Rotating bending machine for high cycle fatigue testing

D. Brandolisio*, G. Poelman, G. De Corte, J. Symynck, M. Juwet, F. De Bal

Department of mechanical engineering, KaHo Technological University Sint-Lieven Ghent, Gebroeders Desmetstraat 1, B-9000 Gent

March 26, 2009

KaHo Sint Lieven - Departement Gent

Technologiecampus GentGebroeders Desmetstraat 1, B-9000 GENT*Corresponding author: daniele.brandolisio@gmail.com

Abstract

The aim of the project is to develop and build an innovative rotating bending (RB) fatigue testing machine. This new apparatus has to cover most of the commercial available machines in testing possibilities, due to its wide range in force, rotation speed and dimensional flexibility. Furthermore it needs to have an open and versatile acquisition for measurements, with the synchronisation ability for a controllable bending moment.

Keywords: rotating bending fatigue, Zwick/Roell Z020, Zwick/Roell testXpert II

1 IntroductionMaterial testing is fundamental for the production and construction sector. As the well-known relation time=money is a common rule, sometimes it's requested to speed up the fatigue's tests. To do this, servo-hydraulic machines are the fastest solution. Because of the extremely high price of these, SME (Small and Medium Enterprises) are obligated to adopt electromechanical systems, more affordable but with the disadvantage of a slower response; often this class of companies has to ask for external support. The aim of this project, beside providing the laboratory with an additional method for fatigue's testing, which gives an alternative way of investigation of material's behaviour under fatigue, is to satisfy the time-saving demand: the solution is proposed in the combination of the rotational motion with the

Zwick/Roell electromechanical actuator (already existing in the laboratory). After an accurate study of the fatigue theory, the next step is the realisation of a general setup. This concerns the study of all the components involved, starting with the specimen's geometry and behavior under test. In detail, the clamping system for the specimen, how the load should be applied, the rotation's transmission, the main frame, plus conventional parts such as bearings and supports, need particular attention: the study of them is fundamental to verify the final feasibility, plus the identification and solution of weak points.The result of the study brings to the real design: with a 3D modeling software all the parts are drawn, taking into account the method of their construction. The subsequent physical realization is carried out. An additional attention is given to the control system: with the TestXpert software, coupled to

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the Zwick/Roell Z020 actuator, and a control device for the motor drive, it is possible to regulate the rotation speed and the intensity of the load; the result of this controlled action is a precise, accurate and valid test.

2 Bending fatigue's theory

2.1 DefinitionThe rotating bending (RB) fatigue test consists in the application of a known constant bending stress (due to a bending moment) to a round sample of the material, combined with the rotation of the sample around the bending stress axis until its failure.

2.2 Main formulaeThe calculation of the bending stress is given by the equation:

y =MI

y

where M is the bending moment, J is the surface moment of inertia (since we're talking about round specimens, this is referred to a circular area), y is the distance between the center and a generic point. The maximum distance is situated on the surface, and correspond to the dimension of the radius, as seen in the figure 2.1.

I=d 4

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Figure 2.1: I formula and cross-section.

2.3 Validation of this methodDifferent methods concerning fatigue's bending testing are compared1 (see figure 2.2):

– the cantilever bending test, which consist in the application of a variable load on an extreme edge of the specimen, while the other edge is embedded;

– the 4 points bending test, where the specimen is bended by two fluctuating loads of the same magnitude applied at the same distance from the two supports;

– the 4 points RB test which has the same configuration of the 4 points bending, but the load applied is static and at the same time the specimen is in rotation;

1On the difference of fatigue strengths from rotating bending, four-point bending, and cantilever bending tests – T. Hassa, Z. Liu

– the 2 points RB test, with the cantilever configuration but static load and rotation.

(a) (b)

constant moment triangular moment

(c) (d)

Figure 2.2: (a) cantilever bending, (b) 4 points bending, (c) 4 points RB and (d) 2 points RB with the respective moments'

diagrams.

Since the failure of the specimen starts from the weakest point, situated in proximity of the surface, we obtain:

– in the RB, because of the rotation, under bending all the portion of material close to the surface of the specimen is tested under the maximum stress;

– in the other tests, only the top and the bottom points of the surface are stressed during the alternate bending.

The conclusion is that in RB test the weakest point is always individuated, while in the other tests it may or may not be contained in the portion of material involved (figure 2.3).As a result, we can underline several advantages in RB:

– more accuracy in the results: the weakest point is always determinate, so more fidelity in investigating the material's behaviour

– less scattering in the results, derived from a coherent examination (weak point on surface)

– less number of specimens for the test to reach reliable results

– in particular, in the 4 points RB the bending moment is constant inside all the length of the specimen; hence a less complex shape of it to assure an homogeneous investigation.

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Figure 2.3: RB and other bending tests weakest point zone.

3 Design of the RB machine

3.1 Four points RB machine's conceptFigure 2.4 shows the basic scheme of a four points RB machine. The main elements are:

– motor drive, which gives the rotation;– two main bearings, which create the two

supports;– two load bearings, where the load is applied.

Figure 2.4: RB machine main scheme.

3.2 Main componentsParticular attention is spent for several elements' choice.

Clamping system It permits the installation of the specimen in the machine. It must be precise (because of the rotation) and adaptable to different dimensions of the specimen, both in the diameter and in the length. As a result, the choice is for collets in figure 3.1. These are used in the milling machines for the tool's clamping. A high precision and resistance are guaranteed, plus they can adapt different diameters. In the end, they're also not expensive therefore replaceable after each test for a better precision and stability.

Figure 3.1: collet clamping system.

Application of the loadIn the reality, an element that works under fatigue's conditions is subjected to an alternate and non-constant load. For laboratory testing, we need to transform this random condition in a more readable and repeatable situation.The idea is the application of a variable and controlled load, this to obtain an automatic variation of the load amplitude between the blocks of cycles, and to give the ability to generate overload and underload's conditions.The choice is the use of the Zwick/Roell Z020 electromechanical actuator (figure 3.2). This is able to guarantee a load which is dynamically adjustable and controlled (by the testXpert software).

Figure 3.2: Zwick/Roell Z020.

3.3 Spreadsheets and calculationsIt is fundamental to solve several basic equations for determining the right dimensions of the different elements that characterize the entire apparatus. With the use of spreadsheets it is possible to manipulate the main fomulae of the bending moment and stress, giving in input the dimensions of the specimen (cross-section and length). Thus to find its theoretical curvature under bending, the axial displacement (figure 3.3) and, more important, the definition of the optimum moment's arm (figure 3.4). Since the goal is to test different materials (with dissimilar mechanical properties), it has been necessary to define an optimum range

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of lengths for the arm to satify all the cases. To obtain this, the starting point was the data of the load cell installed in the actuator, which is the responsible of the setting and control of the amount of load. In particular this load cell can reach 20 kN, and its accuracy is guaranteed from 0.2% of the maximum load, at 40 N. Beside this wide variation, the choice of three different positions for the load's application, which define the arms of the moment, allows to cover a large range of bending moments (and subsequently bending stresses) required for testing different classes of materials.

Figure 3.3: curvature and displacement's calculations.

Figure 3.4: optimum moment's arm.

The dimensions of the critical cross-sections of the main shafts under load are also found applying the fatigue's theory(figure 3.5).

Figure 3.5: shafts' critical cross-sections.

3.4 3D project's drawingsWith the 3D modelling software SolidWorks it is possible to realise the model of the RB machine, from every single component until the final assembly. Here are shown examples of views of the designed machine.

Figure 3.6: frontal view setup with Zwick/Roell actuator.

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specimen dataC40 Ti

210000 120000 [MPa]200 100 [mm]

20 10 [mm]7853,98 490,87 [mm^4]

105 35 [mm]4000 3300 [N]

40 40 [mm]

210000 57750267 588 [MPa]

curvature of specimen 0,000127324 0,000980394 [1/mm]7853,98 1020,00 [mm]

0,012732739 0,049039376 [ ]0,729532234 2,809749251 [°]

200,005404191 100,040092254 [mm]0,005404191 0,040092254 [mm]

112,361025271 53,150729064 [mm]105,500784494 36,918712276 [mm]

0,500784494 1,918712276 [mm]

1001,57 3165,88268,66 620,48 [MPa]

4 points rotating bending fatigue machine

material nameE-modulusparallel lengthdiameter

surface moment of inertia

test environmentOriginal moment's armbending forceheight load-support

constant moment on specimen [Nmm]sigma_max on specimen surface

curvature of specimen (radius)

bending angle (Thèta)bending angle (Thèta)

specimen arc lengthaxial displacement

distance load-supportFinal moment's arm

Variation moment's arm

Variation of moment [Nmm]Final sigma on surface

Definition of the optimum moment's arm

load cell grade 1 (= reliability from 0.2% of capacity)

Fmax 20000 [N] clamp section max 26 [mm]Fmin (0.2%) 40 [N] clamp section min 4 [mm]

diameter_specimen 20 [mm]

@ Fmax, sigma_max, section_maxM_max 1725519,76 [Nmm] arm_min 172,55 [mm]

arm_min_adj 105 [mm]

@ Fmax, arm_min_adj, section_maxsigma_max_obt 608,51 [MPa]

@ Fmin, arm_min_adj, diameter_specimenM_min 2100 [Nmm] sigma_min_obt 2,67 [MPa] lower stress

@ sigma_min, Fmin, arm_min_adjdiameter_specimen obt 7,53 [mm]

@ Fmax, arm_min_adj, diameter_specimensigma_obt 1336,9 [MPa] upper stress

Figure 3.7: general view setup with Zwick/Roell actuator.

Figure 3.8: frontal section view of the machine.

Figure 3.9: section view of a part of machine.

Figure 3.10: clamping system and bearing detail view.

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Load bearingsIf we bend a beam, we obtain an axial displacement along the bending axis. If the beam is embedded at the extreme edges, the result is an axial stress. Since we want to test only in pure bending condition, we need to avoid this axial stress. Thus, the axial displacement is guaranteed by the shifting of the bearings inside the housing. To assure a perfect alignment of the shafts with the specimen, spherical bearings are used.

Figure 3.11: load bearing detail section view.

Support bearingsWhen applying the load, the specimen is subjected (even if small) of a curvature. To allow this, ball bearings are used assupport points. The double row type guarantees the appropriate static load strength.

Figure 3.12: support bearing detail section view.

Figure 3.12: support bearing detail section view.

4 Control of the machineAs mentioned before, the magnitude of the load is given by the electromechanical actuator. This one is controlled by the Zwick/Roell TestXpert II software: since the moment's arm is known, it is easy to control the wanted applied load, and then find the moment for the test.Also the electrical motor must be controlled, thus to set the rotational speed, which is important for the definition of the “speed” of the test: taking into account different factors and considerations, rising the rotation, it is possible to accelerate the experiment, reaching for instance the rupture of the specimen in less time.The revolution counting can be achieved with precision by setting the rotational speed and knowing the time, this to obtain the exact number of cycles at which the specimen reaches the rupture (in other words, to detect the specimen's life). As shown in the 3D sketches, in unload conditions the length of the moment's arm is exactly defined. When the load is applied, due to the turning of the two housings around the support points, the arm is subjected to a small variation, which induces an error in the calculation of the bending moment. This is compensated thanks to the capability to adjust the load at this variation. The bending moment is then constant and well defined. The sketch below shows the entire control system of the apparatus.

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Figure 4.1: control scheme of the system.

4.1 InvestigationsThis apparatus enables the determination of the Wohler's diagram, which describes the fatigue's behaviour of the tested material plotting the applied stress versus the number of cycles. Since the goal is to spot the failure of the specimen, and thus observing the amount of cycles reached to trace the diagram, a particular method must be realised.Several different investigations and studies can be also attained with this machine.

One of these could be the study of the crack growth2 and propagation using the setup shown in figure 4.1 which involves other particular devices such a camera, a shaft encoder and a PC.

Figure 4.2: hypothetical experimental setup.

2A comparison of two experimental methods for assessing the influence of initial defects on fatigue life - H.-P. Gänser, I. Gódor, W. Eichlseder, R. Pippan, R. Ofner, R. Vollgger

5 ConclusionsThe RB test is reliable for determining the fatigue's behaviour of the materials. In particular this project, with the use of the electromechanical actuator, is able to give high precision (due to the controlled loading), time-saving tests for the companies' requests and possibilities to carry out studies and researches between the interaction of different factors. The prospect of development in RB fatigue testing machines is open thanks to the recent technologies.

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