Graphical method for determining of limit and permissible values of drawing and friction coefficients, stress, drawing angle and delta-criterion for shape of plastic deformation zone

The maximum and permissible values of the coefficients of drawing and friction, the Delta criterion of the shape of the deformation center, the index of the deformed state, the angle and drawing stress are determined graphically for different models of hardening and values of the anti-tension stress. For the determination, cartesian graphs were used, on the ordinate axis of which the desired indicators are located, and on the abscissa axis the values of the I.L. Per lin safety factor obtained by varying the extraction coefficient. The permissible values of the drawing coefficient and drawing stress decrease with the growth of the safety factor of I.L. Perlin. The dependence of the limit and permissible values of the Delta criterion for the optimal value of the drawing angle on the deformation parameters and the harden ing model is shown. The maximum and permissible values of the coefficient of friction are higher at the optimal value of the drawing angle. For the first time, the possibility of increasing the limit value of the coefficient of friction from the action of anti-gravity is established. The limit and permissible values of the coefficient of friction decrease with the increase in the value of the coefficient of drawing and increase with the increase in the coefficient of hardening k. Curves for the dependences of the safety factor, the stress state indicator and the absolute safety margin Zap on the value of the drawing angle fix small and large values of the limit drawing angle on the abscissa axis. Small limit values of the drawing angle do not differ significantly in value for different values of the drawing and hardening coefficients, in contrast to large limit values of the angle. The action of counter-gravity increases the small limit angles and decreases the large limit angles. Determination of the limit and permissible values of the coefficients of drawing and friction, the Delta criterion, stress and drawing angle contributes to the rational choice of modes of deformation of the wire (bar).

Effect of deformation hardening intensity, contact friction and back tension on indicators of wire drawing process

Dependences on the hardening factor for the drawing stress, the safety factor of I.L. Perlin and the stress state indicator V.L. Kolmogorov at different values of the drawing angle, coefficient of friction and stress of back tension are presented. For the first time, the nature of the dependences for the limiting and permissible values of delta-criterion is shown for the shape of the deformation zone of round solid profile on the coefficients of friction, hardening and safety factor and the back tension stresses. The limiting and permissible values of the delta-criterion increase from increase in the coefficients of friction and safety factor, the back tension stress and decrease from increase in the hardening coefficient. It is shown that for small values of the criterion ∆ < 1.5, the drawing stress can be higher than the yield point at the die output. As result, the wire material may be destroyed and the drawing process cannot be realized. Assessment of the change degree in the limiting and permissible values of the elongation coefficient and delta-criterion is carried out with increase in the friction coefficient from 0.05 to 0.15, the back tension from 0 to 85 MPa, the safety factor from 1.0 to 1.4, the hardening coefficient from 0 to k.

Determination of limiting and legitimate values of drawing coeffi cient and delta-criterion for deformation zone shape during wire drawing

The limiting and legitimate values of the drawing coefficient and delta-criterion Δ for the deformation zone shape depending on the friction coefficient for different models of hardening and the values of the drawing angle and the back-pull stress are determined by numerically solving the corresponding equations. The limiting and legitimate values of the drawing coefficient decrease with increase in the friction coefficient, while the analogous values of the criterion increase. Increase in the safety factor causes decrease in the allowable drawing and increase in the delta-criterion. The limiting and legitimate values of the drawing coefficient decrease from the application of back tension in the absence of strain hardening. The nature of the effect of back tension on the limiting and legitimate values of the drawing coefficient and the delta-criterion depends on the deformation parameters with intensive hardening and significant value of the friction coefficient. The possibility of the absence of limiting values of the drawing coefficient and criterion Δ under hypothetical drawing conditions is shown: intensive hardening of the wire material at low friction coefficient and the calculation of the limiting values of these indicators based on the value of the I.L. Perlin safety factor, equal to 1. The estimation of the reliability of the approximate equality is carried out to determine the nature of the relationship between the criterion Δ and the index of the deformed state. It is shown that with small value of the delta-criterion (Δ < 2) wire breakage at the die exit is not guaranteed, since the limiting value of the drawing coefficient is slightly greater than 1. The drawing production technologist needs assessment of the limiting and legitimate values of the drawing coefficient and delta-criterion for predicting of wire (rod) breakage at given deformation parameters.

Results for calculation of optimal delta-criteria for deformation zone shape in drawing of round solid profi le

Formulas for calculating of the optimal delta-criterion are proposed, which, in contrast to the two similar formulas of foreign researchers considered, take into account the back-pull stress and the hardening model. The optimal delta-criterion depends on the deformation parameters and the hardening model. Approximate equalities are proposed that refl ect the relationship between the criteria of the deformation zone and the indicators of the strain state. The values of the criteria for the deformation zone and the strain state for the drawing angles is 4 and 9° and the optimal drawing angle are given. According to two formulas of foreign researchers and the proposed formula, dependencies for the optimal delta-criterion on the drawing and friction coeffi cients are constructed. The criteria values for these formulas do not differ signifi cantly. Taking into account the nature of the relationship for the criteria of the deformation zone shape and the strain state contributes to rational choice of drawing modes.

Nature of relationship between simple and integrated indicators of stressed state, safety margin and effi ciency of wire forming

The combined criterion, which includes forming effectiveness indicator and the I.L. Perlin’s safety margin is proposed. Interdependencies for different criteria for the shape of the deformation zone are given. Suggested indicators for assessing of the shape of plastic deformation zone are simpler than delta criterion used in the foreing theory of drawing. For different hardening models, the results for the calculation of the axial stress, the absolute safety margin, the I.L. Perlin’s wire safety margin, V.L. Kolmogorov’s stress state indicator stress state indicator and the proposed criteria for assessing of the forming effectiveness when drawing round solid profile depending on the drawing coefficient, drawing angle and criteria for the shape of the plastic deformation zone. In the plastic deformation zone with equal average yield strength, the equality of the strain indicators of the wire is not ensured if hardening curves of material are different. In particular, when the drawing coefficient ensures equal yield strength for different hardening curves and is equal to the initial yield strength, the drawing stress is more at more convex shape of the hardening curve. At the optimum drawging angle, when the minimum axial stress, the maximum values of the safety margin indicators and the proposed criteria for the forming effectiveness and the minimum stress state indicator are observed. Equal minimum values of the drawing stress when varying the drawing angle, the length of the plastic deformation zone or other criteria. The nature of the relationship between the stress state indicators, the safety margin and the forming effectiveness is shown. With different hardening models of lines for the relationship of the I.L. Perlin’s safety margin and V.L. Kolmogorov’s stress state indicator are located along one curve, as are the lines for the relationship between the dimensionless axial stress and the stress state indicator. With the strain parameters, when the drawing stress under the action of back tension is less than this stress in the absence of back tension, the safety margin and the new combined forming effectiveness indicator are more under the action of back tension. This is possible with intensive hardening of the wire material in the draft of drawing, reduced drawing angles and increased values of drawing and friction coefficients. Different values of strain indicators of steel 12Kh18N10T wire after quenching and annealing are shown.

HAUSDORFF DIMENSION OF GENERALIZED FIBONACCI WORD FRACTALS

Fibonacci word fractals are a class of fractals that have been studied recently, though the words the fractals are generated from are well known in the combinatorics literature. The Fibonacci word can be used to draw a curve which possesses self-similarities determined by the recursive structure of the word. The Hausdorff dimension of the scaling limit of the finite Fibonacci word curves is computed for [Formula: see text]-Fibonacci curves and any drawing angle between [Formula: see text] and [Formula: see text].

Wear characteristics of die surface in deep drawing of stainless steel 304 by using finite element simulation

The characteristics of adhesive wear of TiN coating in drawing process by using finite element method were carried out to investigate the effects of drawing angles and sliding velocities of punch to explained wear index. Bending radius of die was used to increase the contact pressure between stainless sheet and TiN coating surface. Three sliding velocities (0.5, 1 and 5 mm/s) were studied each bending angle between (0O to 90O) by keeping the hardness of material coating to 24 GPa (HV.0.05). The results showed that the wear index were decreased with drawing angle but sliding speed of punch was not affected in slightly speed.

The Influence of the Angle of the Working Part of the Die on the High Speed Drawing Process of Low Carbon Steel Wires

The paper contains the theoretical and experimental analysis of the impact of the drawing angle on the drawing process and the properties of low carbon steel wires. A multi-stage drawing wire rod with a diameter of 5.5 mm on a wire with a diameter of 1.0 mm has been carried out in two stages. The first one consisted of preliminary drawing wire rod for the wire with a diameter of 2.2 mm which was next subjected to the drawing process at a speed of 25 m/sec at the final wire with a diameter of 1.0 mm. The wires were drawn in conventional dies with drawing angle α = 3, 4, 5, 6, 7 degrees. For the wires drawn in respective variants, the investigation of the mechanical properties was performed and the amount of lubricant on the surface of steel wires was determined. Numerical analysis of the process of drawing in the Drawing 2D complemented the experimental studies. It has been shown that when drawing at high speeds, properly chosen the value of the angle of the working part of the die can improve the lubrication conditions and mechanical properties of steel wires.