Kinetostatic analysis,manufacturing,and experimental application of a press machine based on Stephenson II mechanism

Abstract

Press machine tools are often used in important industrial establishments, such as automobiles, aerospace, and aviation; these machine tools must be produced with high precision. Therefore, studies related to improving press tools and enhancing their precision are being conducted. In this study, a press machine tool based on the Stephenson II mechanism is proposed. Compared to that of conventional crank presses, this mechanism increases the slider balance using a ternary link and unique connecting rods. Thus, the slider precision can be improved with a small addition to the mechanism, and load transmission can be ensured in a balanced manner. To test the contribution of the mechanism, dynamic analysis is performed using the kinetostatic method, and the dynamic data of the mechanism are obtained. Subsequently, a press machine prototype is designed and manufactured. The experimental results are verified against the theoretical results, confirming that the proposed press machine tool based on the Stephenson II mechanism has better characteristics than those of the conventional press machine owing to the favorable distribution of forces on the slide and lower reaction to the slide guides.

Keywords

Press manufacturing Stephenson II mechanism kinetostatic analysis dynamic analysis experimental study metal forming

Introduction

Mechanical presses are extensively utilized in metal forming processes. Various types of linkage mechanisms have been proposed to meet the load and stroke characteristics of a particular metal forming process. During metal forming operations, the deep drawing process requires a gradual and extended stroke of the ram, while the shearing process requires a short stroke of the slide.^1,2

The types of mechanical press available for stamping and forming operations vary according to the slide motion.³ A conventional crank press operates based on a slider-crank mechanism, designed for stamping various parts, and can generate a sinusoidal slide motion.^4–6 During the operation of a conventional crank press, substantial heavy dynamic loads occur on the mechanism parts when it is turned on. These loads are related to the crank press operational features, including sudden, almost immediate stops with shock cyclic loads. Therefore, the choice of mechanism structure of the crank press is crucial for decreasing the dynamic load during operation.^7,8

Stamping accuracy is an important parameter of a crank press. The stamping accuracy of a crank press generally depends on two factors, that is, the inclination of the slide under the influence of an eccentric application of the deforming force and the total linear elastic deformation of the construction units of the press and the stamps under the load, which depends on the rigidity of the press structure and stamps.^3–6,9

Various studies related to the design, kinematic modeling, dynamic modeling, and analysis of crank press mechanisms have been reported in the literature.

Erkaya and Uzmay^10,11 performed kinematic and dynamic analyses of a modified slider-crank mechanism. The mechanism had an additional eccentric link between the connecting rod and crank. Anis¹² performed kinematic and dynamic analyses on a slider-crank mechanism using the Adams software with mechanism inertias. Wu et al.¹³ studied a double crank press mechanism. They mathematically modeled the mechanism to evaluate the contact forces in a 3D translational joint with clearance. For the finite element analysis, ANSYS/LS-DYNA was used to prove the accuracy of the proposed model. Li et al.^14–16 studied on the hybrid mechanisms of seven-bar and nine-bar press mechanisms for deep drawing applications. They presented kinematic and dynamic modeling and an analysis of these mechanisms. The Lagrangian method was used for dynamic models, wherein the fourth-order Runge Kutta method was preferred for integration. Kütük et al.¹⁷ optimized an industrial seven-bar hybrid press mechanism for a deep drawing study using a genetic algorithm. They also presented a dynamic analysis using the kinetostatic method.

Abdullah and Telegin¹⁸ studied a dynamic model and its mathematical description of a central slider crank mechanism for a crank press. The clearances at the joints of the mechanism and eccentricity were considered. Liu et al.¹⁹ presented a kinematic and dynamic analysis of a slider-crank mechanism. The dynamic analysis was modeled using static equilibrium (kinetostatic approach). They also built the MATLAB-Simulink model. Jun²⁰ performed the basic theory of the mechanical dynamics method and kinetostatic analysis to obtain the numerical solutions of the slider-crank mechanism. Khemili and Romdhane²¹ were interested in the dynamic behavior of a planar flexible slider-crank mechanism with clearance. They designed a model using the Adams^® based impact-function, and manufactured and presented an experimental setup. Choi et al.²² optimized the eccentric mechanism of a linear guide press based on a nonlinear search method. They modeled an objective function to satisfy the specified conditions of the forming processes. Chen et al.²³ established a dynamic model for the main transmission system of a high-speed precision crank press using Adams^®. The mechanism included a crank and two connecting rods.

Cheng et al.²⁴ designed a double-axis crank servo press system. The slider was adjusted using a multi-axis servo system. The mechanism was designed using two servo motors, two crank shafts, and four connecting rods for slider precision. They also presented the experimental results. Qingyu et al.²⁵ studied the optimization and motion planning of a heavy loading eccentric servo press. Kaya^26,27 improved the sheet metal forming of Al and Mg alloy materials. Warm forming experiments were conducted using a 110 ton servo press. A load cell was used to observe the punch load. The models were developed by calculating the heat transfer coefficients. The computational model was validated using the experimental results. They also studied the non-isothermal warm deep drawing of stainless steel and verified the finite element (FE) predictions. Halicioglu et al.²⁸ studied the dynamic modeling and experimental implantation of a servo crank press. They used the Lagrangian method for dynamic modeling. A manufactured servo press prototype was operated and the experimental results were found to be in good agreement. Halicioglu et al.²⁹ also developed a soft motion scenario that was applied to enhance the forming quality. This press system with optimized motion exhibited good tracking precision for the slider. The optimized motion provided a better surface quality at higher speeds. Gao et al.³⁰ manufactured a servo press with a toggle booster mechanism driven by a tubular permanent magnet linear motor. They modeled the dynamics of the mechanism and analyzed them. Subsequently, they presented the theoretical and experimental results together.

In addition to metal forming and the mechanisms, a model with the maximum undeformed chip thickness was proposed by Zhang et al.³¹ which was in good agreement with the experimental results for brittle materials.^32,33 They also presented an approach of single grain scratching performed on a developed grinder, in which the speed was three to six orders of magnitude higher than that in nanoscratching.³⁴ The force, stress, depth of cut, and size of plastic deformation were calculated on the onset of cutting and brittle-to-ductile transition.³⁵ With the breakthrough in these mechanisms, new manufacturing tools and methods have been developed.^36,37 These explorations are a landmark contribution to conventional manufacturing because it is difficult to develop high-performance surfaces using traditional manufacturing techniques.³⁸

It has been reported in the literature that the precision and slider balance of a crank press machine can be increased by using servo motors, more than one crank with more than one motor or complex mechanisms. These applications increase the press manufacturing cost while improving slider precision. However, an increase in cost is undesirable. Therefore, Jomartov et al.³⁹ proposed the use of a Stephenson II six-bar linkage mechanism to increase the precision of crank presses. A new crank press was synthesized based on the Stephenson II six-bar linkage. This crank press operates based on a simpler mechanism and can be manufactured without increasing the press manufacturing cost. To test the functionality and identify the advantages of the new crank press, it is necessary to dynamically analyze the Stephenson II linkage and perform experimental validation. Previous studies have shown that while MATLAB and Adams software are used as packet programs, Lagrangian and kinetostatic analyses are often used for dynamic analyses.

In this study, the six-bar Stephenson II linkage mechanism, including a ternary additional link with two connecting rods for precision, was dynamically analyzed using the kinetostatic method. A press prototype based on the Stephenson II mechanism was manufactured to test the functionality and identify the advantages of conducting experimental research. It is necessary to develop a method for the experimental research of a press machine based on the Stephenson II mechanism, which is based on modern digital devices with information processing algorithms, and visualization of the measured signals.

Mechanism definition

Figure 1(a) depicts the Stephenson II six-bar linkage mechanism. In contrast to that of the conventional crank press (Figure 1(b)), this mechanism includes a ternary link between the crank and connecting rod. By adding the ternary link, the slide can be balanced with two equal connecting rods.

Figure 1.

Schematics of mechanisms: (a) Stephenson II press mechanism (r: crank length, a: ABB' triangle height, l: parallel connecting rods length, φ: the angle of a crank, ψ: angle of two connecting rods, H: linear coordinate of slider, e: slider eccentricity, andb: distance between joint C and slider center along an axis Ox), (b) Conventional crank press mechanism (r: crank length, l: connecting rod length, φ: the angle of a crank, S: stroke length)

The kinematic position of the mechanism can be analyzed using equation (1).³⁹ $ψ$ denotes the connecting rod angle. The first and second derivations of the equation represent the velocity and acceleration, respectively.

{\begin{matrix} H = a - r \sin φ \pm \sqrt{l^{2} - {(e - r \cos φ)}^{2}} \\ ψ = \pm \arccos [\frac{1}{l} (e - r \cos φ)] \end{matrix}

(1)

Kinetostatic analysis of Stephenson II six-bar linkage

The vector method for solving an important problem related to the dynamic analysis of mechanisms, called kinetostatic analysis, was considered.⁴⁰ Using this method, the external force, mass, and inertia effect during the movement of the mechanism can be balanced by the reaction forces. Kinetostatic analysis is practically significant when selecting electric motors and calculating kinematic pairs’ bearings. For instance, given the constant angular velocity of a driving member ( $ω_{1} = constant$ ), the kinematic and kinetostatic analyses of the mechanism can be performed, and reactions on kinematic pairs and the balance moment can be determined for the entire movement segment, $0 \leq φ_{1} \leq 2 π$ . The parameters of the electric motor are determined according to the average value of the balance moment, and the extreme values of the reactions are used to calculate and select the bearings to be installed on the joints. Also, knowledge regarding the analytical expressions of the reactions facilitate in visually solving the dynamics of mechanisms by considering the frictional force in the kinematic pairs.

${\vec{R}}_{ij} = - {\vec{R}}_{ji}$ , where $i, j = 1, . . ., 5$ (reactions from link $i$ to $j$ ), denotes the desired reactions on the kinematic pairs and $M_{y}$ an unknown balance moment on driving link 1. The link mass is given by $m_{j}$ and the moment of inertia of the links with respect to the center of mass is denoted as $J_{S_{j}}$ . ${\vec{G}}_{i}$ and ${\vec{F}}_{5}$ denote the gravitational force of the links and resistance force at output link 5, respectively. From the solution to the problem of kinematic analysis, the motion law of the remaining links of the mechanism can be determined. The inertia force of the center of mass is $- m_{j} {\vec{W}}_{S_{j}}$ and the moment of inertia force of the links is $- J_{S_{j}} ε_{j}$ . ${\vec{W}}_{S_{j}}$ and $ε_{j}$ denote the acceleration of the center of mass and angular acceleration of the center of mass at point S_J, respectively.

Figure 2 depicts the equilibrium forces of the Stephenson mechanism. Slider eccentricity of e is equal to zero since the mechanism is considered a central mechanism in this study. Based on D’Alembert’s principle, the equilibrium equations of the five links can be written as follows:

{\begin{matrix} \sum {\vec{F}}_{i, j} - m_{j} {\vec{W}}_{S_{j}} = 0, \\ \sum M_{S_{j}} ({\vec{F}}_{i, j}) - J_{S_{j}} ε_{j} \vec{k} = 0, j = 1, . ., 5 \end{matrix}

(2)

Figure 2.

Load representation of Stephenson II six-bar linkage mechanism.

Here, ${\vec{F}}_{i, j}$ denotes the active and reactive forces acting on the $j$ th link. Moreover,

{\vec{F}}_{ij} = - {\vec{F}}_{ji} .

(3)

When equation (2) is used to determine the equilibrium equation for each link, we can derive further equations. For driving link 1, assuming that it is statically balanced (Figure 3(a)), we obtain equation (4).

{\begin{matrix} {\vec{R}}_{01} + {\vec{R}}_{21} + {\vec{G}}_{1} = 0, \\ \vec{r} \times {\vec{R}}_{21} + M_{y} \vec{k} - J_{S_{1}} ε_{1} \vec{k} = 0 \end{matrix}

(4)

Figure 3.

Forces acting on: (a) link 1, (b) link 2, (c) link 3, (d) link 4, and (e) slide 5.

For link 2, the static balance (Figure 3(b)) can be determined using equation (5).

{\begin{matrix} {\vec{R}}_{12} + {\vec{R}}_{32} + {\vec{R}}_{42} + {\vec{G}}_{2} - m_{2} {\vec{W}}_{S_{2}} = 0, \\ - {\vec{r}}_{2} \times {\vec{R}}_{12} + ({\vec{a}}_{2} - {\vec{r}}_{2}) \times {\vec{R}}_{42} + ({\vec{b}}_{2} - {\vec{r}}_{2}) \\ \times {\vec{R}}_{42} - J_{S_{2}} ε_{2} \vec{k} = 0 \end{matrix}

(5)

For links 3 and 4 (Figure 3(c) and (d)), equations (6) and (7) can be written as follows:

{\begin{matrix} {\vec{R}}_{23} + {\vec{R}}_{53} + {\vec{G}}_{3} - m_{3} {\vec{W}}_{S_{3}} = 0, \\ - {\vec{r}}_{3} \times {\vec{R}}_{23} + (\vec{l} - {\vec{r}}_{3}) \times {\vec{R}}_{53} - J_{S_{3}} ε_{3} \vec{k} = 0 \end{matrix}

(6)

{\begin{matrix} {\vec{R}}_{24} + {\vec{R}}_{54} + {\vec{G}}_{4} - m_{4} {\vec{W}}_{S_{4}} = 0, \\ - {\vec{r}}_{4} \times {\vec{R}}_{24} + (\vec{l} - {\vec{r}}_{4}) \times {\vec{R}}_{54} - J_{S_{4}} ε_{4} \vec{k} = 0 \end{matrix}

(7)

For slide 5 (Figure 3(e)), the equilibrium conditions can be written as shown in equation (8).

{\begin{matrix} {\vec{R}}_{35} + {\vec{R}}_{45} + {\vec{G}}_{5} + {\vec{F}}_{5} + {\vec{R}}_{05} - m_{5} {\vec{W}}_{S_{5}} = 0, \\ \vec{x} \times {\vec{R}}_{05} + {\vec{a}}_{5} \times {\vec{R}}_{35} + {\vec{b}}_{5} \times {\vec{R}}_{45} = 0 \end{matrix}

(8)

In these equations, the basis vector of the coordinate axis $Oz$ is denoted by $\vec{k}$ . For simplicity, equation (9) is introduced.

{\vec{Q}}_{i} = {\vec{G}}_{i} - m_{i} {\vec{W}}_{S_{i}}, {\vec{J}}_{i} = J_{S_{i}} ε_{i} \vec{k}, i = 1, 2, . . ., 5

(9)

Accordingly, the equilibrium equation of the mechanism system can be written as shown in equation (10).

{\begin{matrix} {\vec{R}}_{01} + {\vec{R}}_{21} + {\vec{G}}_{1} = 0 \\ \vec{r} \times {\vec{R}}_{21} + M_{y} \cdot \vec{k} - {\vec{J}}_{1} \\ {\vec{R}}_{12} + {\vec{R}}_{32} + {\vec{R}}_{42} + {\vec{Q}}_{2} = 0 \\ - {\vec{r}}_{2} \times {\vec{R}}_{12} + ({\vec{a}}_{2} - {\vec{r}}_{2}) \times {\vec{R}}_{32} + ({\vec{b}}_{2} - {\vec{r}}_{2}) \times {\vec{R}}_{42} - {\vec{J}}_{2} \\ {\vec{R}}_{23} + {\vec{R}}_{53} + {\vec{Q}}_{3} = 0 \\ - {\vec{r}}_{3} \times {\vec{R}}_{23} + (\vec{l} - {\vec{r}}_{3}) \times {\vec{R}}_{53} - {\vec{J}}_{3} = 0 \\ {\vec{R}}_{24} + {\vec{R}}_{54} + {\vec{Q}}_{4} = 0 \\ - {\vec{r}}_{4} \times {\vec{R}}_{24} + (\vec{l} - {\vec{r}}_{4}) \times {\vec{R}}_{54} - {\vec{J}}_{4} = 0 \\ {\vec{R}}_{05} + {\vec{R}}_{35} + {\vec{R}}_{45} + {\vec{F}}_{5} + {\vec{Q}}_{5} = 0 \\ - \vec{x} \times {\vec{R}}_{05} + {\vec{a}}_{5} \times {\vec{R}}_{35} + {\vec{b}}_{5} \times {\vec{R}}_{45} = 0 \end{matrix}

(10)

If ${\vec{R}}_{12} = - {\vec{R}}_{21}$ , we can define ${\vec{R}}_{01}, M_{y}$ from the first two equations of the system.

{\vec{R}}_{01} = - {\vec{G}}_{1} - {\vec{R}}_{21}, M_{y} = (\vec{k}, {\vec{J}}_{1}) - (\vec{k}, \vec{r}, {\vec{R}}_{21})

(11)

After vectorially multiplying the third equation of the system by ${\vec{r}}_{2}$ and adding to the fourth equation, equation (12) can be obtained as:

{\vec{a}}_{2} \times {\vec{R}}_{32} + {\vec{b}}_{2} \times {\vec{R}}_{42} = {\vec{J}}_{2} - {\vec{r}}_{2} \times {\vec{Q}}_{2}

(12)

Similar steps were applied for the fifth and sixth equations and seventh and eighth equations of the system in equation (10). Then, equations (13) and (14) can be obtained.

\vec{l} \times {\vec{R}}_{53} = {\vec{J}}_{3} - {\vec{r}}_{3} \times {\vec{Q}}_{3}

(13)

\vec{l} \times {\vec{R}}_{54} = {\vec{J}}_{4} - {\vec{r}}_{4} \times {\vec{Q}}_{4}

(14)

The relations can be introduced as given in equation (15).

{\vec{P}}_{i} = {\vec{J}}_{i} - {\vec{r}}_{i} \times {\vec{Q}}_{i}, i = 2, 3, 4

(15)

Then, equations (12)–(14) can be written in the following form:

{\begin{matrix} {\vec{a}}_{2} \times {\vec{R}}_{32} + {\vec{b}}_{2} \times {\vec{R}}_{42} = {\vec{P}}_{2}, \\ \vec{l} \times {\vec{R}}_{53} = {\vec{P}}_{3}, \\ \vec{l} \times {\vec{R}}_{54} = {\vec{P}}_{4}, \end{matrix}

(16)

From the system equation (10), we can also derive ${\vec{R}}_{32}$ and ${\vec{R}}_{42}$ .

{\vec{R}}_{32} = {\vec{R}}_{53} + {\vec{Q}}_{3}, {\vec{R}}_{42} = {\vec{R}}_{54} + {\vec{Q}}_{4}

(17)

By substituting equation (17) into the first equation of equation (16), equation (18) can be obtained.

{\vec{a}}_{2} \times {\vec{R}}_{53} + {\vec{b}}_{2} \times {\vec{R}}_{54} = {\vec{P}}_{2} - {\vec{a}}_{2} \times {\vec{Q}}_{3} - {\vec{b}}_{2} \times {\vec{Q}}_{4}

(18)

The last two equations in equation (16) can be written as:

{\begin{matrix} {\vec{R}}_{53} = λ_{3} \cdot \vec{l} + \frac{1}{l^{2}} \cdot {\vec{P}}_{3} \times \vec{l} \\ {\vec{R}}_{54} = λ_{4} \cdot \vec{l} + \frac{1}{l^{2}} \cdot {\vec{P}}_{4} \times \vec{l} \end{matrix}

(19)

By substituting equation (19) into equation (18), equation (20) can be obtained.

{\vec{a}}_{2} \times \vec{l} \cdot λ_{3} + {\vec{b}}_{2} \times \vec{l} \cdot λ_{4} = {\vec{σ}}_{2}

(20)

where

\begin{matrix} {\vec{σ}}_{2} = {\vec{P}}_{2} - {\vec{a}}_{2} \times {\vec{Q}}_{3} - {\vec{b}}_{2} \times {\vec{Q}}_{4} - \frac{1}{l^{2}} \cdot ({\vec{a}}_{3} \times {\vec{P}}_{3} \times \vec{l}) \\ - \frac{1}{l^{2}} \cdot ({\vec{b}}_{2} \times {\vec{P}}_{4} \times \vec{l}) \end{matrix}

(20)

After performing scalar multiplication on the second last equation of the system, that is, equation (10) multiplied by $\vec{j}$ , equation (21) can be obtained.

{\vec{R}}_{53} \cdot \vec{j} + {\vec{R}}_{54} \cdot \vec{j} = {\vec{F}}_{5} \cdot \vec{j} + {\vec{Q}}_{5} \cdot \vec{j}

(21)

Alternatively, by considering equation (19), equation (22) can be obtained.

λ_{3} + λ_{4} = σ_{5}

(22)

Here,

σ_{5} = \frac{{\vec{F}}_{5} \cdot \vec{j} + {\vec{Q}}_{5} \cdot \vec{j}}{\vec{l} \cdot \vec{j}} + \frac{\vec{l} \cdot \vec{i}}{l^{2} (\vec{l} \cdot \vec{j})} ({\vec{P}}_{3} + {\vec{P}}_{4})

(23)

By solving equations (20)–(22), $λ_{3}, λ_{4}$ can be obtained.

Using equation (19) and ${\vec{R}}_{53}$ , ${\vec{R}}_{54}$ can be determined. Then, ${\vec{R}}_{05}$ and $\vec{x}$ can be determined using equation (10) as follows:

\begin{matrix} {\vec{R}}_{05} = {\vec{R}}_{53} + {\vec{R}}_{54} - {\vec{F}}_{5} - {\vec{Q}}_{5} \\ x = \frac{({\vec{a}}_{5} \times {\vec{R}}_{53} + {\vec{b}}_{5} \times {\vec{R}}_{54}) \cdot \vec{k}}{(\vec{j} \times {\vec{R}}_{05}) \cdot \vec{k}} \end{matrix}

(24)

Next, ${\vec{R}}_{24}, {\vec{R}}_{23}, {\vec{R}}_{12}$ can be defined by equation (25).

{\begin{matrix} {\vec{R}}_{24} = - {\vec{R}}_{54} - {\vec{Q}}_{4} \\ {\vec{R}}_{23} = - {\vec{R}}_{53} - {\vec{Q}}_{3} \\ {\vec{R}}_{12} = {\vec{R}}_{23} + {\vec{R}}_{24} - {\vec{Q}}_{2} \end{matrix}

(25)

Thus, the problem of kinetostatic analysis was solved using the vector method. According to the obtained formulas, the balance moment and reactions in kinematic pairs can be determined for the entire part of the movement, $0 \leq φ_{1} \leq 2 π$ . The Stephenson II six-bar linkage kinetostatic analysis program was developed using the Maple^® software package.

Kinetostatic analysis of a prototype crank press based on Stephenson II linkage

Test calculations were performed with the following dimensions of the actuator links of a prototype crank press based on Stephenson II linkage: r = 0.04 m, l = 0.185 m, a = 0.06 m, and b = 0.065 m. The law of motion of the crank is given in the form of $φ_{1} = φ_{1} (t)$ = ωt, ω = 10 rad/s. The mass and moment of inertia of the links of the prototype crank press have the following values: m₁=0.164 kg, J₁ = 100.915 × 10⁻⁶kgm², m₂ = 0.777 kg, J₂ = 1864.63×10⁻⁶kg m², m₃ = m₄ = 0.608 kg, J₃= J₄ = 7125.8×10⁻⁶ kg m², m₅ = 3.8 kg.

The load force, $F_{5}$ [N] (Figure 2), on the slide is directed in the opposite direction of the slide motion, and is determined by the following function ⁴¹:

{\begin{matrix} F_{5} = 0 °, 0 \leq φ_{1} < 145 ° \\ F_{5} = - 8196.7 \cdot (φ_{1} - \frac{145 \cdot π}{180}), 145 ° \leq φ_{1} \leq 180 ° \\ F_{5} = 0, 180 ° < φ_{1} \leq 360 ° \\ F_{5}^{Max} = 5000 N \end{matrix}

(25)

Figure 4(a) depicts a graph of the load force, $F_{5}$ . For clarity, Figure 4(b) also shows a combined graph of motion of the slide and load force on the Stephenson II press. For the analysis results, y axis is assumed as the reference for the crank angle. So, the slider is on top dead center as the start point when the crank angle is zero. Figures 5 and 6 show the resulting calculated graphs of the absolute values of reactions $R_{01}, R_{12}, R_{23}, R_{24}, R_{53}, R_{54}, R_{05}$ [N] and torque $M_{y}$ [Nm]. The reaction forces are presented in the range of 145°–180° because the external force only acts during this period.

Figure 4.

Graphs: (a) load force $F_{5}$ and (b) combined graph of the slide motion and load force on the slide.

Figure 5.

Absolute values of reactions: (a) $R_{01}, R_{12}$ , (b) $R_{23}, R_{24}$ , and (c) $R_{53}, R_{54}$ .

Figure 6.

Graphs: (a) absolute values of reaction $R_{05}$ , (b) crank torque of $M_{y}$ , and (c) values of $R_{05}^{x}, R_{05}^{y}$ .

Figure 6(c) shows graphs $R_{05}^{x}, R_{05}^{y}$ , that is, the projections of reaction $R_{05}$ to the slide guide on the x- and y-axes.

Figure 5(a) indicates that the reaction $R_{01}$ to the crank shaft support increases linearly and reaches a maximum of 5000 N at a crank angle of 180°. Figure 6(c) shows that the maximum value, $R_{05}^{x}$ , is 244 N at crank angle $φ = 163^{°}$ .

At a given load on the slide, that is, $F_{5} = 5000 N$ , the value of $R_{05}^{x}$ was found to be only 4.88% of the load.

From Figure 7,⁴¹ the component of force F acting on the slide guides of a conventional press can be determined.

F_{t} = F \cdot tg β

(26)

where β denotes the angle defining the position of the connecting rod relative to the vertical passing through the center of the crank shaft. In practice, based on the accepted values of the crank and connecting rod dimensions, the maximum value of angle β during stamping should not exceed approximately 8°–10°.⁴¹ From equation (26) with F = 5000 N, $β = 10 °$ , and $F_{t} = 750 N$ ; thus, the value of the reaction from the side of the slide guide is approximately 15% of the force on the slide. In conventional crank presses with one connecting rod, the projection of the reaction to the slide guides on the x-axis can reach 15% of the load. Hence, crank presses with two connecting rods have great advantages over those with one connecting rod owing to the better distribution of forces on the slide, which results in lower loads on the slide guides.

Figure 7.

Forces on a conventional press.

Experimental research for crank press prototype based on Stephenson II linkage

A prototype of a crank press based on the Stephenson II mechanism was manufactured. Figure 8 illustrates a general view of the manufactured prototype of a six-linkage crank press based on Stephenson II.

Figure 8.

Prototype of a crank press based on Stephenson II six-bar linkage.

The experimental setup of the prototype crank press based on the Stephenson II mechanism (Figure 9) was built on the digital devices of the ZETSENSOR^® series⁴² with a CAN^® interface.

Figure 9.

Experimental setup of the press based on Stephenson II mechanism.

The system enables the measurement of the following parameters: motion of slide, force acting on the slide, and stresses on the links of the press.

A digital force sensor was used to measure the force of the crank press. The digital force transducer contained a UU strain gage and a ZET 7111 measuring module.⁶ The linear motion of the slide was determined using a digital motion transducer. The digital motion sensor comprised an RL inductive sensor and a ZET 7111-L measuring module.⁶ Foil strain gages were used to measure the deformations and stresses on the links of the Stephenson II mechanism.

The motion sensor and force sensor were installed directly on the press slide; they transmitted signals proportional to the relative movement of the slide and the force exerted by the slide on the die. Strain gages were mounted on the press links; it is necessary to determine the stresses arising during operation. These signals were processed by ZET 7111 measuring modules, which transmit the measured values via the CAN 2.0 bus to the ZET 7174 interface converter and then to the computer via USB 2.0.

Experimental research results

The experiment was performed on a crank press prototype based on the Stephenson II mechanism, with the following parameters: electric motor power = 1.4 kW and constant crank speed = 95.5 rpm (10 rad/s). The applied experimental setup is presented on the prototype, as depicted in Figure 10(a).

Figure 10.

(a) Prototype of crank press based on Stephenson II linkage and (b) fragment of the strain gage sticker on the connecting rod.

In the course of experimental research, a hole with a diameter of 5 mm was cut by a stamp in a steel sheet with a thickness of 0.8 mm. The punching operation was performed by a single press stroke. Figure 10(b) depicts the connecting rod of the press with a mounted strain gage to determine the stress. The cross-sectional dimension of the connecting rod at the strain gage sticker was 4.2 × 1.0 cm².

The stress was measured three times in the cross-section of the connecting rod when punching a hole with a diameter of 5 mm in a steel sheet with a thickness of 0.8 mm; accordingly, the following maximum values were obtained: P_n1 = 6.796 MPa, P_n2 = 6.803 MPa, and P_n3 = 6.653 MPa. The average value of the maximum stress, ${\bar{P}}_{n}^{max}$ , is determined using equation (27).

{\bar{P}}_{n}^{max} = \frac{1}{3} \sum_{i = 1}^{3} P_{ni}

(27)

The mean square deviation, σ, is determined using equation (28).

σ = \sqrt{\frac{1}{3} \sum_{i = 1}^{3} {(P_{i} - {\bar{P}}_{n}^{max})}^{2}}

(28)

From equations (27) and (28), ${\bar{P}}_{n}^{max} = 6.751 MPa$ and σ = 0.06912 MPa were obtained.

Figure 11 shows an experimental graph of the average stress, ${\bar{P}}_{n}$ , in the cross-section of a connecting rod when punching a 5 mm hole in a steel sheet with a thickness of 0.8 mm. The cross-sectional area of the connecting rod at the measurement point was equal to $S_{n} = 0, 42 \cdot 10^{- 3} m^{2}$ , indicating that the forces in this section were equal, $F_{n}^{max} = {\bar{P}}_{n}^{max} \cdot S_{n} \approx 2835 N$ . The steel sheet was punched with a hole near the bottom dead center; the maximum force on the slide was equal to twice the force on the connecting rod (owing to the presence of two connecting rods), $F_{n}^{max} \approx 5670 N$ .

Figure 11.

Experimental graph of the average stress, ${\bar{P}}_{n}$ , in the section of the connecting rod.

To evaluate the calculated force, $F_{n}^{max}$ , three measurements of the forces acting on the slide were recorded using a digital force sensor UU. The following values were obtained from the measurements: $F_{n 1}^{max} = 5406 N, F_{n 2}^{max} = 5503 N, F_{n 3}^{max} = 5306 N$ . The average value of the force from equation (27), $F_{nav}^{max} = 5405 N$ , and the mean square deviation, $σ = 1.41 N$ , were obtained. Considering the average value of the forces acting on the slide, determined using strain gages and the digital force sensor UU, the value of $F_{n}^{max}$ was found to be $F_{n}^{max} \approx 5538 N$ .

From experimental research, it was found that in the absence of eccentricity, the nominal punching force was uniformly distributed on the connecting rods.

To determine the reaction on the slide guides of the press, a strain gage was mounted on the slide, as shown in Figure 12(a). The strain gage was perpendicular to the direction of motion. The cross-sectional size of the slide at the measurement point was $S_{t} = 1.05 \cdot 10^{- 3} m^{2}$ .

Figure 12.

(a) Fragment of the strain gage sticker on the slide and (b) experimental graph of the average stress ${\bar{P}}_{t}$ on the slide guides of a crank press.

We measured the stress three times in the cross-section of the slide when punching a hole with a diameter of 5 mm in a steel sheet with a thickness of 0.8 mm, and obtained the following maximum values: P_t1 = 0.229 MPa, P_t2 = 0.251 MPa, and P_t3 = 0.296 MPa. The average value of the maximum stress, ${\bar{P}}_{t}^{max}$ = 0.2587, was determined using equation (27) with a mean square deviation σ = 0.0275 MPa by using equation (28).

Figure 12(b) shows an experimental graph of the average stress, ${\bar{P}}_{t}$ , on the slide, perpendicular to the direction of its movement, of the press when punching a hole with a diameter of 5 mm in a steel sheet with a thickness of 0.8 mm.

The maximum stress during punching was observed to be ${\bar{P}}_{t}^{max} = 0.2587 MPa$ . The cross-sectional area of the slide at the measurement point was $S_{t} = 1.05 \cdot 10^{- 3} m^{2}$ , and the force in this section was equal to $F_{t}^{max} = {\bar{P}}_{t}^{max} \cdot S_{t} \approx 271.64 N$ . This force was considered to be equal to the maximum reaction from the side of the slide guide of the press, $R_{t}^{max}$ , that is, $R_{t}^{max} = F_{t}^{max} = 271.64 N$ .

In comparison to the maximum force on the slide, $F_{n}^{max} \approx 5538 N$ was required to punch a hole (diameter = 5 mm) in the steel sheet (thickness = 0.8 mm); the maximum reaction, $R_{t}^{max} = 271.64 N$ , from the slide rail of the crank press was observed to be 4.91% of the maximum force on the slide. Previous theoretical calculations of the kinetostatics of the crank press based on Stephenson II linkage showed that the maximum value of the reaction on the slide guides was 4.88% of the maximum force on the slide. In the conventional crank press with one connecting rod, the projection of the reaction on the slide guides on the x-axis could be more than 15% of the technological load on the slide.

We measured the crank torque three times, whose graphs are shown in Figure 13; here, the solid blue line denotes the theoretical torque. Experimental torques are represented by the brown dashed, red dotted, and green starry lines. As evident from Figure 13, the theoretical results are significantly consistent with the experimental results.

Figure 13.

Experimental and theoretical results of torque $M_{y}$ .

Moreover, experimental research confirmed that the crank press based on Stephenson II linkage exhibits better characteristics in comparison to those of conventional presses owing to the favorable distribution of forces on the slide, resulting in lower reactions to the slide guides.

Conclusion

Metal forming is an important application in several industries that requires production precision. By improving the metal forming production quality, a new press machine based on the Stephenson II mechanism was considered in this study. Kinetostatic analysis was performed for dynamic analysis. Accordingly, this machine was manufactured and experiments were conducted for its evaluation. The theoretical results were validated by the experimental results. Moreover, an experimental research method was developed for the press machine based on the Stephenson II mechanism; it is based on the digital devices of the ZETSENSOR series with a CAN interface. The information processing algorithm and visualization of the measured signals were performed using the ZETLAB SENSOR software and its subprograms. Investigations on an experimental industrial model of the proposed press machine demonstrated that the maximum reaction from the slide rails of the press was 4.91% of the maximum force on the slide.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (Grant No.: AP09259339).

ORCID iD

Recep Halicioglu

References

Mitsi

Tsiafis

Bouzakis

. Dynamic analysis of six-bar mechanical press for deep drawing. IOP Conf Ser Mater Sci Eng 2017; 174: 012006.

Atul

Babu

. A review on effect of thinning, wrinkling and spring-back on deep drawing process. Proc IMechE, Part B: J Engineering Manufacture 2019; 233: 1011–1036.

Altan

S-I

Gegel

. Metal forming fundamentals and applications. Am Soc Metal 1983; 1983: 353.

Hoffman

. Metal forming handbook. Berlin: Springer Science & Business Media, 1998.

Osakada

Mori

Altan

, et al. Mechanical servo press technology for metal forming. CIRP Annals 2011; 60: 651–672.

Halicioglu

Dulger

Bozdana

. Mechanisms, classifications, and applications of servo presses: a review with comparisons. Proc IMechE, Part B: J Engineering Manufacture 2016; 230: 1177–1194.

Jomartov

Tuleshov

Kuatova

. Dynamic model of a crank press in the process of braking. In: Kuo

C-H

Lin

P-C

Essomba

, et al. (eds) IFToMM international symposium on robotics and mechatronics. Cham: Springer, 2019, pp.141–150.

Wang

X-S

. Analysis of thermally induced machine tool errors of a crank press. Proc IMechE, Part B: J Engineering Manufacture 2012; 226: 1465–1478.

Bocharev

Matvienko

. Mashiny i oborudovaniye kuznechno-shtampovochnogo i liteynogo proizvodstva: [Machines and equipment for press-forging and foundry]. Mashinostroyeniye [Engineering]. Moscow: Mashinostroyeniye, 2005.

10.

Erkaya

Uzmay

. Dynamic analysis of a slider–crank mechanism with eccentric connector and planetary gears. Mech Mach Theory 2007; 42: 393–408.

11.

Erkaya

Uzmay . Experimental investigation of joint clearance effects on the dynamics of a slider-crank mechanism. Multibody Syst Dyn 2010; 24: 81–102.

12.

Anis

. Simulation of slider crank mechanism using ADAMS software. Int J Eng Technol 2012; 12: 108–112.

13.

Sun

Wang

, et al. Dynamic analysis of the double crank mechanism with a 3D translational clearance joint employing a variable stiffness contact force model. Nonlinear Dyn 2020; 99: 1937–1958.

14.

Zhang

Zheng

. Dynamics modeling and simulation of a new nine-bar press with hybrid-driven mechanism. J Mech Sci Technol 2008; 22: 2436–2444.

15.

Zhang

. Seven-bar mechanical press with hybrid-driven mechanism for deep drawing; part 1: kinematics analysis and optimum design. J Mech Sci Technol 2010; 24: 2153–2160.

16.

Zhang

. Seven-bar mechanical press with hybrid-driven mechanism for deep drawing; part 2: dynamic modeling and simulation. J Mech Sci Technol 2010; 24: 2161–2167.

17.

Kütük

Artan

Dülger

. Hybrid seven-bar press mechanism: link optimization and kinetostatic analysis. Tehnički Glasnik 2018; 12: 181–187.

18.

Abdullah

Telegin

. Modeling of dynamic processes of the main executive mechanism of the hot-crank press. Al-Rafidain Eng J 2011; 19: 1–10.

19.

Liu

Cao

Zhang

, et al. Kinematics and dynamics simulation of the Slider-Crank mechanism based on MATLAB/Simulink. In: 2010 international conference on IEEE computer application and system modeling (ICCASM), Taiyuan, China, 22–24 October 2010, P.V9-557–V9-63. New York: IEEE.

20.

Jun

. A study of the dynamic of slider-crank mechanism. J Shanghai Dianji Univ 2006; 9: 24–28.

21.

Khemili

Romdhane

. Dynamic analysis of a flexible slider–crank mechanism with clearance. Eur J Mech A Solids 2008; 27: 882–898.

22.

Choi

Jang

, et al. A study on the optimization of a mechanical press drive. Proc IMechE, Part B: J Engineering Manufacture 2004; 218: 189–196.

23.

Chen

Zhang

. Analysis on dynamic precision degradation mechanism of high-speed precision press. J Phys Conf Ser 2021; 1948: 012073.

24.

Cheng

P-Y

Chen

P-J

Lin

Y-T

. Small mechanical press with double-axis servo system for forming of small metal products. Int J Adv Manuf Technol 2013; 68: 2371–2381.

25.

Qingyu

Baofeng

Jian

. Drawing motion profile planning and optimizing for heavy servo press. Int J Adv Manuf Technol 2013; 69: 2819–2831.

26.

Kaya

. Improving the formability limits of lightweight metal alloy sheet using advanced processes-finite element modeling and experimental validation. Industrial and Systems Engineering, Ohio State University, 2008.

27.

Kaya

. Nonisothermal warm deep drawing of SS304: FE modeling and experiments using servo press. Int J Adv Manuf Technol 2016; 83: 1047–1056.

28.

Halicioglu

Dulger

Bozdana

. Modeling, design, and implementation of a servo press for metal-forming application. Int J Adv Manuf Technol 2017; 91: 2689–2700.

29.

Halicioglu

Dulger

Bozdana

. Improvement of metal forming quality by motion design. Robot Comput Integr Manuf 2018; 51: 112–120.

30.

Gao

Zhao

, et al. Study on dynamic characteristic and forging capacity of the direct drive press with symmetrical toggle booster mechanism driven by TPMLM. Proc IMechE, Part B: J Engineering Manufacture 2021; 235: 1800–1809.

31.

Zhang

Huo

Guo

. A model for nanogrinding based on direct evidence of ground chips of silicon wafers. Sci China Technol Sci 2013; 56: 2099–2108.

32.

Zhang

Huo

Zhang

, et al. Fabrication and size prediction of crystalline nanoparticles of silicon induced by nanogrinding with ultrafine diamond grits. Scr Mater 2012; 67: 657–660.

33.

Zhang

Song

, et al. A novel model for undeformed nanometer chips of soft-brittle HgCdTe films induced by ultrafine diamond grits. Scr Mater 2012; 67: 197–200.

34.

Zhang

Wang

Kang

, et al. Changes in surface layer of silicon wafers from diamond scratching. CIRP Ann Manuf Technol 2015; 64: 349–352.

35.

Zhang

Guo

Wang

, et al. A novel approach of high speed scratching on silicon wafers at nanoscale depths of cut. Sci Rep 2015; 5(1): 16395.

36.

Zhang

Cui

Wang

, et al. A novel approach of mechanical chemical grinding. J Alloys Comp 2017; 726: 514–524.

37.

Zhang

Huang

Wang

, et al. A novel approach of high-performance grinding using developed diamond wheels. Int J Adv Manuf Technol 2017; 91: 3315–3326.

38.

Cui

Zhang

Liu

, et al. Unprecedented piezoresistance coefficient in strained silicon carbide. Nano Lett 2019; 19: 6569–6576.

39.

Jomartov

Tuleshov

Jamalov

, et al. Designing of the Stephenson II six-link linkage actuator for servo mechanical press. Int J Mech Prod Eng Res Dev 2020; 10: 601–612.

40.

Jomartov

Tuleshov

. Vector method for kinetostatic analysis of planar linkages. J Braz Soc Mech Sci Eng 2018; 40: 56.

41.

Bocharov

. Kuznechno-shtampovochnoe oborudovanie. M.: Izdatel’skij centr «Akademija», 2008 (in Russian).

42.

ZETLAB company [electronic resource].