Angular Velocity Meters Research Articles

Method for Increasing the Accuracy of a Gyroscope with a Spherical Ball Bearing Suspension

The article is devoted to the development of a method for improving the accuracy of a gyro with a spherical ball bearing suspension operating in the mode of a deflection angle meter of the base on which it is installed. When operating a gyroscope as part of an information-measuring and control system, such an operational characteristic as the accuracy of readings, depending on the noise component of the gyroscope output signal, is of decisive importance. The purpose of the article is to solve the problem of reducing the noise component of the output signal while maintaining a wide bandwidth of the device and a minimum phase delay of the output signal in relation to the measured value. The paper provides an overview of the existing device construction schemes. A mathematical description of the functioning of the gyroscope is presented, on the basis of which the transfer functions for the moment (disturbing, controlling or total) along the direct and cross channels are obtained. Transfer functions are also obtained, which are the ratio of the output signal to the measured value through direct and cross channels. It is noted that the predominant frequencies of the noise component of the output signal correspond to the rotational frequency of the gyroscope rotor, the rotation frequency of the gyroscope rotor and the multiple rotation frequencies of the gyroscope rotor. The structure of the system is proposed in which the signal from the gyroscope angle sensor with a spherical ball bearing suspension is summed up with the output signal of an additional angular velocity sensor according to the corresponding coordinate and then the total signal is smoothed using an aperiodic link of the first order. The results are obtained for determining the parameters of the channel of the angular velocity meter, at which it is possible to compensate for the bandwidth limitations in the channel of the angle measurement due to the time constant of the smoothing filter and at the same time ensure effective suppression of the noise component of the output signal. The proposed construction scheme of the meter provides attenuation of noise components in the output signal of a gyroscope with a spherical ball bearing suspension at a rotation frequency of the gyroscope rotor 250 Hz by 156 times, at a frequency of nutation oscillations of the gyroscope rotor 404 Hz by 256 times, at a frequency of 500 Hz by 316 times, at a frequency of 750 Hz by 474 times, at a frequency of 1000 Hz by 630 times, at a frequency of 1250 Hz by 785 times while maintaining a wide bandwidth of 285 Hz when measuring an angle with a phase lag of the output signal from the measured one close to zero degrees in the bandwidth.

Synthesis and verification of the method of finding a faulty sensor in redundant meters

The reliability of the method for determining a failed sensor in a redundant angular velocity meter (AVM) by means of its experimental verification is considered. The mutual non-orthogonal arrangement of six axes of sensor sensitivity has been optimized to reduce the instrumental errors of each sensitive element and ensure the equality of their contribution. Provides approximately the same sensitivity to the level of error in case of failure. One of the six experimentally obtained sensor signals contains an error that exceeds the specified permissible limit. The algorithm for searching for a sensor is checked, the error of which exceeds the specified one, and which, for this reason, is considered faulty.

Simulation of a multifunctional micromechanical gyroscope

The possibility of constructing a multifunctional inertial navigation device based on a hybrid-type modulation micromechanical gyroscope is considered. A mathematical model of the device ("heavy" gyroscope) as a high-quality three-dimensional oscillatory system is constructed. It is numerically shown that, under certain conditions, the reaction of the system to the motion of an object has, along with precession, the observed nutation, which carries information about the linear motion of the gyroscope base. It is noted that the possibility of measuring linear accelerations is ensured by the presence of a small symmetrical distance between the axes of the elastic suspension relative to the center of mass of the sensing element. The results obtained make it possible to implement a two-component angular velocity meter and a two-component linear acceleration meter in one device.

Verification of the method of finding a faulty sensor in reduced meters

The reliability of the method for determining a failed sensor in a redundant angular velocity meter (AVM) by means of its experimental verification is considered. The mutual non-orthogonal arrangement of six axes of sensor sensitivity has been optimized to reduce the instrumental errors of each sensitive element and ensure the equality of their contribution. Provides approximately the same sensitivity to the level of error in case of failure. One of the six experimentally obtained sensor signals contains an error that exceeds the specified permissible limit. The algorithm for searching for a sensor is checked, the error of which exceeds the specified one, and which, for this reason, is considered faulty.

Research of Precision of Non-collinear Inertial Measurement Devices

The non-collinear measurement devices based on the inertial triaxial devices, and structural units such as the triangular, and quadrangular polyhedrons are presented. The corresponding matrices of guide cosines are obtained. In contrast to the known non-collinear measurement devices, the measurements of all sensors that are part of the triaxial devices are taken into account. A description of the relative position of the measurement axes of the individual sensors in the proposed measurement devices is given. Theoretical estimation of non-collinear measurement devices of MEMS-sensors on the basis of uniaxial and triaxial angular velocity meters using correlation matrices of measurement errors is obtained. The obtained results are useful because they are aimed at providing high-precision and reliable measurements that is important for unmanned aerial vehicles, which are currently widely used in Ukraine.

Choice of configuration and parameters of the vibration protection system for gyroscopic angular velocity meters

The rationale for the choice of a technical solution to the issue of vibration protection of gyroscopic angular velocity meters, built on the basis of dynamically tuned gyroscopes (DTG) is presented. The proposed vibration protection system consists of shock absorbers with high elasticity and dynamic vibration dampers (DVD) with nonlinear elastic and damping characteristics. The main factors that determine the peculiarities of choosing a vibration protection system for precision gyroscopic devices are indicated. Keywords dynamically tuned gyroscope (DTG); dynamic vibration damper (DVD); vibration protection system; gyroscopic angular velocity meter

Features of dynamics and errors of vibrating gyroscopes

The obtained generalized mathematical model of micromechanical and rotary vibrating gyroscopes as meters of angular velocity and transfer functions of meters. The features of the dynamics of vibration gyros according to the generalized model and their influence on the properties of the transfer function of the angular velocity meter are determined.
 The properties of the constant error and the trend of the output signal of micromechanical gyroscopes are investigated.

Algorithm for Spacecraft Angular and Translational Motion Control with use of Orientation Thrusters

The paper discusses the algorithm of spacecraft orientation and docking thrusters control for simultaneous spatial and angular motion. The solution of control velocity formation problem and the problem of required engines configuration determination along with the optimization of control vector execution accuracy are considered. The formation of control velocity is carried out using a phase plane with switching lines and a zone of inactivity. The calculation of thrusters working duration time is based on the method of least squares with non-negative resulting solution vector and additional boundary conditions. In the paper, the necessary control parameters were chosen to ensure the necessary accuracy of spacecraft stabilization. To demonstrate the developed algorithm, mathematical modelling of various considered spacecraft's orbital flight stages was executed, including damping of initial angular velocities, spatial motion, and stabilization under the influence of continuous perturbations. The simulation took into account the disturbing moments acting on the spacecraft, thrusters mounting errors and the characteristics of the angular velocity meter. The elastic characteristics of the structure were not taken into account. The results of mathematical modelling showed that the proposed algorithm coped well with the task, and was able to ensure the movement of the spacecraft center of masses in a given direction and simultaneous angular stabilization with required accuracy.

Improving the efficiency of the search methods of the refused sensor in an excessive angular speed meters

In control systems of launch vehicles, satellites, it is important to ensure the operability of the system in the presence of failures. In the units of angular velocity or acceleration sensors, redundancy can be used, that is, the installation of sensors in the amount of four to six, the sensitivity axis of any three of them are not coplanar. In addition to reliability improvement the redundant meters improve the accuracy characteristics of systems. To determine the failed sensors, special algorithms which influence the efficiency of the failed sensor search have been developed. The following search methods are considered: the method of the failed sensor determining by the minimum of average values of the residual modules; method for the failed sensor determining by the minimum of mean values of squared residuals method for the failed sensor determining by the minimum of the squares deviations average values of the angular velocity components; method for the failed determining sensor by the maximum modulus of the difference of the calculated and measured data. The probabilities of determining failures, false failures, and undetected failures are given. The methods of finding a failed sensor in the redundant angular velocity meters given in the article take into account the presence of errors in the transmittance of sensors.

Theoretical prerequisites for substantiation of the possibility of using the Kovalev gyroscope as a three-component angular velocity meter

Theoretical prerequisites for substantiation of the possibility of using the Kovalev gyroscope as a three-component angular velocity meter

Theoretical Background of Rationale for the Possibility of the Kovalevskaya Gyroscope Usage by a Three-Component Angular Velocity Meter

The TGAVM schemes based on the Kovalevskaya gyroscope with both spherical electrostatic and spring suspensions are described. The differential equations of motion of the gyroscope are given, formulae for the output information on the three components of the angular velocity of MO. The formula for determining the third component includes the first and second derivatives on the coordinates of the translational movements of the gyroscope in the equatorial plane. To determine them, an algorithm is used to filter the interference of derivatives, based on the Luenberger identification device. The results of mathematical simulation by the derivation of the three components of the angular velocity, which confirmed the validity of the premises, are given. An analytical approximate solution of the problem is given for the self-centering mode of the gyroscope rotor and for the resonance mode. It is shown that in the second case the sensitivity of the device can be an order of magnitude higher than in the first. The approximate solution is confirmed by calculations of the third component of the angular velocity based on measuring only the coordinates of the translational movement of the gyroscope, without derivatives.

The Theoretical Basis of the Possible Application of a Kovalevsky Gyroscope as Three-Component Angular-Velocity Meter

Two schemes of the three-component angular-velocity meter based on the Kovalevsky gyroscope are described: on the electrostatic and mechanical spring suspensions. The gyroscopic degrees of freedom are restricted on the observation coordinates, and there is a rapid rotation around its principal axis. A mathematical model of the device motion along three translational coordinates and two angular coordinates is presented. The formulas for determining the two components of the mobile-object angular velocities lying in the equatorial plane are derived by using the signals in the channels of the radial interaxial correction as well as the algorithm of calculation with the help of an onboard controller of the angular-velocity component of rotation around the object axis, which practically coincides with the principal one. The algorithm includes the coordinates of the relative translational equatorial motions of the rotor and their first and second time derivatives. The algorithms of their determination with the interference filtering based on the Leuenberger observing identification device are given.

Procedure of estimating characteristics of angular velocity meter using the Kalman filter and Allan variance

A procedure of assessing the main characteristics of angular velocity inertial meters of middle and low accuracy classes, including measuring channel noise terms is proposed. The procedure is based on the processing of the meter output information by means of the Kalman discrete filter and the Allan variance method. The characteristics to be estimated are: scale coefficient errors and zero signal shifts, as well as series of standard noise terms. Estimates of the method error level for the procedure under consideration are given on the basis of mathematical simulation of the measurement information and its correction with different estimated errors. An example of approbation of the technique is processing the results of tests conducted for two inertial meters based on different operating principles. One of them is the ADIS16405 device developed by Analog Devices (USA) on the basis of three micromechanical gyroscopes of low- accuracy class and the other is the ВГ910-МК470 device designed by Fizoptika, CJSC (Arzamas city) which consists of one fiber-optic gyroscope of the middle -accuracy class.

Some Dimensions of the Angular Acceleration Receptor Systems of Cephalopods

The shapes and dimensions of the statocysts of cephalopods have been measured and compared with the semi-circular canals of vertebrates. The cavities grow much more slowly than the body as a whole, but there are knobs, anticristae, which restrict the cavity, and these grow relatively faster. This ensures that the flow of endolymph across the cupulae remains small. Where the liquid is constrained within canals the radius of curvature of the whole canal,R, is similar to that of fishes, whereas its internal radius, r, is twice as large in non-buoyant and four times as large in deep-sea buoyant cephalopods as in fishes of similar size. As in fishes the restriction is greatest in the horizontal plane, providing for operation at higher frequencies in turning about the yaw axis.The statocysts of seven species ofLoligoall have similar proportions. The largest individuals of 16 genera of non-buoyant squids also have these same relative dimensions. The statocyst ofSepiais more like that of non-buoyant than of other buoyant cephalopods but yet differs significantly from that ofLoligoat all sizes. On the other hand 21 genera of squids known to be neutrally buoyant are very different. Their statocysts are often larger than in the non-buoyant forms and there is less restriction of the cavity by anticristae. The greater flow of endolymph acting across the cupulae presumably provides greater sensitivity at the lower frequencies of turning of these deep-sea animals.The data suggest that the cristae of the cephalopod statocyst may operate in the frequency band where they act as angular accelerometers whereas the vertebrate semi-circular canals operate at higher frequencies as angular velocity meters.

The fluid mechanics of the semicircular canals

A mathematical model for the unsteady fluid-dynamic response of the semicircular canals is developed. The endolymph is assumed to be an incompressible Newtonian fluid and the presence and effects of both the utricle and the cupula are specifically accounted for. A first approximate solution is obtained using a singular perturbation method. It is shown that the canal can be modelled as a heavily damped, second-order system which behaves as an angular-velocity meter. A comparison of the model response with experimental results is made; fairly good agreement is found.

Method of increasing the accuracy of an angular velocity meter

Method of increasing the accuracy of an angular velocity meter

On the general equations of inertial navigation

Derived and investigated are the equations of ideal (unperturbed) and perturbed operation of a generalized system of inertial navigation which determines the coordinates of a moving object from the measurements of three linear accelerometers and three angular velocity meters measuring absolute angular velocity. The instruments are located along the axes of an orthogonal trihedron, the origin of which coincides with a certain point in the moving object. In contrast to [1 and 2], the orientation of the trihedron axes is arbitrary. The equations of ideal operation take into account the non-central nature of the Earth's gravitational field. The equations of perturbed operation include instrument error effects. Error equations are derived and investigated not only for small but also for the finite values of the variables of the perturbed operating conditions. The particular cases are the equations and the results of investigation of the particular control systems considered in [1 to 7].

On a Method of Measuring a Ship's Oscillations

There are many sorts of apparatus for measuring the oscillations of ships around and in the direction of the three axes. The ordinary type of apparatus measures directly the displacement itself, but it is very difficult to get any sort of pendulum that has a period sufficiently long enough to measure the displacement of a body that is oscillating slowly, such as a ship at the period of 45 seconds to about 20 seconds. Moreover here are some cases in studying the motion of ships, when knowledge of the velocity or acceleration of oscillations is necessary.So, utilizing the operating circuit of electronic analogue computers, we succeeded in setting up a system of measuring capable of getting displacement, velocities and accelerations at once. By integrating or differentiating once or twice the easiest of these three measurements to obtain, the remaining two measurements will automatically be obtained.We made a set of integrators, differentiatars and multipliers by the circuit of ana-com., and by using an angular velocity meter of a rate gyroscope unit as a pick up, we established a measuring system of angular oscillations of ships.We used this set on the voyage of a certain ship, and because we received excellent results, we want to report our method and conclusions in the following paper.