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To cite this version :

Olabanji, Olayinka and Mpofu, Khumbulani and Battaïa, Olga

Design, simulation and experimental investigation of a novel reconfigurable

assembly fixture for press brakes. (2016) The International Journal of Advanced

Manufacturing Technology, 82 (1). pp. 663-679. ISSN 0268-3768

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Design, simulation and experimental investigation

of a novel reconfigurable assembly fixture for press brakes

Olayinka Olabanji1&Khumbulani Mpofu1 &Olga Battaïa2

Abstract A reconfigurable assembly fixture is a major and im-portant component of a reconfigurable assembly system. It is required for the assembly of a variety of press brake models in order to reduce the assembly time and overall production time. The stages and requirements for the design of an assembly fixture and understanding of the assembly process for press brake models were used to design a reconfigurable assembly fixture. A detailed design analysis of parts of the fixture and the hydraulic system is considered and presented in this article. The stress and displacement analysis of the parts is executed using Solidworks express simulation. The parameters of the hydraulic components were determined from force requirements, and the hydraulic sys-tem was modelled physically using Matlab Simscape hydraulics. The response of the hydraulic system was obtained for each actuator in the system in order to depict the output of the actua-tors from the spool displacement of the valves. Stress analysis conducted on parts of the fixture showed that it can withstand maximum stresses that are lesser than the yield strength of the material used for the part. It was also established that synchroni-zation of hydraulic actuators can best be achieved by the use of a sine input to the electrohydraulic valve. An experimental inves-tigation was done using FESTO hydraulic test bench in order to observe the synchronized extension and retraction of the hydrau-lic actuators. The simulation of the hydrauhydrau-lic system, electric

system and the programmable logic controller was prepared using automation studio. The design is envisaged to provide the industries with relevant information on accurate location and gripping of press brake frames rather than turning and repo-sitioning of the frame in order to fit other parts during assembly. The article provides relevant information on the design analysis of a reconfigurable assembly fixture for press brakes which is novel because articles on reconfigurable assembly fixtures have not considered its application to press brake assembly.

Keywords Design . Reconfigurable assembly fixture . Assembly systems . Manufacturing . Hydraulic system . Stress analysis

1 Introduction

Manufacturers of press brakes face the problem of inconsistent demand in terms of model varieties needed by the customer, and as such, the question arises as to which system is needed in order to reduce non-recurring costs, reduce time to market and improve capacity and flexibility of the manufacturing equipment [1–3]. The design of an assembly fixture is an integral part of process planning for workpiece set-up in a manufacturing plant. Assem-bly fixtures are used to reduce production cycle time, improve the product quality and in turn reduce production cost. Traditionally, assembly operations in industries are achieved with the help of fixtures which are large and permanent structures that are costly to design and manufacture [4–6]. The primary function of fixtures in manufacturing is to facilitate production and assembly operations by reducing the repetitive layout set-up time for assembly of the products, which are time-consuming activities and require consid-erable skills [7–10]. Sometimes, assembly fixtures are also pro-vided with assembly tools for fastening and welding operations. They facilitate the employment of unskilled labour in assembly

* Khumbulani Mpofu mpofuk@tut.ac.za; khumblani@gmail.com Olayinka Olabanji obayinclox@gmail.com; MohammedOO@tut.ac.za Olga Battaïa battaia@emse.fr 1

Tshwane University of Technology, Pretoria, Gauteng, South Africa

2

Henri Fayol Institute, Ecole des Mines de Saint-Etienne, France, Saint-Etienne, France

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operations, mostly when there are visual aids or computer-aided process planning for the assembly procedures [11–13].

In the manufacturing of press brakes, assembly fixtures are used to uniquely locate, support and secure the main or heavi-er part of the press brake (which is the frame). The support is usually in the correct orientation and position while other components are added to the part to make the whole product [14,15]. They are used to ensure that each part is assembled correctly within the specified limits and the correct relation-ship and alignment between the parts is maintained. In es-sence, they are designed to be precision tools, usually large and with materials that provide good resistance to wear. More so, their use is limited to job requirements and the imagination of the designer [12,16]. They are accurately designed and positioned in the assembly floor to prevent accidental damage. They are designed to withstand the operational and assembly forces experienced during joining processes and the weight of the product. They are usually kept clean, undamaged and free from chips and grit components, so that they will not be forced into the moving parts of the fixture [8,17]. Reconfigurable assembly fixtures are designed around a specific part family of products to allow rapid change in machine configurations or structure. The change may be in terms of functionality or scalability, according to changes in product requirements [18–20]. Generally, when it is required to design a fixture, the features usually considered are

1. The type of fixture (machining or assembly fixture) 2. The shape of the workpiece (rectangular, square,

cylindri-cal or sphericylindri-cal)

3. The size and weight of the workpiece (housing dimensions)

4. The workpiece material

Manufacturing of press brakes can be decomposed into two steps. Firstly, component parts are fabricated using different methods such as machining, casting, injection moulding, or metal forming. Secondly, these components are assembled or joined together using welding, riveting, fastening or other joining methods [21]. It is usually a batch production system [22]. The main or heaviest part of the press brake is the frame; other components such as the ram, actuators and bolster plate are fitted to the frame. To avoid vibration of the press brake during operation, the frame needs to be firmly and safely secured during the assembly process, while other components are fitted by welding, fastening and other joining processes. As presented in Fig.1, during assembly of press brakes, other components of the press brake are fitted to the frame on the floor. This causes the challenge of accessibility to the assem-bly in progress, thereby increasing the assemassem-bly time and in turn increasing the production time [23].

In essence, changes in press brake models require a reconfigurable assembly fixture (RAF). The RAF will change

in scale so as to accommodate different frame sizes, working length, overall weight and tonnage of the various press brakes during assembly [24]. In this article, a detailed mechanical design of the critical parts of a reconfigurable assembly fixture was conducted. Stress analysis of the parts was done, and a hydraulic system was developed which was modelled using Simscape to determine the response of the system to step input, ramp input and sine input. The hydraulic and electrical system was simulated using automation studio. An experi-ment was set up to investigate the extension of the actuators. The results obtained are discussed in the rest of the manu-script. A literature review of prior work done in this area will be presented in the next section, then a description of the RAF will be given, then the mechanical and control design details will be presented before a discussion and conclusions are made on the research work carried out.

2 Literature review

The factors considered in the development of fixtures for workholding and assembly operations are geometry, mate-rial, mechanical properties and tolerances of the workpiece or product [25]. Another important factor is the machining and assembly process involved in the manufacturing envi-ronment; this process includes tool paths, machining/ assembly forces and environmental concerns, e.g., coolant liquids [26]. Advanced factors that need to be incorporated into the design are the target set-up cost, which dictates the complexity and high accuracy needed in the equipment [27]. Most fixtures are designed to hold or assemble a workpiece or product for a long time of use, in order to recover the cost of development and to make a profit [17, 28–30]. Thus, in many instances, they do not cater for

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product variation which is a constant reality in today’s manufacturing world. The design of a fixture is divided into three stages, which are set-up planning, fixture plan-ning and fixture configuration. Set-up planplan-ning is done in order to determine the number of set-ups required for manufacturing of a product and to specify the position and orientation of the product or workpiece during opera-tion [28,31]. The locating, supporting and clamping points on the product or workpiece are specified in the fixture planning stage. In the configuration stage, the motions of the parts of the fixture are specified in order to achieve the required support and clamping operation. This stage is fo-cused on the process and principles of power generation in the fixture [32]. In reconfigurable fixtures, the final stage is usually a difficult task because it encompasses develop-ment of models that will allow for different modules of the changeable component to be added to the main fixture in line with the shape and size of the product or workpiece. Sometimes, the configuration may not necessarily be changing of modules; it may be the development of models that will set instructions to change the arrangements of components in the fixture to fit the new product [8, 33]. Maniar [34] reviewed fixture designing and manufacturing as a complex process that demands the knowledge of dif-ferent areas such as geometry, tolerances, dimensions, pro-cedures and manufacturing processes [35]. The basic re-quirements of a fixture were identified in the article as the accurate locating of the workpiece, total restraint of the workpiece during machining and other manufacturing processes, limited deformation of the workpiece and no interference during manufacturing processes [3]. An as-sembly set up for the modular fixture machining process was developed by Kršulja et al. [16]. In their design, loca-tors were positioned relative to the force applied during machining and the fixture was able to reduce cost and production cycle time by reducing the number of tool regrinds and set-up times. However, the stress analysis of the locators was not considered in order to determine its behaviour and response to the machining forces.

Jonsson and Ossbahr [36] reviewed different approaches to reconfigure a flexible fixture, ranging from manual to special built machinery, and presented different methods used to po-sition and reconfigure flexible fixtures. The article also report-ed that hand-driven screws or separate screws can be usreport-ed for manual reconfiguration of the flexapod, while measurements can be done either by using an external system or by scales on the legs of the flexapod and the changeover time is typically a quarter of an hour per device. Izquierdo et al. [37] propose a new approach for fixture configuration design for a family of products assembled in a single reconfigurable line. The chal-lenge is formulated as a constraint optimization problem by considering part geometry, fixture workspace and the align-ment of the pins. Sequential quadratic programming was used

to solve the optimization problem, and a relaxed formulation of the problem allowed searching for a robust layout. The strength of the work done in the article is in the area of fixture planning. The article did not consider issues in the fixture configuration stage which plays an important role in the de-sign of a fixture [9]. An improved design of modular steel beam construction (called the boxjoint system) was presented by Helgosson et al. [38]. The system uses different types of boxjoint connection concepts which can be built using a lim-ited set of basic elements. The forces, torque, moments and displacement of each joint in the box were analysed with respect to the load supported by the joint. However, the stress induced in each member of the joint was not analysed in order to depict the behaviour of the joint to loading conditions. In order to demonstrate the satisfaction of demands for a configurable fixture system, the system was used on the airbus A380 subassembly system as a case study, and it was proven that the boxjoint system enabled suitable fix-ture design.

Kairan Prathap and Srihari [11] developed an assembly fixture for mounting circlip to grooves of piston holes. Four concepts were designed and one was selected after the concept selection exercise. The chosen concept was developed and the total cost incurred to manufacture the fixture was approxi-mately US$556. The fixture was able to assemble 2160 pis-tons in a day at an average time of 33 s for installing circlips in piston holes. A reconfigurable pin clamping, integrated with specially developed CAD/CAM software, was developed by Afzeri et al. [39]. A clamping evaluation using a CAD model was conducted in order to achieve the pin configuration auto-matically for a particular part geometry. A detail analysis was done on the workpiece holding and pin configuration, which are part of the fixture planning stage. However, the article elaborated on the fixture configuration stage and not the other stages in assembly.

In all the articles reviewed, the mechanical design and stress analysis of the parts of the fixture have been silent. However, a lot of work has been done on the set-up planning, fixture planning and fixture configuration, but these articles did not consider the design, stress analysis and motion speci-fication of the fixture which is the major activity in the fixture configuration stage. In essence, the novelty in this article is the mechanical design, stress analysis of the component parts of the fixture and the hydraulic system design for the multi-actuator system used in the reconfigurable assembly fixture.

3 Description of the reconfigurable assembly fixture

The reconfigurable assembly fixture (RAF) is designed to locate and secure the frame of press brakes using four fingers that are moved by four hydraulic cylinders (finger cylinders). The movable frame is also moved by two hydraulic cylinders

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(movable frame cylinders), which are different in sizes from the finger cylinders. The function of the finger cylinder and movable frame cylinder is to increase the workspace of the RAF to accommodate press brakes of different working lengths and widths. The minimum and maximum widths of press brakes that the reconfigurable assembly fixture can as-semble are 1500 and 2900 mm respectively. The minimum and maximum ranges of press brake lengths that can be as-sembled on it are 1500 and 5500 mm respectively. Figure2 shows the isometric view of the designed fixture using Solidworks CAD modelling software and (Table1) describes the number components of Figure2. A pictorial view of the reconfigurable assembly fixture gripping a C-frame press brake is shown in Fig.3.

4 Design analysis of components

in the reconfigurable assembly fixture

The components of the RAF are the finger, the fixed frame, the movable frame and the fasteners (supporting the cylinders to the frames of the fixture). Components of the hydraulic system are the finger cylinder (FC), movable frame cylinder

(MFC), hydraulic hose, directional control valves and pump unit.

4.1 Finger

The finger locates the workpiece and transmits the required clamping force from the finger cylinders. The material used for the design of the fingers is carbon steel with 0.85–1.18 % carbon and is oil hardened (to RC 62–63) to prevent wear [8]. The compressive stress and maximum bending stress on the base plate of the finger due to the forces of the press brake are obtained as 4 MN/m2and 2143 N/m2respectively [40–43]. The modal analysis of the finger was done using Solidworks CAD software to ascertain the failure mode of the finger dur-ing operation. This is necessary because the press brake rests on the fingers during the assembly operation. The load was applied on the base plate of the finger, and a mesh was applied using 14,845 nodes and 9093 elements with an element size of 34.7317 mm and a tolerance of 1.73658 mm in order to obtain as accurate results as possible [44,45]. The maximum and minimum stresses in line with the displacement obtained from the simulation are presented in Table2. The mesh displace-ment and stress diagram are presented in Fig.4.

The maximum displacement and stress of 0.014922 mm and 1.4367e+7 N/m2respectively occur at the tip of the finger base plate as shown in Fig.4c, d. The reason is because the tip of the finger base is not supported by the base support of the finger. Optimization of the finger by extending the base sup-port will increase the material and overall weight of the finger and also increase the load of the finger cylinder.

Fig. 2 Isometric view of the reconfigurable assembly fixture

Press brake frame

RAF

Fig. 3 Isometric view of the RAF gripping a press brake frame

Table 2 Table of results for finger simulation

Name Type Minimum Maximum

Displacement URES: resultant displacement

0 mm 0.0149222 mm

Node: 1 Node: 372 Stress VON: von Mises

stress

5340.72 N/m2 1.43676e+007 N/m2 Node: 271 Node: 13,727 Table 1 Description of Fig.2RAF parts

Items Description

1 Movable frame cylinder 2 Movable frame support

3 Movable frame

4 Fixed frame

5 Finger cylinder support

6 Hydraulic hose supplying the finger cylinder from the pump 7 Finger cylinder

8 Fingers

9 Hydraulic hose supplying the movable frame cylinder from the pump

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4.2 Supports for movable frame cylinder and finger cylinder

The hydraulic cylinders are supported in order to eliminate vibration or twisting of the piston rods during extension. The supports (of length Lcand area Asc) are subjected to

compres-sive forces equal to the weight of the cylinder. Factors that affect the buckling load (Wbuck) of the supports are the end

fixity (C), modulus of elasticity of the material ECand least

radius of gyration k. Using Euler’s equation, as deduced in Eq.1, the buckling loads of the movable frame cylinder and finger cylinder were obtained as 82.5 and 243 MN respective-ly. When the cross-sectional area and least radius of gyration are large, the buckling load increases. This implies that the beams with larger cross-sectional areas and least radius of gyration can withstand a large buckling load. The summation of the weights of cylinder, its base plate and push plate must not be more than the buckling load so that the support will not fail [42]. Wbuck¼ πk Lc  2 CECAsc ð1Þ

The modal analysis of the support column was also done using Solidworks simulation to know how it will fail during operation. Tables3and4present the results of the simulation

for the movable frames and finger cylinder supports respec-tively. Figures5and6show pictures of the mesh, stress and displacement diagram for the movable frame and finger cyl-inder support respectively.

4.3 Fasteners joining the hydraulic cylinders to the frame of the fixture

The base plates of the finger cylinders and movable jaw cyl-inders are fitted to the frames of the RAF by means of bolts and nuts. The nominal diameter of the bolt is a function of the external load acting on it [43,46]. The bolts are subjected to an initial tension load due to the tensioning during tightening and an external load as a result of the cylinder weight tending to pull the base plate away from the fixture wall like a cantilever and to pull the support plate away from the piston rod in either case [47,48]. The external load acting on the bolts is the weight of the cylinders acting in the axis of the bolts. More so, since the bolts are used to prevent movement of the cylin-ders from the frames, they are subjected to a shear stress which tends to shear the shank of the bolt. In order to reduce the effect of the shearing load on the bolt, four bolts are used per cylinder (at the corners of the base plate) in the fastening so that the effect of the shearing load will be shared among the bolts as shown in Figs.7and8. The type of bolt used in the

(b) Mesh Diagram (c) Displacement Diagram (a) Stress Diagram (d) Maximum Stress

Fig. 4 Simulation results for finger

Table 3 Results of simulation for movable frame cylinder support

Name Type Minimum Maximum

Displacement URES: resultant displacement

0 mm 7.11624 mm

Node: 1119 Node: 571

Stress VON: von Mises

stress

44616.4/m2 1.17847e+008 N/m2 Node: 581 Node: 19,646 Parameters Total nodes 21,666 12,108

Element size 25.2322 mm Tolerance 1.26161

Table 4 Results of simulation for finger cylinder support

Name Type Minimum Maximum

Displacement URES: resultant displacement

0 mm 0.0111636 mm

Node: 991 Node: 195

Stress VON: von Mises

stress

753.2 N/m2 4.01947e+006 N/m2 Node: 7049 Node: 10,839

Parameters Total nodes 12,459 7368

Element size 20.4009 mm Tolerance 1.02005

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design of the fixture is a through bolt which is made from mild steel SA 36 with fine square threads. The reason for using this type of bolt is because it gives more strength due to a large core area and it provides resistance to unscrewing due to a low helix angle. In essence, the nominal diameter (db) of the bolt is

deduced as presented in Eq.2. It is designed as a function of the external load (Pext), initial tension due to tightening (PI),

number of bolts (n) and yield strength for the bolt material (σys). A factor of safety (F.S) is considered based on the tensile

strength of the material and the loading condition reference. Since the material used for the design of the bolt is mild steel, then the length of the nut will be equal to the nominal diameter of the bolt [43,46]. The method used in the determination of the nominal diameter and other parameters of the bolt is presented in Fig.9. db¼ 1:8 F :S σys PIþ Pext n    12 ð2Þ 4.4 Hydraulic system

The function of the hydraulic system in the fixture is to pro-vide the necessary clamping force required during the

assembly operation. The components of the hydraulic system are the movable frame cylinder, finger cylinder, hose, direc-tional control valve, pressure relief valve, pumping unit, flow divider valve and pressure-reducing valves. The hydraulic components used in the fixture are designed considering the safety of operation, functional requirements and efficiency [49,50]. Physical modelling of the hydraulic circuit was done using Simscape hydraulics as shown in Figs.10and11. In the circuit, directional control valves (A) (feeding the finger cyl-inders) pick the supply from the pump unit and supply the finger cylinders through the flow dividers and pressure-reducing valves which ensure uniform extension of the finger cylinders to the required length. After this operation, direc-tional control valve (B) (supplying the movable frame cylin-ders) also collects the supply from the pump unit and delivers it to the cylinders until the required extended length is attained [51]. The purpose of the modelling is to observe the output of the cylinders to various inputs from the directional control valve. The extension and retraction of the cylinders are a func-tion of the spool displacement [52–54]. Hence, if the direc-tional control valves (DCV) are subjected to a sine input, a step input and a ramp input, then the scope of the cylinders should also be in the form of the inputs. More so, in order to confirm the synchronization of the cylinders, their scope must

Mesh Diagram Displacement Diagram

Stress Diagram Fig. 5 Simulation of movable

frame cylinder support

Fig. 6 Simulation of finger cylinder support

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be of the same pattern [55]. The scheme developed for design of the hydraulic components in the system is presented in Fig.12. The length of the cylinders is obtained from the di-mensions of the fixture as presented in Figs.13and14.

The pressure in the system from DCV (A) to the finger cylinder (Ps) and from DCV (B) to the movable frame

cylin-der (Psm) was determined from the total dynamic column of

hydraulic fluid in the system [56]. The diameter of the piston

is obtained from the weight of the load, the total pressure developed in the cylinder and the pressure in the system. The movable frame cylinder pushes the movable frame of weight (Wmf) and two fingers of weight (Wfinger) [57].

The load due to the movable frame cylinder is uniformly shared by the two movable frame cylinders. If the total pressure developed in the movable frame cylinder is represented by Phcm,

then the diameter of the movable frame cylinder (dmfc) is

de-duced as shown in Eq.3.

Similarly, the diameter of the finger cylinder (dfc) is

obtain-ed from the weight of the finger (WFC) and the pressure

de-veloped in the cylinder (Phc), as presented in Eq.4. The

ex-ternal diameter (dec) and wall thickness (twc) of the cylinders

are deduced from Eqs.5and6respectively. They are a func-tion of the design pressure in the system (Pdes), diameter of the

piston (Dpiston) and the yield point strength of the material

(σyp) [58]. The design pressure is a summation of the pressure

in the section of the system and the pressure developed in the cylinder [59,60]. More so, the force required by the piston rod of the cylinders (Fpe) to push the external loads is obtained

from the crushing stress of the piston rod material (σc), the free

bucking length (Lfb) and the area of the piston rod (Apr) as

presented in Eq.7. The crushing stress of the piston rod ma-terial is expressed in terms of the Rankine constant (α).

dm f c¼ 0:64 Wm fþ 2Wfinger  Phcmþ Psm  12 ð3Þ

Table 5 Description of Fig.15

Part Description

a Finger cylinders

b Movable jaw cylinders

c Limit switch

d Pump unit

e Directional control valve B

f Hose connector (discharging to the tank)

g Flow distributor to inlet ports of movable jaw cylinders

h Pump switch

i Directional control valve A

j Hose connector (supplying from the pump) k Flow distributor to outlet ports of finger cylinders l Electrical connection unit

m Flow distributor to outlet ports of movable jaw cylinders n Flow distributor to inlet ports of finger cylinders

Legend

Determine total external load acting on all the bolts in the assembly.

Express the elasticity of connected parts to the elasticity of the bolt in terms of the ratio.

Determine external force acting on each bolt in the assembly by dividing the external load by the number of bolts in the assembly.

Express initial tension in each bolt as a function of the nominal diameter of the bolt.

Determine the total force acting on each bolt in terms of the external load acting on each bolt.

Obtain the permissible or allowable tensile stress for the bolt from the yield point of the bolt material.

Determine the total force acting on each bolt in terms of the allowable tensile stress and the core diameter of the bolt.

Compare total force due to the external load and allowable stress in order to obtain the nominal diameter of the bolt.

Determine the length of the nut from the nominal diameter and material of the bolt.

Determine maximum tensile load on heavily loaded bolt from external load and bolt distances. Also determine direct shear load on each bolt from external and number of bolt in the assembly as shown in figure 8.0

Comparison stage of the analysis Process flow

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dfc¼ 1:27WFC Phcþ Ps  12 ð4Þ dec¼ Dpiston 2 4Pdesþ 0:8σy 0:8σy−4Pdes  12 ð5Þ twc¼ Dpiston 2 0:8σyp 0:8σypþ 8Pdes  12 −1 ( ) ð6Þ Fpe¼ σc F:S Apr− πaLf b2 4   ð7Þ

4.5 Simulation and experimental set-up

In order to simulate the electrical connection and rung circuit for the programmable logic controller, the hydraulic and electrical system was simulated using automation studio, as presented in

Figs.15and16. Proximity switches F2 and F1 control solenoids B and D respectively. Solenoids B and D control the flow of hydraulic fluid for extension and retraction of the movable jaw cylinders respectively. Similarly, solenoids A and C control the flow of hydraulic fluid for extension and retraction of the finger cylinders respectively. The programmable logic controller (PLC) is controlled by the reconfiguration model which is installed on a computer. A fault diagnosis system will be used with the PLC in order to improve its reliability [61,62]. The picture of the experimental set-up is presented in Figs.17and 18. In the experimental set-up, flow distributors are used as flow dividers in order to obtain the pressure difference during exten-sion and retraction of the actuators. The pressure reading on the flow distributors for the piston and annulus sides of the finger actuators increases gradually from 0 to 20 bars during extension and retraction. The reason for the gradual increase is because at the beginning of extension, the pressure and flow required by the distributor to feed the four finger cylinders equally are not

Bolt assembly nomenclature presented in figure 9.0

Fig. 8 Eccentric load due to the weight of the movable jaw cylinder

Fig. 9 Bolt and nut assembly joining the actuator base plate and fixture frame. LMsummation of

the widths for the cylinder base metal plate and fixture frame, Lgripthe grip length which is

equal to the summation of the bolted members’ width and the washers, LTthreaded length of the

bolt, LUTunthreaded length of the

bolt, Lextraextra length of the bolt

outside the nut after assembly, Lnutlength of the nut, Lw

thickness of washers, LM1

thickness of the fixture frame, LM2thickness of the cylinder base

plate, Lbhlength of bolt head, Dbh

diameter of the bolt head, Dnut

diameter of the nut, dbdiameter of

the bolt, Lboltfull length of the

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attained instantly. In essence, during the experimental investiga-tion, it was observed that all the finger cylinders extend equally but at the start there was a small difference in the displacement of the actuators. However, the difference only occurred for 3 s. Similarly, the pressure reading on the flow distributor for the pistons and annulus sides of the movable jaw cylinders increases gradually from 0 to 10.8 bars because the cylinders in the test bench are of the same size. The difference in values of the pressure reading is because the number of cylinders supported by the distributor is different. This is an indication that, during operation of the fixture, the pressure in the system from DCV (A) to the finger cylinders will be different from that of DCV (B) to the movable jaw cylinders.

5 Results and discussion

Considering the yield strength of the material from which the supports of the movable frame and finger cylinders are made (ASTM 36 with a yield strength of 2.5e +008 N/m2) and comparing it with the maximum stress obtained from the von Mises stress analysis done with the Solidworks sim-ulation, it can be concluded that the supports of the cyl-inders will not fail during operation because the maxi-mum stress induced is lower than the yield strength of the material. Also, since the buckling length of the piston rod (for the movable frame cylinder) under a load of 246320.76 N is 7975 mm and the length of the piston rod used in the design is 2230 mm, this implies that the design length of the movable frame cylinder will not buckle during operation. Similarly, the length of the pis-ton rod (for the finger cylinder) under a load of 125, 625 N is 3969 mm and the length of the piston rod used in the design is 650 mm; this implies that the design length of the finger cylinder will not buckle during op-eration. In essence, there will be a long life span of the cylinders during operation, also especially given they are reconfigurable and can be customized to the various de-mands at a specific juncture.

The pressure in the hydraulic system is divided into two sections because the hydraulic fluid leaving the pump is channelled to power two different arrangements of hydrau-lic cylinders (the finger cylinders and the movable frame cylinders). In essence, pressure in the system from DCV (A) to the finger cylinders is different from the pressure in the system from DCV (B) to movable frame cylinders. The pressure in the system for both sections was obtained as 65 bars by considering the equivalent total column of hydrau-lic fluid in motion in each section. The static discharge column from the pump outlet to the inlet of the four finger cylinders was obtained by determining the length of the hydraulic hose. The volumetric flow rate in each section was determined from the velocity of fluid flow, and the total volumetric flow rate required from the pump was obtained by summing individual flows from each section. The effi-ciency of the pump was determined in terms of output hy-draulic power and the input electrical (at the motor termi-nals) power. The output power of the pump was obtained as 96 KW, while the input power is 120 KW, both yielding an efficiency of 80 %.

The length of the finger cylinder and movable frame cyl-inder was determined by considering the geometry of the fix-ture and the range of press brakes required to be assembled on it. In addition, considering the results of the velocities of the cylinders and the time spent to extend and retract fully, it is evident that the velocity of the cylinders depends on the flow from the pump and the area filled by the hydraulic fluid in it. Ideally, the velocity of a hydraulic cylinder during its

Fig. 10 Travel distance of the movable frame cylinder in the fixture. Lmf

length of the movable frame, Wmfwidth of the movable frame, fwtfixture

wall thickness, fwdfinger width distance, fwwfixture wall width, fwlfixture

wall length, cb cylinder base plate thickness, Lfflength of the fixed frame,

Lffo length of the fixed frame open space, F=D−(E+fwd+cb),

E¼ fwl2þ fww2

12, D¼ 1

2Lm fþ Wm f2

12

1 2

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extension stroke is expected to be lower than the velocity during the retraction stroke, because the volume of fluid re-quired by the cylinder during extension is high and as such it takes more time for the flow from the pump to feel the blank space of the piston, unlike during the retraction where the

annulus area is filled. This implies that the time spent during extension will be greater than the time spent during retraction. The output response of the cylinders following a ramp, step and sine input to the directional control valve is presented in Figs.19,20,21, and22.

Obtain velocity of fluid in the system from the pump inlet to the inlet of the finger cylinders using Bernoulli’s equation. Likewise from the pump inlet to the inlet of the movable frame

Determine the input and output power of the pump and its efficiency.

Obtain pressure in the finger cylinder as a result of the piston movement. Likewise the same for the movable frame cylinder

Determine the pressure at the inlet of the finger cylinder and movable frame cylinder from load

Determine the total pressure developed in the

Determine the pressure required by the cylinders to push external load

Determine the area of the piston. Select diameter of piston rod corresponding to the piston diameter from manufacturer’s catalogue. Determine other parameters such as maximum force, buckling load, buckling length, thickness of cylinder wall, extending force, time and velocity, retracting force, time and velocity, leakage flow and leakage flow coefficient, volume of oil under compression in both chambers, coefficient of viscous friction, and total stiffness.

Obtain pressure in the system from directional control valve (A) to the inlet ports of the finger cylinders, and likewise from directional control valve (B) to the inlet ports of the movable frame cylinders

Determine the total dynamic column of hydraulic line from pump inlet to finger cylinders, and likewise to the movable frame cylinders.

Determine the volumetric flow rate of fluid in the system from pump outlet to the inlet of the finger cylinders, and likewise from the pump outlet to the inlet of the movable frame

Add the volumetric flow rate in each section in order to obtain the required flow rate of the pump, and obtain the mass flow rate of the fluid in the

Determine the pressure difference across the ports of the valves

Determine valve coefficient knowing the specific gravity, piping geometry and numerical constant based on units.

Determine flow coefficient of the valve knowing the coefficient of discharge, density of the fluid and length of spool

Determine pressure coefficient of the valve knowing the coefficient of discharge, length of spool, and density of the hydraulic fluid

Obtain the pressure sensitivity of the valve, as a ratio of the flow coefficient to the pressure coefficient

Determine the force spring rate of the spool knowing the length of spool.

Determine the damping coefficient of the valve due to transient flow force, knowing the spool length, coefficient of discharge, and density of the fluid

Section for estimating parameters of the directional control valves Section for estimating parameters of the finger cylinders and movable frame cylinders

Section for estimating parameters of the pump and system pressure

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Considering Fig.19, when the system is subjected to a unit gradient, the output response of the finger cylinders is 1 *

10−10m in 10 s. This implies that it takes the finger cylinders

10 s to respond linearly to a linear input from the directional

Fig. 13 Physical modelling of the hydraulic system from DCV (A) to finger cylinders using Simscape Hydraulics

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control valve in order to extend or retract synchronously. Sim-ilarly, a unit step input to DCV (A) yields an output approxi-mately equal to that of the ramp input. Considering Figs.20 and21, when the directional control valve (A) is subjected to a sine input, it is observed that it took the cylinders 5 s to extend to displacement of 12 * 10-12m. This implies that with a sine input to the directional control valve (A), it takes the finger cylinders 5 s to respond to the spool displacement of the valve thus extending or retracting synchronously. The results of simulation for the movable frame cylinders are similar to those for the finger cylinders. However, there are differences in the response time and displacement for different inputs at the DCV (B). Considering Fig.22b, when the directional control valve (B) is subjected to a sine input, it is observed that it took the movable frame cylinders 3 s to extend to displacement of 12 * 10−12. This implies that with a sine input to the directional

control valve (B), it takes the movable frame cylinders 3 s to respond to the spool displacement of the valve thus extending or retracting synchronously. The change in time is due to the fact that the total volume of oil under compression in both chambers of the movable frame cylinders is less compared to that of the finger cylinders. More so, the number of flow

dividers present in the system to distribute the flow from the valve to the finger cylinders increases the response time to the spool displacement.

6 Conclusion

In conclusion, a reconfigurable assembly fixture is needed in reconfigurable assembly systems in order to locate and support the workpiece during assembly. The stages involved in the development of fixtures are set-up planning, fixture planning and fixture configuration. The design of a reconfigurable as-sembly fixture is a task that can be associated with the fixture configuration stage. Recent articles reviewed in the field of fixture design have considered a large amount of work in set-up planning and fixture planning. This article deals extensively with the mechanical design and stress analysis of parts of a reconfigurable assembly fixture which are part of the fixture configuration stage. The components of the designed fixture were simulated using Solidworks express simulation to analyse the mode of failure during operation. von Mises stress analysis conducted on the components yields results as presented in each section of the component design. The results obtained from the stress analysis do not exceed the yield strength of the materials from which the parts were made. This signifies that the components will not fail during operation. The article also presents a detailed analysis of the bolting system which pro-vides a simplified approach to bolt connection design.

The components of the hydraulic system and a comprehen-sive scheme for design of hydraulic components were devel-oped which give an overview on the design of hydraulic equipment. The hydraulic system uses a one-directional con-trol valve to concon-trol multi-actuating cylinders. In order to en-sure efficient synchronization, the system uses presen-sure- pressure-reducing valves with the flow dividers so as to regulate the pressure of fluid entering and leaving each cylinder. The

Fig. 15 Experimental setup for the hydraulic system

Finger cylinders extending uniformly

Flow distributor for Finger cylinders

Flow distributor for movable jaw cylinders

Movable jaw cylinders extending uniformly

Fig. 16 Synchronized extension of finger cylinders and movable jaw cylinders during the experimental setup

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Fig. 17 Synchronized extension of finger cylinders, and simulation of the programmable logic controller using IEC Standard

Fig. 18 Synchronized extension of movable jaw cylinders, and simulation of the programmable logic controller using IEC Standard

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hydraulic system was modelled and simulated. Physical modelling of the hydraulic system shows that the actuating

cylinders will respond fast to the spool displacement of the directional control valves when there is a sine input to the

Fig. 19 Response of the finger cylinders to ramp input at DCV (A)

Fig. 20 Response of the finger cylinders to sine input at DCV (A)

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valves compared to other inputs used in the simulation. Future research in progress on the reconfigurable assembly fixture is

a detailed and effective control system for the hydraulic sys-tem incorporating the use of appropriate controllers and

Fig. 21 Response of the finger cylinders to step input at DCV (A)

22b: Sine 22c: Step

22a: Ramp Fig. 22 Response of the movable

frame cylinders to sine, step and ramp input at DCV (B)

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sensors to compare the actual extension of the actuators to the desired extension for proper gripping of press brake frames. Further to this, a model for reconfiguration of the fixture is in progress. The model will determine the travel lengths and operating parameters of the actuators for every press brake dimension within the limit of the fixture.

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Figure

Fig. 3 Isometric view of the RAF gripping a press brake frame
Table 3 Results of simulation for movable frame cylinder support
Fig. 6 Simulation of finger cylinder support
Fig. 7 Process flow for determining bolt parameters
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