Roller Trace Design in Multi-Pass Conventional Spinning Based on Cylindrical Part

Conventional spinning is a kind of ancient revolving process which controls the product’s shape by roller trace design. It is also widely used in civil, military, automobile, aerospace and other fields. Unlike the power spinning process, the roller trace used in conventional spinning is complex. Both thickness uniformity and crack defects are affected by it. However, roller trace design is still based on experience without a solid theoretical basis. This paper simulated five different roller trace curves: involute curve, circular curve, Bezier curve, conchoids and line. Experiments using superalloy GH3030 were conducted in conjunction with a multi-pass conventional spinning simulation model. Blank thickness variations, mandrel and roller forces of different roller traces in the first pass are analyzed and assessed through the verification experiments. The results suggest that the curve trace parameters play a key role on the product thickness uniformity. And the distribution of Bezier and conchoid roller traces is more uniform than the other traces. The axial force of mandrel is a very important factor in the design of tool load capability. Larger roller feed ratio and proper roller traces can reduce the thinning which may avoid the cracks.

Spherical Indicatrices of Involute of a Space Curve in Euclidean 3-Space

In this work, we studied the properties of the spherical indicatrices of involute curve of a space curve and presented some characteristic properties in the cases that involute curve and evolute curve are slant helices and helices, spherical indicatrices are slant helices and helices and we introduced new representations of spherical indicatrices.

A Mathematical Model for Parametric Tooth Profile of Spur Gears

Spur gears are widely used transmission components. In the traditional design process, the noninvolute part of the tooth profile curve is difficult to describe with mathematical equations. This article puts forward a new parametric modeling method, which can describe the modified involute part of spur gears and parameterize and optimize the transition part of the involute curve of the spur gear. And this model of the spur gear can be created by parameters which is input in Scilab software and the spur gear graphic can be completed correspondingly. The experiments show that this modeling method can more quickly produce the standard spur or modified spur gear, and it also improves the efficiency and accuracy of spur gear modeling.

An Analytic Expression for the Inverse Involute

This article introduces new types of rational approximations of the inverse involute function, widely used in gear engineering, allowing the processing of this function with a very low error. This approximated function is appropriate for engineering applications, with a much reduced number of operations than previous formulae in the existing literature, and a very efficient computation. The proposed expressions avoid the use of iterative methods. The theoretical foundations of the approximation theory of rational functions, the Chebyshev and Jacobi polynomials that allow these approximations to be obtained, are presented in this work, and an adaptation of the Remez algorithm is also provided, which gets a null error at the origin. This way, approximations in ranges or degrees different from those presented here can be obtained. A rational approximation of the direct involute function is computed, which avoids the computation of the tangent function. Finally, the direct polar equation of the circle involute curve is approximated with some application examples.

Involute Curve Roller Trace Design and Optimization in Multipass Conventional Spinning Based on the Forming Clearance Compensation

In industrial production, the roller trace design is still based on the trial-and-error method that is more like an art than science. In this paper, we establish the mathematical model of the involute curve roller trace and adopted the forming clearance compensation in the attaching-mandrel process. The backward pass roller trace is optimized to avoid the roller interference due to blank springback. The spinning simulation model of seven forming passes is set up and verified by the experiments with superalloy GH3030. The wall thickness, the strain distribution, and the tool forces are analyzed. The results show that the forming clearance compensation can greatly shorten the forming time and enhance the production efficiency and saving energy. The metal accumulates at the edge of the blank, and the maximum thinning zone appeared near the edge and is prone to crack. In the straightening pass, the tool forces of both the roller and the mandrel are larger than those in the other passes.

On the Sabban frame belonging to involute-evolute curves

In this paper, we investigate special Smarandache curves with regard to Sabban frame of involute curve. We create Sabban frame belonging to spherical indicatrix of involute curve. Smarandache curves are explained by Sabban vectors belonging to spherical indicatrix. Then, we calculate geodesic curvatures of this Smarandache curves. The results found for each curve is given depending on evolute curve. The example related to the subject is given and their figures are drawn with MAPPLE program.