1. Introduction

2. Experimental Measurements

3. Results and Discussions

3.1. Forming Process of the Clinch-Rivet Joint

During the clinch-riveting process the forming force was measured and recorded for each joint combination seven times. For determining the mean values ($\overline{x_n}$), standard deviation ($s$) and coefficient of variation ($c_v$) five recorded values were taken into account. Calculated parameters (Equations (1)–(4)) are presented in Table 4. For each sheet thickness and width forming force-displacement diagrams are presented in Figure 11.

Figure 11. The force-displacement diagrams of clinch-riveting process for one sample combination (b=20 mm, t=1mm) – diagrams move by each other of 0.5mm.

Figure 11. The force-displacement diagrams of clinch-riveting process for one sample combination (b=20 mm, t=1mm) – diagrams move by each other of 0.5mm.

$$\overline{x_n}=\frac{\sum _{i=1}^n{x}_i}{n}$$

(1)

$$s=\sqrt{\frac{1}{n-1}·\sum _{i=1}^n{\left(x_i-\overline{x_n}\right)}^2}$$

(2)

$$c_v=\frac{s}{\overline{x_n}}·100\%$$

(3)

where:

$\overline{x_n}$ – mean values of forming force (kN),

$x_i$ – simple values of forming force (kN),

$n$ – number of measurements,

$s$ – standard deviation (kN),

$c_v$ – coefficient of variation (%).

$$E_f=\underset{s=0}{\overset{s_{Fmax}}{\int }}{F}_f·ds$$

(4)

where:

$E_f$ – forming energy (J),

$s$ – displacement (mm),

$s_{Fmax}$ – displacement for maximum forming force (mm),

$F_f$ – forming force (kN),

Table 4. Mean values of forming force and statistical parameters.

Table 4. Mean values of forming force and statistical parameters.

Sample nomenclature	Sheet width b, [mm]	Sheet thickness t, [mm]	Forming force Ff, [kN]	Standard deviation s, [kN]	Coefficient of variation cv, [%]	Forming energy Ef, [J]
1-2	20	1	85.18	0.398	0.467	232
1-3	30	1	87.35	0.397	0.454	236
1-4	40	1	87.77	0.426	0.485	237
2-2	20	1.5	72.32	0.398	0.550	210
2-3	30	1.5	74.57	0.356	0.477	218
2-4	40	1.5	74.29	0.416	0.560	213

Figure 12. The comparison of the force-displacement diagrams of clinch-riveting process.

Figure 12. The comparison of the force-displacement diagrams of clinch-riveting process.

Changing the distance of the joint from the sheet edge from 20 mm to 10 mm caused the sheet material to flow more freely in the radial direction outside the die, which resulted in the lowering the force necessary to form the joint by 2.95% for sheets with a thickness of 1 mm, and by 2.65% for sheets with a thickness 1.5mm.

By reducing the distance of the joint from the edge of the sheet, the forming force and, consequently, the demand for forming energy can be reduced. Another way to reduce the energy absorption of the joint formation process is to use a rivet of a different hardness [30], use a tubular rivet [27], change the insertion depth of the rivet [56].

3.3. Sheet Deformation Measurement after Joining Process

Based on the permanent elements of the die - the flat surface of the die bottom, the groove on the die bottom and the side surface of the sheets, coordinate systems were created for all joints. The surface and torus fitting parameters are presented in Table 6.

In the area close to the rivet the measurement system didn’t ensure appropriate values. For the position of the punch system at the level of the upper surface of the sheet, as recommended by TOX manufacturer, the joints made of 1 mm sheet thickness at the point contact with the punch had a larger size. This was due to the greater pressing of the rivet – the distance between die and punch was smaller than for 1.5 mm sheet thicknesses. In addition, the Rmin value of 3.75 mm was selected to eliminate defects on the mesh after the process of polygonization of measurement data, presented in Figure 14 below as sub-points 1 to 3 (places where light reflections occurred resulting in the lack of the scanned area or representation deviating from reality) in connection with adopted measurement method.

For determine the sheet deformation, after clinch riveting process, all joint were scanned by using ATOS scanner. Deformation of lower and upper sheet in the area of joint were analyzed on the base of 3d model obtained from measurement. The part of the samples in the equipment grip area was didn’t take into account for results analyzing. In Figure 15 the views of 3D model from lower and upper sheet were presented.

For each samples the shape of the deformation, in the area close to the rivet, reproduces the shape of the die with movable segments. For fixed segments of the die, from rivet side close to the rivet, the sheet deformation along the measurement angle α equal 45°, 135°, 225° and 315° was bigger than for angles 0°, 90°, 180° and 270°. The movement of die sliding element caused that the more sheet material can flow in the space between fixed part of the die and movable segments. Hence the sheet deformation in this places is smaller than for die fixed element – sheet material is less compressed. Deformations of the sheet, with the increase of the distance between rivet axis and measuring point, were changing to circular shape. By increasing the sheet width the area of upper and lower sheet deformation lower than ±0.1 mm significantly decrease. The material close to the sheet edges, for 40 mm sheet width, didn’t allow to change the sheet dimensions.

For the sheets thickness 1.5 mm and width 20 mm the bulk (rivet pressed in the sheets caused the sheet material flow) of the sheet appear along the 180° angle - Figure 16b. For lower sheet dimension between rivet axis and sheet edge (angle 180°) increase of 0.11 mm and upper sheet increase of 0.09 mm – the linearity deviation. The sheet width at the sheet corners was also changed form 20 mm to 20.34 for lower sheet and 20.19 for upper sheet. For the 90° and 270° angles the sheet material was partially blocked by sheet material along to the measurement grip area – the sample was changes to 20.34 for lower sheet and 20.19 for upper sheet. The material of the sheet along the 0° angle didn’t allow to push outside the sheet material. For other sheet width (30, 40 mm) and the sheet thickness 1.5 mm and for all samples of 1.00 mm the change of width observed was on the 0.03 mm. The linearity deviation of the sheet was presented in Table 7. For the sheet thickness 1.0 mm and 1.5 mm and width 40 mm the measured deformations were presented in Table 8. The measurement points coordinates for 3D models for all joints were presented in Figure 7. The origin point of the axis system was always in the center point of the die bottom. The linearity deviations for other sheet width and thickness was at similar level – about 0.02 mm. So the sheet dimension after joining process significantly change only for sheet thickens 20 mm and thickness of 1.0 mm.

For all joint, based on the 3d models, the sheet profile after clinch-riveting joining process were determined along the angles α=0°, 45°, 90°, 180°, 225° and 270° – Figure 17.

For a sheets width of 20 mm (Figure 18 – red line) and a thickness of 1.5, it can be seen that the deformation of the upper and lower sheets in the area of the rivet is greater than for the widths of 30 mm (Figure 18 – green line) and 40 mm (Figure 18 – black line). The smaller amount of material around the joint causes the sheet to deform more freely than in the case of wider sheet samples.

Figure 17. Profiles of the sheet with 1.5 mm thickness (α=45°): a) half of the cross-section, b) 10x zoom in y axis of A area.

Figure 17. Profiles of the sheet with 1.5 mm thickness (α=45°): a) half of the cross-section, b) 10x zoom in y axis of A area.

Figure 18. Profiles of the sheet with 1.0 mm thickness (α =45°): a) half of the cross-section, b) 10x zoom in y axis of A area.

Figure 18. Profiles of the sheet with 1.0 mm thickness (α =45°): a) half of the cross-section, b) 10x zoom in y axis of A area.

For sheets with a thickness of 1 mm, the blank holder causes that for smaller widths, the sheet material around it is pressed deeper – Figure 18.

Changing the thickness of the joined sheets from 1.0 mm (Figure 19 – red line) to 1.5 mm (Figure 19 – green line) with the same geometry of the forming die and the rivet causes that more material fills the same space in the die, which causes greater deformations in the joint area. For the angle α=225° the deformation in higher due to less stiffness of the sheet than for angle α=45°.

Figure 19. Profiles of the sheet with 20 mm width and angle α=45° and α=225° (sheet thickness 1.5 mm - green line and 1 mm - red line).

Figure 19. Profiles of the sheet with 20 mm width and angle α=45° and α=225° (sheet thickness 1.5 mm - green line and 1 mm - red line).

The range and size of sheet deformation for the angle α=0° and α =180° is almost identical for all tested variants. Slight differences are visible for the width of 20 mm and the thickness of 1.5mm. For all angles the course of sheet deformation were the same. There were slight differences in values of deformation caused by the sheet material flow during the joint formation. In Figure 20 the joint profile in the die groove (green line) and profile in the space of movable segments (red line) were compared.

Figure 20. Profiles of the sheet with 20 mm width (α=0° - green line and α=45° - red line).

Figure 20. Profiles of the sheet with 20 mm width (α=0° - green line and α=45° - red line).

4. Conclusions

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