New method for determining singularities on enveloped surface and its application to study curvature interference theory of involute worm drive

In this paper, a more computationally convenient singularity condition of the enveloped surface is proposed using the theory of linear algebra. Its preconditions are only the tangential vector of the enveloping surface, the relative velocity vector, and the total differential of the meshing function. It avoids calculating the curvature parameters of the enveloping surface. It is proved that the singularity conditions of enveloped surface from different references are equivalent to each other and the relational equations among them are obtained. The curvature interference theory for the involute worm drive is established using the proposed singularity condition. The equation for the singularity trajectory is obtained. The calculation method for the singularity trajectory is proposed and its numerical result is obtained. The influence of the design parameters on the singularity trajectory is studied using the proposed curvature interference theory. The study results show that the risk of curvature interference is high when the transmission ratio is too small, especially in the case of the single-threaded worm and large modulus. The proposed singularity condition can also be applied to study the curvature interference mechanism in other types of the worm drive and to study the undercutting mechanism when machining the worm drive.

Analysis of the Torque Loss of High-Speed Transmission Mechanism with a Stacked Roller Set

Two-dimensional pumps have broad application prospects in aerospace. However, the performance of the pump is degraded because of the clearance problem of the current 2D transmission mechanism. In order to eliminate the clearance between the cam rail and the rollers, a high-speed transmission mechanism with a stacked roller set is proposed. The stacked roller set is compressed by the load pressure. The axial inertia force is balanced when the transmission mechanism works at high speed, via the equal acceleration and reverse movement of two cam rail sets. Thus, the transmission mechanism meets the high-speed demand. In this paper, the mathematical model of the transmission mechanism is established based on the enveloping surface theory and the differential geometry principle. Afterwards, numerical analysis of the mathematical model is performed based on MATLAB, combined with the experiment, to study the influence of load pressure and rotational speed on the torque loss. Then, the torque characteristics of the transmission mechanism is obtained. According to a test, the deviation between theoretical data and experimental data is 11.9%; therefore, the mathematical model can predict the torque of the transmission mechanism effectively. It is concluded that the torque loss of the transmission mechanism increases linearly with the load pressure, and the rotational speed has a slight effect on the torque loss.

Quality improvement of calibrated steelby surface deformation. Part 2. Effect of enveloping surface deformation on residual stresses in cylindrical bars

Cold-drawn metal has a number of undeniable advantages over the hot-rolled one. Increased hardness, high surface quality, stability of the diametrical dimension along the length of the workpiece are the basis for choosing calibrated metal as effective workpieces for the manufacture of long parts such as shafts, axles, and rods. In some cases, such workpieces require a small amount of machining, for example, threading or making necks at the ends of a bar. The wider use of the calibrated metal is hindered by residual stresses that are formed during its manufacture. In the first part of this article, it was proposed to use small plastic deformations to control residual stresses. By the example of a new process of surface plastic deformation, which is called orbital burnishing, the working and residual stresses in cylindrical workpieces are determined. In the second part of the article, the process of enveloping surface plastic deformation is considered, which, at high productivity, makes it possible to reduce the residual tensile stresses in the calibrated metal or form the surface layers of the workpiece compressive stress. A technique for the experimental determination of residual stresses in the volume of a body is based on layer-by-layer removal of the inner and outer layers of cylindrical samples. Influence of the main parameters of the enveloping deformation process on the components of the residual stress tensor is established. A range of relative compressions (0.1 – 1.0 %) is revealed, at which residual compressive stresses are formed in the surface layers of the workpiece. It was found that at a relative compression of 0.5 %, the maximum residual compression stresses are created. Enveloping surface deformation has a positive effect on the residual stress state and on colddrawn metal – the residual tensile stresses can be reduced, removed or converted into compressive ones.

A Fault-Tolerant Offset Algorithm for Measured Data with Defects

Offsetting of measured data, as a basic geometric operation, has already been widely used in many areas, like reverse engineering, rapid prototyping and NC machining. However, measured data always carry typical defects like caves and singular points. A fault-tolerant offset method is proposed to create the high quality offset surface of measured data with such defects. Firstly, we generated an expansion sphere model of measured data with the radius equivalent to the offset length. Secondly, using the computational geometry application of convex hull, we acquire the data of outermost enveloping surface of this expansion sphere model. Finally, we use local MLS projection fitting method to wipe out existing defects, and generate the high-quality triangular mesh surface of the offset model. The offset surface generated by this method is suitable for practical engineering application due to its high efficiency and accuracy.