Dynamically coupled models of the sliding and spinning friction based on padé expansions

It is presented a new approach for dry friction modeling under conditions of combined kinematics. The main distinguish feature of this approach is building of friction models which are suitable for using in differential equations of motion. Under the proposed models of friction are understudied the interrelations between friction force components, torques and velocities which are represented be the analytical functions. The procedure of the models constructing consists of the two parts. In the first part, the exact integral expressions for the net vector and torque are formed with the assumption that Coulomb's friction law in classical forms or generalized differential forms is valid at each point of the contact area. In addition, in process of the exact integral models construction there are is used well known results from the theory of elasticity that tangent stresses lead to shift in the symmetric diagram of the normal contact stresses in the direction of the instantaneous sliding velocity. To use the theory of elasticity results in the dynamics problems, it is proposed the simple asymptotic representations for the contact stresses distributions based on their general properties known from the theoretical results of the theory of elasticity. In the second part the exact integral models are replaced by appropriate Pade expansions. The approximate models preserve all properties of the models based on the exact integral expressions and correctly describe the behaviour of the net vector and torque of the friction forces and their first derivatives at zero and infinity. Moreover, one does not have even to calculate the integrals to determine the coefficients of the Pade approximations. The corresponded coefficients can be identified from experiments. Consequently, the models based on Pade expansions may be considered as phenomenological models of combined dry friction

Combined dry friction models in the case of random distribution of the normal contact stresses inside contact patches

We propose a further development of the theory of multi-component dry friction [5-10] by offering a dry friction model with random distribution of contact stresses across the contact spot. Special attention is devoted to investigation of the dry friction effects that arise in the traditional systems that consist of solid disks and spheres sliding or rolling on a horizontal plane. Applications of the proposed model for description of the interaction between a pneumatic aviation tire and the surface of a landing strip are outlined

Numeric-analytical methods of the coefficients definition of the rolling friction model of the pneumatic aviation tire

A new approximate models of the tire rolling accounting for coupled longitudinal and lateral sliding as well as the spinning and the deformed state resulting in elastic forces were proposed in previous works [1-7]. The main goal of this investigation consists in the development of the numeric-analytical methods of these models coefficients definition

Controllability of a rigid body in a perfect fluid in the presence of friction

We study a mechanical system that consists of a 2D rigid body immersed in an unbounded volume of perfect fluid. The body is controlled by two internal point masses. The fluid's influence manifests itself through the added mass effect and dissipation (whose magnitude is small) described by the Rayleigh dissipation function. These assumptions allow for an analytical study of the problem using the small parameter method. Indeed, the unperturbed system (no dissipation) has, according to the Noether's theorem, a complete set of integrals of motion. For a fixed value of the integrals, the equations of motion reduce to a non-autonomous system of ordinary differential equations. The controllability of the system is then studied. In the presence of small dissipative friction these linear in velocities integrals (given their evolution is slow and can therefore be determined via a standard averaging procedure) can still be used to adopt non-dissipative strategies for the dissipative case

CENTRAL WAVELENGTH ADJUSTMENT OF LIGHT EMITTING SOURCE IN INTERFEROMETRIC SENSORS BASED ON FIBER-OPTIC BRAGG GRATINGS

The paper is focused on the investigation of fiber-optic interferometric sensor based on the array of fiber Bragg gratings. Reflection spectra displacement mechanism of the fiber Bragg gratings under the external temperature effects and the static pressure is described. The experiment has shown that reflection spectra displacement of Bragg gratings reduces the visibility of the interference pattern. A method of center wavelength adjustment is proposed for the optical radiation source in accord ance with the current Bragg gratings reflection spectra based on the impulse relative modulation of control signal for the Peltier element controller. The semiconductor vertical-cavity surface-emitting laser controlled by a pump driver is used as a light source. The method is implemented by the Peltier element controller regulating and stabilizing the light source temperature, and a programmable logic-integrated circuit monitoring the Peltier element controller. The experiment has proved that the proposed method rendered possible to regulate the light source temperature at a pitch of 0.05 K and adjust the optical radiation source center wavelength at a pitch of 0.05 nm. Experimental results have revealed that the central wavelength of the radiation adjustment at a pitch of 0.005 nm gives the possibility for the capacity of the array consisting of four opticalfiber sensors based on the fiber Bragg gratings. They are formed in one optical fiber under the Bragg grating temperature change from 0° C to 300° C and by the optical fiber mechanical stretching by the force up to 2 N

Combined dry friction models in the case of random distribution of the normal contact stresses inside contact patches

We propose a further development of the theory of multi-component dry friction [5-10] by offering a dry friction model with random distribution of contact stresses across the contact spot. Special attention is devoted to investigation of the dry friction effects that arise in the traditional systems that consist of solid disks and spheres sliding or rolling on a horizontal plane. Applications of the proposed model for description of the interaction between a pneumatic aviation tire and the surface of a landing strip are outlined