Robotics Seminar ME EN 7960
Popular in Course
Popular in Mechanical Engineering
This 29 page Class Notes was uploaded by Miss Leatha Gottlieb on Monday October 26, 2015. The Class Notes belongs to ME EN 7960 at University of Utah taught by Staff in Fall. Since its upload, it has received 34 views. For similar materials see /class/230017/me-en-7960-university-of-utah in Mechanical Engineering at University of Utah.
Reviews for Robotics Seminar
Report this Material
What is Karma?
Karma is the currency of StudySoup.
Date Created: 10/26/15
Design of Machine Structures ME EN 7960 Precision Machine Design Topic 14 l ME EN 796D e Preeisiun Maenine Design 7 Design ur Maenine structures izH Topics Overall design approach for the structure Stiffness requirements Damping requirements Structural configurations for machine tools Other structural system considerations ME EN 796D e Preeisiun Maenine Design 7 Design ur Maenine structures 1472 Design Strategies Strategies for Accuracy Accuracy obtained 39om component accuracy Most machine tools are built this way Accuracy obtained by error mappin Most coordinate measuring machines are built this way Accuracy obtained 39om a metrolog y 39ame usually 39139 quot quot39 noobject machines Kinematic design Deterministic Less reliance on manufacturing Stiffness and load limited unless pot in epoxy ME EN 796D e Preeisiun Mannine Design 7 Design er Mannine structures Design Strategies contd Elastically averaged design Nondeterministic More reliance on manufacturing Stiffness and load not limited Passive temperature control Minimize and isolate heat sources Minimize coef cient of thermal expansion Maximize thermal diffusivity Insulate critical components Use indirect lighting Use PVC curtains to shield the machine from infrared sources ME EN 796D e Preeisiun Mannine Design 7 Design er Mannine structures Design Strategies contd Active temperature control Air showers irculating temperature controlled uid Thermoelectric coolers to cool hot spots Use proportional control Structural con gurations the center ofmass 39iction and stiffness located What does the structural loop look like Open frames G type Closed 39ames Portal type Spherical NIST39s M3 Tetrahedral Lindsey39s Tetraform Hexapods Stewart platforms Compensating curvatures Counterweights I ME EN 79m 7 Preeisiun Mannine Design 7 Design at Mannine Strumures 1475 Design Strategies contd Damping Passive Material andjointuslip damping Constrained layers tuned mass dampers Active Servocontrolled dampers counter masses Active constrained layer dampers ME EN 79m 7 Preeisiun Mannine Design 7 Design at Mannine Strumures 147B Summary of Strategies for Accuracy Accuracy obtained from component accuracy Inexpensive once the process is perfected Accuracy is strongly coupled to thermal and mechanical loads on the mac 39ne Accuracy obtained by error mapping Inexpensive once the process is perfected Accuracy is moderately coupled to thermal and mechanical loads on the machine Accuracy obtained from a metrology frame Expensive but sometimes the only choice Accuracy is uncoupled to thermal and mechanical loads on the machine ME EN 796D e Preeisiun Maenine Design 7 Design er Maenine structures Stiffness Requirements Engineers commonly ask quothow stiff should it bequot A minimum specified static stiffness is a useful but not sufficient specification Static stiffness and damping must be specified Static stiffness requirements can be predicted Damping can be specified and designed into a machine ME EN 796D e Preeisiun Maenine Design 7 Design er Maenine structures Minimum Static Stiffness For heavily loaded machine tools the required stiffness may be a function of cutting force For lightly loaded machines and quasistatically positioning use the following First make an estimate of the system39s time constant Tmech 277g The control system loop time rm7 must be at least twice as fast to avoid aliasing Faster servo times create an averaging effect by the factor rm 27 echamcal loop I ME EN 796D e Preeisiun Maenine Design 7 Design at Maenine Strumures i479 Minimum Static Stiffness contd For a controller with N bits of digital to analog resolution the incremental force input is F AF quotx 2N Tmech 21 servo The minimum axial stiffness is thus F 1 2N7z39yzmx ME EN 796D e Preeisiun Maenine Design 7 Design at Maenine Strumures MA El Minimum Static Stiffness contd While the controller is calculating the next value to send to the DAC the power signal equals the last value in the The motor is receiving an old signal and is therefore running open loop Assume that there is no damping in the system The error QM due to the mass being accelerated by the force resolution of the system for a time increment 4 IS erva l rz M 2 M xervo ME EN 796D e Preeisiun Maenine Design 7 Design er Maenine Strumures Mell Minimum Static Stiffness contd The maximum allowable servoloop time is thus T 7 mm SEN07 AF The minimum axial stiffness is thus 5 gt max M K 2N70 25 51A It must also be greaterthan the stiffness to resist cutting loads or static loads not compensated for by the servos ME EN 796D e Preeisiun Maenine Design 7 Design er Maenine Strumures MA 2 Minimum Static Stiffness contd The maximum servoloop time is thus 2N0755 m5 F max TEEN S Typically one would set 6K 6M WO Usually 136N005 twoL WhereL is the number of past values used in a recursive digital control algorithm Example Required static stiffness for a machine with 800 N max axial force 250 kg system mass and 14 bit DAC ME EN 7BBE 7 F39recisiun Machine Design 7 Design Elf Machine Structures NJ 3 Exam ple Minimum Save Update Time and Static Stiffness a E E E E E l la a l m 5 a 3 7 0 1 ln 8 g E E E a a E E e l m5 E E E 1 ms 1 m Total allowable servor error m ME EN 7BBE 7 F39recisiun Machine Design 7 Design Elf Machine Structures l47l Servo System Force Output E E g a t a g E i E E g 2 Lower force drive system for a given servo error e thereases the servo update trrhe e Lowers the statrc strrrhess requrrerh eht ME EN 79m 7 Preersroh Maehhe Desrgh e Desrgh or Maehhe structure 144 5 System Mass E E g a t a g E 32 E E g 2 Lower mass 7 Decreases the servo update trrhe 7 Does hot arrect statrc strrthess requrrerheht ME EN 796D e Precrsruh Machrhe Desrgh e Desrgh or Machrhe Strumures 144 E Servo DAC Resolution E E g a 1 3 e a g i 2 dedlmahlesememdm Lo er DAC resolution 7 Decreases the servo update tirne 7 increases static stiffness requirement ME EN men 7 PrEElSan Maenine Design 7 Design er Maenine Structures 11H 7 Dynamic Stiffness Dynamic stiffness is a necessary and sufficient specification Dynamic stiffness Stiffness of the system measured using an excitation force with a frequency equal to the damped natural frequency of the structure Dynamic stiffness can also be said to be equal to the static stiffness divided by the amplification Q at resonance ME EN 796D e Preeisiun Machine Design 7 Design at Machine structure 144 E Dynamic Stiffness contd It takes a lot of damping to r duce the ampli cation ham to a low level Ampiineatian raetar outputinput Freeman mm oeng mmii ME EN 796D 7 Preeisiun Maenine Design 7 Design er Maenine Structures 1448 Same Nemndevslmm i Dynamic Stiffness contd Material and joint damping factors are difficult to predict and are too low anyway For high speed or high accuracy machines Damping mechanisms must be designed into the structure in order to meet realistic damping levels The damped natural frequency and the frequency at which maximum amplification occurs are a M wdpzak a V12 2 ME EN 796D 7 Preeisiun Maenine Design 7 Design er Maenine structures M7ZEI Dynamic Stiffness contd The ampli cation at the damped natural frequency and the peak frequency can thus be shown o be Q 7 3th 7 1 Input 441 7 344 Ownrm 7 1 km 1 Input 2 1741 16mm 24 For unity gain or less must be greater than 0707 Cast iron can have a damping factor of 00015 Epoxy granite can have a damping factor of 001005 All the components bolted to the structure eg slides on bearings help to damp the system To achieve more damping a tuned mass damper or a shear damper should be used ME EN 7060 7 Preeisiun Machine Design 7 Design of Machine structures i472i Material Damping alumina 6063 aiuminum lead I polymer concrete 0 000 0 001 0 002 0 003 0 004 0 005 0 006 loss factor ME EN 7060 7 Preeisiun Machine Design 7 Design of Machine structures M722 Effects of Changing System Mass scarce Alexamer Siammi Prensaquot Machine oesan Adding rnass Add rig sand or head s i hut increases rnass and damping Via the Eanicies rubbing on Each Ell er 7 Higher rnass siuvvs res ENSE but hei hig frequencynui Decreasing rnass 7 Faster respund tci cummand signais 7 increases a higher naturai frequency e Higheispeed ccnirciier signais rn used ust be impruved c the increased iciss factor the ins factor 5 cZm 7 uvvever iEIW shuvv iess nciis higherfrequen T is sug eststhat the rnass systems e reiecticin at cies nuate noise and yibvatiun l ME EN 796D 7 Precision Machine Design 7 Design of Machine structures M723 the serve ps attenuates s amping a resuit or Effects of Adding Stiffness to the Machine System scarce Alexamer Siammi Prensaquot Machine oesan Higher stiffness ives a atter res onse atlow requen0ies an give sma er displacements for a given force Input he com romise 9f decreased lowering the system mass 7 This is shown bythe sirniiar shapes in the three response cury s athigh frequencies his suggests that raisin the tiffness ofa system is aways a desirable course of action However acousticai noise a stiffness frequency of yioration is moved to the audibie region of the human ear I ME EN 796D 7 Precision Machine Design 7 Design of Machine structures M724 Effects of Adding Damping to the Machine System Increasing the system mping can make a dramatic improvement in the system response The trend is for decreasing ampli cation ofthe output at resonance with increasing amping The plot shows the dramatic improvement available by doubling the system damping Although a damping coef cient of 04 may be dif cult to obtain in ac Ice sum Alexamev Slammi Freeman Machine Desgn l ME EN 796D e Preeisiun Maenine Design 7 Design er Maenine structures i445 Summary For a servo controlled machine The stiffness of the machine structure should be maximized to improve positioning accuracy The mass should be minimized to reduce controller effort and improve the frequency response and loss factor Damping however must be present to attenuate vibration in the machine system I ME EN 796D e Preeisiun Maenine Design 7 Design er Maenine structures i446 Open Frame Structures Easy access to Spmd e work zone I Too Structural loop prone to Abbe errors like calipers Sauce Alexander S amm ME EN 796D 7 Premsmn Machme Desrgnr Desrgn ur Macmne Strumures 14727 Structu rar r0 0p Freeman Machme new Open Frame Structures contd Spmme huusmg Facepram Carnage Same Newnders mm Freeman mm Desgn ME EN 796D 7 Premsmn Machme Desrgn r Desrgn ur Macmne Strumures 14728 Closed Frame Structures Structural iuup Vex carriage ME EN 796D e Preeisiun Mannine Designr Design er Mannine structures Moderately easy access to work zone Moderately strong structural loop like a micrometer Primaryfollower actuator o en required for the bridge Easier to obtain common centers of mass stiffness friction sime Alexander Slammi Precision Machine Desgn i449 Closed Frame Structures ME EN 796D e Preeisiun Mannine Design 7 Design er Mannine structures Source Pveusian Design Lab Man Tetrahedral Structures Composed OfSlX legs icined atspherical nodes Workzorie in centerof tetrahe l Ol l Bearing Ways boltedto le 5 Hign thermal stability Hign stiffness Viscous Sheardarnpirig mechanisms builtirito thelegs Dampi g btairied at the iegiOinis by means of Sliding bearing material appliedto the self centering spherical icini lrihereritlystable Shape Source Alemndevslacmi Premium mm new ME EN 796D 7 Preeisiun Machine Design 7 Design er Machine structures Mai Tetrahedral Structures Like the tetrahedron the c ahedron is a stable truss type geometry comprised of triangles As the work volume increases the structure grows less fast than a tetrahedron The hexapod Stewart platform concept originally develo ed or ig simula ors gives six limited degrees of freedom The tool angle is limited to about 2 degrees from the ertical Advanced controller architecture and algorithms m K S N m 5 make programming possible Freeman Machine Desgn ME EN 796D 7 Preeisiun Machine Design 7 Design er Machine structures i432 Cast Iron Structures Linear guide inning niregiei nay for Sliding einrimr Beng at hjr39dwstau bearing r Inna regions for rqriiceien interim i tSCOUS dampers shaped LthdEd aluminum Round man 11le is El uzrurzillv LL12 mcsl emrieiir EC ii fm resisting rorsierini loads Widely used Stable with thermal anneal aging or vibration stress relieve Good damping and heat transfer Modest cost for modest sizes Integral ways can be cast in place Design rules are well established see text Economical in medium to large quantities Suurce Alexander Slucumr Precision Machine uesgn ME EN 7960 7 Precision Macnine Design 7 Design ofMacnine Structures 14733 Welded Structures Linear gunk mllmg Integral ii ny rnr sliding eignieiir bearing nr hydraslanc bearing Inukfregmns rnr rrphcated Interim riscniis dampers Round inner iiibe ls r mmllyrtie masr s m ef cient sectmn for mining rorsmnal lands Often used for larger structures or smalllot sizes Stable with thermal anneal Low damping improved with shear dampers Modest cost Integral ways can be welded in place Structures can be made from tubes and plates Suuice Alexander Slucumr Frecicron Machine pecan ME EN 7960 7 Precision Macnine Design 7 Design of Macnine Structures 14734 Epoxy Granite Structures 39 E Can be cast with intricate passages and inserts epoxy ganiLeEcast tron 5 Exterior surface can be smooth and is ready to paint Cast iron or steel weldments can be cast in place but beware of differential thermal expansion effects Epoxy granite s lower modulus and use of foam cores means that local plate modes require special care when designing inserts to which other structures are bolted Sliding contact bearing surfaces can be replicated onto the epoxy granite ME EN 796D 7 Precisicin Machine Design 7 Design cir Machine structures M735 Epoxy Granite Structures Foam cores reduce weight EDD EDD V U sime Alexarder Slammi Freeman Machine Desgn For some large oneof a kind machines A mold is made 39om thin welded steel plate that remains an integral part of the machine alter the ma erial is cast Remember to use symmetry to avoid thermal warping Consider the effects of differential thermal expansion when designing the eel shell The steel shell should be fully annealed a er it is welded together ME EN 796D 7 Precisicin Machine Design 7 Design cir Machine structures M736 Epoxy Granite Structures Instead of ribs polymer concrete structures usually use internal foam cores to maximize the stiffness to weight ratio Polymer concrete castings can accommodate cast in place components Courtesy of Fritz Studer AG Saw2 Nemnda Slammi Precxsmri Machine oesgn i437 ME EN 796D e Preeisiun Machine Design 7 Design er Machine structures Epoxy Granite Structures With appropriate section design Polymer concrete structures can have the stiffness of cast iron structure They can have much greater damping Highly loaded machine substructures eg carriages are still best made from cast iron Polymer concrete does not diffuse heat as well as cast Iron Attention must be paid to the isolation of heat sources to prevent the formation of hot spots When bolting or grouting nonepoxy granite components to an epoxy granite bed consider the bimaterial effect ME EN 796D e Preeisiun Machine Design 7 Design er Machine structures i438 Granite Dimensionally very stable Must be sealed to avoid absorption of water Can be obtained from a large number of vendors providing excellent atness and orthogonality Cannot be tapped therefore bolt holes consist of steel plugs that have been potted in place that are drilled and tapped after the epoxy has cured Can chip Provides excellent damping ME EN 7960 Precision Machine Design Design of Machine Structures 1439 Granite contd Seuree Standridge Granite Seuree PrEElSan Design Lab ME EN 7960 Precision Machine Design Design of Machine Structures 1440 2O Constrained Layer Damping How does it work Tup Cunsiiaining Layer Aw bi 5 Viscueiastic Damping Materiai Gm n Structure A i E i y w Butturn Cunsiiaining Layer Azi 2i 5 x Viscoelastic layer damps motion between structure and constraining layer from bending or torsion by dissipating kinetic energy into heat ME EN 796D e Preeisiun Mannine Design 7 Design er Mannine Strumures Mm Design parameters to tune damper Elm Elo EEAlty3 y x yi y b EIW r 7 EIU ME EN 796D e Preeisiun Mannine Design 7 Design er Mannine Strumures MAI How is it implemented B D constraining 39L 5 Layer1c ic Thickness S w y Structure A K5 e VA mxv y Damping Material Thickness rd I39Ul inner L ShearDamperTM Constraining layer is wrapped with damping material Coated inner tube is inserted and gap lled with epoxy ME EN 796D e Preeisiun Maenine Designr Design er Maenine Strumures MAS ShearDamperT39V39 step by step Step 1 split tube Step 2 wrap damping sheet around v i444 Any tradeoffs Labor intensive inner tube needs to be split Inner tube and epoxy are expensive Added weight lowers modal frequencies Challenging if bottom is not accessible for sealing Constraining layer performance depends on available wall thickness Only works for round or rectangular structures where a matching split tube is available ME EN 796D e Preeisien Maenine Design 7 Design er Maenine Strumures MAE How can we make it better Replace steel tube AND epoxy with cheaper material that has better internal damping Make the need for splitting the constraining layer obsolete Make design more flexible in terms of shape and required stiffness Remove design constraints ME EN 796D e Preeisien Maenine Design 7 Design er Maenine Strumures MAB But how Four sausage between the outer structural and the inner WWW v 1 WM i I M support tube 1 Dampers are 4 3 lled With expanding concrete E BambetgiAH Slamm canaelebased mnsminailavemanipingh Wm WWW 2m omizuuz W um I ME EN 7BBE 7 Precision Machine Design 7 Design of Machine Structures MAW Concrete cast it s simple Flexible constraining layer thickness Wide range of standard tubes can be used as support tube wall thickness is no longer a design constraint Concrete provides additional damping Cheap Fast I ME EN 796D e Preeisien Machine Design 7 Design at Machine structures MAE How is it done part 1 step 1 Ct dampmg sheet step 2 Make tap 10ml and turn sheet mto tube ME EN 796D 7 Premsmn Machme Destgnr Desrgn uf Macmne Strumures MAB How is it done part 2 step 6 After concrete has cured 7 out step 5 Pour expandmg concrete MEEN 7BED7F39rEmsmn Machme DestgnrDEstgn ufMachmE Strumures MVEEI Dynamic compliance lower is better Steel constraining layer is better because it has a higher Young s modulus than concrete an equally stiff layer is thinner and hence further away from system neutral axis a increased stiffness ratio r ME EN 796D 7 Precisicin Machine Design 7 Design er Machine structures i475i Reinforced works even better R m i i r I mm mm imam t I ME EN 796D 7 Precisicin Machine Design 7 Design er Machine Structures 1452 Concrete cast rocks Virtually ME EN 796D 7 Preclslun Macnlne DESlgn 7 DESlgn ur Macnlne Structures 1453 Reinforced concrete cast Cable ties press damping sleeve against fixture Hot glue seals rebars ME EN 796D 7 Preclslun Macnlne DESlgn 7 DESlgn ur Macnlne Structures 1454 Test setup HP 4channel frequency analyzer 3axis accelerometer 28 data points Freefree setup ME EN 796D 7 Premsmn Machme Deswgn 7 Deswgn uf Macmne Strumures 14755 Response to impulse ummm 3mm 5m led 5mm swag mm mm E amuseAH swammwcanaaabaeumnwnmwaveyuampmgw Preasan Engmeermg 25m OcTnbevZEIEIZ W mum MEEN 7BED7F39remsmn Machme DeswgniDeswgn ufMachme Strumures 14756 Transfer Functions Cari27212 Fitted Strmure x2 Spin Yme Damped Stru ure x12 mama mum Camvete caa Damped Strmure xis Rnaeirituvoed Camrete Cast Damped Stmdme xii in E E irr 1 7 r 7 7 7 r 7 1 xiiiiii xiiiiii mama mum I ME EN 7060 e Preeisiun Maenine Design 7 Design er Maenine structures i457 Measured performance Split Tube f1530 Hz and 710055 predicted 0032 Material cost 100 Concrete Cast f1260 Hz and 710145 predicted 0035 Material cost 235 Reinforced Concrete Cast f1640 Hz and 03 predicted 0044 Material cost 288 I ME EN 7060 e Preeisiun Maenine Design 7 Design er Maenine structures i458