy of the angular velocity signals. This paper discusses the development of an optimal state estimator for sensing inertial velocity using low-cost micro-electro-mechanical systems （MEMS） sensors. A low-bandwidth gyroscope is used alone with two low-performance accelerometers to obtain the estimation. The gyroscope has its own limited dynamics and mainly contributes to the low-frequency components of the estimation. The accelerometers have inherent biases and mainly contribute to the high-frequency components of the estimation. Extensive experimental results show that the state estimator can achieve high-performance signals over a wide range of velocities without drifts in both the t- and s-domains. Furthermore, with applications in miniature inertially stabilized platforms, the control characteristic presents a significantly improvement over the existing methods. The method can be also applied to robotics, attitude estimation, and friction compensation.展开更多
The tracking of orientation and angular velocity is a primary attitude control task for an on-orbit spacecraft.The problem for a rigid spacecraft tracking a desired angular velocity profile is addressed using an adapt...The tracking of orientation and angular velocity is a primary attitude control task for an on-orbit spacecraft.The problem for a rigid spacecraft tracking a desired angular velocity profile is addressed using an adaptive feedback control.An angular velocity feedback tracking algorithm is firstly developed based on the precisely known attitude dynamics of the spacecraft,and the global tracking of the control algorithm is proved based on the Lyapunov analysis.An adaptation mechanism is then designed to deal with the dynamic uncertainties of the spacecraft.Such an adaptation mechanism enables the controller to track any desired angular velocity trajectories even in the presence of uncertain inertia parameters,although it does not guarantee the inertia tensor being precisely identified.To verify the effectiveness of the proposed adaptive control policy,computer simulations on dynamic equations of a spacecraft are conducted and their results are discussed.展开更多
Angular velocity stabilization control and attitude stabilization control for an underactuated spacecraft using only two single gimbal control moment gyros （SGCMGs） as actuators is investigated. First of all, the dy...Angular velocity stabilization control and attitude stabilization control for an underactuated spacecraft using only two single gimbal control moment gyros （SGCMGs） as actuators is investigated. First of all, the dynamic model of the underactuated spacecraft is established and the singularity of different configurations with the two SGCMGs is analyzed. Under the assumption that the gimbal axes of the two SGCMGs are installed in any direction, and that the total system angular momentum is not zero, a state feedback control law via Lyapunov method is designed to globally asymptotically stabilize the angular velocity of spacecraft. Under the assumption that the gimbal axes of the two SGCMGs are coaxially installed along anyone of the three principal axes of spacecraft inertia, and that the total system angular momentum is zero, a discontinuous state feedback control law is designed to stabilize three-axis attitude of spacecraft with respect to the inertial frame. Furthermore, the singularity escape of SGCMGs for the above two control problems is also studied. Simulation results demonstrate the validity of the control laws.展开更多
In this paper,the estimator-based Global Positioning System(GPS)attitude and angular velocity determination is presented.Outputs of the attitude estimator include the attitude angles and attitude rates or body angular...In this paper,the estimator-based Global Positioning System(GPS)attitude and angular velocity determination is presented.Outputs of the attitude estimator include the attitude angles and attitude rates or body angular velocities,depending on the design of estimator.Traditionally as a position,velocity and time sensor,the GPS also offers a free attitude-determination interferometer.GPS research and applications to the field of attitude determination using carrier phase or Doppler measurement has been extensively conducted.The rawattitude solution using the interferometry technique based on the least-squares approach is inherently noisy.The estimator such as the Kalman filter(KF)or extended Kalman filter(EKF)can be incorporated into the GPS interferometer,potentially providing several advantages,such as accuracy improvement,reliability enhancement,and real-time characteristics.Three estimator-based approaches are investigated for performance comparison,including(1)KF with measurement involving attitude angles only;(2)EKF with measurements based on attitude angles only;(3)EKF with measurements involving both attitude angles and body angular rates.The assistance from body mounted gyroscopes,if available,can be utilized as the measurements for further performance improvement,especially useful for the case of signal-challenged environment,such as the GPS outages.Modeling of the dynamic process involving the body angular rates and derivation of the related algorithm will be presented.Simulation results for various estimator-based approaches are conducted;performance comparison is presented for the case of GPS outages.展开更多
In order to find out the influence of the instability of angular velocity of the rotating carrier itself on the stability of silicon micromachined gyroscope, the digital models for relative error of the high and low d...In order to find out the influence of the instability of angular velocity of the rotating carrier itself on the stability of silicon micromachined gyroscope, the digital models for relative error of the high and low damping gyroscope's output signal are given respectively, based on the motion equations of the silicon micromachined gyroscope. Theory proves that the output signal error of the silicon micromachined sensor is mainly caused by the instability of damping factor and the angular velocity of the rotating carrier itself. The experiment result indicates that the error of proportionality coefficient of output voltage which is caused by the instability of the angular velocity of the rotating carrier itself reaches to 4.1 %. Theoretical demonstration and experimental verification show that the instability of angular velocity of the rotating carrier itself has an important effect on the stability of low damping silicon micromachined gyroscope.展开更多
The loss of Baryonic Matter through Black Holes from our spatial 3-D Universe into its 4th dimension as Dark Matter, is used along with the Conservation of Angular Momentum Principle to prove theoretically the acceler...The loss of Baryonic Matter through Black Holes from our spatial 3-D Universe into its 4th dimension as Dark Matter, is used along with the Conservation of Angular Momentum Principle to prove theoretically the accelerated expansion of the 3-D Universe, as has already been confirmed experimentally being awarded the 2011 Nobel Prize in Physics. Theoretical calculations can estimate further to indicate the true nature of the acceleration;that the outward acceleration is due to the rotation of the Universe caused by Dark Energy from the Void, that the acceleration is non-linear, initially increasing from zero for the short period of about a Million years at a constant rate, and then leveling off non-linearly over extended time before the outward acceleration begins to decrease in a non-linear fashion until it is matched by the gravitational attraction of the matter content of 4D Space and the virtual matter in 3-D Vacuum Space. m = m(4D) + m(Virtual). The rotation of our 3D Universe will become constant once all 3D matter has entered 4D space. As the 3-D Universe tries to expand further it will be pulled inward by its gravitational attraction and will then keep on oscillating about a final radius r<sub>f</sub> while it also keeps on oscillating at right angles to the radius r<sub>f</sub> around final angular velocity ω<sub>f</sub>, until it becomes part of the 4-D Universe. The constant value of the Angular Momentum of our Universe is L = .展开更多
The study object is the angular output velocity of the drive shaft which is made up of two series-wound cross universal joints. We have deduced the function relation between the angular output velocity and initiative ...The study object is the angular output velocity of the drive shaft which is made up of two series-wound cross universal joints. We have deduced the function relation between the angular output velocity and initiative input angle of the drive shaft with double cross universal joints that is based on the calculation formula of the angular output velocity of a single cross universal joint, and by analyzing the relation between the two input angles. By using this function relation, the constant velocity condition of the drive shaft with double cross universal joints＂ is verified. The step-by-step searching algorithm is adopted to obtain the optimal phase angle that leads to the minimum fluctuate index of the angular output velocity in the vary velocity condition. At the same time, we worked out the maximal and minimum value of the angular output velocity, and their initiative input angle. The correctness of the function of the angular output velocity and the step-by-step search algorithm are verified by an ADAMS simulation example.展开更多
In simulation,sometimes we wish to stipulate a specified angular velocity applied to a given frame.Although position,linear velocity and orientation interpolations are well studied,less attention is paid on angular ve...In simulation,sometimes we wish to stipulate a specified angular velocity applied to a given frame.Although position,linear velocity and orientation interpolations are well studied,less attention is paid on angular velocity interpolation.In this paper,a new method to smoothly interpolate angular velocity using quaternions is presented.This method can be easily incorporated into a key frame animation system.The angular velocity at an arbitrary time can be calculated easily by our method.This method can also be generalized to smoothly interpolate orientations.展开更多
In this paper, we derive non-classical continuum theory for physics of compressible and incompressible thermoviscous non-classical fluent continua using the conservation and balance laws (CBL) by incorporating additio...In this paper, we derive non-classical continuum theory for physics of compressible and incompressible thermoviscous non-classical fluent continua using the conservation and balance laws (CBL) by incorporating additional physics of internal rotation rates arising from the velocity gradient tensor as well as their time varying rates and the rotational inertial effects. In this non-classical continuum theory time dependent deformation of fluent continua results in time varying rotation rates i.e., angular velocities and angular accelerations at material points. Resistance offered to these by deforming fluent continua results in additional moments, angular momenta and inertial effects due to rotation rates i.e., angular velocities and angular accelerations at the material points. Currently, this physics due to internal rotation rates and inertial effects is neither considered in classical continuum mechanics (CCM) nor in non-classical continuum mechanics (NCCM). In this paper, we present a derivation of conservation and balance laws in Eulerian description: conservation of mass (CM), balance of linear momenta (BLM), balance of angular momenta (BAM), balance of moment of moments (BMM), first and second laws of thermodynamics (FLT, SLT) that include: (i) Physics of internal rotation rates resulting from the velocity gradient tensor;(ii) New physics resulting due to angular velocities and angular accelerations due to spatially varying and time dependent rotation rates. The balance laws derived here are compared with those that only consider the rotational rates but neglect rotational inertial effects and angular accelerations to demonstrate the influence of the new physics. Constitutive variables and their argument tensors are established using conjugate pairs in the entropy inequality, additional desired physics and principle of equipresence when appropriate. Constitutive theories are derived using Helmholtz free energy density as well as representation theorem and integrity (complete basis). It is shown that the mathematical model consisting of the conservation and balance laws and constitutive theories presented in this paper has closure. Influence of new physics in the conservation and balance laws on compressible and incompressible thermoviscous fluent continua is demonstrated due to presence of angular velocities and angular accelerations arising from time varying rotation rates when the deforming fluent continua offer rotational inertial resistance. The fluent continua are considered homogeneous and isotropic. Model problem studies are considered in a follow-up paper.展开更多
The relative characteristics of motion of the fuel and shell upon launching is analyzed. By means of mechanical analysis and calculation, it is proposed that relative motion exists not only in the ranges between the f...The relative characteristics of motion of the fuel and shell upon launching is analyzed. By means of mechanical analysis and calculation, it is proposed that relative motion exists not only in the ranges between the fuel and shell of the warhead, but also in the fuel in different positions. The result of study indicates that the position of the fuel in the warhead has a marked influence on the relative motion, while the frictional coefficient between the fuel and shell has less influence upon it.展开更多
The exact thermoelastic analysis of a functionally graded piezoelectrical （FGP） rotating cylinder is investigated analytically. The cylinder is subjected to a com- bination of electrical, thermal, and mechanical loa...The exact thermoelastic analysis of a functionally graded piezoelectrical （FGP） rotating cylinder is investigated analytically. The cylinder is subjected to a com- bination of electrical, thermal, and mechanical loads simultaneously. The structure is a simplified model of a rotational sensor or actuator. The basic governing differential equation of the system is obtained by using the energy method. A novel term, named as the additional energy, is introduced to exact the evaluation of the energy functional. The solution to the governing differential equation is presented for two types of boundary conditions including free rotating and rotating cylinders exposed to the inner pressure. The effect of the angular velocity is investigated on the radial distribution of various components. The mentioned structure can be considered as a sensor for measuring the angular velocity of the cylinder subjected to the pressure and temperature. The obtained results indicate that the electrical potential is proportional to the angular velocity.展开更多
A rotating axisymmetric circular nanoplate is modeled by the Mindlin plate theory.The Mindlin plate theory incorporates the nonlocal scale and strain gradient effects.The shear deformation of the circular nanoplate is...A rotating axisymmetric circular nanoplate is modeled by the Mindlin plate theory.The Mindlin plate theory incorporates the nonlocal scale and strain gradient effects.The shear deformation of the circular nanoplate is considered and the nonlocal strain gradient theory is utilized to derive the governing differential equation of motion that describes the out-of-plane free vibration behaviors of the nanoplate.The differential quadrature method is used to solve the governing equation numerically,and the natural frequencies of the out-of-plane vibration of rotating nanoplates are obtained accordingly.Two kinds of boundary conditions are commonly used in practical engineering,namely the fixed and simply supported constraints,and are considered in numerical examples.The variations of natural frequencies with respect to the thickness to radius ratio,the angular velocity,the nonlocal characteristic scale and the material characteristic scale are analyzed in detail.In particular,the critical angular velocity that measures whether the rotating circular nanoplate is stable or not is obtained numerically.The presented study has reference significance for the dynamic design and control of rotating circular nanostructures in current nano-technologies and nano-devices.展开更多
In order to satisfy the requirement of high precision measurement in a high dynamic environment, a kind of gyro aided multi-accelerometer inertial measurement unit （GAMA-IMU） with six accelerometers and two gyros （...In order to satisfy the requirement of high precision measurement in a high dynamic environment, a kind of gyro aided multi-accelerometer inertial measurement unit （GAMA-IMU） with six accelerometers and two gyros （6A2G） was proposed in this paper. The available configurations have the problem of low measurement precision In a high dynamic environment due to channel coupling. The three channels were decoupled when calculating the angular velocity in the proposed configuration. The yawing and pitching angular velocity were directly measured by gyros, while only the rolling angular velocity was obtained by the GAMA-IMU indirectly from the rolling angular acceleration and quadratic component of rolling angular velocity. Then a single channel rolling angular velocity calculation model was established and the extended Kalman filter （EKF） was used to do state esti- mation. Simulations were carried out and results indicated that the calculation precision of the proposed 6A2G configuration could meet the demand of high precision measurement for a high-speed rotating carrier.展开更多
Lattice Boltzmann method was used to numerically investigate the motion and orientation distribution of cylindrical and cubic particles in pipe flow with high concentration and high particle to pipe size ratio. The tr...Lattice Boltzmann method was used to numerically investigate the motion and orientation distribution of cylindrical and cubic particles in pipe flow with high concentration and high particle to pipe size ratio. The transient impulse model of 3D collisions between particles and between particle and wall is proposed. The numerical results are qualitatively in agreement with and quantitatively comparable to the experiment data. The results show that the increases of both the cylindrical particle to pipe size ratio and the particle aspect ratio decrease the rotation about all axes. All rotations of cubic particles decrease with increasing the particle concentration. The cubic particles, rotating more drastically in the flow with large Reynolds number, rotate faster than the cylindrical particles with the same size. The cylindrical particles align with the flow direction more obviously with decreasing Reynolds numbers. However, the orientations of cubic particles are spread all over the range with no significant difference in magnitude, and the Reynolds numbers have no obvious effect on the orientations of cubic particles.展开更多
The fundamental principles of the gyroscope theory contain the system of the inertial torques generated by the rotating mass of the spinning disc that interrelated by the ratio of its angular velocities rotation aroun...The fundamental principles of the gyroscope theory contain the system of the inertial torques generated by the rotating mass of the spinning disc that interrelated by the ratio of its angular velocities rotation around axes. The action of the centrifugal, common inertial Coriolis forces and the change in the angular momentum generate the system of inertial torques. These four dynamical components make up the system of the eight torques acting simultaneously on the spinning disc. They manifest their action in gyroscopic effects. The ratio of the precessed motions of the gyroscope presents one of the gyroscopic effects around axes of rotation. The known mathematical model for this ratio contains an error that was corrected in this work.展开更多
The star identification algorithm usually identifies stars by angular distance matching.However,under high dynamic conditions,the rolling shutter effect distorts the angular distances between the measured and true sta...The star identification algorithm usually identifies stars by angular distance matching.However,under high dynamic conditions,the rolling shutter effect distorts the angular distances between the measured and true star positions,leading to plethoric false matches and requiring complex and time-consuming verification for star identification.Low identification rate hinders the application of low-noise and cost-effective rolling shutter image sensors.In this work,we first study a rolling shutter distortion model of angular distances between stars,and then propose a novel three-stage star identification algorithm to identify distorted star images captured by the rolling shutter star sensor.The first stage uses a modified grid algorithm with adaptive error tolerance and an expanded pattern database to efficiently eliminate spurious matches.The second stage performs angular velocity estimation based on Hough transform to verify the matches that follow the same distortion pattern.The third stage applies a rolling shutter error correction method for further verification.Both the simulation and night sky image test demonstrate the effectiveness and efficiency of our algorithm under high dynamic conditions.The accuracy of angular velocity estimation method by Hough transform is evaluated and the root mean square error is below 0.5(°)/s.Our algorithm achieves a 95.7% identification rate at an angular velocity of 10(°)/s,which is much higher than traditional algorithms.展开更多
This paper reported a silicon micromachined gyroscope which is driven by the rotating carrier's angular velocity,the silicon was manufactured by anisotropy etching.The design,fabrication and packing of the sensing...This paper reported a silicon micromachined gyroscope which is driven by the rotating carrier's angular velocity,the silicon was manufactured by anisotropy etching.The design,fabrication and packing of the sensing element were introduced in the paper.The imitation experimentation and performance test have certificated that the principle of the gyroscope is correct and the gyroscope can be used to sense yawing or pitching angular velocity of the rotating carrier,and the angular velocity of the rotating carrier itself.展开更多
文摘In engineering,all movable expanse revolving objects manifest gyroscopic effects.These effects are created by the action of the outer load on the revolving items whose rotating mass originates eight inertial torques about two axes.Two torques of centrifugal forces,one torque of the Coriolis force originated by the rotating distributed mass,and the torque of the change in the angular momentum of the center mass act about each axis.The inertial torques activate rotations of the gyroscope by the determined correlation.Inertial torques depend on their geometry and orientation at the spatial coordinate system.The known analytical model for the rotation of the revolving disc about axes contains a mechanical error.This error was obtained by the incorrect integration of the centrifugal inertial torque.The corrected inertial torque yields the accurate expression for the interacted rotations of the revolving disc about axes.
基金supported by the Program for Liaoning Excellent Talents in University of China(LJQ2014013)the Liaoning Natural Science Foundation of China(2015020066)
文摘This study proposes a new nonlinear tracking control method with safe angular velocity constraints for a cushion robot. A fuzzy path planning algorithm is investigated and a realtime desired motion path of obstacle avoidance is obtained. The angular velocity is constrained by the controller, so the planned path guarantees the safety of users. According to Lyapunov theory, the controller is designed to maintain stability in terms of solutions of linear matrix inequalities and the controller's performance with safe angular velocity constraints is derived.The simulation and experiment results confirm the effectiveness of the proposed method and verify that the angular velocity of the cushion robot provided safe motion with obstacle avoidance.
基金Foundation item： National Natural Science Foundation of China （50805144）
文摘The performance of any inertially stabilized platform （ISP） is strongly related to the bandwidth and accuracy of the angular velocity signals. This paper discusses the development of an optimal state estimator for sensing inertial velocity using low-cost micro-electro-mechanical systems （MEMS） sensors. A low-bandwidth gyroscope is used alone with two low-performance accelerometers to obtain the estimation. The gyroscope has its own limited dynamics and mainly contributes to the low-frequency components of the estimation. The accelerometers have inherent biases and mainly contribute to the high-frequency components of the estimation. Extensive experimental results show that the state estimator can achieve high-performance signals over a wide range of velocities without drifts in both the t- and s-domains. Furthermore, with applications in miniature inertially stabilized platforms, the control characteristic presents a significantly improvement over the existing methods. The method can be also applied to robotics, attitude estimation, and friction compensation.
基金Supported by the Innovation Fund of Shanghai Aerospace Science and Technology(SAST 201308)
文摘The tracking of orientation and angular velocity is a primary attitude control task for an on-orbit spacecraft.The problem for a rigid spacecraft tracking a desired angular velocity profile is addressed using an adaptive feedback control.An angular velocity feedback tracking algorithm is firstly developed based on the precisely known attitude dynamics of the spacecraft,and the global tracking of the control algorithm is proved based on the Lyapunov analysis.An adaptation mechanism is then designed to deal with the dynamic uncertainties of the spacecraft.Such an adaptation mechanism enables the controller to track any desired angular velocity trajectories even in the presence of uncertain inertia parameters,although it does not guarantee the inertia tensor being precisely identified.To verify the effectiveness of the proposed adaptive control policy,computer simulations on dynamic equations of a spacecraft are conducted and their results are discussed.
文摘Angular velocity stabilization control and attitude stabilization control for an underactuated spacecraft using only two single gimbal control moment gyros （SGCMGs） as actuators is investigated. First of all, the dynamic model of the underactuated spacecraft is established and the singularity of different configurations with the two SGCMGs is analyzed. Under the assumption that the gimbal axes of the two SGCMGs are installed in any direction, and that the total system angular momentum is not zero, a state feedback control law via Lyapunov method is designed to globally asymptotically stabilize the angular velocity of spacecraft. Under the assumption that the gimbal axes of the two SGCMGs are coaxially installed along anyone of the three principal axes of spacecraft inertia, and that the total system angular momentum is zero, a discontinuous state feedback control law is designed to stabilize three-axis attitude of spacecraft with respect to the inertial frame. Furthermore, the singularity escape of SGCMGs for the above two control problems is also studied. Simulation results demonstrate the validity of the control laws.
基金This work has been partially supported by the Ministry of Science and Technology,Taiwan[Grant Numbers MOST 109-2221-E-019-010 and MOST 110-2221-E-019-042].
文摘In this paper,the estimator-based Global Positioning System(GPS)attitude and angular velocity determination is presented.Outputs of the attitude estimator include the attitude angles and attitude rates or body angular velocities,depending on the design of estimator.Traditionally as a position,velocity and time sensor,the GPS also offers a free attitude-determination interferometer.GPS research and applications to the field of attitude determination using carrier phase or Doppler measurement has been extensively conducted.The rawattitude solution using the interferometry technique based on the least-squares approach is inherently noisy.The estimator such as the Kalman filter(KF)or extended Kalman filter(EKF)can be incorporated into the GPS interferometer,potentially providing several advantages,such as accuracy improvement,reliability enhancement,and real-time characteristics.Three estimator-based approaches are investigated for performance comparison,including(1)KF with measurement involving attitude angles only;(2)EKF with measurements based on attitude angles only;(3)EKF with measurements involving both attitude angles and body angular rates.The assistance from body mounted gyroscopes,if available,can be utilized as the measurements for further performance improvement,especially useful for the case of signal-challenged environment,such as the GPS outages.Modeling of the dynamic process involving the body angular rates and derivation of the related algorithm will be presented.Simulation results for various estimator-based approaches are conducted;performance comparison is presented for the case of GPS outages.
基金The author would like to thank the Nature Science Foundation of China (Grant No.60627001)the Beijing Key Laboratory for Sensor(No.KM200810772001)
文摘In order to find out the influence of the instability of angular velocity of the rotating carrier itself on the stability of silicon micromachined gyroscope, the digital models for relative error of the high and low damping gyroscope's output signal are given respectively, based on the motion equations of the silicon micromachined gyroscope. Theory proves that the output signal error of the silicon micromachined sensor is mainly caused by the instability of damping factor and the angular velocity of the rotating carrier itself. The experiment result indicates that the error of proportionality coefficient of output voltage which is caused by the instability of the angular velocity of the rotating carrier itself reaches to 4.1 %. Theoretical demonstration and experimental verification show that the instability of angular velocity of the rotating carrier itself has an important effect on the stability of low damping silicon micromachined gyroscope.
文摘The loss of Baryonic Matter through Black Holes from our spatial 3-D Universe into its 4th dimension as Dark Matter, is used along with the Conservation of Angular Momentum Principle to prove theoretically the accelerated expansion of the 3-D Universe, as has already been confirmed experimentally being awarded the 2011 Nobel Prize in Physics. Theoretical calculations can estimate further to indicate the true nature of the acceleration;that the outward acceleration is due to the rotation of the Universe caused by Dark Energy from the Void, that the acceleration is non-linear, initially increasing from zero for the short period of about a Million years at a constant rate, and then leveling off non-linearly over extended time before the outward acceleration begins to decrease in a non-linear fashion until it is matched by the gravitational attraction of the matter content of 4D Space and the virtual matter in 3-D Vacuum Space. m = m(4D) + m(Virtual). The rotation of our 3D Universe will become constant once all 3D matter has entered 4D space. As the 3-D Universe tries to expand further it will be pulled inward by its gravitational attraction and will then keep on oscillating about a final radius r<sub>f</sub> while it also keeps on oscillating at right angles to the radius r<sub>f</sub> around final angular velocity ω<sub>f</sub>, until it becomes part of the 4-D Universe. The constant value of the Angular Momentum of our Universe is L = .
文摘The study object is the angular output velocity of the drive shaft which is made up of two series-wound cross universal joints. We have deduced the function relation between the angular output velocity and initiative input angle of the drive shaft with double cross universal joints that is based on the calculation formula of the angular output velocity of a single cross universal joint, and by analyzing the relation between the two input angles. By using this function relation, the constant velocity condition of the drive shaft with double cross universal joints＂ is verified. The step-by-step searching algorithm is adopted to obtain the optimal phase angle that leads to the minimum fluctuate index of the angular output velocity in the vary velocity condition. At the same time, we worked out the maximal and minimum value of the angular output velocity, and their initiative input angle. The correctness of the function of the angular output velocity and the step-by-step search algorithm are verified by an ADAMS simulation example.
文摘In simulation,sometimes we wish to stipulate a specified angular velocity applied to a given frame.Although position,linear velocity and orientation interpolations are well studied,less attention is paid on angular velocity interpolation.In this paper,a new method to smoothly interpolate angular velocity using quaternions is presented.This method can be easily incorporated into a key frame animation system.The angular velocity at an arbitrary time can be calculated easily by our method.This method can also be generalized to smoothly interpolate orientations.
文摘In this paper, we derive non-classical continuum theory for physics of compressible and incompressible thermoviscous non-classical fluent continua using the conservation and balance laws (CBL) by incorporating additional physics of internal rotation rates arising from the velocity gradient tensor as well as their time varying rates and the rotational inertial effects. In this non-classical continuum theory time dependent deformation of fluent continua results in time varying rotation rates i.e., angular velocities and angular accelerations at material points. Resistance offered to these by deforming fluent continua results in additional moments, angular momenta and inertial effects due to rotation rates i.e., angular velocities and angular accelerations at the material points. Currently, this physics due to internal rotation rates and inertial effects is neither considered in classical continuum mechanics (CCM) nor in non-classical continuum mechanics (NCCM). In this paper, we present a derivation of conservation and balance laws in Eulerian description: conservation of mass (CM), balance of linear momenta (BLM), balance of angular momenta (BAM), balance of moment of moments (BMM), first and second laws of thermodynamics (FLT, SLT) that include: (i) Physics of internal rotation rates resulting from the velocity gradient tensor;(ii) New physics resulting due to angular velocities and angular accelerations due to spatially varying and time dependent rotation rates. The balance laws derived here are compared with those that only consider the rotational rates but neglect rotational inertial effects and angular accelerations to demonstrate the influence of the new physics. Constitutive variables and their argument tensors are established using conjugate pairs in the entropy inequality, additional desired physics and principle of equipresence when appropriate. Constitutive theories are derived using Helmholtz free energy density as well as representation theorem and integrity (complete basis). It is shown that the mathematical model consisting of the conservation and balance laws and constitutive theories presented in this paper has closure. Influence of new physics in the conservation and balance laws on compressible and incompressible thermoviscous fluent continua is demonstrated due to presence of angular velocities and angular accelerations arising from time varying rotation rates when the deforming fluent continua offer rotational inertial resistance. The fluent continua are considered homogeneous and isotropic. Model problem studies are considered in a follow-up paper.
文摘The relative characteristics of motion of the fuel and shell upon launching is analyzed. By means of mechanical analysis and calculation, it is proposed that relative motion exists not only in the ranges between the fuel and shell of the warhead, but also in the fuel in different positions. The result of study indicates that the position of the fuel in the warhead has a marked influence on the relative motion, while the frictional coefficient between the fuel and shell has less influence upon it.
基金supported by National Outstanding Youth Science Foundation(61125306)National Natural Science Foundation of Major Research Plan(91016004,61034002)+2 种基金Specialized Research Fund for the Doctoral Program of Higher Education of China(20110092110020)Open Fund of Key Laboratory of Measurement and Control of Complex Systems of Engineering(Southeast University)Ministry of Education(MCCSE2013B01)
文摘The exact thermoelastic analysis of a functionally graded piezoelectrical （FGP） rotating cylinder is investigated analytically. The cylinder is subjected to a com- bination of electrical, thermal, and mechanical loads simultaneously. The structure is a simplified model of a rotational sensor or actuator. The basic governing differential equation of the system is obtained by using the energy method. A novel term, named as the additional energy, is introduced to exact the evaluation of the energy functional. The solution to the governing differential equation is presented for two types of boundary conditions including free rotating and rotating cylinders exposed to the inner pressure. The effect of the angular velocity is investigated on the radial distribution of various components. The mentioned structure can be considered as a sensor for measuring the angular velocity of the cylinder subjected to the pressure and temperature. The obtained results indicate that the electrical potential is proportional to the angular velocity.
基金supported by the Natural Science Foundation of China(No.11972240)the China Postdoctoral Science Foundation(No.2020M671574)the University Natural Science Research Project of Anhui Province(No.KJ2018A0481).
文摘A rotating axisymmetric circular nanoplate is modeled by the Mindlin plate theory.The Mindlin plate theory incorporates the nonlocal scale and strain gradient effects.The shear deformation of the circular nanoplate is considered and the nonlocal strain gradient theory is utilized to derive the governing differential equation of motion that describes the out-of-plane free vibration behaviors of the nanoplate.The differential quadrature method is used to solve the governing equation numerically,and the natural frequencies of the out-of-plane vibration of rotating nanoplates are obtained accordingly.Two kinds of boundary conditions are commonly used in practical engineering,namely the fixed and simply supported constraints,and are considered in numerical examples.The variations of natural frequencies with respect to the thickness to radius ratio,the angular velocity,the nonlocal characteristic scale and the material characteristic scale are analyzed in detail.In particular,the critical angular velocity that measures whether the rotating circular nanoplate is stable or not is obtained numerically.The presented study has reference significance for the dynamic design and control of rotating circular nanostructures in current nano-technologies and nano-devices.
文摘In order to satisfy the requirement of high precision measurement in a high dynamic environment, a kind of gyro aided multi-accelerometer inertial measurement unit （GAMA-IMU） with six accelerometers and two gyros （6A2G） was proposed in this paper. The available configurations have the problem of low measurement precision In a high dynamic environment due to channel coupling. The three channels were decoupled when calculating the angular velocity in the proposed configuration. The yawing and pitching angular velocity were directly measured by gyros, while only the rolling angular velocity was obtained by the GAMA-IMU indirectly from the rolling angular acceleration and quadratic component of rolling angular velocity. Then a single channel rolling angular velocity calculation model was established and the extended Kalman filter （EKF） was used to do state esti- mation. Simulations were carried out and results indicated that the calculation precision of the proposed 6A2G configuration could meet the demand of high precision measurement for a high-speed rotating carrier.
基金Project (No. 10632070) supported by the National Natural Science Foundation of China
文摘Lattice Boltzmann method was used to numerically investigate the motion and orientation distribution of cylindrical and cubic particles in pipe flow with high concentration and high particle to pipe size ratio. The transient impulse model of 3D collisions between particles and between particle and wall is proposed. The numerical results are qualitatively in agreement with and quantitatively comparable to the experiment data. The results show that the increases of both the cylindrical particle to pipe size ratio and the particle aspect ratio decrease the rotation about all axes. All rotations of cubic particles decrease with increasing the particle concentration. The cubic particles, rotating more drastically in the flow with large Reynolds number, rotate faster than the cylindrical particles with the same size. The cylindrical particles align with the flow direction more obviously with decreasing Reynolds numbers. However, the orientations of cubic particles are spread all over the range with no significant difference in magnitude, and the Reynolds numbers have no obvious effect on the orientations of cubic particles.
文摘The fundamental principles of the gyroscope theory contain the system of the inertial torques generated by the rotating mass of the spinning disc that interrelated by the ratio of its angular velocities rotation around axes. The action of the centrifugal, common inertial Coriolis forces and the change in the angular momentum generate the system of inertial torques. These four dynamical components make up the system of the eight torques acting simultaneously on the spinning disc. They manifest their action in gyroscopic effects. The ratio of the precessed motions of the gyroscope presents one of the gyroscopic effects around axes of rotation. The known mathematical model for this ratio contains an error that was corrected in this work.
基金supported by the National Key Research and Development Program of China(No.2019YFA0706002).
文摘The star identification algorithm usually identifies stars by angular distance matching.However,under high dynamic conditions,the rolling shutter effect distorts the angular distances between the measured and true star positions,leading to plethoric false matches and requiring complex and time-consuming verification for star identification.Low identification rate hinders the application of low-noise and cost-effective rolling shutter image sensors.In this work,we first study a rolling shutter distortion model of angular distances between stars,and then propose a novel three-stage star identification algorithm to identify distorted star images captured by the rolling shutter star sensor.The first stage uses a modified grid algorithm with adaptive error tolerance and an expanded pattern database to efficiently eliminate spurious matches.The second stage performs angular velocity estimation based on Hough transform to verify the matches that follow the same distortion pattern.The third stage applies a rolling shutter error correction method for further verification.Both the simulation and night sky image test demonstrate the effectiveness and efficiency of our algorithm under high dynamic conditions.The accuracy of angular velocity estimation method by Hough transform is evaluated and the root mean square error is below 0.5(°)/s.Our algorithm achieves a 95.7% identification rate at an angular velocity of 10(°)/s,which is much higher than traditional algorithms.
基金supported by the National Natural Science Foundation of China(No.60272001)the Beijing Natural Science Foundation of China(No.4032010).
文摘This paper reported a silicon micromachined gyroscope which is driven by the rotating carrier's angular velocity,the silicon was manufactured by anisotropy etching.The design,fabrication and packing of the sensing element were introduced in the paper.The imitation experimentation and performance test have certificated that the principle of the gyroscope is correct and the gyroscope can be used to sense yawing or pitching angular velocity of the rotating carrier,and the angular velocity of the rotating carrier itself.
