Rigidity through a Projective Lens

In this paper, we offer an overview of a number of results on the static rigidity and infinitesimal rigidity of discrete structures which are embedded in projective geometric reasoning, representations, and transformations. Part I considers the fundamental case of a bar–joint framework in projective d-space and places particular emphasis on the projective invariance of infinitesimal rigidity, coning between dimensions, transfer to the spherical metric, slide joints and pure conditions for singular configurations. Part II extends the results, tools and concepts from Part I to additional types of rigid structures including body-bar, body–hinge and rod-bar frameworks, all drawing on projective representations, transformations and insights. Part III widens the lens to include the closely related cofactor matroids arising from multivariate splines, which also exhibit the projective invariance. These are another fundamental example of abstract rigidity matroids with deep analogies to rigidity. We conclude in Part IV with commentary on some nearby areas.

Vibroacoustic Assessment of an Innovative Composite Material for the Roof of a Coupe Car

The objective of this paper is the vibroacoustic evaluation of an innovative material for a sports car roof, aiming at replacing fiberglass composite materials. Such evaluation was carried out using numerical and experimental analysis techniques, with cross-comparison between the corresponding results. The innovative material under analysis is a composite material, with a thermoplastic polypropylene matrix and reinforcement made of cellulose fibers. In order to validate the virtual dynamic modeling of the new material, the inertance on different points of some sheets made of the material under analysis was evaluated by an in-house made experimental activity, performed in the CRF (Fiat Research Center) test room, and cross-compared with corresponding results from a numerical analysis performed with the MSC Nastran software. Then, a realistic model of the car roof of the Alfa Romeo 4C car, made with the new material, was implemented and analyzed from the vibroacoustic point of view. The mere switch to the new material, with no changes in the geometry/structure of the car roof, did not allow preserving the original values of static rigidity, dynamic rigidity, and configuration of modal shapes. For this reason, a geometric/structural optimization of the component was performed. Once the new geometry/structure was defined, a vibroacoustic analysis was carried out, checking for a possible coupling between the fluid cavity modes and the structure car body modes. Finally, the vibroacoustic transfer functions to the driver’s ear node were assessed, considering two different excitation points on the structure. The excellent damping capacity of the proposed material led to an improvement in the vibroacoustic transfer functions and to a reduction in the weight of the pavilion.

Research and improvement of methods of testing machines for geometric and kinematic accuracy

Purpose. To analyze and check for adequacy the known calculation formulas in determining the geometric and kinematic accuracy, statistical and dynamic rigidity and testing the machine for technological reliability. To carry out comparative calculations to simplify the methodology of complex tests of metal-cutting machines of the universal group. To select and improve the measuring equipment during the complex tests of the milling machine. Methodology. The research is based on the use of analytical methods for calculating the static rigidity coefficient, additional calculation of the measuring instrument design due to the gear ratio, the angle of rotation of the lever and the theoretical error of the displacement mechanism based on the known probability distribution theorem. Findings. The formulas of researches of the coefficient of static rigidity, the mechanism of the measuring device, the angle of rotation of the lever, the theoretical error of the mechanism of movement and the density of probability of distribution of the angle of the lever mechanism of the indicator of tangent type has been obtained. Originality. The research has been carried out and the parametric relationship between the static rigidity coefficient in the design of the spindle assembly of the vertical milling machine with the error of the calculations of the design, the departure of the spindle cone and the location between the supports has been established. The values and functional dependences of the amplitude of oscillations on the maximum allowable spindle speeds and feed rates at which the surface roughness of the workpiece reaches the specified geometric limits has been obtained. It is experimentally confirmed that the parameters of the system of pre-planned repairs are directly related to the reliability of the machine. The resource on the accuracy of the machine determines the need for overhaul, and the repair period depends on the service life of parts and elements of the machine. The actual service life should be a multiple of the repair period, as the restoration of the part is planned during the current repair. Practical value. The practical achievement of the obtained results is to confirm the adequacy of the known calculation formulas in determining the geometric and kinematic accuracy, statistical and dynamic rigidity and testing the machine for technological reliability. On the basis of the received analytical and settlement data was made the simplified complex technique of test of the metal-cutting machine during the: testing the machine at idle; testing of the machine when working under load; testing of the machine for geometric and kinematic accuracy; determination of statistical and dynamic rigidity; research of vibration-resistant vertical milling machine; testing of the machine for technological reliability.

Some Aspects about Theoretical Static Rigidity and Experimental Static Rigidity of a New Elastic Coupling with Cylindical Bolts and Nonmetallic Elements

The elastic couplings are frequently used in mechanical transmissions design, to take over the radial, axial and angular misalignments and also to take over the shocks and the overloads that could appear. In this paper is presenting some aspects about the construction of couplings with bolts using non-metallic elements, e.g. rubber, having different hardness, the elements involved in torque transmission, in this case elastic elements, having also different dimensions or forms, in the way to have a good elasticity and capacity of vibration absorbtion, determining theoretical static rigidity and experimental static rigidity of a new elastic coupling with cylindrical bolts and nonmetallic elements and compare of results for these values.

Foot Function Disorders in Children with Severe Spondylolisthesis of L5 Vertebra

Background. In children with spondylolisthesis, there are still unexplained aspects in the relationship of the degree of displacement of the L5 vertebra with the severity of the clinical picture and neurological disorders. At the same time, aspects of the mutual aggravating influence of the indicated spinal disorder on the condition of the feet have not been studied. Therefore, the problem of identifying disorder of foot function in children with spinal spondylolisthesis of the L5 vertebra is relevant.Aim of the study — to evaluate the deviations in parameters of the transverse and longitudinal arches of feet in children suffering from severe spondylolisthesis of the L5 vertebra.Materials and Methods. In the period from 2016 to 2018, 12 children aged 14.1 y.o. [12,7; 15,5] were examined with spondylolisthesis of the L5 vertebral body of grade III-IV, accompanied by stenosis of the spinal canal at the same level and by compression of the roots of the spinal cord. Imaging diagnostics included multispiral computed tomography (MSCT) and magnetic resonance imaging (MRI). To estimate the function of the feet, double-bearing and single-bearing plantography was used. The data for the control group included only plantographic examinations of 12 healthy children of the same age.Results. In patients with spondylolisthesis, the mean value of the anterior t and intermediate s plantographic bearing indices were significantly lower than those of healthy children. At the same time, in tests with an increased load on the foot in patients, there was no significant increase in the mean anterior t and medial m indices, which indicates the dynamic rigidity of the transverse and medial longitudinal arches. The value of the lateral plantographic index l showed its significant pathological increase compared with the normal value at double-bearing load, which indicates the static rigidity of the lateral longitudinal arch. Correlation analysis demonstrated that, against the normal state, the bearing ability of the feet in sick children is realized through a pathological strengthening of the functional relationship between the arches of the foot at double-bearing load and a non-physiological reduction of the interaction between arches at single-bearing load.Conclusion. In children with severe forms of vertebra spondylolisthesis, the parameters of plantographic characteristics indicate the rigidity of the arches of the feet and the distortion of their bearing pattern. It is necessary to take into account the aggravating effect of rigid feet on the state of the spine and include the examination of the bearing function of the feet in the algorithm for the comprehensive diagnosis of children with spondylolisthesis.

Investigation of the fluctuation of the static axial rigidity for double-nut preloaded ball screws

This article aims to investigate the fluctuation of the static rigidity for preloaded ball screws. Based on the correlation between preload and friction torque, a new model to calculate the contact rigidity by friction torque is proposed. Meanwhile, a novel test bench is constructed to measure the static stiffness at different positions. The experimental results agree well with the theoretical values, which proves the validity of the model. Furthermore, it is found that the screw shaft rigidity has the greatest influence on the system stiffness fluctuation, compared to the bearing rigidity, and the torsional rigidity. For the feed system, increasing the bearing rigidity, which is the lowest stiffness of the whole system, is an effective method to increase the system stiffness. The study provides an accurate method to obtain the stiffness fluctuation in the effective travel of ball screws, which is significant for improving the positioning accuracy of ball screws and computer numerical control machine tools.

Production Aspects Affecting the Final Precision Machining of Advanced Materials

When creating products of modern construction materials has a great influence on their endpoints right way and the quality of working on machine tools. The article deals with positioning accuracy of machine tools which is carried out in an unloaded condition, according to international standard ISO 230-2. Overall accuracy of working machining is determined mainly static rigidity, geometrical accuracy of mechanical components, positioning accuracy and dynamic stiffness. Static stiffness is defined in new machine tools in a limited workspace. Therefore, the article deals with the definition of static stiffness in the expanded work area and also defines its impact on the positioning accuracy at individual points in workspace of the machine tool.

The amortization of vibrations on machines - case study

When determining the static rigidity of the machine, only loads of constant forces are taken into account. However, machine details are not loaded only with static forces but also with external and internal dynamic forces. Components of static forces affect the form errors, while dynamic instability, and as a result of dynamic forces have negative impact on: the severity of processed surface, the wear of the metal cut-ting tool, wear of the machine details and productivity.