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Path Planning for Robotic Grinding on a Large Forged Workpiece
Control 9th IFAC Conference on Manufacturing Modelling, Management and Berlin, Germany, August 28-30, 2019 9th IFAC Conference on Manufacturing Modelling, Management and Control Available online at www.sciencedirect.com Control 9th IFAC Conference on Manufacturing Modelling, Management and Berlin, Germany, August 28-30, 2019 9th IFAC Conference on Manufacturing Modelling, Management and Berlin, Germany, August 28-30, 2019 Control Control Berlin, Germany, August 28-30, 2019 Berlin, Germany, August 28-30, 2019
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Path Planning forIFAC Robotic Grinding on a Large Forged Workpiece PapersOnLine 52-13 (2019) 1162–1167 Path Planning Planning for for Robotic Robotic Grinding Grinding on aa Large Large Forged Forged Workpiece Workpiece Path Mohamed Didi Chaoui, Françoison Léonard and Gabriel Abba Path for Grinding on aa Large Forged Workpiece Path Planning PlanningMohamed for Robotic Robotic Grinding on Large Forged Workpiece Didi Chaoui, François Léonard and Gabriel Abba Mohamed Didi Chaoui, François Léonard and Gabriel Abba Mohamed Didi Chaoui, Léonard and Gabriel Abba Université de Lorraine, Arts etFrançois Métiers ParisTech, LCFC, F-57000 Metz, Mohamed Didi Chaoui, François Léonard and Gabriel Abba France (email: [email protected]) Université de de Lorraine, Lorraine, Arts Arts et et Métiers Métiers ParisTech, LCFC, LCFC, F-57000 F-57000 Metz, Metz, Université ParisTech, France (email: [email protected]) Université de Lorraine, et Métiers ParisTech, LCFC, F-57000 Metz, France (email: Arts [email protected]) Université de Lorraine, Arts et Métiers ParisTech, LCFC, F-57000 Metz, France (email: [email protected]) France (email: [email protected])
Abstract: Abstract: In this paper a robotic grinding system which can produce a finished workpiece that respects some Abstract: product geometric specifications proposed. It iscan composed 1 DoF active compliance actuator some fixed Abstract: In this paper paper robotic grindingissystem system which produceofaaa finished finished workpiece that respects respects In this aa robotic which can produce workpiece that some Abstract: between the grinder and grinding the robot. The 1 DoF actuator associated toDoF the active tool can be mounted at existing product geometric specifications is proposed. It is composed of a 1 compliance actuator fixed In this paper a robotic grinding which can produce thatindustrials. respects product geometric specifications issystem proposed. It isvery composed ofaaand a finished 1 DoF active compliance actuator some fixed robotic installations which this flexible easy toworkpiece use by The In this paper a robotic grinding system which can produce finished workpiece that respects some between the grinder grinder and the make robot. The solution 1 DoF DoF actuator associated toDoF the active tool can be the mounted at existing existing product geometric specifications is proposed. It is composed of a 1 compliance actuator fixed between the and the robot. The 1 actuator associated to the tool can be mounted at grinding system composed of the robot and the actuator is able to apply a constant contact force between product installations geometric specifications is this proposed. It isvery composed of and a 1 DoF active compliance actuator fixed robotic which make solution flexible easy to use use by the industrials. The between the grinder and the make robot.tool. TheAsolution 1 path DoF actuator associated toeasy the presented tool canby beinthe mounted at existing robotic installations which this very flexible and to The the workpiece and the grinding planning method isapply thisindustrials. article. Using between the grinder and theofrobot. The and 1 DoF actuator associated toalso theatool can be mounted at between existing grinding system composed the robot the actuator is able to constant contact force robotic installations which make this is solution very for flexible use bycontact the industrials. The grinding system composed of the robot the actuator isgrinding able and to apply a to constant between analytical calculations, the robot path determined aeasy rounded corner on a force parallelepiped robotic installations which make this Aand solution very flexible and easy to use byinthe The the workpiece and the grinding tool. path planning method isapply also presented thisindustrials. article.between Using grinding system composed of the robot and the actuator is able to a constant contact force the workpiece and the grinding tool. A path planning method is also presented in this article. Using workpiece with a given precision of the surface shape. Copyright © 2019 IFAC grinding system composed of the robot and the actuator is able to apply a constant contact force between analytical calculations, the robot tool. path A is determined determined for method grindingisaaalso rounded cornerinon on the workpiece and the the grinding path planning presented thisa parallelepiped article. Using analytical calculations, robot path is for grinding rounded corner the workpiece and the precision grinding tool. A path planning method is 2019 also presented in thisa parallelepiped article. Using workpiece with a given of the surface shape. Copyright © IFAC Keywords: Path planning, Robotic grinding, Disc grinding, Roughness, Rounds. © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All reserved. analytical calculations, the robot of path issurface determined for grinding©a2019 rounded corner onrights a parallelepiped workpiece with a given precision the shape. Copyright IFAC analytical calculations, the robot path is determined for grinding a rounded corner on a parallelepiped workpiece with a given precision of the surface shape. Copyright © 2019 IFAC Keywords: Path Path planning, planning, Robotic Robotic grinding, grinding, Disc Disc grinding, grinding, Roughness, Rounds. Rounds. Keywords: Roughness, workpiece with a given precision of the surface shape. Copyright © 2019 IFAC position and force control. This combination is referred to as Keywords: Path planning, Robotic grinding, Disc grinding, Roughness, Rounds. Keywords: Path planning, Robotic grinding, Disc grinding, Roughness, Rounds. 1. INTRODUCTION hybrid control (or hybrid position/force control). position and and force force control. control. This combination combination is referred referred to to as as position This is 1. INTRODUCTION In order to reduce the number of tedious operations affected 1. INTRODUCTION hybrid control (or hybrid position/force control). Thomessen al.hybrid (2001)position/force presents a robot system position and et force control. This combination iscontrol referred to as (or control). to the operators, their working conditions by hybrid positioncontrol and force control. This combination is referred to as 1. INTRODUCTION In order to reduce reduce to theimprove number of of tedious operations affected dedicated toetgrinding large Francisa turbines. The control hybrid control (or hybrid position/force control). 1. INTRODUCTION In order to the number tedious operations affected Thomessen al. (2001) presents robot control system reducing dangerous operations andworking to improve quality hybrid control hybrid position/force control). et (or al. presents a robot control systema to the operators, operators, to improve their conditions by Thomessen system is based on (2001) an active force feedback system In order to reduce theimprove number workpieces, of tedious operations affected to the to their working conditions by dedicated toetgrinding grinding large Francis turbines. The using control consistency of manufactured many industrials Thomessen al. (2001) presents a robot control system In order to reduce the number of tedious operations affected dedicated to large Francis turbines. The control reducing dangerous operations andworking to improve improve quality axes force sensor attached to feedback the robot’s end effector. Thomessen et al. (2001) presents a robot control systema to the tooperators, to different improve their conditions by three reducing dangerous operations and to quality system is based based on an active active force system using chose automatize kinds of processes. Grinding dedicated to grinding large Francis turbines. The control to the operators, to improve their working conditions by system is on an force feedback system using a consistency of manufactured workpieces, many industrials This system offers high flexibility and robustness against dedicated to grinding large Francis turbines. The control reducing dangerous operations and to improve quality consistency of of manufactured workpieces, many industrials three axes force on sensor attached to feedback the robot’s robot’s end effector. effector. processtoisautomatize one those processes thatofrepresented aGrinding serious system is based an active force system using reducing dangerous operations and toprocesses. improve quality three axes force sensor attached to the end chose different kinds workpiece positioning and theforce grinding tool wear. Using theaa system is based on an active feedback system using consistency of manufactured many industrials chose to (Andersson automatize different kinds of et processes. Grinding This system offers high flexibility androbot’s robustness against problem (1990) andworkpieces, Huang al. (2002)). Royal This three axes force sensor attached to the end effector. consistency of of manufactured workpieces, many industrials system offers high flexibility and robustness against process is one those processes that represented a serious Dai and etattached al.the(1993) developed and tested an three axes models, force sensor to the robot’s endUsing effector. chose tofor automatize different kinds processes. aGrinding process one of those processes thatof serious identified workpiece positioning grinding tool wear. the Society the Prevention ofand Accidents Surveillance Systems This system offers high andtool robustness against chose tois(Andersson automatize different kinds ofrepresented processes. Grinding positioning andflexibility the controller grinding wear. Using the problem (1990) Huang et al. (2002)). (2002)). Royal workpiece adaptive pole placement using computer This system offers high flexibility and robustness against process is one of those processes that represented a serious problem (Andersson (1990) and Huang et al. Royal identified models, Dai and et al. al.the(1993) (1993) developed andUsing tested the an data showed angle processes grinders were the most dangerous workpiece models, positioning grinding tooliswear. process is one of those that represented aSystems serious identified Dai et developed tested an Society for thethat Prevention ofand Accidents Surveillance simulations. The purpose ofthethecontroller controller toand regulate the workpiece positioning and grinding toolusing wear. Using problem (Andersson (1990) Huang etrecorded al. (2002)). Royal Society for the Prevention of Accidents Surveillance Systems adaptive pole placement computer tools with an average of 5,400 injuries yearly in identified models, Dai et al. (1993) developed and tested an problem (Andersson (1990) and Huang et al. (2002)). Royal adaptive pole force, placement controller usingand computer data showed that angle grinders grinders were Surveillance the most most dangerous dangerous normal grinding Minami etdeveloped al. (1996). the basis identified models, Dai see et al. (1993) tested an Society for thethat Prevention of Accidents Systems data showed angle were the simulations. The purpose purpose of thecontroller controller is to to On regulate the Great Britain. According to this research, the most injured adaptive pole placement using computer Society for the Prevention of Accidents Surveillance Systems simulations. The of the controller is regulate the tools with an an that average ofgrinders 5,400 injuries injuries recorded yearly in in of a detailed analysis ofsee theMinami grinding process, motions ofbasis the adaptive pole placement controller using computer data showed angle were the most dangerous tools with average of 5,400 recorded yearly normal grinding force, et al. (1996). On the areas are face, head andgrinders upper extremity (Sozbilen et al. normal simulations. Theforce, purpose theacontroller is to On regulate the data that angle were the the most dangerous grinding see of Minami et al. (1996). the basis Greatshowed Britain. According to this injuries research, most injured dynamic system of grinding robot is modelled simulations. The purpose of the controller is to regulate the tools with an average of to 5,400 recorded in constrained Great Britain. According this research, the most injured of a detailed detailed analysis ofsee the grinding process, motions ofbasis the (2018)). Removal of Excess material, surfacing andyearly creating normal grinding force, Minami et al. (1996). On the tools with an average of 5,400 injuries recorded yearly in of a analysis of the grinding process, motions of the areas are face, head and upper extremity (Sozbilen et al. in this paper. In the model, the constrained generalized forces normal grinding force, see Minami et al. (1996). On the basis Great Britain. According to this research, the most injured areas face, head and (Sozbilen et al. constrained dynamic system of aa grinding grinding robot is modelled modelled rounds inRemoval workpieces aretoupper dangerous and the time consuming of aincluded detaileddynamic analysis of theasgrinding process, motions ofstate the Great are Britain. According this extremity research, most injured system of robot is (2018)). of Excess Excess material, surfacing and creating are and expressed an obvious function of theforces of a detailed analysis of thethe grinding process, motions of the areas are Removal face, head and upper extremity (Sozbilen et do al. constrained (2018)). of material, surfacing and creating in this paper. In the model, constrained generalized grinding operations affected to skilled operators to constrained dynamic system of a grinding robot is modelled areas are face, head and upper extremity (Sozbilen et al. in this paper. In the model, the constrained generalized forces rounds in workpieces are dangerous and time consuming and included input generalized forces. Agrinding controller then built constrained dynamic system of aobvious robotis isof modelled (2018)).inRemoval of Excess material,a surfacing and creating rounds workpieces are dangerous and time consuming are and expressed as an function theforces state manually. These operations become bigger problem in this paper. In the model, thean constrained generalized (2018)). Removal of Excess material, surfacing and creating included and expressed as obvioussensors. function of the state grinding operations affected to skilled skilled operators towhen do are without involving any force feedback Simulations in this paper. In the model, the constrained generalized forces rounds in workpieces are dangerous and time consuming grinding operations affected to operators to do and input generalized forces. A controller is then built the size of the ground workpieces is very large. are included and expressed as an obvious function of the state rounds in workpieces are dangerous and time consuming input generalized forces. A controller is of then manually. These operations operations become bigger problem towhen when haveincluded been done for justification of the feasibility ofbuilt the are and expressed as an obvious function the state grinding operations affected to skilled operators do and manually. These become aa bigger problem without involving any force feedback sensors. Simulations and input generalized forces. A controller is then built grinding operations affected to skilled operators to do involving any force sensors. the size of the the ground ground workpieces is very very large. controller by taking an feedback articulated planar two-link In size literature, proposed automation solutions canwhen be without and input generalized forces. A of controller is Simulations then built manually. These operations become a bigger problem the of workpieces is large. have been done for justification the feasibility of the without involving anyjustification force feedback sensors. Simulations manually. These operations become a bigger problem when have been done for ofet the feasibility of the manipulator as antaking example Tönshoff al. (1992). categorized two groups. Theisfirst concerns the without involving any force feedback sensors. Simulations the size of theinground workpieces very group large. controller by an articulated planar two-link In literature, proposed automation solutions can be have been done for justification of the feasibility of the the size of the ground workpieces is very large. by taking an articulated planar two-link In literature, proposed automation solutions thecan be controller automation using CNC special-purpose second have been done for justification ofet the feasibility of the manipulator as hand, antaking example Tönshoff al. (1992). (1992). categorized in two two groups. The first first machines, group concerns the On the other an active or passive compliance end controller by an articulated planar two-link In literature, proposed automation solutions can be manipulator as an example Tönshoff et al. categorized in groups. The group concerns the group concerns the automation using robots. But the first controller by taking an articulated planar two-link In literature, proposed automation solutions can be automation using CNC special-purpose machines, the second second effector control the endoreffector tooling having end the manipulator as hand, aninvolves example Tönshoff et al. (1992). categorized in two groups. The first group concerns the automation using CNC special-purpose machines, the On the other an active passive compliance solution is normally quite expensive. robots have manipulator as hand, an example Tönshoff et al. (1992). categorized in two groups. Theusing firstIndustrial group concerns the On thetoother active or passive compliance end group concerns the automation robots. But the first ability control the an applied force by measuring the force automation using CNC special-purpose machines, the second group concerns the automation using robots. But the first effector control involves the end effector tooling having the been proven to CNC bequite a expensive. more economical solution for effector On theThis other hand, an active passive compliance end automation using special-purpose machines, the second control involves the endor effector tooling having the solution is normally normally Industrial robots have error. is done independently from the robot's position On the other hand, an active or passive compliance end group concerns the automation using robots. But the first solution is quite expensive. Industrial robots have ability to control the applied force by measuring the force automation. Thetothe robot can be programmed to carry out first the effector involves the end effector tooling having the group concerns using robots. But the tocontrol control the applied force by measuring the force been proven beautomation more economical solution for ability controller and depend only on the force control. In other effector control involves the end effector tooling having the solution isjobs normally quite Industrial robots have been proven to can be aa expensive. more economical solution for error. This is done done independently from the robot's position grinding and achieve the required surface quality ability to control the applied force by measuring the force solution is normally quite expensive. Industrial robots have error. This is independently from the robot's position automation. The robot can be programmed to carry out the words, the force and position control are dissociated in active ability to control the applied force by measuring the force been proven to be a more economical solution for automation. Theconsistency be programmed to force carry out the controller and depend only on on the thefrom force control. In other and machining with active contact control. This is done independently thecontrol. robot's position been proven torobot be can a more economical solution for error. and depend only force In other grinding jobsThe and can achieve the required surface quality control. Active compliance actuators can classified as error. This is done independently from the be robot's position automation. robot can be programmed to carry out the controller grinding jobs and can achieve the required surface quality words, the force and position control are dissociated in active The existing active force control methods can be broadly controller only control on the are force control. In active other automation. Theconsistency robot can with be programmed to force carry control. out the words, the and forcedepend and non-programmable. position dissociated in and machining active contact programmable and The programmable controller and depend only on the force control. In other grinding jobs and can achieve the required surface quality and machining consistency with active contact force control. control. Active compliance actuators can be classified classified as categorized asactive through-the-arm and active end effector force control. words, the force and position control arecan dissociated in active grinding jobs and can achieve the methods required surface quality Active compliance actuators be as The existing force control can be control. broadly type can accomplish trajectory grinding-force tracking, words, the force and position control are dissociated in active and machining consistency with active contact force The existing active force control methods can be broadly programmable and non-programmable. The programmable control. control. Active compliance actuators can be classified as and machining consistency with active contact force control. and non-programmable. Theeffectors categorized asactive through-the-arm and methods active end end effector force programmable whereas theaccomplish non-programmable active end cannot. control. Active compliance actuators can beprogrammable classified as The existingas force control caneffector be broadly categorized through-the-arm and active force type can trajectory grinding-force tracking, programmable and non-programmable. The programmable The existing active force control methods can be broadly can compliance accomplish trajectory grinding-force tracking, control. A passive tool would alsoend beeffectors suitable, which Through-the-arm force control and is aactive well-known technique programmable and non-programmable. The programmable categorized as through-the-arm end effector force type control. whereas the non-programmable active cannot. type can accomplish trajectory grinding-force categorized as through-the-arm and active end effector force whereas non-programmable active end effectors cannot. to athe tool composedtool of awould particular material thattracking, enables where feedback to determinetechnique the tool- refers typepassive can accomplish trajectory grinding-force tracking, control.force sensory A compliance alsoend beeffectors suitable, which Through-the-arm force controlis is isused a well-known well-known whereas the non-programmable active cannot. control. A passive compliance tool would also be suitable, which Through-the-arm force control a technique compliance. Tocomposed calculateofthe grinding force, athat simplified to-part contact, andfeedback the robot's position is the adjusted whereas the non-programmable active end effectors cannot. refers to a tool a particular material enables where force sensory is used to determine toolA passive compliance tool alsomaterial be suitable, which Through-the-arm force controlis isused a well-known technique to a model tool composed ofand awould particular thatprogram enables where force sensory feedback to determine the toolgrinding is used a path planning accordingly. One can immediately the combination of refers A passive compliance tool would also force, be suitable, which Through-the-arm force control is notice a well-known compliance. Tocomposed calculate the grinding athat simplified to-part contact, andfeedback the robot's position is technique adjusted refers to a toolTo ofthe a particular material enables where force sensory is used position to determine the tool- compliance. calculate grinding force, a simplified to-part contact, and the robot's is adjusted refers to a tool composed of a particular material that enables where force sensory feedback is used to determine the toolgrinding model is used used the and grinding path force, planning program accordingly. One can can immediately notice the combination combination of grinding compliance. To calculate a simplified to-part contact, andimmediately the robot's position is adjusted model is and aa path planning program accordingly. One notice the of compliance. To calculate the grinding force, a simplified to-part contact, and the robot's position is adjusted Copyright © 2019 IFAC 1179 accordingly. One can immediately notice the combination of grinding model is used and a path planning program grindingby Elsevier model Ltd. is used andreserved. a path planning program accordingly. OneIFAC can (International immediatelyFederation notice theofcombination of Hosting 2405-8963 © 2019, Automatic Control) All rights
Copyright © 2019 IFAC 1179 Peer review©under of International Federation of Automatic Copyright 2019 responsibility IFAC 1179Control. 10.1016/j.ifacol.2019.11.357 Copyright © 2019 IFAC 1179 Copyright © 2019 IFAC 1179
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determined the efficient path of the robot that minimizes the grinding time and achieve the wanted shape of the workpiece (Radius of the corners, surface roughness, etc). Nomenclature Fp' grinding force, N K1,K2 experimental coefficients Qw material removal rate, m3/s θ surface contact angle, deg θ0 surface contact position, deg R radius of the grinding wheel, m h distance between the center of the grinding wheel and the surface contact, m α tilt angle of the grinding wheel, deg S area of the surface contact, m² Vf grinding speed in the Y axis, m/s d depth of cut, m K experimental coefficient Za Length of the pneumatic actuator, m Zp position of the contact surface on the Z axis, m ZR0 initial Z position of the robot, m d0 initial depth of cut, m β experimental coefficient f viscous friction m mass of the moving part of the actuator k experimental coefficient
case, we simplifier the problem to grinding a radius R=4mm on the corners (Fig. 1 (b)). The round is located on the superior surface of the parallelepiped workpiece. The grinding wheel will be at a constant angle α compared to the ground surface as illustrated in Fig. 2.
(a) Pressure
Different grinding tool holders can be used by opening the chuck of the tool holder and inserting a different grinding tool. A diagram is shown in Fig. 1 (a) to illustrate the dynamic interaction involved in this system. Pressurized air and electric current enter the pneumatic cylinders and the angle grinder respectively. The air pressure causes the piston to extend, moving in the XZ plan the grinding tool toward the workpiece in a direction that creates an angle α=5° with grinded surface. The main objective of the pneumatic actuator is to obtain a constant contact force. The electric current is supplied to the grinding wheel and determines its power output. Finally, based on the tool/part position, a particular material removal rate (MRR) is obtained. The relationship between the normal grinding force and the grinding parameters is presented later in this paper. 3. GRINDING PROCESS We chose in this work a rounded corner grinding on a large parallelepiped workpiece as case study. Such operation is usually done manually by industrial partners and can take several days to finish for a complex workpiece. This makes the process automation much needed. As an example in our
Contact force Pneumatic Cylinder
Tool/Part interaction
Electric current Angle grinder
(b)
Grinding force
Material Removal Rate
Finished workpiece Material to be ground
R
2. GRINDING SYSTEM Prior to modelling, a grinding system is developed. This system is composed of a serial robot and an active grinding end effector. The used robot is a 6 axis serial robot ABB IRB 7600 with a maximum carrying charge of 500 Kg. The grinding end-effector is attached to the end of arm of the robot. The grinding end-effector is equipped with a 1 DoF pneumatic cylinder attached to the angle grinder. The actuator alloys the movement of the grinding tool along the Z axis. A rigid grinding wheel is mounted on the electric angle grinder.
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Fig. 1 (a) Relation between the components of the grinding system (b) 4 mm rounded corner on the workpiece The grinding process is done in two steps in order to reduce the needed time for this operation. The first step is roughing step, in which the material removal rate is maximized. The area of the contact surface between the grinding wheel and the workpiece is consequently maximized (Smax) taking into consideration different criterion. The second step is finishing operation. In this step the quality of the final surface is more important than the material removal rate.
4. MODELING OF THE GRINDING FORCE Grinding is a subject that gained great attention in the last decades. Many research works were interested in studying this process. Today, in the literature, numerous models are used to describe different parameters of the grinding operation. There are temperature models, force models, surface roughness models, energy models, etc. The material removal rate, the dynamic behaviour of the grinding tools, the surface quality and tool wear are greatly influenced by the grinding forces, see Durgumahanti et al. (2010). Therefore, many research developments were focalized on calculating this latter. Salje (1953) considered that grinding force model is directly linked to the shear strength of the grinded workpiece. Brach et al. (1988) took into consideration the effect of the shape of the grinding wheel. Ono (1961) proposed a model that considered the distance between cutting edges of the grinding wheel. Lindsay (1971) used two different grinding models.
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The first model is used when the grinded material is easy to grind, the second one is used when the grinded material is hard to grind. Werner (1978) superimposed all instantaneous frictional and chip formation forces of the individual edges in contact with the workpiece. The grinding force model is derived as a function of the main grinding parameters. The model of the normal grinding force Fp has an exponent that is ε=0.5 when the phenomenon is purely frictional and it is ε=1 when the phenomenon is purely a chip formation force (1). 𝐹𝐹𝑝𝑝 = 𝐾𝐾𝑤𝑤 [𝐶𝐶1
]𝛾𝛾
𝑄𝑄𝑤𝑤 ′ [ ] 𝑣𝑣𝑠𝑠
2ԑ−1
[𝑑𝑑]1−ԑ [2𝑅𝑅]1−ԑ
(1)
Where, Kw is a proportionality factor, ԑ is an exponent taking values in the range of 0.5 to 1, γ is another exponent taking values from 0 to 1 depending on the grinding parameter and finally C1 is the cutting edge density. Those experimental parameters must be determined according to the application. Q’w is the specific material removal rate, vs is the grinding wheel speed, d is the cut depth and R is the radius of the grinding wheel. Previous works supposed that grit distribution in the grinding wheel is uniform. Chang and Wang (2008) developed a stochastic grinding force model that considered the random distribution of grits.
(a)
Fp ′ = K 1 + K 2 Q w
(2)
Fig. 3 Grinding tool in contact with the workpiece (the angle θ is exaggerated for illustration purposes) In reality, the contact surface between the grinding wheel and the workpiece is small (Fig. 3), therefore the angle θ is very small and can be approximated using (3). We have: 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 =
√𝑅𝑅2 − ℎ2 ≈ 𝜃𝜃 𝑅𝑅
(3)
𝑅𝑅2 𝜃𝜃 ≈ 𝑅𝑅√𝑅𝑅2 −ℎ2
(4)
And due to the tilt angle α of the grinding disc: d h= R− cosα
(5)
With d is the cut depth. The contact surface between the wheel and the workpiece is calculated by eq. (6) π (6) S = 2R√R2 − h2 − h√ R 2 − h2 2π
Suppose that R+h≈2R the equation can be transformed to: 3
3
S = (R − h)2 √R + h = (R − h)2 √2R 3
2 d = (R − (R − )) √2R cosα
(7)
The simplified force model can be then written as follows: (8) Fp ′ = K1 + K 2 Q w = K1 + K 2 SV𝑓𝑓
(b)
β
d )) √2R = Kdβ Fp = K 2 SVf = K 2 Vf (R − (R − cosα
(9)
Because α, R , Vf are constants. With K =
K2 Vs √2R 3
(cosα)2
, Fp = Fp ′ − K1 and β = 3/2.
The dynamic behaviour of the PA and the grinding process (9) were used to control the grinding system and are implemented in Matlab simulation in order to observe the dynamic behaviour of the system (Chaoui et al.(2019)). Fig. 2 (a) Grinding configuration in the YZ plan and (b) in the XZ plan The used process model for the chosen grinding application is that of Persoons and Vanherck (1996) defined by eq. (2) with K1 and K2 experimentally determined. It is widely used for disc and cup grinding applications. This model is similar to the models proposed by Nasri and Bolmsjo (1995) and Hahn and Lindsay (1969). For simulation and control, a simplification of the model is needed.
5. PATH PLANNING 5.1 Position of the grinding wheel The grinding path can be described by defining the succession of point where the center of the grinding disc must be. The rounds while be ground in multiple layers that have the same thickness. Each layer is ground with multiple passes of the grinding wheel (Fig. 4).
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The number of layers and passes depends on the grinding process parameters as well as the grinding wheel and the workpiece geometry. The grinding wheel, while doing one pass will leave an elliptic groove on the surface of the workpiece (Fig. 3) due to the incline angle.
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To place the first ellipse in the first layer (E1L1) (Fig. 5). The contact surface between the grinding wheel and the workpiece is calculated to insure a maximum material removal rate. This surface area is linked to the depth of cut d (9). The robot is doing a back and forth motion along the y axis. Consequently, the contact area is function only of (x,z) position of the center of the grinding wheel. The position of the next passes of the grinding wheel depends on the position of the previous passes. As a result of this, calculating the intersection between the ellipses of different layers is needed and can be done using work of Schneider and Eberly (2003). Limits of the grinding wheel
•
•
•
The blank
L1 L2 L3 • • •
Grinding layers
Ln-1 Ln Fig. 5 The limits of the grinding wheel in different layers
Fig. 4 (a) Perimeter of the grinding wheel in first step in blue and second step in red (b) a close up look to the perimeter In the first grinding step, the material removal rate must be maximized to reduce the time needed for this operation. Using the force model developed in the previous section(9), we can calculate the maximum cut depth dmax that the robot can do in order to have the maximum MRR for a given value of the grinding force Fp (in our case Fp= 200N). Using (7) we can calculate the surface area of the ellipse that is going to be emerged inside the workpiece (surface highlighted in grey colour in Fig. 3). This surface will help determine the position of the ellipse using (5). The next pass will be placed directly next to the first pass until the whole layer is covered. For the second layer and for the other layers, the grinding wheel will be placed between two passes of the previous layer as shown in Fig. 5. The objective of the grinding program, for the first step, is to obtain in each grinding pass the same contact area Smax to maximize the MRR.
The number of layers N is dependent on the amount of material that has to ground (10). Where dmax is the maximum depth of cut. 𝑁𝑁 =
𝑅𝑅(√2 − 1) 𝑑𝑑𝑚𝑚𝑚𝑚𝑚𝑚
(10)
6. GRINDING PROGRAM In order to determine the trajectory of the robot. it is necessary to determine the position of the grinding wheel as a function of time. Matlab program uses the grinding process parameters and the geometry of the ground workpiece to determine the robot path and to evaluate the quality of the final workpiece using the previously described method. This program needs as inputs: the grinding wheel dimensions, the grinding advance speed, the ground workpiece dimension and the grinding force parameter K (Fig. 6). The grinder rotation speed, material properties and other constant parameters are taken into consideration while determining the parameter K of the force model.
5.2 Calculation of the intersection surfaces 1182
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For the finishing step, two different strategies are compared in order to choose the efficient one Fig. 8.
Fig. 7 Effect of grinding force on the efficiency of the process
(a)
(b)
Fig. 8 Grinding wheel perimeter for 3 consecutive passes with (a) First finishing strategy (b) Second finishing strategy Fig. 6 Flow diagram of path planning and surface quality evaluation 7. RESULTS The number of passes and consequently the time needed for the grinding operation is directly linked to normal grinding force applied on the grinding wheel. Fig. 7 shows the effect of varying this parameter on the number of grinding pass and therefore on the efficiency of the process. Increasing the grinding force will increase the area of the contact surface, therefore the number of passes and the time needed for the grinding operation decreases. Fig. 4 shows the tool path followed by the grinding wheel. The most important feature of the rounds along the width of the workpiece is the circularity C. The formula used to calculate this coefficient is as follows: 𝑃𝑃2 𝐶𝐶 = 𝜋𝜋 × 𝐴𝐴
(11)
Where, P is the perimeter and A is the surface of rounds. The closer C is to 1, the closer the rounds surface is to a perfect quarter of a circle. In addicting to that, the surface finish roughness is evaluated by Ra. Fixing the grinding force to 200N and the grinding feed speed to 0.5 m/s. we were able to achieve rounds circularity equal to 1.0021 and a medium radius of 4.005mm in simulation during the roughing step.
Fig. 9 Comparison between 1st and 2nd finish strategies The most intuitive one is placing the second pass j+1 in the same radius as the previous one j but at a slightly bigger angle Δθ that is a function of the wanted surface quality: 𝜃𝜃𝑗𝑗+1 = 𝜃𝜃𝑗𝑗 + ∆𝜃𝜃 . We can observe also, when done manually, that operators choose to place the j+1 pass between the two 𝜃𝜃𝑗𝑗 +𝜃𝜃𝑗𝑗−1
last pass j and j-1:𝜃𝜃𝑗𝑗+1 = . The choice of the strategy 2 depends on the wanted surface quality Ra (Fig. 9). The wanted surface quality we fixed is Ra=5μm, therefore the chosen grinding strategy for the finishing step is the 2 nd . This step accounts for 40% of the time need in the robotic grinding operation. Fig. 10 shows a comparison between finished and
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unfinished rounds. The circularity is reduced from 1.0021 to 1.0001 and a medium radius of 4mm. using the path planning program we were able to estimate the grinding operation to be 10 min 56 s. Grinding the same workpiece manually will take approximately 20min to finish. The solution we propose helped reduce the time needed by 45%.
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ROMANSY 22 – Robot Design, Dynamics and Control., 584, 363-369. Dai, H., Yuen, K.M. and Elbestawi, M.A. (1993). Parametric modelling and control of the robotic grinding process. International Journal of Advanced Manufacturing Technology, 8, 182-192. Durgumahanti, U.S.P., Singh, V. and Rao, P.V. (2010). A New Model for Grinding Force Prediction and Analysis. International Journal of Machine Tools and Manufacture, 50, 231-240. Hahn, R.S., Lindsay, R.P. (1969). The influence of process variables on material removal, surface integrity, surface finish and vibration in grinding. Advances in Machine Tool Design and Research, 95-117 Huang, H., Gong, Z.M., Chen, X.Q. and Zhou, L. (2002). Robotic grinding and polishing for turbine-vane overhaul. Journal of Materials Processing Technology, 127, Issue 2, 140-145. Lindsay,R.P. (1971). On the metal removal and wheel removal parameters—surface finish, geometry and thermal damage in precision grinding, Ph.D.Thesis, Worcester Polytechnic Institute.
Fig. 10 Finished and unfinished workpiece in blue and red respectively 8. CONCLUSION In this paper, we properly presented a robotic grinding solution that can be applied easily on different robots. This practical solution helped reduce vibrations and improve sufficiently surface quality. In addition to that, we proposed a robotic grinding method that was implemented in a Matlab program. This program was used in order to grind a corner on a parallelepiped workpiece and is able to reliably produce the most efficient robot path for this operation. The grinding is done in two steps, to efficiently have a good finished surface. The next goal of this work is the experimental validation of the robotic grinding process and the actuator models, as well as the grinding method. ACKNOWLEDGEMENT We would like to thank the Robotix Academy, contract number N°002-4-09-001 for funding this work as a part of the project funded by INTERREG V-A Grande Région program. REFERENCES Andersson, E.R. (1990). Design and testing of a vibration attenuating handle. International journal of industrial ergonomics, 6, 119-125.
Minami, M., Asakura, T., Dong, L.X. and Huang, Y.M. (1996) Position control and explicit force control of constrained motions of a manipulator for accurate grinding tasks, Advanced Robotics, 11:3, 285-300 Nasri, H., Bolmsjo, G. (1995). A process model for robotic disc grinding. International Journal of Machine Tools and Manufacture, 35, Issue 4, 503-510. Ono, K. (1961). Analysis of the grinding force. Bulletin of the Japan Society of Grinding Engineers, 1, 19–22. Persoons, W., Vanherck, P. (1996) A Process Model for Robotic Cup Grinding. CIRP Annals, 45, Issue 1, 319325. Salje, E. (1953). Grundlagen des schleifvorganges, Werkstatt und Betrieb, 86, 177–182. Schneider, P.J. and Eberly, D.H. (2003). Geometric tools for computer graphics, chapter 7. Morgan Kaufmann Publishers, United States of America. Sozbilen, M.C., Dastan, A.E., Gunay, H. and Kucuk, L. (2018). A prospective study of angle grinder injuries in the hands and forearms during a one-year period. Hand Surgery and Rehabilitation, 37, Issue 5, 300-304.
Brach, K., Pai, D.M., Ratterson, E. and Shaw, M.C. (1988). Grinding forces and energy. Journal of Engineering for Industry, 110, 25–31.
Thomessen, T., Lien, T.K. and Sannæs, P.K. (2001). Robot control system for grinding of large hydro power turbines. Industrial Robot: An International Journal, 28 Issue: 4, 328-334.
Chang, H.-C. and Wang, J.-J.J. (2008). A stochastic grinding force model considering random grit distribution, International Journal of Machine Tools and Manufacture, 48, 1336-1344.
Tönshoff, H.K., Peters, J., Inasaki, I. and Paul, T. (1992). Modelling and Simulation of Grinding Processes, CIRP Annals, 41, Issue 2, 677-688.
Chaoui, M.D., Léonard, F., Abba, G. (2019). Improving Surface Roughness in Robotic Grinding Process.
Werner, G. (1978). Influence of work material on grinding forces. Annals of CIRP, 27, 243-248.
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Path Planning forIFAC Robotic Grinding on a Large Forged Workpiece PapersOnLine 52-13 (2019) 1162–1167 Path Planning Planning for for Robotic Robotic Grinding Grinding on aa Large Large Forged Forged Workpiece Workpiece Path Mohamed Didi Chaoui, Françoison Léonard and Gabriel Abba Path for Grinding on aa Large Forged Workpiece Path Planning PlanningMohamed for Robotic Robotic Grinding on Large Forged Workpiece Didi Chaoui, François Léonard and Gabriel Abba Mohamed Didi Chaoui, François Léonard and Gabriel Abba Mohamed Didi Chaoui, Léonard and Gabriel Abba Université de Lorraine, Arts etFrançois Métiers ParisTech, LCFC, F-57000 Metz, Mohamed Didi Chaoui, François Léonard and Gabriel Abba France (email: [email protected]) Université de de Lorraine, Lorraine, Arts Arts et et Métiers Métiers ParisTech, LCFC, LCFC, F-57000 F-57000 Metz, Metz, Université ParisTech, France (email: [email protected]) Université de Lorraine, et Métiers ParisTech, LCFC, F-57000 Metz, France (email: Arts [email protected]) Université de Lorraine, Arts et Métiers ParisTech, LCFC, F-57000 Metz, France (email: [email protected]) France (email: [email protected])
Abstract: Abstract: In this paper a robotic grinding system which can produce a finished workpiece that respects some Abstract: product geometric specifications proposed. It iscan composed 1 DoF active compliance actuator some fixed Abstract: In this paper paper robotic grindingissystem system which produceofaaa finished finished workpiece that respects respects In this aa robotic which can produce workpiece that some Abstract: between the grinder and grinding the robot. The 1 DoF actuator associated toDoF the active tool can be mounted at existing product geometric specifications is proposed. It is composed of a 1 compliance actuator fixed In this paper a robotic grinding which can produce thatindustrials. respects product geometric specifications issystem proposed. It isvery composed ofaaand a finished 1 DoF active compliance actuator some fixed robotic installations which this flexible easy toworkpiece use by The In this paper a robotic grinding system which can produce finished workpiece that respects some between the grinder grinder and the make robot. The solution 1 DoF DoF actuator associated toDoF the active tool can be the mounted at existing existing product geometric specifications is proposed. It is composed of a 1 compliance actuator fixed between the and the robot. The 1 actuator associated to the tool can be mounted at grinding system composed of the robot and the actuator is able to apply a constant contact force between product installations geometric specifications is this proposed. It isvery composed of and a 1 DoF active compliance actuator fixed robotic which make solution flexible easy to use use by the industrials. The between the grinder and the make robot.tool. TheAsolution 1 path DoF actuator associated toeasy the presented tool canby beinthe mounted at existing robotic installations which this very flexible and to The the workpiece and the grinding planning method isapply thisindustrials. article. Using between the grinder and theofrobot. The and 1 DoF actuator associated toalso theatool can be mounted at between existing grinding system composed the robot the actuator is able to constant contact force robotic installations which make this is solution very for flexible use bycontact the industrials. The grinding system composed of the robot the actuator isgrinding able and to apply a to constant between analytical calculations, the robot path determined aeasy rounded corner on a force parallelepiped robotic installations which make this Aand solution very flexible and easy to use byinthe The the workpiece and the grinding tool. path planning method isapply also presented thisindustrials. article.between Using grinding system composed of the robot and the actuator is able to a constant contact force the workpiece and the grinding tool. A path planning method is also presented in this article. Using workpiece with a given precision of the surface shape. Copyright © 2019 IFAC grinding system composed of the robot and the actuator is able to apply a constant contact force between analytical calculations, the robot tool. path A is determined determined for method grindingisaaalso rounded cornerinon on the workpiece and the the grinding path planning presented thisa parallelepiped article. Using analytical calculations, robot path is for grinding rounded corner the workpiece and the precision grinding tool. A path planning method is 2019 also presented in thisa parallelepiped article. Using workpiece with a given of the surface shape. Copyright © IFAC Keywords: Path planning, Robotic grinding, Disc grinding, Roughness, Rounds. © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All reserved. analytical calculations, the robot of path issurface determined for grinding©a2019 rounded corner onrights a parallelepiped workpiece with a given precision the shape. Copyright IFAC analytical calculations, the robot path is determined for grinding a rounded corner on a parallelepiped workpiece with a given precision of the surface shape. Copyright © 2019 IFAC Keywords: Path Path planning, planning, Robotic Robotic grinding, grinding, Disc Disc grinding, grinding, Roughness, Rounds. Rounds. Keywords: Roughness, workpiece with a given precision of the surface shape. Copyright © 2019 IFAC position and force control. This combination is referred to as Keywords: Path planning, Robotic grinding, Disc grinding, Roughness, Rounds. Keywords: Path planning, Robotic grinding, Disc grinding, Roughness, Rounds. 1. INTRODUCTION hybrid control (or hybrid position/force control). position and and force force control. control. This combination combination is referred referred to to as as position This is 1. INTRODUCTION In order to reduce the number of tedious operations affected 1. INTRODUCTION hybrid control (or hybrid position/force control). Thomessen al.hybrid (2001)position/force presents a robot system position and et force control. This combination iscontrol referred to as (or control). to the operators, their working conditions by hybrid positioncontrol and force control. This combination is referred to as 1. INTRODUCTION In order to reduce reduce to theimprove number of of tedious operations affected dedicated toetgrinding large Francisa turbines. The control hybrid control (or hybrid position/force control). 1. INTRODUCTION In order to the number tedious operations affected Thomessen al. (2001) presents robot control system reducing dangerous operations andworking to improve quality hybrid control hybrid position/force control). et (or al. presents a robot control systema to the operators, operators, to improve their conditions by Thomessen system is based on (2001) an active force feedback system In order to reduce theimprove number workpieces, of tedious operations affected to the to their working conditions by dedicated toetgrinding grinding large Francis turbines. The using control consistency of manufactured many industrials Thomessen al. (2001) presents a robot control system In order to reduce the number of tedious operations affected dedicated to large Francis turbines. The control reducing dangerous operations andworking to improve improve quality axes force sensor attached to feedback the robot’s end effector. Thomessen et al. (2001) presents a robot control systema to the tooperators, to different improve their conditions by three reducing dangerous operations and to quality system is based based on an active active force system using chose automatize kinds of processes. Grinding dedicated to grinding large Francis turbines. The control to the operators, to improve their working conditions by system is on an force feedback system using a consistency of manufactured workpieces, many industrials This system offers high flexibility and robustness against dedicated to grinding large Francis turbines. The control reducing dangerous operations and to improve quality consistency of of manufactured workpieces, many industrials three axes force on sensor attached to feedback the robot’s robot’s end effector. effector. processtoisautomatize one those processes thatofrepresented aGrinding serious system is based an active force system using reducing dangerous operations and toprocesses. improve quality three axes force sensor attached to the end chose different kinds workpiece positioning and theforce grinding tool wear. Using theaa system is based on an active feedback system using consistency of manufactured many industrials chose to (Andersson automatize different kinds of et processes. Grinding This system offers high flexibility androbot’s robustness against problem (1990) andworkpieces, Huang al. (2002)). Royal This three axes force sensor attached to the end effector. consistency of of manufactured workpieces, many industrials system offers high flexibility and robustness against process is one those processes that represented a serious Dai and etattached al.the(1993) developed and tested an three axes models, force sensor to the robot’s endUsing effector. chose tofor automatize different kinds processes. aGrinding process one of those processes thatof serious identified workpiece positioning grinding tool wear. the Society the Prevention ofand Accidents Surveillance Systems This system offers high andtool robustness against chose tois(Andersson automatize different kinds ofrepresented processes. Grinding positioning andflexibility the controller grinding wear. Using the problem (1990) Huang et al. (2002)). (2002)). Royal workpiece adaptive pole placement using computer This system offers high flexibility and robustness against process is one of those processes that represented a serious problem (Andersson (1990) and Huang et al. Royal identified models, Dai and et al. al.the(1993) (1993) developed andUsing tested the an data showed angle processes grinders were the most dangerous workpiece models, positioning grinding tooliswear. process is one of those that represented aSystems serious identified Dai et developed tested an Society for thethat Prevention ofand Accidents Surveillance simulations. The purpose ofthethecontroller controller toand regulate the workpiece positioning and grinding toolusing wear. Using problem (Andersson (1990) Huang etrecorded al. (2002)). Royal Society for the Prevention of Accidents Surveillance Systems adaptive pole placement computer tools with an average of 5,400 injuries yearly in identified models, Dai et al. (1993) developed and tested an problem (Andersson (1990) and Huang et al. (2002)). Royal adaptive pole force, placement controller usingand computer data showed that angle grinders grinders were Surveillance the most most dangerous dangerous normal grinding Minami etdeveloped al. (1996). the basis identified models, Dai see et al. (1993) tested an Society for thethat Prevention of Accidents Systems data showed angle were the simulations. The purpose purpose of thecontroller controller is to to On regulate the Great Britain. According to this research, the most injured adaptive pole placement using computer Society for the Prevention of Accidents Surveillance Systems simulations. The of the controller is regulate the tools with an an that average ofgrinders 5,400 injuries injuries recorded yearly in in of a detailed analysis ofsee theMinami grinding process, motions ofbasis the adaptive pole placement controller using computer data showed angle were the most dangerous tools with average of 5,400 recorded yearly normal grinding force, et al. (1996). On the areas are face, head andgrinders upper extremity (Sozbilen et al. normal simulations. Theforce, purpose theacontroller is to On regulate the data that angle were the the most dangerous grinding see of Minami et al. (1996). the basis Greatshowed Britain. According to this injuries research, most injured dynamic system of grinding robot is modelled simulations. The purpose of the controller is to regulate the tools with an average of to 5,400 recorded in constrained Great Britain. According this research, the most injured of a detailed detailed analysis ofsee the grinding process, motions ofbasis the (2018)). Removal of Excess material, surfacing andyearly creating normal grinding force, Minami et al. (1996). On the tools with an average of 5,400 injuries recorded yearly in of a analysis of the grinding process, motions of the areas are face, head and upper extremity (Sozbilen et al. in this paper. In the model, the constrained generalized forces normal grinding force, see Minami et al. (1996). On the basis Great Britain. According to this research, the most injured areas face, head and (Sozbilen et al. constrained dynamic system of aa grinding grinding robot is modelled modelled rounds inRemoval workpieces aretoupper dangerous and the time consuming of aincluded detaileddynamic analysis of theasgrinding process, motions ofstate the Great are Britain. According this extremity research, most injured system of robot is (2018)). of Excess Excess material, surfacing and creating are and expressed an obvious function of theforces of a detailed analysis of thethe grinding process, motions of the areas are Removal face, head and upper extremity (Sozbilen et do al. constrained (2018)). of material, surfacing and creating in this paper. In the model, constrained generalized grinding operations affected to skilled operators to constrained dynamic system of a grinding robot is modelled areas are face, head and upper extremity (Sozbilen et al. in this paper. In the model, the constrained generalized forces rounds in workpieces are dangerous and time consuming and included input generalized forces. Agrinding controller then built constrained dynamic system of aobvious robotis isof modelled (2018)).inRemoval of Excess material,a surfacing and creating rounds workpieces are dangerous and time consuming are and expressed as an function theforces state manually. These operations become bigger problem in this paper. In the model, thean constrained generalized (2018)). Removal of Excess material, surfacing and creating included and expressed as obvioussensors. function of the state grinding operations affected to skilled skilled operators towhen do are without involving any force feedback Simulations in this paper. In the model, the constrained generalized forces rounds in workpieces are dangerous and time consuming grinding operations affected to operators to do and input generalized forces. A controller is then built the size of the ground workpieces is very large. are included and expressed as an obvious function of the state rounds in workpieces are dangerous and time consuming input generalized forces. A controller is of then manually. These operations operations become bigger problem towhen when haveincluded been done for justification of the feasibility ofbuilt the are and expressed as an obvious function the state grinding operations affected to skilled operators do and manually. These become aa bigger problem without involving any force feedback sensors. Simulations and input generalized forces. A controller is then built grinding operations affected to skilled operators to do involving any force sensors. the size of the the ground ground workpieces is very very large. controller by taking an feedback articulated planar two-link In size literature, proposed automation solutions canwhen be without and input generalized forces. A of controller is Simulations then built manually. These operations become a bigger problem the of workpieces is large. have been done for justification the feasibility of the without involving anyjustification force feedback sensors. Simulations manually. These operations become a bigger problem when have been done for ofet the feasibility of the manipulator as antaking example Tönshoff al. (1992). categorized two groups. Theisfirst concerns the without involving any force feedback sensors. Simulations the size of theinground workpieces very group large. controller by an articulated planar two-link In literature, proposed automation solutions can be have been done for justification of the feasibility of the the size of the ground workpieces is very large. by taking an articulated planar two-link In literature, proposed automation solutions thecan be controller automation using CNC special-purpose second have been done for justification ofet the feasibility of the manipulator as hand, antaking example Tönshoff al. (1992). (1992). categorized in two two groups. The first first machines, group concerns the On the other an active or passive compliance end controller by an articulated planar two-link In literature, proposed automation solutions can be manipulator as an example Tönshoff et al. categorized in groups. The group concerns the group concerns the automation using robots. But the first controller by taking an articulated planar two-link In literature, proposed automation solutions can be automation using CNC special-purpose machines, the second second effector control the endoreffector tooling having end the manipulator as hand, aninvolves example Tönshoff et al. (1992). categorized in two groups. The first group concerns the automation using CNC special-purpose machines, the On the other an active passive compliance solution is normally quite expensive. robots have manipulator as hand, an example Tönshoff et al. (1992). categorized in two groups. Theusing firstIndustrial group concerns the On thetoother active or passive compliance end group concerns the automation robots. But the first ability control the an applied force by measuring the force automation using CNC special-purpose machines, the second group concerns the automation using robots. But the first effector control involves the end effector tooling having the been proven to CNC bequite a expensive. more economical solution for effector On theThis other hand, an active passive compliance end automation using special-purpose machines, the second control involves the endor effector tooling having the solution is normally normally Industrial robots have error. is done independently from the robot's position On the other hand, an active or passive compliance end group concerns the automation using robots. But the first solution is quite expensive. Industrial robots have ability to control the applied force by measuring the force automation. Thetothe robot can be programmed to carry out first the effector involves the end effector tooling having the group concerns using robots. But the tocontrol control the applied force by measuring the force been proven beautomation more economical solution for ability controller and depend only on the force control. In other effector control involves the end effector tooling having the solution isjobs normally quite Industrial robots have been proven to can be aa expensive. more economical solution for error. This is done done independently from the robot's position grinding and achieve the required surface quality ability to control the applied force by measuring the force solution is normally quite expensive. Industrial robots have error. This is independently from the robot's position automation. The robot can be programmed to carry out the words, the force and position control are dissociated in active ability to control the applied force by measuring the force been proven to be a more economical solution for automation. Theconsistency be programmed to force carry out the controller and depend only on on the thefrom force control. In other and machining with active contact control. This is done independently thecontrol. robot's position been proven torobot be can a more economical solution for error. and depend only force In other grinding jobsThe and can achieve the required surface quality control. Active compliance actuators can classified as error. This is done independently from the be robot's position automation. robot can be programmed to carry out the controller grinding jobs and can achieve the required surface quality words, the force and position control are dissociated in active The existing active force control methods can be broadly controller only control on the are force control. In active other automation. Theconsistency robot can with be programmed to force carry control. out the words, the and forcedepend and non-programmable. position dissociated in and machining active contact programmable and The programmable controller and depend only on the force control. In other grinding jobs and can achieve the required surface quality and machining consistency with active contact force control. control. Active compliance actuators can be classified classified as categorized asactive through-the-arm and active end effector force control. words, the force and position control arecan dissociated in active grinding jobs and can achieve the methods required surface quality Active compliance actuators be as The existing force control can be control. broadly type can accomplish trajectory grinding-force tracking, words, the force and position control are dissociated in active and machining consistency with active contact force The existing active force control methods can be broadly programmable and non-programmable. The programmable control. control. Active compliance actuators can be classified as and machining consistency with active contact force control. and non-programmable. Theeffectors categorized asactive through-the-arm and methods active end end effector force programmable whereas theaccomplish non-programmable active end cannot. control. Active compliance actuators can beprogrammable classified as The existingas force control caneffector be broadly categorized through-the-arm and active force type can trajectory grinding-force tracking, programmable and non-programmable. The programmable The existing active force control methods can be broadly can compliance accomplish trajectory grinding-force tracking, control. A passive tool would alsoend beeffectors suitable, which Through-the-arm force control and is aactive well-known technique programmable and non-programmable. The programmable categorized as through-the-arm end effector force type control. whereas the non-programmable active cannot. type can accomplish trajectory grinding-force categorized as through-the-arm and active end effector force whereas non-programmable active end effectors cannot. to athe tool composedtool of awould particular material thattracking, enables where feedback to determinetechnique the tool- refers typepassive can accomplish trajectory grinding-force tracking, control.force sensory A compliance alsoend beeffectors suitable, which Through-the-arm force controlis is isused a well-known well-known whereas the non-programmable active cannot. control. A passive compliance tool would also be suitable, which Through-the-arm force control a technique compliance. Tocomposed calculateofthe grinding force, athat simplified to-part contact, andfeedback the robot's position is the adjusted whereas the non-programmable active end effectors cannot. refers to a tool a particular material enables where force sensory is used to determine toolA passive compliance tool alsomaterial be suitable, which Through-the-arm force controlis isused a well-known technique to a model tool composed ofand awould particular thatprogram enables where force sensory feedback to determine the toolgrinding is used a path planning accordingly. One can immediately the combination of refers A passive compliance tool would also force, be suitable, which Through-the-arm force control is notice a well-known compliance. Tocomposed calculate the grinding athat simplified to-part contact, andfeedback the robot's position is technique adjusted refers to a toolTo ofthe a particular material enables where force sensory is used position to determine the tool- compliance. calculate grinding force, a simplified to-part contact, and the robot's is adjusted refers to a tool composed of a particular material that enables where force sensory feedback is used to determine the toolgrinding model is used used the and grinding path force, planning program accordingly. One can can immediately notice the combination combination of grinding compliance. To calculate a simplified to-part contact, andimmediately the robot's position is adjusted model is and aa path planning program accordingly. One notice the of compliance. To calculate the grinding force, a simplified to-part contact, and the robot's position is adjusted Copyright © 2019 IFAC 1179 accordingly. One can immediately notice the combination of grinding model is used and a path planning program grindingby Elsevier model Ltd. is used andreserved. a path planning program accordingly. OneIFAC can (International immediatelyFederation notice theofcombination of Hosting 2405-8963 © 2019, Automatic Control) All rights
Copyright © 2019 IFAC 1179 Peer review©under of International Federation of Automatic Copyright 2019 responsibility IFAC 1179Control. 10.1016/j.ifacol.2019.11.357 Copyright © 2019 IFAC 1179 Copyright © 2019 IFAC 1179
2019 IFAC MIM Berlin, Germany, August 28-30, 2019 Mohamed Didi Chaoui et al. / IFAC PapersOnLine 52-13 (2019) 1162–1167
determined the efficient path of the robot that minimizes the grinding time and achieve the wanted shape of the workpiece (Radius of the corners, surface roughness, etc). Nomenclature Fp' grinding force, N K1,K2 experimental coefficients Qw material removal rate, m3/s θ surface contact angle, deg θ0 surface contact position, deg R radius of the grinding wheel, m h distance between the center of the grinding wheel and the surface contact, m α tilt angle of the grinding wheel, deg S area of the surface contact, m² Vf grinding speed in the Y axis, m/s d depth of cut, m K experimental coefficient Za Length of the pneumatic actuator, m Zp position of the contact surface on the Z axis, m ZR0 initial Z position of the robot, m d0 initial depth of cut, m β experimental coefficient f viscous friction m mass of the moving part of the actuator k experimental coefficient
case, we simplifier the problem to grinding a radius R=4mm on the corners (Fig. 1 (b)). The round is located on the superior surface of the parallelepiped workpiece. The grinding wheel will be at a constant angle α compared to the ground surface as illustrated in Fig. 2.
(a) Pressure
Different grinding tool holders can be used by opening the chuck of the tool holder and inserting a different grinding tool. A diagram is shown in Fig. 1 (a) to illustrate the dynamic interaction involved in this system. Pressurized air and electric current enter the pneumatic cylinders and the angle grinder respectively. The air pressure causes the piston to extend, moving in the XZ plan the grinding tool toward the workpiece in a direction that creates an angle α=5° with grinded surface. The main objective of the pneumatic actuator is to obtain a constant contact force. The electric current is supplied to the grinding wheel and determines its power output. Finally, based on the tool/part position, a particular material removal rate (MRR) is obtained. The relationship between the normal grinding force and the grinding parameters is presented later in this paper. 3. GRINDING PROCESS We chose in this work a rounded corner grinding on a large parallelepiped workpiece as case study. Such operation is usually done manually by industrial partners and can take several days to finish for a complex workpiece. This makes the process automation much needed. As an example in our
Contact force Pneumatic Cylinder
Tool/Part interaction
Electric current Angle grinder
(b)
Grinding force
Material Removal Rate
Finished workpiece Material to be ground
R
2. GRINDING SYSTEM Prior to modelling, a grinding system is developed. This system is composed of a serial robot and an active grinding end effector. The used robot is a 6 axis serial robot ABB IRB 7600 with a maximum carrying charge of 500 Kg. The grinding end-effector is attached to the end of arm of the robot. The grinding end-effector is equipped with a 1 DoF pneumatic cylinder attached to the angle grinder. The actuator alloys the movement of the grinding tool along the Z axis. A rigid grinding wheel is mounted on the electric angle grinder.
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Fig. 1 (a) Relation between the components of the grinding system (b) 4 mm rounded corner on the workpiece The grinding process is done in two steps in order to reduce the needed time for this operation. The first step is roughing step, in which the material removal rate is maximized. The area of the contact surface between the grinding wheel and the workpiece is consequently maximized (Smax) taking into consideration different criterion. The second step is finishing operation. In this step the quality of the final surface is more important than the material removal rate.
4. MODELING OF THE GRINDING FORCE Grinding is a subject that gained great attention in the last decades. Many research works were interested in studying this process. Today, in the literature, numerous models are used to describe different parameters of the grinding operation. There are temperature models, force models, surface roughness models, energy models, etc. The material removal rate, the dynamic behaviour of the grinding tools, the surface quality and tool wear are greatly influenced by the grinding forces, see Durgumahanti et al. (2010). Therefore, many research developments were focalized on calculating this latter. Salje (1953) considered that grinding force model is directly linked to the shear strength of the grinded workpiece. Brach et al. (1988) took into consideration the effect of the shape of the grinding wheel. Ono (1961) proposed a model that considered the distance between cutting edges of the grinding wheel. Lindsay (1971) used two different grinding models.
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The first model is used when the grinded material is easy to grind, the second one is used when the grinded material is hard to grind. Werner (1978) superimposed all instantaneous frictional and chip formation forces of the individual edges in contact with the workpiece. The grinding force model is derived as a function of the main grinding parameters. The model of the normal grinding force Fp has an exponent that is ε=0.5 when the phenomenon is purely frictional and it is ε=1 when the phenomenon is purely a chip formation force (1). 𝐹𝐹𝑝𝑝 = 𝐾𝐾𝑤𝑤 [𝐶𝐶1
]𝛾𝛾
𝑄𝑄𝑤𝑤 ′ [ ] 𝑣𝑣𝑠𝑠
2ԑ−1
[𝑑𝑑]1−ԑ [2𝑅𝑅]1−ԑ
(1)
Where, Kw is a proportionality factor, ԑ is an exponent taking values in the range of 0.5 to 1, γ is another exponent taking values from 0 to 1 depending on the grinding parameter and finally C1 is the cutting edge density. Those experimental parameters must be determined according to the application. Q’w is the specific material removal rate, vs is the grinding wheel speed, d is the cut depth and R is the radius of the grinding wheel. Previous works supposed that grit distribution in the grinding wheel is uniform. Chang and Wang (2008) developed a stochastic grinding force model that considered the random distribution of grits.
(a)
Fp ′ = K 1 + K 2 Q w
(2)
Fig. 3 Grinding tool in contact with the workpiece (the angle θ is exaggerated for illustration purposes) In reality, the contact surface between the grinding wheel and the workpiece is small (Fig. 3), therefore the angle θ is very small and can be approximated using (3). We have: 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 =
√𝑅𝑅2 − ℎ2 ≈ 𝜃𝜃 𝑅𝑅
(3)
𝑅𝑅2 𝜃𝜃 ≈ 𝑅𝑅√𝑅𝑅2 −ℎ2
(4)
And due to the tilt angle α of the grinding disc: d h= R− cosα
(5)
With d is the cut depth. The contact surface between the wheel and the workpiece is calculated by eq. (6) π (6) S = 2R√R2 − h2 − h√ R 2 − h2 2π
Suppose that R+h≈2R the equation can be transformed to: 3
3
S = (R − h)2 √R + h = (R − h)2 √2R 3
2 d = (R − (R − )) √2R cosα
(7)
The simplified force model can be then written as follows: (8) Fp ′ = K1 + K 2 Q w = K1 + K 2 SV𝑓𝑓
(b)
β
d )) √2R = Kdβ Fp = K 2 SVf = K 2 Vf (R − (R − cosα
(9)
Because α, R , Vf are constants. With K =
K2 Vs √2R 3
(cosα)2
, Fp = Fp ′ − K1 and β = 3/2.
The dynamic behaviour of the PA and the grinding process (9) were used to control the grinding system and are implemented in Matlab simulation in order to observe the dynamic behaviour of the system (Chaoui et al.(2019)). Fig. 2 (a) Grinding configuration in the YZ plan and (b) in the XZ plan The used process model for the chosen grinding application is that of Persoons and Vanherck (1996) defined by eq. (2) with K1 and K2 experimentally determined. It is widely used for disc and cup grinding applications. This model is similar to the models proposed by Nasri and Bolmsjo (1995) and Hahn and Lindsay (1969). For simulation and control, a simplification of the model is needed.
5. PATH PLANNING 5.1 Position of the grinding wheel The grinding path can be described by defining the succession of point where the center of the grinding disc must be. The rounds while be ground in multiple layers that have the same thickness. Each layer is ground with multiple passes of the grinding wheel (Fig. 4).
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The number of layers and passes depends on the grinding process parameters as well as the grinding wheel and the workpiece geometry. The grinding wheel, while doing one pass will leave an elliptic groove on the surface of the workpiece (Fig. 3) due to the incline angle.
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To place the first ellipse in the first layer (E1L1) (Fig. 5). The contact surface between the grinding wheel and the workpiece is calculated to insure a maximum material removal rate. This surface area is linked to the depth of cut d (9). The robot is doing a back and forth motion along the y axis. Consequently, the contact area is function only of (x,z) position of the center of the grinding wheel. The position of the next passes of the grinding wheel depends on the position of the previous passes. As a result of this, calculating the intersection between the ellipses of different layers is needed and can be done using work of Schneider and Eberly (2003). Limits of the grinding wheel
•
•
•
The blank
L1 L2 L3 • • •
Grinding layers
Ln-1 Ln Fig. 5 The limits of the grinding wheel in different layers
Fig. 4 (a) Perimeter of the grinding wheel in first step in blue and second step in red (b) a close up look to the perimeter In the first grinding step, the material removal rate must be maximized to reduce the time needed for this operation. Using the force model developed in the previous section(9), we can calculate the maximum cut depth dmax that the robot can do in order to have the maximum MRR for a given value of the grinding force Fp (in our case Fp= 200N). Using (7) we can calculate the surface area of the ellipse that is going to be emerged inside the workpiece (surface highlighted in grey colour in Fig. 3). This surface will help determine the position of the ellipse using (5). The next pass will be placed directly next to the first pass until the whole layer is covered. For the second layer and for the other layers, the grinding wheel will be placed between two passes of the previous layer as shown in Fig. 5. The objective of the grinding program, for the first step, is to obtain in each grinding pass the same contact area Smax to maximize the MRR.
The number of layers N is dependent on the amount of material that has to ground (10). Where dmax is the maximum depth of cut. 𝑁𝑁 =
𝑅𝑅(√2 − 1) 𝑑𝑑𝑚𝑚𝑚𝑚𝑚𝑚
(10)
6. GRINDING PROGRAM In order to determine the trajectory of the robot. it is necessary to determine the position of the grinding wheel as a function of time. Matlab program uses the grinding process parameters and the geometry of the ground workpiece to determine the robot path and to evaluate the quality of the final workpiece using the previously described method. This program needs as inputs: the grinding wheel dimensions, the grinding advance speed, the ground workpiece dimension and the grinding force parameter K (Fig. 6). The grinder rotation speed, material properties and other constant parameters are taken into consideration while determining the parameter K of the force model.
5.2 Calculation of the intersection surfaces 1182
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For the finishing step, two different strategies are compared in order to choose the efficient one Fig. 8.
Fig. 7 Effect of grinding force on the efficiency of the process
(a)
(b)
Fig. 8 Grinding wheel perimeter for 3 consecutive passes with (a) First finishing strategy (b) Second finishing strategy Fig. 6 Flow diagram of path planning and surface quality evaluation 7. RESULTS The number of passes and consequently the time needed for the grinding operation is directly linked to normal grinding force applied on the grinding wheel. Fig. 7 shows the effect of varying this parameter on the number of grinding pass and therefore on the efficiency of the process. Increasing the grinding force will increase the area of the contact surface, therefore the number of passes and the time needed for the grinding operation decreases. Fig. 4 shows the tool path followed by the grinding wheel. The most important feature of the rounds along the width of the workpiece is the circularity C. The formula used to calculate this coefficient is as follows: 𝑃𝑃2 𝐶𝐶 = 𝜋𝜋 × 𝐴𝐴
(11)
Where, P is the perimeter and A is the surface of rounds. The closer C is to 1, the closer the rounds surface is to a perfect quarter of a circle. In addicting to that, the surface finish roughness is evaluated by Ra. Fixing the grinding force to 200N and the grinding feed speed to 0.5 m/s. we were able to achieve rounds circularity equal to 1.0021 and a medium radius of 4.005mm in simulation during the roughing step.
Fig. 9 Comparison between 1st and 2nd finish strategies The most intuitive one is placing the second pass j+1 in the same radius as the previous one j but at a slightly bigger angle Δθ that is a function of the wanted surface quality: 𝜃𝜃𝑗𝑗+1 = 𝜃𝜃𝑗𝑗 + ∆𝜃𝜃 . We can observe also, when done manually, that operators choose to place the j+1 pass between the two 𝜃𝜃𝑗𝑗 +𝜃𝜃𝑗𝑗−1
last pass j and j-1:𝜃𝜃𝑗𝑗+1 = . The choice of the strategy 2 depends on the wanted surface quality Ra (Fig. 9). The wanted surface quality we fixed is Ra=5μm, therefore the chosen grinding strategy for the finishing step is the 2 nd . This step accounts for 40% of the time need in the robotic grinding operation. Fig. 10 shows a comparison between finished and
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unfinished rounds. The circularity is reduced from 1.0021 to 1.0001 and a medium radius of 4mm. using the path planning program we were able to estimate the grinding operation to be 10 min 56 s. Grinding the same workpiece manually will take approximately 20min to finish. The solution we propose helped reduce the time needed by 45%.
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ROMANSY 22 – Robot Design, Dynamics and Control., 584, 363-369. Dai, H., Yuen, K.M. and Elbestawi, M.A. (1993). Parametric modelling and control of the robotic grinding process. International Journal of Advanced Manufacturing Technology, 8, 182-192. Durgumahanti, U.S.P., Singh, V. and Rao, P.V. (2010). A New Model for Grinding Force Prediction and Analysis. International Journal of Machine Tools and Manufacture, 50, 231-240. Hahn, R.S., Lindsay, R.P. (1969). The influence of process variables on material removal, surface integrity, surface finish and vibration in grinding. Advances in Machine Tool Design and Research, 95-117 Huang, H., Gong, Z.M., Chen, X.Q. and Zhou, L. (2002). Robotic grinding and polishing for turbine-vane overhaul. Journal of Materials Processing Technology, 127, Issue 2, 140-145. Lindsay,R.P. (1971). On the metal removal and wheel removal parameters—surface finish, geometry and thermal damage in precision grinding, Ph.D.Thesis, Worcester Polytechnic Institute.
Fig. 10 Finished and unfinished workpiece in blue and red respectively 8. CONCLUSION In this paper, we properly presented a robotic grinding solution that can be applied easily on different robots. This practical solution helped reduce vibrations and improve sufficiently surface quality. In addition to that, we proposed a robotic grinding method that was implemented in a Matlab program. This program was used in order to grind a corner on a parallelepiped workpiece and is able to reliably produce the most efficient robot path for this operation. The grinding is done in two steps, to efficiently have a good finished surface. The next goal of this work is the experimental validation of the robotic grinding process and the actuator models, as well as the grinding method. ACKNOWLEDGEMENT We would like to thank the Robotix Academy, contract number N°002-4-09-001 for funding this work as a part of the project funded by INTERREG V-A Grande Région program. REFERENCES Andersson, E.R. (1990). Design and testing of a vibration attenuating handle. International journal of industrial ergonomics, 6, 119-125.
Minami, M., Asakura, T., Dong, L.X. and Huang, Y.M. (1996) Position control and explicit force control of constrained motions of a manipulator for accurate grinding tasks, Advanced Robotics, 11:3, 285-300 Nasri, H., Bolmsjo, G. (1995). A process model for robotic disc grinding. International Journal of Machine Tools and Manufacture, 35, Issue 4, 503-510. Ono, K. (1961). Analysis of the grinding force. Bulletin of the Japan Society of Grinding Engineers, 1, 19–22. Persoons, W., Vanherck, P. (1996) A Process Model for Robotic Cup Grinding. CIRP Annals, 45, Issue 1, 319325. Salje, E. (1953). Grundlagen des schleifvorganges, Werkstatt und Betrieb, 86, 177–182. Schneider, P.J. and Eberly, D.H. (2003). Geometric tools for computer graphics, chapter 7. Morgan Kaufmann Publishers, United States of America. Sozbilen, M.C., Dastan, A.E., Gunay, H. and Kucuk, L. (2018). A prospective study of angle grinder injuries in the hands and forearms during a one-year period. Hand Surgery and Rehabilitation, 37, Issue 5, 300-304.
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Chang, H.-C. and Wang, J.-J.J. (2008). A stochastic grinding force model considering random grit distribution, International Journal of Machine Tools and Manufacture, 48, 1336-1344.
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Chaoui, M.D., Léonard, F., Abba, G. (2019). Improving Surface Roughness in Robotic Grinding Process.
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