Error Modeling. Error Budgets. Start with basics
|
|
- Dina Lamb
- 5 years ago
- Views:
Transcription
1 Error Modeling Error Budgets Low cost method to help evaluate concepts before detailed solid models, FEA (which will not catch geometric errors ), because: Nothing is perfect Need to estimate accuracy and repeatability of concepts Need to better predict loads/life of bearings! Start with basics Stick figures Structural loop Error budget spreadsheets Simple error models If in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics Roger Bacon Bumpy path as measured by sensor Ideal path Y Circle traced out by X and Y axes moving with sine and cosine paths X Non-perfect rollers Non-perfect surface High frequency straightness error (smoothness) Straightness error Bumps caused by axis reversal 2016 Alexander Slocum 2-1
2 Stick figure: The sticks join at centers of stiffness, mass, friction, and help to: Define the sensitive directions in a machine Locate coordinate systems Error Modeling: Stick Figures Set the stage for error budgeting The designer is no longer encumbered by cross section size or bearing size It helps to prevent the designer from locking in too early on a concept Error budget and preliminary load analysis can then indicate the required stiffness/load capacity required for each stick and joint Appropriate cross sections and bearings can then be deterministically selected 2016 Alexander Slocum 2-2
3 Error Modeling: Structural Loops The Structural Loop is the path that a load takes from the tool to the work It contains joints and structural elements that locate the tool with respect to the workpiece It can be represented as a stick-figure to enable a design engineer to create a concept Subtle differences can have a HUGE effect on the performance of a machine The structural loop gives an indication of machine stiffness and accuracy The product of the length of the structural loop and the characteristic manufacturing and component accuracy (e.g., parts per million) is indicative of machine accuracy (ppm) Long-open structural loops have less stiffness and less accuracy 2016 Alexander Slocum 2-3
4 Structural Loops: Equivalent Springs Structural stiffness between two coordinate systems is modeled as stiffness of the structure between the two (6x6 matrix) & stiffness of the attachment (6x1 vector) 2016 Alexander Slocum 2-4
5 Bearings Error Motions Bearings are not perfect, and when they move, errors occur in their motion Accuracy standards are known as ABEC (Annular Bearing Engineers Committee) or RBEC (Roller Bearing Engineers Committee) of the American Bearing Manufacturers Association (ABMA) ABEC 3 & RBEC 3 rotary motion ball and roller bearings are common and low cost ABEC 9 & RBEC 9 rotary motion ball and roller bearings are used in high precision machines The International Standards organization (ISO) has a similar standard (ISO 492) An error budget is used to keep track of all the error motions in a machine Remember Abbe and sine errors and how they can amplify bearing angular errors! 50 Parallelism P (mm) Rail length (mm) Normal (N) High (H) Precision (P) Super precision (SP) Ultra Precision (UP) Amplitude (m) 2.50E E E E-07 // P Peaks likely due to rolling elements (ball and cam roller surface errors) Surface finish effects // P // P Overall bow in rail 5.00E Alexander Slocum E E E E-01 Wavelength (m)
6 Error Motions: Linear Bearings Error motions of a carriage supported by a kinematic arrangement of bearings (exact constraint) can be determined "exactly" Error motions of a carriage supported by an elastically averaged set of bearings can be estimated by assuming the bearings act in pairs Calculations are done using the running parallelism error information from the bearing supplier Running parallelism number is usually a systematic (repeatable) error Roll: εxparallelism Assume all Random error motion may typically be 10% of the running bearings on each rail Roll: εx Assume all move vertically in an bearings on each Z rail x opposite direction Roll: ε Assume all move vertically in an x bearings direction on each rail opposite move vertically in an opposite direction ε = 2δ/L Horizontal Straightness: δy Assume all bearings move horizontally Horizontal Straightness: δ Assume Y y δh move horizontally all bearings δh Z Y Z X YL X w w L Vertical Straightness: δz Assume all bearings move vertically Vertical Straightness: δ Assume all z qz (Pitch) δv bearings move vertically δv Z 2016 Alexander Slocum qy (Yaw) LZ LX ε = 2δ/L Pitch: εz Assume Z and rear bearing X front Pitch: εz Assume pairs move in opposite front and rear bearing vertical directions pairs in opposite Pitch:move εz Assume vertical directions front and rear bearing pairs move in opposite vertical directions εy = 2δ/LX qx (Roll) Yaw: ε Assume y front and rear bearing Yaw: y Assume pairs εmove in opposite front and bearing horizontalrear directions X pairs in opposite Yaw:move εy Assume horizontal directions front and rear bearing 2-6 pairs move in opposite
7 Error Motions: Linear Bearing Rotation Analysis When all the bearings are in a plane defined by the CS axes, angular error motions are simple to model: ε x = 2δ/L Z ε Y = 2δ/L X ε Z = 2δ/L X When the bearings are not in a plane, a simple algorithm can be fooled Conditional IF statements can be used to avoid issues Roll about X axis in this example is Y ε x = 2δ/L Y REMEMBER Calculations are done using the running parallelism error information from the bearing supplier Running parallelism error is a systematic (repeatable) error Random error motion is typically 10% of the running parallelism Parallelism P (mm) Rail length (mm) Normal (N) High (H) Precision (P) Super precision (SP) Ultra Precision (UP) 2016 Alexander Slocum 2-7 // P // P // P X -Z
8 Error Motions: Rotary Bearings Standards exist for describing and measuring the errors of an axis of rotation: Axis of Rotation: Methods for Specifying and Testing, ANSI Standard B89.3.4M-1985 Radial, Axial, and Tilt error motions are of concern Upper bound: Radial error motion equals bore roundness Lower Bound: Radial bearings act as elastic averaging elements and radial error motion is bore roundness/averaging factor (3-5 for rolling elements, for hydrostatic or aerostatic) Precision Machine Designers measure error motions and use Fourier transforms to determine what is causing the errors MRS center error motion value PC center error motion value PC center 500 Inner motion Displacement (nanometers) Displacement due to machine deformation MRS center Total Error Motion Outer motion Frequency (Hz) Alexander Slocum 2-8 Average Error Motion Fundamental Error Motion
9 Error Motions: Rotary Motion Estimates Rotary bearings usually only come with an overall quality rating (e.g., ABEC 9, ISO 5) The rating indicates ID and OD tolerance of the bearing The accuracy of the supported element (e.g., shaft) axis of rotation is usually dominated by the accuracy of the bore, shaft, alignment, and clamping method. Mel Liebers at Professional Instruments has tremendous insight on bearing measurement and mounting As he points out, screw-actuated locknuts can also be used to preload a bearing and deform a shaft to correct for errors and thus achieve greater accuracy» E.g. As a first order estimate, assume the root square sum of the bore and shaft roundness are representative of the radial accuracy of the supported shaft. Similar for axial accuracy Tilt accuracy can be estimated by radial accuracy divided by spacing between bearing sets If just a single bearing set is used, tilt accuracy can be estimated by the flatness of the bearing mount (bore) divided by the bearing pitch diameter 2016 Alexander Slocum 2-9
10 Sensor Placement Effects If a linear encoder is used to measure an axis position, it can reduce the Abbe error To model the effect of sensor placement, scale the angular error that affects error motions in the direction of sensor action Add sensor location effect as an input in the Error Budget spreadsheet a b δ Abbe = aα δ Abbe with sensor = (a-b)α α is scaled by (a-b)/a 2016 Alexander Slocum 2-10
11 Thermal Growth Errors: Heat sources and paths There are many different types of thermal errors and paths Thermal effects in manufacturing and metrology (After Bryan.): Heat source/ sinks Room environment Heat added or removed by coolant systems Coolants Electronic Hydraulic Frame Cutting Lubricating systems oil stabilizing fluid oil People Electrical and electronic Friction Heat created by the machine Frame stabilization Motors, transducers Amplifiers, control cabnets Spindle bearings Other Hydraulic Miscellaneous Heat created by the cutting process Heat flow paths Conduction Convection Radiation Conduction Convection Radiatio Conduction Convection Radiatio Temperature gradiants or static effects Temperature variations or dynamic effects Temperature field Uniform temperature other than 20 degrees C Nonuniform temperatures Memory of previous environment Affected Structure Part Master Frame Station-change effect Error components Form error Total thermal error 2016 Alexander Slocum 2-11 Size error
12 Very troublesome They are always changing Thermal Growth Errors Time constants can be from seconds to many hours Very troublesome because components' heat transfer coefficients can vary from machine to machine Surface finish and joint preload can have an effect Design strategies to minimize effects: Isolate heat sources and temperature control the system Maximize conductivity, OR insulate Combine one of above with mapping and real time error correction May be difficult for thermal errors because of changing boundary conditions. Combine two of the above with a metrology frame 2016 Alexander Slocum 2-12
13 Thermal Growth Errors: Linear Expansion Simple to estimate Axial expansion of tools, spindles and columns, caused by bulk temperature change ΔT, is often a significant error At least it does not contribute to Abbe errors δ = αlδt Axial expansion in a gradient (one end stays at temperature, while the other end changes) ( 1 2) αl T T δ = 2 For a meter tall cast iron structure in a 1 C o /m gradient, δ= 5.5 µm This is a very conservative estimate, because the column will diffuse the heat to lessen the gradient 2016 Alexander Slocum 2-13
14 Thermal Growth Errors: Bimaterial Effect Deformation of a bimaterial plate moved from one uniform temperature to another: δ = α = t t ( α1 α 2) ΔT( L ) 2 4( EI 1 1+ EI 2 2) t + + t1 EA 1 1 EA 2 2 ( α1 α 2) ΔT( L ) 2 + t 2( EI 1 1+ EI 2 2) t1 EA 1 1 EA 2 2 Example: 1m x 1m x 0.3m with 0.03 m wall thickness surface plate If not properly annealed, after top is machined and the bottom retains a 0.5 cm layer of white iron: δ = 0.10 µm/c o, α = 0.41 µrad Similar effects are incurred by steel bearing rails grouted to epoxy granite structures Consider using a symmetrical design (steel on the bottom) to offset this effect Two materials may have similar expansion coefficients, but very different conduction coefficients and density! For a quick estimate of transient effect, assume that the coefficient of expansion of one member is scaled by the ratio of the conduction coefficients Beware placing a precision surface on top of a cabinet that contains electronics! Alexander Slocum 2-14
15 Thermal Growth Errors: Bimaterial Effect Example: Two size 55 linear guides bolted to a granite bed, later used at a different temperature (e.g., in the summer) How can these errors be counteracted? How can symmetry be used? Does segmenting steel members reduce the effect? Example: steel bearing rails attached to granite beam Two materials may have similar expansion coefficients, but very different conduction coefficients and density! For a quick estimate of transient effect, assume that the coefficient of expansion of one member is scaled by the ratio of the conduction coefficients BiMat.xls Determine thermal errors in a bi-material beam Written by Alex Slocum. Last modified by AS Enter numbers in BLACK outputs in RED Be consistent with units Beam and environment Units Value Length of beam: L mm 1000 Change in temperature: DT C 4.0 Cross section 1 (e.g., bearing rails) properties Modulus of Elasticity: E_1 mm 2.00E+05 Coefficient of thermal expansion: alpha_1 1/C 1.20E-05 Enter YES if entering just moment of inertia and X section area, else NO NO User entered values for I, A TOTAL (e.g., if 2 bearing rails) Moment of inertia, I_1ue mm^ TOTAL (e.g., if 2 bearing rails) Cross section area, A_1ue mm^2 750 TOTAL flange thickness (top + bottom) (0 for rect. beam): ft_1 mm 0 Height: h_1 mm 20 Width: b_1 mm 40 TOTAL web thickness (left + right) (bi=bo for rect. beam): wt_1 mm 0 Moment of inertia: I1 mm^ Area: Ar1 mm^2 800 Cross section 2 (e.g., structure) properties Modulus of Elasticity: E_2 N/mm^2 6.67E+04 Coefficient of thermal expansion: alpha_2 2.40E-05 Enter YES if entering just moment of inertia and X section area, else NO NO User entered values for I, A TOTAL (e.g., if 2 bearing rails) Moment of inertia, I_2ue mm^ TOTAL (e.g., if 2 bearing rails) Cross section area, A_2ue mm^ TOTAL flange thickness (top + bottom) (0 for rect. beam): ft_2 mm 6 Height: h_2 mm 100 Width: b_2 mm 100 TOTAL web thickness (left + right) (bi=bo for rect. beam): wt_2 mm 6 Moment of inertia: I_2 mm^ Area: A_2 mm^2 800 Results Max. displacement error mm Max. slope error radians Alexander Slocum 2-15
16 Thermal Growth Errors: Bimaterial Effect Note its not the ratio of CTEs but the difference! How can these errors be counteracted? How can symmetry be used? Does segmenting steel reduce the effect? What would size 20 linear guides do to a 100mm square aluminum tube? What if there were an axis mounted orthogonal to the tube? 2016 Alexander Slocum 2-16
17 Thermal Growth Errors: Thermal Gradients One of the most common and insidious thermal errors Beam length = L, height = h, section I, gradient ΔT, straightness error: ε T M y α yδt = = ρ h EI = ρ ( L ) 2 2 M 2 L αδt δ T = = 2EI 2h Slope error at the ends of the beam (α=m(l/2)/ei): αδtl θ T = 2h For a 1x1x0.3 m cast iron surface plate with ΔT=1/3 C o (1 C o /m), δ = 1.5 µm and θt = 6.1 µrad This is a very conservative estimate, because the plate will diffuse the heat to lessen the gradient In a machine tool with coolant on the bed, thermal warping errors can be significant Angular errors are amplified by the height of components attached to the bed 2016 Alexander Slocum 2-17
18 Thermal Growth Errors: Thermal Gradient Causes of gradients A machine tool structure may be subjected to a flood of temperature controlled fluid Evaporative cooling (common on large grinders and milling machines) Room temperature may vary wildly during the day Overhead lights can create gradients in sensitive structures Plastic PVC curtains are extremely effective at reducing infrared heat transmission A large machine on a deep foundation (relies on the concrete for support), can have problems: Several meters under the ground, the concrete is at constant temperature The top of the machine and the concrete are at room temperature Internal heat sources (motors, spindles, ballscrews, process) 2016 Alexander Slocum 2-18
19 Thermal Growth Errors: Design Strategies Example Conduction: Use thermal breaks (insulators) Keep the temperature the same in the building all year! Channel heat-carrying fluids (coolant coming off the process) away Convection: Use sheet metal or plastic cowlings to control heat flow Radiation: Plastic PVC curtains (used in supermarkets too!) are very effective at blocking infrared radiation Use indirect lighting outside the curtains, & never turn the lights off! Always ask yourself if symmetry can be used to minimize problems 62.5 grams of prevention is worth a kilo of cure! Workpiece zone Wheel zone Flood coolant Flood coolant Insulation layer (5 mm foam) Sheet metal trough 2016 Alexander Slocum 2-19
20 Thermal Growth Errors: Symmetry and Thermocentric Design Symmetry: Avoid inducing angular displacements Cause differential expansion to cancel Beware aluminum structure and steel bearing rails Steel on granite can also be an issue if not careful Thermocentric design: Expansion in one direction cancels effect of expansion in another Always ask yourself if symmetry can be used to minimize problems Contact angle Effective width CL Effective width Face-to-face Back-to-back 2016 Alexander Slocum 2-20
21 Dynamic Errors from Rotating Components Rotating components can cause errors Out-of-balance induced forces (e.g., motors, leadscrews ) Bowed-components (e.g., leadscrews) Modal analysis and frequency analysis can be used to help determine the source of the error The spindle speed was 1680 rpm (28 Hz) Was the 2x speed error from out-of-round bore or shaft, or is it a balancing problem? 500 Displacement (nanometers) Displacement due to machine deformation Frequency (Hz) Alexander Slocum 2-21
22 Dynamic Errors from Accelerating Componennts Accelerating components can cause errors Force from the acceleration Impulse from the starting or stopping of an acceleration (jerk) Round those motion profiles! 2016 Alexander Slocum 2-22
23 Which Error is it? Temperatures of different principle components and locations need to be plotted along side a quality control parameter (e.g., part diameter) In addition, all other functions on the machine should also be plotted E.g., lubricators that squirt oil to bearings every N minutes can cause a sudden temporary expansion of the machine Predictions can be made using fundamental theory or finite element models However, nothing beats real data from a real system The problem lies in interpolating the data Constant adjustment (via SPC) does not address the problem Temperature 0 0 Δ T environment Part error. Δ T top and bottom structure. etc.. Part error Time Sliding bearing lubricator cycle 2016 Alexander Slocum 2-23
24 The Fourier Transform: Your Error Hunting Companion The Fourier transform, when plotted as error amplitude as a function of wavelength, is an invaluable diagnostic tool It can help identify the dominant sources of error, so design attention can be properly allocated For a system with rolling elements, the center of the rolling element moves πd, while the element that rolls upon it moves 2πD! Amplitude (m) 2.50E E E E E-08 Peaks likely due to rolling elements (ball and cam roller surface errors) Surface finish effects Overall bow in rail 0.00E E E E-01 Wavelength (m) 2016 Alexander Slocum 2-24
Precision Machine Design
Precision Machine Design Topic 3 Examples of errors Purpose: This lecture provides detailed examples of different types of errors, and shows how estimates can be made of their magnitude. Outline: Geometric
More informationAXTRUSION SUPPLEMENTARY MATERIALS. An approximate formula for estimating a bearing s stiffness is 1. P s A 2 h
Appendix A AXTRUSION SUPPLEMENTARY MATERIALS A. Carriage Stiffness Estimates This section describes the steps to predict the stiffness performance of the carriage. First an accurate stiffness model of
More informationLinear guide drives. Synchronous shafts The use of synchronous shafts enables several linear axes to be operated with one drive.
Linear guide drives Drive concept The linear guides are driven via the hollow shaft in the drive head. The drive head is used to directly install a motor or alternatively (in connection with a center shaft)
More information[7] Torsion. [7.1] Torsion. [7.2] Statically Indeterminate Torsion. [7] Torsion Page 1 of 21
[7] Torsion Page 1 of 21 [7] Torsion [7.1] Torsion [7.2] Statically Indeterminate Torsion [7] Torsion Page 2 of 21 [7.1] Torsion SHEAR STRAIN DUE TO TORSION 1) A shaft with a circular cross section is
More informationTopic 6 Power Transmission Elements II
Topic 6 Power Transmission Elements II Topics: Screws! Gears! 000 Alexander Slocum 6-1 Screws! The screw thread is one of the most important inventions ever made HUGE forces can be created by screw threads,
More informationSOLUTION (17.3) Known: A simply supported steel shaft is connected to an electric motor with a flexible coupling.
SOLUTION (17.3) Known: A simply supported steel shaft is connected to an electric motor with a flexible coupling. Find: Determine the value of the critical speed of rotation for the shaft. Schematic and
More informationTWISTING (TORSIONAL) STIFFNESS. Barry T. Cease Cease Industrial Consulting
TWISTING (TORSIONAL) STIFFNESS Barry T. Cease Cease Industrial Consulting ceasevibration@icloud.com 843-200-9705 USUAL STIFFENING PRACTICES Most vibration analysts are familiar with methods of how to increase
More informationMechanical Vibrations Prof. Rajiv Tiwari Department of Mechanical Engineering Indian Institute of Technology, Guwahati
Mechanical Vibrations Prof. Rajiv Tiwari Department of Mechanical Engineering Indian Institute of Technology, Guwahati Module - 12 Signature analysis and preventive maintenance Lecture - 3 Field balancing
More informationPERIYAR CENTENARY POLYTECHNIC COLLEGE PERIYAR NAGAR - VALLAM THANJAVUR. DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK
PERIYAR CENTENARY POLYTECHNIC COLLEGE PERIYAR NAGAR - VALLAM - 613 403 - THANJAVUR. DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK Sub : Strength of Materials Year / Sem: II / III Sub Code : MEB 310
More informationDYNAMICS ME HOMEWORK PROBLEM SETS
DYNAMICS ME 34010 HOMEWORK PROBLEM SETS Mahmoud M. Safadi 1, M.B. Rubin 2 1 safadi@technion.ac.il, 2 mbrubin@technion.ac.il Faculty of Mechanical Engineering Technion Israel Institute of Technology Spring
More informationPrecision Ball Screw/Spline
58-2E Models BNS-A, BNS, NS-A and NS Seal Outer ring Shim plate Seal Spline nut Seal Collar Shim plate Seal End cap Ball Outer ring Ball screw nut Outer ring Ball Retainer Retainer Outer ring Point of
More informationClausing Industrial, Inc. Variable Speed 20" Single and Multi-spindle, Belt Drive Industrial Drill Presses
www.clausing-industrial.com Variable Speed 20" Single and Multi-spindle, Belt Drive Industrial Drill Presses Clausing Industrial, Inc. Two Speed Variable Speeds 150-2000rpm Variable Speeds 200-1300rpm
More informationThe Torsion Pendulum (One or two weights)
The Torsion Pendulum (One or two weights) Exercises I through V form the one-weight experiment. Exercises VI and VII, completed after Exercises I -V, add one weight more. Preparatory Questions: 1. The
More informationKNIFE EDGE FLAT ROLLER
EXPERIMENT N0. 1 To Determine jumping speed of cam Equipment: Cam Analysis Machine Aim: To determine jumping speed of Cam Formulae used: Upward inertial force = Wvω 2 /g Downward force = W + Ks For good
More informationBalancing of Masses. 1. Balancing of a Single Rotating Mass By a Single Mass Rotating in the Same Plane
lecture - 1 Balancing of Masses Theory of Machine Balancing of Masses A car assembly line. In this chapter we shall discuss the balancing of unbalanced forces caused by rotating masses, in order to minimize
More informationEXPERIMENT 7: ANGULAR KINEMATICS AND TORQUE (V_3)
TA name Lab section Date TA Initials (on completion) Name UW Student ID # Lab Partner(s) EXPERIMENT 7: ANGULAR KINEMATICS AND TORQUE (V_3) 121 Textbook Reference: Knight, Chapter 13.1-3, 6. SYNOPSIS In
More informationSliding Contact Bearings
Sliding Contact Bearings Classification of Bearings 1. According to the direction of load to be supported. The bearings under this group are classified as: (a) Radial bearings (b) Thrust bearings. In radial
More informationUpgrade of 5m-Bench System for Traceable Measurements of Tapes and Rules at SASO-NMCC Dimensional Laboratory
Upgrade of 5m-Bench System for Traceable Measurements of Tapes and Rules at SASO-NMCC Dimensional Laboratory Bülent ÖZGÜR 1,*, Okhan GANİOĞLU 1, Nasser Al-Qahtani 2, Faisal Al-Qahtani 2 1 TÜBİTAK, National
More informationClass XI Physics Syllabus One Paper Three Hours Max Marks: 70
Class XI Physics Syllabus 2013 One Paper Three Hours Max Marks: 70 Class XI Weightage Unit I Physical World & Measurement 03 Unit II Kinematics 10 Unit III Laws of Motion 10 Unit IV Work, Energy & Power
More informationLab Partner(s) TA Initials (on completion) EXPERIMENT 7: ANGULAR KINEMATICS AND TORQUE
TA name Lab section Date TA Initials (on completion) Name UW Student ID # Lab Partner(s) EXPERIMENT 7: ANGULAR KINEMATICS AND TORQUE 117 Textbook Reference: Walker, Chapter 10-1,2, Chapter 11-1,3 SYNOPSIS
More informationExperiment Instructions. Deformation of Frames
Experiment Instructions SE 0.20 Deformation of Frames Experiment Instructions This manual must be kept by the unit. Before operating the unit: - Read this manual. - All participants must be instructed
More informationFine Alignment of the ATF Damping Ring
Fine Alignment of the ATF Damping Ring M. Takano, S. Araki (a), Y. Funahashi (a), H. Hayano (a), T. Matsui (b), J. Urakawa (a) Toho University 2 2 1 Miyama, Funabashi, Chiba 275, Japan (a) KEK, High Energy
More informationTOPIC D: ROTATION EXAMPLES SPRING 2018
TOPIC D: ROTATION EXAMPLES SPRING 018 Q1. A car accelerates uniformly from rest to 80 km hr 1 in 6 s. The wheels have a radius of 30 cm. What is the angular acceleration of the wheels? Q. The University
More information1 High precision, high rigidity positioning table
TSHM CTHM 11 116 Precision Positioning Table H Ball screw TSH M Ball screw Slide table inear Way Bed inear Points 1 High precision, high rigidity positioning table High precision, high rigidity positioning
More informationHeat Transfer Analysis of Machine Tool Main Spindle
Technical Paper Heat Transfer Analysis of Machine Tool Main Spindle oshimitsu HIRASAWA Yukimitsu YAMAMOTO CAE analysis is very useful for shortening development time and reducing the need for development
More informationR-Plus System Frontespizio_R_PlusSystem.indd 1 11/06/ :32:02
R-Plus System R-Plus System R-Plus system R-Plus system description Fig. R-Plus system R-Plus System is Rollon s series of rack & pinion driven actuators. Rollon R-Plus System series linear units are designed
More informationStress Analysis Lecture 3 ME 276 Spring Dr./ Ahmed Mohamed Nagib Elmekawy
Stress Analysis Lecture 3 ME 276 Spring 2017-2018 Dr./ Ahmed Mohamed Nagib Elmekawy Axial Stress 2 Beam under the action of two tensile forces 3 Beam under the action of two tensile forces 4 Shear Stress
More informationSNL plummer block housings, 2, 3, 5 and 6 series Other bearing housings Large SNL plummer block housings
Bearing housings SNL plummer block housings, 2, 3, 5 and 6 series... 1033 Other bearing housings... 1058 Large SNL plummer block housings... 1058 SONL plummer block housings... 1059 SDG plummer block housings...
More informationPhysics 12. Unit 5 Circular Motion and Gravitation Part 1
Physics 12 Unit 5 Circular Motion and Gravitation Part 1 1. Nonlinear motions According to the Newton s first law, an object remains its tendency of motion as long as there is no external force acting
More informationENGINEERING INFORMATION TABLE OF CONTENTS SHAFT AND HOUSING FITS LUBRICATION LIFE AND LOAD RATINGS RADIAL CLEARANCE CHART
ENGINEERING INFORMATION TABLE OF CONTENTS ENGINEERING INFORMATION SHAFT AND HOUSING FITS LUBRICATION LIFE AND LOAD RATINGS RADIAL CLEARANCE CHART SHAFT AND HOUSING FITS FOR METRIC RADIAL BALL AND ROLLER
More informationSelection Calculations For Linear & Rotary Actuators
H-8 For Electric Linear Slides and Electric Cylinders First determine your series, then select your product. Select the actuator that you will use based on the following flow charts: Selection Procedure
More informationCam Roller Guides. The Drive and Control Company. Service Automation. Electric Drives and Controls. Linear Motion and Assembly Technologies
Industrial Hydraulics Electric Drives and Controls Linear Motion and Assembly Technologies Pneumatics Service Automation Mobile Hydraulics Cam Roller Guides The Drive and Control Company Linear Motion
More informationNATIONAL CERTIFICATE (VOCATIONAL) APPLIED ENGINEERING TECHNOLOGY NQF LEVEL 4 NOVEMBER 2009
NATIONAL CERTIFICATE (VOCATIONAL) APPLIED ENGINEERING TECHNOLOGY NQF LEVEL 4 NOVEMBER 2009 (6021024) 30 October (Y-Paper) 13:00 16:00 A non-programmable scientific calculator may be used. This question
More informationDownloaded from Downloaded from / 1
PURWANCHAL UNIVERSITY III SEMESTER FINAL EXAMINATION-2002 LEVEL : B. E. (Civil) SUBJECT: BEG256CI, Strength of Material Full Marks: 80 TIME: 03:00 hrs Pass marks: 32 Candidates are required to give their
More informationStep 1: Mathematical Modeling
083 Mechanical Vibrations Lesson Vibration Analysis Procedure The analysis of a vibrating system usually involves four steps: mathematical modeling derivation of the governing uations solution of the uations
More informationCharacterization of Fixture-Workpiece Static Friction
Characterization of Fixture-Workpiece Static Friction By Jose F. Hurtado Shreyes N. Melkote Precision Manufacturing Research Consortium Georgia Institute of Technology Sponsors: NSF, GM R&D Center Background
More informationPHYSICS 221 Fall 2013 EXAM 2: November 6, :15pm 10:15pm. Name (printed): Recitation Instructor: Section #:
PHYSICS 221 Fall 2013 EXAM 2: November 6, 2013 8:15pm 10:15pm Name (printed): Recitation Instructor: Section #: INSTRUCTIONS: This exam contains 25 multiple choice questions, plus two extra credit questions,
More informationAn investigation into the relative accuracy of ball-screws and linear encoders over a broad range of application configurations and usage conditions
An investigation into the relative accuracy of ball-screws and linear encoders over a broad range of application configurations and usage conditions A.J. White, S.R. Postlethwaite, D.G. Ford Precision
More informationSTRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS
1 UNIT I STRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS 1. Define: Stress When an external force acts on a body, it undergoes deformation. At the same time the body resists deformation. The
More informationCEE 271: Applied Mechanics II, Dynamics Lecture 9: Ch.13, Sec.4-5
1 / 40 CEE 271: Applied Mechanics II, Dynamics Lecture 9: Ch.13, Sec.4-5 Prof. Albert S. Kim Civil and Environmental Engineering, University of Hawaii at Manoa 2 / 40 EQUATIONS OF MOTION:RECTANGULAR COORDINATES
More informationNAME: Given Formulae: Law of Cosines: Law of Sines:
NME: Given Formulae: Law of Cosines: EXM 3 PST PROBLEMS (LESSONS 21 TO 28) 100 points Thursday, November 16, 2017, 7pm to 9:30, Room 200 You are allowed to use a calculator and drawing equipment, only.
More informationUNIT 1 STRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS 1. Define stress. When an external force acts on a body, it undergoes deformation.
UNIT 1 STRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS 1. Define stress. When an external force acts on a body, it undergoes deformation. At the same time the body resists deformation. The magnitude
More informationMembers Subjected to Torsional Loads
Members Subjected to Torsional Loads Torsion of circular shafts Definition of Torsion: Consider a shaft rigidly clamped at one end and twisted at the other end by a torque T = F.d applied in a plane perpendicular
More informationSECOND ENGINEER REG. III/2 APPLIED MECHANICS
SECOND ENGINEER REG. III/2 APPLIED MECHANICS LIST OF TOPICS Static s Friction Kinematics Dynamics Machines Strength of Materials Hydrostatics Hydrodynamics A STATICS 1 Solves problems involving forces
More informationPiedmont Chapter Vibration Institute Training Symposium 10 May, 2012 FIELD BALANCING OF ROTATING MACHINERY.
Piedmont Chapter Vibration Institute Training Symposium 10 May, 2012 FIELD BALANCING OF ROTATING MACHINERY WWW.PdMsolutions.com Presenter: William T. Pryor III Senior Technical Director PdM Solutions,
More informationMetrology Prof. Dr Kanakuppi Sadashivappa Bapuji Institute of Engineering and Technology Davangere
Metrology Prof. Dr Kanakuppi Sadashivappa Bapuji Institute of Engineering and Technology Davangere Lecture 32 Introduction To Comparators, Mechanical Comparators (Refer Slide Time: 00:15) I welcome you
More informationENG1001 Engineering Design 1
ENG1001 Engineering Design 1 Structure & Loads Determine forces that act on structures causing it to deform, bend, and stretch Forces push/pull on objects Structures are loaded by: > Dead loads permanent
More informationCalculating the Applied Load
The LM Guide is capable of receiving loads and moments in all directions that are generated due to the mounting orientation, alignment, gravity center position of a traveling object, thrust position and
More informationMechanics Topic D (Rotation) - 1 David Apsley
TOPIC D: ROTATION SPRING 2019 1. Angular kinematics 1.1 Angular velocity and angular acceleration 1.2 Constant-angular-acceleration formulae 1.3 Displacement, velocity and acceleration in circular motion
More informationPhysical Pendulum, Torsion Pendulum
[International Campus Lab] Physical Pendulum, Torsion Pendulum Objective Investigate the motions of physical pendulums and torsion pendulums. Theory ----------------------------- Reference --------------------------
More informationTribology Prof. Dr. Harish Hirani Department of Mechanical Engineering Indian Institute of Technology, Delhi
Tribology Prof. Dr. Harish Hirani Department of Mechanical Engineering Indian Institute of Technology, Delhi Lecture No. # 29 Rolling Element Bearings (Contd.) Welcome to 29 th lecture of video course
More informationCTV series CHARACTERISTICS LINEAR UNITS
CTV series CHARACTERISTICS The CTV series describes s with a precision ball screw drive and two parallel, integrated, Zerobacklash rail guides. Compact dimensions allow high performance features such as,
More informationOverview. Dry Friction Wedges Flatbelts Screws Bearings Rolling Resistance
Friction Chapter 8 Overview Dry Friction Wedges Flatbelts Screws Bearings Rolling Resistance Dry Friction Friction is defined as a force of resistance acting on a body which prevents slipping of the body
More informationEMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 3 Torsion
EMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 3 Torsion Introduction Stress and strain in components subjected to torque T Circular Cross-section shape Material Shaft design Non-circular
More informationVariable Speed 20" Single and Multi-spindle, Belt Drive Industrial Drill Presses
www.clausing-industrial.com Variable Speed 20" Single and Multi-spindle, Belt Drive Industrial Drill Presses Two Speed Variable Speeds 150-2000rpm Variable Speeds 200-1300rpm Variable Speeds 300-2000rpm
More informationNew Representation of Bearings in LS-DYNA
13 th International LS-DYNA Users Conference Session: Aerospace New Representation of Bearings in LS-DYNA Kelly S. Carney Samuel A. Howard NASA Glenn Research Center, Cleveland, OH 44135 Brad A. Miller
More informationThe basic dynamic load rating C is a statistical number and it is based on 90% of the bearings surviving 50 km of travel carrying the full load.
Technical data Load Rating & Life Under normal conditions, the linear rail system can be damaged by metal fatigue as the result of repeated stress. The repeated stress causes flaking of the raceways and
More informationControlling Thermal Expansion
Controlling Thermal Expansion Strategies for Maximizing the Repeatability of your Linear Stage By David Goosen, Mechanical Engineering Team INTRODUCTION Most of us are aware that all common engineering
More informationA deeper investigation into the thermal drift of a linear axis
A deeper investigation into the thermal drift of a linear axis O Beltrami STANIMUC Ente Federate UNI via A. Vespucci 7725 Torino, Italia Abstract This presentation shows the results of actual tests performed
More informationIncreasing of the Stern Tube Bushes Precision by On-Line Adaptive Control of the Cutting Process
Increasing of the Stern Tube Bushes Precision by On-Line Adaptive Control of the Cutting Process LUCIAN VASILIU, ALEXANDRU EPUREANU, GABRIEL FRUMUŞANU, VASILE MARINESCU Manufacturing Science and Engineering
More informationTopic 3 FUNdaMENTAL Principles
Topic 3 FUNdaMENTAL Principles θz Z Y θy θx X Topics Occam s Razor Saint-Venant s Principle Golden Rectangle Abbe s Principle Maxwell & Reciprocity Self-Principles Stability Symmetry Parallel Axis Theorem
More informationNR ROTARY RING TABLE: FLEXIBLE IN EVERY RESPECT
NR FREELY PROGRAMMABLE ROTARY TABLES NR ROTARY RING TABLE All NR rings allow customer-specific drive motors to be connected NR ROTARY RING TABLE: FLEXIBLE IN EVERY RESPECT WHEN IT S GOT TO BE EXACT We
More informationNew Way Porous Gas Bearings as Seals. Bearings Seals
New Way Porous Gas Bearings as Seals Bearings Seals 1 New Way Overview Founded January 1994. Aston, Pa. 15 miles south of Philadelphia 54 employees 35,000 sq ft facility, Environmentally Controlled Precision
More informationConcepts in Physics. Wednesday, November 04th
1206 - Concepts in Physics Wednesday, November 04th Request from Mark Brown Those of you who will miss the LAB tomorrow, please let Mark B. know - either stopping by or a quick email will be fine. State
More informationTopic wise Tests. Complex Variables, Numerical Methods and Probability and Statistics.
ME-01 ME-02 ME-03 ME-04 GEM-1 GEM-2 GMC 1 Mechanics) GHT 1 Topic wise Tests Each test carries 25 marks and 45 minutes duration Test consists of 5 one mark questions and 10 two marks questions Tests will
More informationSCHOOL OF COMPUTING, ENGINEERING AND MATHEMATICS SEMESTER 1 EXAMINATIONS 2012/2013 XE121. ENGINEERING CONCEPTS (Test)
s SCHOOL OF COMPUTING, ENGINEERING AND MATHEMATICS SEMESTER EXAMINATIONS 202/203 XE2 ENGINEERING CONCEPTS (Test) Time allowed: TWO hours Answer: Attempt FOUR questions only, a maximum of TWO questions
More informationLT130LDGS Single table
T0DGS Single table K(mounting hole: pitch) 0 30 S(stroke) 0 0 4-M Depth 9( 1 ) Hole for n-m4 3. 43 imit 87. 1 K n T0DGS- 240 240 80 0 8 7.6 T0DGS- 7 7 1 000 80 840 16. T0DGS-0 1 1 480 80 24 19.4 T0DGS-1680
More informationAnalysis of a High-Precision Grinding Machine
ISSN 47-98 International Journal of Emerging Trends in Engineering Research (IJETER), Vol. No.1, Pages : 1 16 (015) Analysis of a High-Precision Grinding Machine Seon-Yeol Oh 1, Joon Jang, Woo Chun Choi
More informationPHYSICS I RESOURCE SHEET
PHYSICS I RESOURCE SHEET Cautions and Notes Kinematic Equations These are to be used in regions with constant acceleration only You must keep regions with different accelerations separate (for example,
More informationROLLER BEARING FAILURES IN REDUCTION GEAR CAUSED BY INADEQUATE DAMPING BY ELASTIC COUPLINGS FOR LOW ORDER EXCITATIONS
ROLLER BEARIG FAILURES I REDUCTIO GEAR CAUSED BY IADEQUATE DAMPIG BY ELASTIC COUPLIGS FOR LOW ORDER EXCITATIOS ~by Herbert Roeser, Trans Marine Propulsion Systems, Inc. Seattle Flexible couplings provide
More informationEngineering Science OUTCOME 1 - TUTORIAL 4 COLUMNS
Unit 2: Unit code: QCF Level: Credit value: 15 Engineering Science L/601/10 OUTCOME 1 - TUTORIAL COLUMNS 1. Be able to determine the behavioural characteristics of elements of static engineering systems
More informationSimulation, Prediction and Compensation of Transient Thermal Deformations of a Reciprocating Linear Slide for F8S Motion Error Separation
Proceedings of the 3 rd International Conference on Mechanical Engineering and Mechatronics Prague, Czech Republic, August 14-1, 2014 Paper No. 139 Simulation, Prediction and Compensation of Transient
More informationFoundations of Ultraprecision Mechanism Design
Foundations of Ultraprecision Mechanism Design S.T. Smith University of North Carolina at Charlotte, USA and D.G. Chetwynd University of Warwick, UK GORDON AND BREACH SCIENCE PUBLISHERS Switzerland Australia
More informationPHYSICS LAB Experiment 9 Fall 2004 THE TORSION PENDULUM
PHYSICS 83 - LAB Experiment 9 Fall 004 THE TORSION PENDULUM In this experiment we will study the torsion constants of three different rods, a brass rod, a thin steel rod and a thick steel rod. We will
More informationVisual Physics Rotational Dynamics Lab 5
You have been asked to think of objects as point particles rather than extended bodies up to this point in the semester. This assumption is useful and sometimes sufficient, however, the approximation of
More informationAPPENDIX. SELECTING THE SureServo SERVO SYSTEM. In This Appendix... Selecting the SureServo Servo System...B 2. Leadscrew - Example Calculations...
SELECTING THE SureServo SERVO SYSTEM APPENDIX B In This Appendix... Selecting the SureServo Servo System............B 2 The Selection Procedure......................................B 2 How many pulses
More informationS.C. Rulmenti S.A. Barlad Romania Republicii Street No
SELECTION OF BEARING SIZE Basic load ratings The size of a bearing is selected considering the load in the used rolling bearing and also depends on the operational rating life and prescribed operating
More informationStudy of Rupture Directivity in a Foam Rubber Physical Model
Progress Report Task 1D01 Study of Rupture Directivity in a Foam Rubber Physical Model Rasool Anooshehpoor and James N. Brune University of Nevada, Reno Seismological Laboratory (MS/174) Reno, Nevada 89557-0141
More informationQUESTION BANK SEMESTER: III SUBJECT NAME: MECHANICS OF SOLIDS
QUESTION BANK SEMESTER: III SUBJECT NAME: MECHANICS OF SOLIDS UNIT 1- STRESS AND STRAIN PART A (2 Marks) 1. Define longitudinal strain and lateral strain. 2. State Hooke s law. 3. Define modular ratio,
More informationMechanics of Materials Primer
Mechanics of Materials rimer Notation: A = area (net = with holes, bearing = in contact, etc...) b = total width of material at a horizontal section d = diameter of a hole D = symbol for diameter E = modulus
More informationIdentification system for short product names. Changes/amendments at a glance. 2 Bosch Rexroth AG OBB omega modules R ( )
Omega Modules OBB 2 OBB omega modules R9990079 (206-05) Identification system for short product names Short product name Example: O B B - 085 - N N - System = Omega module Guideway = Ball Rail System Drive
More informationHRN/HRN-C Series Hydraulic Vane Rotary Actuators
HRN/ Hydraulic Vane Rotary Actuators Vane Actuators Tork-Mor HRN Contents Features... 2 Ordering Information... Engineering Data / Specifications... Dimensions... Features... 1 Ordering Information...12
More informationEffective Measurement Method of Thermal Deformation of Machine Tools Caused by Linear Axis Motion
Effective Measurement Method of Thermal Deformation of Machine Tools aused by inear Axis Motion 1. Introduction Shinji Shimizu Noboru Imai Department of Mechanical Engineering Sophia University Tokyo The
More informationMatlab Sheet 2. Arrays
Matlab Sheet 2 Arrays 1. a. Create the vector x having 50 logarithmically spaced values starting at 10 and ending at 1000. b. Create the vector x having 20 logarithmically spaced values starting at 10
More informationwhere G is called the universal gravitational constant.
UNIT-I BASICS & STATICS OF PARTICLES 1. What are the different laws of mechanics? First law: A body does not change its state of motion unless acted upon by a force or Every object in a state of uniform
More informationForce and Motion 20 N. Force: Net Force on 2 kg mass = N. Net Force on 3 kg mass = = N. Motion: Mass Accel. of 2 kg mass = = kg m/s 2.
Force and Motion Team In previous labs, you used a motion sensor to measure the position, velocity, and acceleration of moving objects. You were not concerned about the mechanism that caused the object
More informationGyroscopes and statics
Gyroscopes and statics Announcements: Welcome back from Spring Break! CAPA due Friday at 10pm We will finish Chapter 11 in H+R on angular momentum and start Chapter 12 on stability. Friday we will begin
More informationManufacturing Equipment Control
QUESTION 1 An electric drive spindle has the following parameters: J m = 2 1 3 kg m 2, R a = 8 Ω, K t =.5 N m/a, K v =.5 V/(rad/s), K a = 2, J s = 4 1 2 kg m 2, and K s =.3. Ignore electrical dynamics
More informationName: Fall 2014 CLOSED BOOK
Name: Fall 2014 1. Rod AB with weight W = 40 lb is pinned at A to a vertical axle which rotates with constant angular velocity ω =15 rad/s. The rod position is maintained by a horizontal wire BC. Determine
More informationSample Final Exam 02 Physics 106 (Answers on last page)
Sample Final Exam 02 Physics 106 (Answers on last page) Name (Print): 4 Digit ID: Section: Instructions: 1. There are 30 multiple choice questions on the test. There is no penalty for guessing, so you
More informationStrain Gages. Approximate Elastic Constants (from University Physics, Sears Zemansky, and Young, Reading, MA, Shear Modulus, (S) N/m 2
When you bend a piece of metal, the Strain Gages Approximate Elastic Constants (from University Physics, Sears Zemansky, and Young, Reading, MA, 1979 Material Young's Modulus, (E) 10 11 N/m 2 Shear Modulus,
More informationThe Torsion Pendulum
Page 1 of 9 The Torsion Pendulum Introduction: This experiment helps to relate many of the concepts that we see in everyday life. Damped oscillations and pendulums are an everyday occurrence. You will
More information1. A pure shear deformation is shown. The volume is unchanged. What is the strain tensor.
Elasticity Homework Problems 2014 Section 1. The Strain Tensor. 1. A pure shear deformation is shown. The volume is unchanged. What is the strain tensor. 2. Given a steel bar compressed with a deformation
More informationTheory & Practice of Rotor Dynamics Prof. Rajiv Tiwari Department of Mechanical Engineering Indian Institute of Technology Guwahati
Theory & Practice of Rotor Dynamics Prof. Rajiv Tiwari Department of Mechanical Engineering Indian Institute of Technology Guwahati Module - 8 Balancing Lecture - 1 Introduce To Rigid Rotor Balancing Till
More informationPHYSICS 221 Fall 2016 FINAL EXAM: December 12, :30pm 6:30pm. Name (printed): Recitation Instructor: Section #:
PHYSICS 221 Fall 2016 FINAL EXAM: December 12, 2016 4:30pm 6:30pm Name (printed): Recitation Instructor: Section #: INSTRUCTIONS: This exam contains 25 multiple-choice questions, plus two extra-credit
More informationANALYSIS OF GATE 2018*(Memory Based) Mechanical Engineering
ANALYSIS OF GATE 2018*(Memory Based) Mechanical Engineering 6% 15% 13% 3% 8% Engineering Mathematics Engineering Mechanics Mechanics of Materials Theory Of Machines Machine Design Fluid Mechanics 19% 8%
More information2. a) Explain the equilibrium of i) Concurrent force system, and ii) General force system.
Code No: R21031 R10 SET - 1 II B. Tech I Semester Supplementary Examinations Dec 2013 ENGINEERING MECHANICS (Com to ME, AE, AME, MM) Time: 3 hours Max. Marks: 75 Answer any FIVE Questions All Questions
More informationRotational Mechanics Part III Dynamics. Pre AP Physics
Rotational Mechanics Part III Dynamics Pre AP Physics We have so far discussed rotational kinematics the description of rotational motion in terms of angle, angular velocity and angular acceleration and
More informationTextbook Reference: Wilson, Buffa, Lou: Chapter 8 Glencoe Physics: Chapter 8
AP Physics Rotational Motion Introduction: Which moves with greater speed on a merry-go-round - a horse near the center or one near the outside? Your answer probably depends on whether you are considering
More information(Refer Slide Time: 1: 19)
Mechanical Measurements and Metrology Prof. S. P. Venkateshan Department of Mechanical Engineering Indian Institute of Technology, Madras Module - 4 Lecture - 46 Force Measurement So this will be lecture
More information