Designing an outer toothed gear whose wheel teeth are outlined by the logarithmic spiral arcs

Toothed gears are the most common mechanical gears in machine building, which are characterized by high reliability and durability, a constant transfer number, and which can transmit high torque. During toothed gear operation, the surfaces of the teeth slide, which gives rise to friction forces and wears their working surfaces. To prevent this, the surfaces of the teeth need constant lubrication. This paper considers the design of a gear tooth engagement, which does not have friction between the surfaces of the teeth since they roll over each other without slipping. The profile of the tooth of such a gear is outlined by congruent arcs, symmetrical relative to the line that connects the center of rotation of the toothed wheel with the top of the tooth. These symmetrical curves at the top of the tooth intersect at the predefined angle. In the depressions of the wheel, adjacent teeth also intersect at the same angle. Such a condition can be ensured by a curve that at all its points crosses the radius-vector emanating from the coordinate origin, also at a stable angle equal to half of the given one. This curve is a logarithmic spiral. If the number of teeth of the drive and driven wheels is the same, then their teeth are congruent. Otherwise, the profiles of the teeth would differ but they could be outlined by congruent arcs of the same logarithmic spiral of the same length taken from different areas of the curve. The minimum possible angle at the top of the teeth is straight. At acute angle, the toothed gear operation is impossible. To build gear wheels with a right angle at the top of the tooth, it would suffice to set the number of teeth of the drive and driven wheels. The center-to-center distance is calculated using the derived formula. The transfer number of such a gear is variable but, with an increase in the number of teeth, the range of its change decreases. The algorithm of wheel construction is given.

Study of lithium-conducting ceramics Li1.3Al0.3Ti1.7(PO4)3 with the nasicon structure

NASICON-type Li1.3Al0.3Ti1.7(PO4)3 ceramics with a high-density was obtained from powders synthesized from a liquid-phase precursor. The technological scheme of Li1.3Al0.3Ti1.7(PO4)3 solid electrolyte production is given. It is established that at 800 °C a single-phase well-crystallized Li1.3Al0.3Ti1.7(PO4)3 is formed. The ionic conductivity of the sintered Li1.3Al0.3Ti1.7(PO4)3 tablets (density 88–90 %) was 1,9·10–4 S/cm at room temperature, and the electronic conductivity did not exceed 5·10–10 S/cm. The Li+ ion transfer number, measured by potentiostatic chronoamperometry, was 0.99, indicating that the solid electrolyte Li1.3Al0.3Ti1.7(PO4)3 is a purely ionic conductor.

Network dynamics on the Chinese air transportation multilayer network

Air transportation networks play important roles in human mobility. In this paper, from the perspective of multilayer network mechanism, the dynamics of the Chinese air transportation network are extensively investigated. A multilayer-based passengers re-scheduling model is introduced, and a multilayer cooperation (MC) approach is proposed to improve the efficiency of network traffic under random failures. We use two metrics: the success rate and the extra transfer number, to evaluate the efficiency of re-scheduling. It is found that a higher success rate of passengers re-scheduling can be obtained by MC, and MC is stronger for resisting the instability of the capacity of links. Furthermore, the explosion of the number of extra transfer can be well restrained by MC. Our work will highlight a better understanding of the dynamics and robustness of the Chinese air transportation network.

Transfer stability of urban subway network with passenger flow: Evidence in Beijing

Stability of urban subway systems is a crucial issue in daily operation. This paper proposes a node failing process to test the stability of subway network by structure-based and flow-based node evaluation indicators. Furthermore, three network evaluation indicators are used to measure the network performance. The average transfer number of times (ATT) that is strongly associated with network structure and passenger flow will be discussed specifically. The results show that removing nodes with large inbound passenger flow cannot effectively damage the subway network structure, but it can result in significant increment of the ATT in the whole network. Another finding is that the ATT is smaller in peak hours compared with off-peak hours.