Design and characterization of an assembly to obtain a linkage pivot by crimping process

– The purpose of this research is to design and test a linkage pivot assembled by metal forming process. The assembly is obtained by crimping a tubular component onto a cylindrical grooved component using an experimental instrumented device. The quality of the linkage pivot is evaluated by a pullout test which measures the force required to break or dismantle the assembly. The study is focused on analysing the eﬀect of the main process parameter (i.e. the crimping depth) and geometrical parameters (i.e. the tubular component thickness and the groove radius). For one set of geometrical parameters, an appropriate crimping depth leading to the maximum assembly strength and assembly stiﬀness is determined. The study of the geometrical parameters shows that the tubular component thickness and the groove radius do not aﬀect much the assembly strength. However, the tubular component thickness aﬀects considerably the forming load, the assembly stiﬀness and the failure mode. According to the obtained results, one set of parameters that meets industrial requirements is selected to design the linkage pivot.


Introduction
In recent years, a growing interest in mechanical assembly operations is set to reduce additional components such as screws, pegs, rivets, pins, spurs, bolts and nuts.Consequently, assemblies obtained by metal forming processes have been widely used in mechanical design [1,2].For several applications, clinching and hemming are the possible alternatives [3,4].Particularly for tubular components, crimping is the most popular of the metal forming processes used to obtain a mechanical assembly such as the fixed joint.
In the literature, several researchers have done much work on joining tubular components by crimping process.Shirgaokar et al. [5] studied the effect of various process variables to optimize the process so that the effect of springback could be reduced and the assembly quality, as indicated by the pullout force, could be improved.By another work, Shirgaokar et al. [6] investigated the crimping process using a polyurethane tool and hydraulic pressure to enhance the performance of the assembly by determining the optimum process and geometrical parameters.In these two studies, the analysed parameters are the geometry, alignment and stroke of the crimper, friction, material properties and also manufacturing errors.Recently, Fresnel et al. [7] studied the structural response of the airbag inflator tubes from the crimping to destructive burst test stages.It was found that the numerical damage maps obtained after the crimping process and during the burst tests are in good agreement with the experimental data.On the other hand, Park et al. [8] performed finite element simulations and strength tests in order to design an axial joint and a torque joint made by the electromagnetic forming which is described by Psyk et al. [9].The authors concluded that multiple grooves with different radii or depths should be combined in the design of the crimped region to manufacture a link according to the desired strength.
The present study deals with obtaining an assembly between two cylindrical rods without the use of additional components.The assembly is obtained by crimping the end of a tubular rod onto the end of a grooved rod.In this work, the aim of the crimping process is not to obtain a fixed joint as the case of the major previous works, but rather to obtain a revolute joint.Crimping process is performed by means of an experimental instrumented device in order to determine the forming load.To make sure of the final performance and the safety of the linkage, the maximum pullout force during a destructive testing phase is analysed.Several assemblies with various sets of process and geometrical parameters are tested to find the appropriate values that meet some performance and industrial requirements.

Assembly components
To obtain an assembly by crimping, a female component and a male component were designed as shown in Figure 1.The female component has an inner diameter of φ i , a wall thickness of t and an axial length of l 1 as shown in Figure 1a.The male component, designed with a groove, has a φ e outer diameter and a l 2 axial length.The geometrical parameters of the groove are the groove width W g , the groove depth D g and the groove radius R g .
The boring of the female component which has the inner diameter φ i and the male component which has the outer diameter φ e were designed with the same nominal diameter φ n .With a view to obtain a linkage pivot, they were designed to fit together with a clearance value set to 0.1 mm.
From an economical point of view, the increase of the groove width W g and the groove depth D g is needless.The increase of these two parameters causes the increase of manufacturing cost.In this work, W g and D g were minimized and were set to their lower limits as indicated in Table 1.Accordingly, the effect of only two geometrical parameters (t and R g ) was studied, while keeping constant the other parameters.The nomenclature of the geometrical parameters and the considered values are summarized in Table 1.
A commercial brass rod was used as the component linkage material.Uniaxial tensile test was used to describe the stress-strain relationship.The tensile tests were carried out on bone-shaped specimens with a diameter of 6 mm and a gauge length of 50 mm.The tests were performed under displacement control at a constant rate of 5 mm.min −1 .The true stress was calculated by the ratio of the load over the current section of the sample.The current section was determined from the initial section of the sample by assuming both isochoric plastic deformation and a homogeneous distribution of strain along the gauge length of the sample.The true strain is equal to the natural logarithm of the ratio of length at any instant to original length.Figure 2 shows the obtained stress-strain curve.The mechanical properties determined from these tests are shown in Table 2.
To manufacture the female and male components, two parts were cut from a commercial brass cylindrical rod with a diameter of φ = 10 mm.Only one end of each part was machined using a computerized numerical control (CNC) lathe.The tubular part of the female component   was manufactured by drilling operation preceded by a center-drilling operation to obtain a hole precisely centered in the cylindrical rod.The male component was machined by turning and grooving operations.

Assembly procedure
The technique used to assemble the male and female components by crimping consists of pushing partially the tubular part into the groove as shown in Figure 3.This operation was performed by applying firstly a local deformation on the female component using a narrow roller tool and then rotating the female component so as to deform the workpiece along a circular path.To achieve the desired shape, these actions were repeated until reaching the required value of the crimping depth P c as shown in Figure 3.To prevent components bending during forming, a cylinder was mounted in the opposite side of the roller tool.Note that, both the roller tool and the opposite cylinder were free to rotate about their axis.In addition to t and R g , the crimping depth P c was counted as a process parameter to be also studied.The considered values of P c are 0.6, 0.8, 1 and 1.2.
A specific instrumented device was manufactured for crimping as shown in Figure 4.This device was equipped with a displacement gauge and a load cell to measure the roller tool displacement p and the opposite cylinder reaction R, respectively.The experimental procedure of crimping was performed as follows.Firstly, a good alignment between the roller tool and the groove was set.Secondly, the male component was inserted into the female component until its shoulder.Thirdly, a local deformation of the female component was induced by applying a displacement increment Δp to the roller tool by a leadscrew that induced also a reaction force increment ΔR.This stage was performed under reaction force control at a constant increment ΔR = 0.1 kN.Fourthly, a single rotation was applied to the female component by a handwheel to deform the workpiece along a circular path.The third and the forth stages were repeated in the same manner until the imposed displacement reached progressively the required value of the crimping depth P c .The values of P c  were set in such a way to not constraint completely the assembly.Figure 4 shows a typical example of the manufactured components, the experimental device of crimping and an actual half section view of the obtained assembly.

Pullout test
To analyse the maximum assembly strength after crimping, the assembly was subjected to a pullout test.
The male component was totally embedded while an uniaxial tension was applied to the female component until failure as shown in Figure 1b.This destructive test was performed to check the minimum limit value stipulated by a local industry aimed at producing a strong assembly that bears heavy external loading.a constant low rate of 5 mm.min −1 .The outputs of the displacement gauge and the load cell were continuously stored in a data acquisition system.

Process validation
After crimping, it was usually found that the female part is free to rotate around the male part.Thus, as excepted, a linkage pivot and not a fixed joint was obtained in all cases.It was also found that the desired geometry is achieved without defects.To illustrate the final geometry of the assembly, an actual half section view of a typical finished product is presented in Figure 4c.
Moreover, the assembly procedure was inspected by analysing the relationship between the opposite cylinder reaction R and the roller tool displacement p.This relationship was obtained by measuring the values of R and p after applying an increment ΔR and before rotating the female component to deform the workpiece along a circular path.Figure 5 shows a typical relationship between R and p for t = 1.To ensure that the crimping operation is repeatable, some curves are superimposed in Figure 5 for different samples designed, manufactured and crimped in the same conditions.It can be seen that the four superimposed curves are very close to each other that proves the good repeatability of the assembly procedure.From an industrial point of view, this experimental curve can be also used to determine the maximum forming load that seems to be advantageous in the tool design.
After the validation of the process, attention is paid to the effect of the process and geometrical parameters in order to determine the appropriate linkage design leading to the maximum pullout force.

Effect of design parameters
The considered parameters are the process parameter (P c ) and the geometrical parameters (t and R g ).A first study is focused on analysing the effect of the crimping depth P c for a constant preselected values of the geometrical parameters (i.e.t = 1 mm and R g = 0 mm).Based on this first study, an appropriate value of P c is determined.Then, a second study is focused on analysing the effect of the geometrical parameters for the determined value of P c .

Effect of process parameter (P c )
To investigate the effect of the process parameter P c , four values of this parameter are considered (i.e.0.6, 0.8, 1 and 1.2 mm), while the geometrical parameters are kept constant.A value of φ n equal to 8 mm is selected to obtain a wall thickness t of about the unity.This value is chosen according to industrial recommendations.A value of R g equal to 0 mm is selected to reduce the manufacturing cost of the male component.Sectional views of typical finished products are presented in Figure 6 for the different considered values of P c .
To study the effect of P c on the assembly strength after crimping, the load-displacement curve obtained from the pullout test is investigated.Before that, the repeatability of the pullout test is inspected.Figure 7 shows the load-displacement curves resulted from three trials of a pullout test for an assembly with P c equal to 1 mm.It can be seen that a good repeatability of the values is obtained.The shapes of the curves are similar.That is also observed in the other cases.However, some dispersions are observed in the maximum force F max .In all cases, the dispersion does not exceed 20% of the mean value.
To illustrate the effect of P c on the load-displacement curve, four typical curves corresponding to P c equal to 0.6, 0.8, 1 and 1.2 mm are plotted in Figure 8.It is clearly seen that P c affects considerably the relationship between load and displacement in the pullout test.The assembly stiffness which corresponds to the slope at the beginning of the curve is very low for the lower values of P c (i.e.0.6 mm).This result indicates that in this case the crimping is at a primary stage.From P c equal to 0.8 mm, the stiffness increases notably and becomes almost constant.
After reaching the maximum force, the assembly fails.For lower values of P c (i.e.0.6 mm), the male component is pulled from the female component without crack as shown in Figure 9a.However, for the other cases, an axial crack is usually observed on the outer surface of the female part as shown in Figure 9b.
To study the effect of P c on the maximum assembly strength, the variation of F max versus P c is plotted in Figure 10.It can be seen that as P c increases F max increases.From a value of P c equal to 1 mm, the effect of P c on the resistance of the assembly becomes no significant.Indeed, F max increases by about 2.7% when increasing P c from 1 mm to 1.2 mm.Accordingly, a value of P c equal to 1 mm is chosen since a higher value than the unity does not affect much the maximum assembly strength.

Effect of geometrical parameters
It is obvious that the reduction of the wall thickness t decreases the forming load and thus makes easier the crimping process.It also well known that a value of R g equal to zero leads to a geometrical singularity that is undesirable in most industrial practices.Therefore, this section will focus on studying the effect of the reduction   of the wall thickness t and the effect of changing the value of the groove radius R g .In other words, the aim is to prove or disapprove the preselected values of geometrical parameters (i.e.t = 1 mm and R g = 0 mm).
Firstly, an assembly was designed with a wall thickness t equal to 0.75 mm.To obtain such assembly, samples were manufactured with φ n equal to 8.5 mm.The other parameters were kept constant (i.e.P c equal to the unity and R g equal to zero).To evaluate the effect of the reduction of the wall thickness t on the forming load, a typical curve of the opposite cylinder reaction R versus the roller tool displacement p for t equal to 0.75 mm is superimposed in Figure 5.As excepted, it can be seen that the reduction of the wall thickness decreases considerably the forming load.Namely, to obtain an assembly with P c equal to 1 mm, the forming load decreases by about 30% when the value of t decreases from 1 mm to 0.75 mm.
To illustrate the effect of the reduction of t on the pullout test results, Figure 11 shows the load-displacement curves for t = 0.75 mm and t = 1 mm.In addition to the good repeatability of the curves observed for t = 0.75 mm, it can be seen that t does not affect significantly the maximum strength (i.e.F max ).However, the assembly stiffness decreases as t decreases.It can be also noted that, for the case of t equal to 0.75 mm, a radial crack followed by a radial brutal rupture is observed as shown in Figure 9c.According to the above results, it can be concluded that the value of t = 1 mm can be considered as the best suited to obtain a stiffer assembly and to avoid a brutal rupture of the assembly.However, a value of t = 0.75 mm is more appropriate when a reduction of forming load is desired.
On the other hand, several samples were manufactured with different values of R g (i.e.0, 0.2, 0.5 and 1 mm).Both P c and t were set equal to 1 mm.After performing the pullout test, the variation of F max with R g is plotted in Figure 12.It can be seen that R g affects slightly F max .Indeed, F max decreases by about 7% when R g increases from 0 mm to 1 mm.It is also found that whatever the value of R g , the assembly fails by an axial crack.It can be concluded that a value of R g equal to 0 mm can be considered when a maximum assembly strength and a reduction of manufacturing cost are required.However, an appropriate value of R g can be determined more accurately by testing the assembly under a rotary motion combined with an axial loading.

Conclusion
An assembly is designed to obtain a linkage pivot by crimping a tubular component onto a cylindrical grooved component.The assembly is manufactured by an experimental crimping device using a narrow roller tool.The analyse of the forming load during the crimping process and the final shape leads to the validation of the assembly design and processing.This validation shows that a typical revolute joint can be obtained successfully when a reduced number of components is needed.
The assembly is characterized by the means of a pullout test carried out until failure.The analysis of the results of the pullout test allows to choice the appropriate process and geometrical parameters leading to the maximum assembly strength and stiffness as well as avoiding the brutal rupture.An appropriate value of the process parameter (i.e.crimping depth) is determined for preselected geometrical parameters that fulfill certain industrial requirements notably the manufacturing cost.The preselected values of geometrical parameters are proved by studying the effect of a reduction of the wall thickness and the effect of changing the value of the groove radius.
Finally, it seems interesting to optimize the process and geometrical parameters by the means of a finite element model and a further characterization based on applying a rotary motion combined with an axial loading to the assembly.This will be done in future works.

Fig. 5 .
Fig. 5.The opposite cylinder reaction versus the roller tool displacement.

Fig. 8 .
Fig. 8.The pullout force versus the displacement for different values of Pc.

Fig. 12 .
Fig. 12. Bar graph of the maximum pullout force Fmax versus the groove radius Rg.

Table 1 .
Geometrical parameters of the assembly.

Table 2 .
Mechanical properties of the brass rod.