AfM - Accuracy for Machines

Size: px
Start display at page:

Download "AfM - Accuracy for Machines"

Transcription

1 Praxisbericht / Case Study / Gantry type AfM - Accuracy for Machines Page 1

2 Volumetric Compensation Volumetrische Vermessung und Kompensation einer Gantry Fräsmaschine mit FIDIA CNC C20 und Option VAC Volumetric Calibration and Compensation of a gantry type machine tool with FIDIA CNC C20 and option VAC Verbesserung der volumetrischen Genauigkeit um: 92% 359µm Improvement of volumetric accuracy by: 92% 359µm Page 2

3 Zeitplan / Schedule Montag Monday Anreise / journey there Aufbau LaserTRACER / setup of the LaserTRACER system in the machine tool Installation der volumetrischen Korrekturoption durch den Steuerungshersteller / Installation of the Volumetric Compensation Option by the control manufacturer Erstellung / Anpassung der Messstrategie an das Maschinenvolumen und die Gegebenheiten vor Ort / Creation and modification of the measurement strategy Temperaturmesssystem an Maschinenmaßstäben installieren / setup of the temperature measuring system Dienstag Tuesday Mittwoch Wednesday Donnerstag Thursday Kalibriermessung der Maschine / Calibration measurement of the machine tool Auswertung der volumetrischen Abweichung / Evaluation of the volumetric deviation Erstellung des Korrekturfiles / Creation of the compensation file for the CNC Control Verifizierungsmessung des kompensierten Volumens / Verification measurement of the compensated machine tool Auswertung der volumetrischen Restabweichung / Evaluation of the remaining volumetric deviation Dokumentation / Documentation Abreise / Return trip Page 3

4 Maschine / Machine tool Kompensationsvolumen / Compensated workspace: 15m³ X-Achse / X-Axis: 5000mm Y-Achse / Y-Axis: 2500mm Z-Achse / Z-Axis: 1200mm Maschine ohne Temperaturkompensation Machine without temperature compensation Page 4

5 Ergebnisse / Results Verification of VolumetricAxisCalibration on 5 axis machine tool 400,0 300,0 200,0 100,0 0,0-100,0-200,0 Without VolumetricAxisCalibration With VolumetricAxisCalibration Page 5

6 Ergebnisse / Results Parameter position deviation [µm] straightness deviation [µm] rotational deviation [µrad] orthogonality [µrad] spatial deviation (Simulation) Without With U (max) Improvement VolumetricAxisCalibration VolumetricAxisCalibration Tracer absolut percentage xtx / EXX 77,4 18,6 0,8-58,9-76% yty / EYY 53,6 9,6 0,8-44,0-82% ztz / EZZ 59,9 6,8 0,8-53,1-89% xty / EYX 52,3 7,1 1,0-45,3-87% xtz / EZX 80,4 7,3 1,2-73,0-91% ytx / EXY 52,7 7,0 0,3-45,7-87% ytz / EZY 43,0 4,0 0,9-39,0-91% ztx / EXZ 16,9 2,9 0,4-14,0-83% zty / EYZ 132,4 3,5 0,3-128,9-97% xrx / EAX 153,6 5,2 0,7-148,4-97% xry / EBX 88,3 5,5 0,5-82,7-94% xrz / ECX 28,0 2,4 0,4-25,6-91% yrx / EAY 69,5 7,2 0,6-62,3-90% yry / EBY 100,7 6,6 0,3-94,1-93% yrz / ECY 83,3 28,5 1,3-54,8-66% zrx / EAZ 123,4 6,3 1,0-117,0-95% zry / EBZ 44,2 5,8 1,1-38,4-87% zrz / ECZ 30,8 7,3 1,2-23,6-76% xwy / COY -52,5 1,7 0,3-50,8-97% xwz / BOZ -120,9 7,3 0,5-113,6-94% ywz / AOZ -30,1 1,5 0,4-28,6-95% L mea 180,0 40,0 2,0-140,0-78% 1D sim 180,0 33,0 2,0-147,0-82% 3D sim 389,0 30,0 2,0-359,0-92% Page 6

7 Positionsabweichungen / Position deviations 0,070 0,060 0,050 0,040 0,030 0,020 0,010 0,000-0,010-0,020-0,030-0,040-0,050-0,060 0,040 0,030 0,020 0,010 0,000-0,010-0,020-0,030-0,040-0,050-0,060 xtx xtx with VAC ztz ztz with VAC 0,060 0,050 0,040 0,030 0,020 0,010 0,000-0,010-0,020-0,030-0,040 Abweichungen bezogen auf 20 C Deviations related to 20 C yty yty with VAC Page 7

8 Geradheitsabweichungen / Straightness dev. X-Achse / x-axis 0,040 0,020 0,000-0,020-0,040 0,040 0,020 0,000-0,020-0,040-0,060-0,080 xty xty with VAC xtz xtz with VAC Page 8

9 Geradheitsabweichungen / Straightness dev. Y-Achse / y-axis 0,040 0,020 0,000-0,020-0,040 0,040 0,020 0,000-0,020-0,040-0,060-0,080 ytx ytx with VAC ytz ytz with VAC Page 9

10 Geradheitsabweichungen / Straightness dev. Z-Achse / Z-axis 0,040 0,020 0,000-0,020-0,040 ztx ztx with VAC 0,060 0,040 0,020 0,000-0,020-0,040-0,060-0,080-0,100 zty zty with VAC Page 10

11 Rotationsabweichungen / Rotational deviation 0, , , , , , , , , , , , , , , , , , xrx xrx with VAC xrz xrz with VAC 0, , , , , , X-Achse / x-axis -0, xry xry with VAC Page 11

12 Rotationsabweichungen / Rotational deviation 0, , , , , , , , , , , , , , , , , yrx yrx with VAC yrz yrz with VAC 0, , , , , Y-Achse / y-axis -0, , yry yry with VAC Page 12

13 Rotationsabweichungen / Rotational deviation 0, , , , , , , , , , , , , , zrx zrx with VAC zrz zrz with VAC 0, , , , , Z-Achse / z-axis -0, , zry zry with VAC Page 13

14 Rechtwinkligkeiten / Orthogonality 1, deviation xwy 1, deviation ywz xwy without VAC xwy with VAC ywz ohnevac ywz mit VAC 0, , , , deviation xwz xwz without VAC xwz with VAC Definition Vorzeichen: Positiver Winkel ist größer 90 Definition of sign: Positive angle is greater than 90 Page 14

15 1D Abweichung / 1D deviation without Volumetric Compensation maximum 180 µm deviation 1D deviation: The maximum deviation of measuring lines along the axes, in all planes and spatial diagonals of the machine tool with Volumetric Compensation maximum 33 µm deviation 1D Abweichung: Es wurden die Abweichungen entlang achsparalleler Geraden, in allen Ebenen- und Raumdiagonalen berechnet. Page 15

16 3D Abweichung / 3D volumetric deviation without Volumetric Compensation maximum 389 µm deviation 3D deviation: The maximum volumetric deviation in the whole workspace of the machine tool with Volumetric Compensation maximum 31 µm deviation 3D Abweichung: Es wurde die maximale volumetrische Abweichung im gesamten Arbeitsraum berechnet Page 16

17 volumetrisches Umkehrspiel / volumetric backlash Position 1 0,0150 0,0100 0,0050 0,0000-0,0050-0,0100-0,0150 3D backlash and drift [mm] Xq - 3s [mm] Xq [mm] Xq + 3s [mm] thermal drift 0,0150 0,0100 0,0050 0,0000-0,0050-0,0100-0,0150 Position 3 Position 2 0,0150 0,0100 0,0050 0,0000-0,0050-0,0100-0,0150 3D backlash and drift [mm] Xq - 3s [mm] Xq [mm] Xq + 3s [mm] thermal drift 0,0150 0,0100 0,0050 0,0000-0,0050-0,0100-0,0150 Position 4 3D backlash and drift [mm] Xq - 3s [mm] 3D backlash and drift [mm] Xq - 3s [mm] Xq [mm] Xq + 3s [mm] Xq [mm] Xq + 3s [mm] thermal drift thermal drift Page 17

18 volumetrisches Umkehrspiel / volumetric backlash 0,0150 0,0100 0,0050 0,0000-0,0050-0,0100-0,0150 Position 5 0,0150 0,0100 0,0050 0,0000-0,0050-0,0100-0,0150 Position 6 0,0150 0,0100 0,0050 0,0000-0,0050-0,0100-0,0150 3D backlash and drift [mm] Xq - 3s [mm] Xq [mm] Xq + 3s [mm] thermal drift Position 7 3D backlash and drift [mm] Xq [mm] thermal drift Xq - 3s [mm] Xq + 3s [mm] 3D backlash and drift [mm] Xq [mm] thermal drift Xq - 3s [mm] Xq + 3s [mm] Page 18

19 Temperatur Bedingungen / Temperature conditions Calibration Measurement Position Actual Nominal Date Start time End time Duration tp [s] Start temp. End temp. Temp. diff. Gradient [ C/h] Average :47:21 10:18:00 0:30:39 2,91 22,319 22,370 0,051 0,100 22, :40:55 13:11:03 0:30:08 2,88 22,691 22,810 0,119 0,237 22, :04:08 14:34:47 0:30:39 2,93 23,148 23,120-0,028-0,055 23, :00:44 15:31:28 0:30:44 2,94 23,462 23,260-0,201-0,393 23, :03:51 17:35:06 0:31:15 2,85 23,604 23,570-0,034-0,065 23, :44:19 18:03:33 0:19:14 2,68 23,444 23,500 0,056 0,174 23, :14:31 18:33:34 0:19:03 2,65 23,507 23,480-0,027-0,086 23,494 Verification Measurement Position Actual Nominal Date Start time End time Duration tp [s] Start temp. End temp. Temp. diff. Gradient [ C/h] Average :25:03 10:45:12 0:20:09 2,81 20,414 21,370 0,956 2,847 20, :51:21 11:12:17 0:20:56 2,91 21,981 22,590 0,609 1,746 22, :17:32 11:51:23 0:33:51 3,08 22,562 22,620 0,058 0,104 22, :02:57 12:35:47 0:32:50 3,12 22,750 22,930 0,180 0,328 22, :02:39 13:34:54 0:32:15 3,09 23,201 23,390 0,189 0,352 23, :56:00 14:27:47 0:31:47 3,04 23,415 23,500 0,085 0,161 23, :24:35 15:57:35 0:33:00 3,16 23,785 23,780-0,005-0,009 23,783 Measuring schedule Duration [hh:mm:ss] Calibration Verification measurement time 3:11:42 3:24:48 setup time 5:34:31 2:07:44 total time 8:46:13 5:32:32 Page 19

20 16:47:00 17:39:00 18:31:00 19:23:00 20:15:00 21:07:00 21:59:00 22:51:00 23:43:00 00:35:00 01:27:00 02:19:00 03:11:00 04:03:00 04:55:00 05:47:00 06:39:00 07:31:00 08:23:00 09:15:00 10:07:00 10:59:00 11:51:00 12:43:00 13:35:00 14:27:00 15:19:00 16:11:00 17:03:00 17:55:00 18:47:00 19:39:00 20:31:00 21:23:00 22:15:00 23:07:00 23:59:00 00:51:00 01:43:00 02:35:00 03:27:00 04:19:00 05:11:00 06:03:00 06:55:00 07:47:00 08:39:00 09:31:00 10:23:00 11:15:00 12:07:00 12:59:00 13:51:00 14:43:00 15:35:00 16:27:00 28 Temperatur Bedingungen / Temperature conditions 27 Calibration Verification 26 Z- Achse 25 Y- Achse 24 X- Achse 23 Page 20

21 Thank you for your attention Vielen Dank für Ihre Aufmerksamkeit AfM Technology GmbH Gartenstraße Aalen Fon: +49 (0) Fax: +49 (0) Page 21

Static and dynamic testing of machine tools

Static and dynamic testing of machine tools Static and dynamic testing of machine tools Thomas Liebrich, Michael Gebhardt, Stefan Thoma, Hop Nguyen, Sascha Weikert, Wolfgang Knapp, Konrad Wegener Institute for Machine Tools and Manufacturing (IWF),

More information

Economics 204 Summer/Fall 2017 Lecture 1 Monday July 17, 2017

Economics 204 Summer/Fall 2017 Lecture 1 Monday July 17, 2017 Economics 04 Summer/Fall 07 Lecture Monday July 7, 07 Section.. Methods of Proof We begin by looking at the notion of proof. What is a proof? Proof has a formal definition in mathematical logic, and a

More information

Notes 2: Fluid Mechanics Introduction

Notes 2: Fluid Mechanics Introduction Low Speed Aerodynamics Notes 2: Fluid Mechanics Introduction FLUID DYNAMICS http://www.andes.org.uk/andes-information-files/condor-puna-2005.jpg Types of Fluid Motion 1. Fluids, like most other forms of

More information

Relations (3A) Young Won Lim 3/27/18

Relations (3A) Young Won Lim 3/27/18 Relations (3A) Copyright (c) 2015 2018 Young W. Lim. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later

More information

Relations MATH Relations. Benjamin V.C. Collins, James A. Swenson MATH 2730

Relations MATH Relations. Benjamin V.C. Collins, James A. Swenson MATH 2730 MATH 2730 Benjamin V.C. Collins James A. Swenson among integers equals a = b is true for some pairs (a, b) Z Z, but not for all pairs. is less than a < b is true for some pairs (a, b) Z Z, but not for

More information

MATH 433 Applied Algebra Lecture 14: Functions. Relations.

MATH 433 Applied Algebra Lecture 14: Functions. Relations. MATH 433 Applied Algebra Lecture 14: Functions. Relations. Cartesian product Definition. The Cartesian product X Y of two sets X and Y is the set of all ordered pairs (x,y) such that x X and y Y. The Cartesian

More information

Relations and Equivalence Relations

Relations and Equivalence Relations Relations and Equivalence Relations In this section, we shall introduce a formal definition for the notion of a relation on a set. This is something we often take for granted in elementary algebra courses,

More information

9 RELATIONS. 9.1 Reflexive, symmetric and transitive relations. MATH Foundations of Pure Mathematics

9 RELATIONS. 9.1 Reflexive, symmetric and transitive relations. MATH Foundations of Pure Mathematics MATH10111 - Foundations of Pure Mathematics 9 RELATIONS 9.1 Reflexive, symmetric and transitive relations Let A be a set with A. A relation R on A is a subset of A A. For convenience, for x, y A, write

More information

Reproducibility of machine tools' circularity test according to ISO with respect to testing position

Reproducibility of machine tools' circularity test according to ISO with respect to testing position Arch. Mech. Tech. Mater.Vol. 37 (2017) 22-26 Archives of Mechanical Technology and Materials www.amtm.put.poznan.pl Reproducibility of machine tools' circularity test according to ISO 230-4 with respect

More information

Foundations of Mathematics Worksheet 2

Foundations of Mathematics Worksheet 2 Foundations of Mathematics Worksheet 2 L. Pedro Poitevin June 24, 2007 1. What are the atomic truth assignments on {a 1,..., a n } that satisfy: (a) The proposition p = ((a 1 a 2 ) (a 2 a 3 ) (a n 1 a

More information

A SPRT Intercomparison at Hg, TPW, Ga, Sn and Zn ITS-90 Fixed Points between PTB and LATU with PTB as Pilot Laboratory

A SPRT Intercomparison at Hg, TPW, Ga, Sn and Zn ITS-90 Fixed Points between PTB and LATU with PTB as Pilot Laboratory A SPRT Intercomparison at Hg, TPW, Ga, Sn and Zn ITS-90 Points between PTB and LATU with PTB as Pilot Laboratory O. Robatto, Departamento de Metrología Científica, Laboratorio Tecnológico del Uruguay(LATU),

More information

AN3002 Thermocouple measurement

AN3002 Thermocouple measurement AN3002 Thermocouple measurement This application note illustrates the correct measurement of thermocouple sensors. Contents 1 Introduction......................................... 3 2 Test configuration....................................

More information

ISO defines the Rockwell superficial hardness value, HRN, as:

ISO defines the Rockwell superficial hardness value, HRN, as: Rockwell Hardness Coefficients HR30N ISO 6508-1 defines the Rockwell superficial hardness value, HRN, as: HRN = 100 h where: h = permanent depth of indentation under preliminary test force after removal

More information

Simulation and Verification of bionic heat exchangers with COMSOL Multiphysics. A. Kremers, M. Pieper

Simulation and Verification of bionic heat exchangers with COMSOL Multiphysics. A. Kremers, M. Pieper Simulation and Verification of bionic heat exchangers with COMSOL Multiphysics A. Kremers, M. Pieper The idea Bionic heat exchanger Analogy to blood vessel system Low pressure losses Low energy consumption

More information

Chapter 3. Cartesian Products and Relations. 3.1 Cartesian Products

Chapter 3. Cartesian Products and Relations. 3.1 Cartesian Products Chapter 3 Cartesian Products and Relations The material in this chapter is the first real encounter with abstraction. Relations are very general thing they are a special type of subset. After introducing

More information

Discrete Mathematics with Applications MATH236

Discrete Mathematics with Applications MATH236 Discrete Mathematics with Applications MATH236 Dr. Hung P. Tong-Viet School of Mathematics, Statistics and Computer Science University of KwaZulu-Natal Pietermaritzburg Campus Semester 1, 2013 Tong-Viet

More information

TEMPERATURE COMPENSATION DURING CMM INSPECTION

TEMPERATURE COMPENSATION DURING CMM INSPECTION TEMPERATURE COMPENSATION DURING CMM INSPECTION E. Ratajczyk, M. Dobosz Institute of Metrology and Measuring Systems, Faculty of Mechatronics Warsaw University of Technology, Chodkiewicza 8 Str. 02-525

More information

Guide to Proofs on Discrete Structures

Guide to Proofs on Discrete Structures CS103 Handout 17 Spring 2018 Guide to Proofs on Discrete Structures In Problem Set One, you got practice with the art of proofwriting in general (as applied to numbers, sets, puzzles, etc.) Problem Set

More information

Deutschen Kalibrierdienst D-K

Deutschen Kalibrierdienst D-K akkreditiert durch die / accredited by the Deutsche Akkreditierungsstelle GmbH als Kalibrierlaboratorium im / as calibration laboratory in the Deutschen Kalibrierdienst Kalibrierschein Kalibrierzeichen

More information

Heat flux and temperature distribution in gear hobbing operations

Heat flux and temperature distribution in gear hobbing operations Available online at www.sciencedirect.com Procedia CIRP 8 (2013 ) 456 461 14 th CIRP Conference on Modeling of Machining Operations (CIRP CMMO) Heat flux and temperature distribution in gear hobbing operations

More information

Sets. A set is a collection of objects without repeats. The size or cardinality of a set S is denoted S and is the number of elements in the set.

Sets. A set is a collection of objects without repeats. The size or cardinality of a set S is denoted S and is the number of elements in the set. Sets A set is a collection of objects without repeats. The size or cardinality of a set S is denoted S and is the number of elements in the set. If A and B are sets, then the set of ordered pairs each

More information

Unit 3, Lesson 1: How Well Can You Measure?

Unit 3, Lesson 1: How Well Can You Measure? Unit 3, Lesson 1: How Well Can You Measure? Lesson Goals Decide whether a relationship is proportional using a graph and a quotient. Understand that due to measurement error, if a graph of two associated

More information

Gauss-Seidel method. Dr. Motilal Panigrahi. Dr. Motilal Panigrahi, Nirma University

Gauss-Seidel method. Dr. Motilal Panigrahi. Dr. Motilal Panigrahi, Nirma University Gauss-Seidel method Dr. Motilal Panigrahi Solving system of linear equations We discussed Gaussian elimination with partial pivoting Gaussian elimination was an exact method or closed method Now we will

More information

Basics of Relation Algebra. Jules Desharnais Département d informatique et de génie logiciel Université Laval, Québec, Canada

Basics of Relation Algebra. Jules Desharnais Département d informatique et de génie logiciel Université Laval, Québec, Canada Basics of Relation Algebra Jules Desharnais Département d informatique et de génie logiciel Université Laval, Québec, Canada Plan 1. Relations on a set 2. Relation algebra 3. Heterogeneous relation algebra

More information

XMA2C011, Annual Examination 2012: Worked Solutions

XMA2C011, Annual Examination 2012: Worked Solutions XMA2C011, Annual Examination 2012: Worked Solutions David R. Wilkins 1. (a) Let A, B and C be sets. Prove that A (B \ C) = (A B) \ (A C). We show that every element of A (B \ C) is an element of (A B)

More information

CSE Discrete Structures

CSE Discrete Structures CSE 2315 - Discrete Structures Homework 1- Fall 2010 Due Date: Sept. 16 2010, 3:30 pm Statements, Truth Values, and Tautologies 1. Which of the following are statements? a) 3 + 7 = 10 b) All cars are blue.

More information

Forschungszentrum Karlsruhe

Forschungszentrum Karlsruhe Forschungszentrum Karlsruhe Technik und Umwelt Wissenschaftliche Berichte FZK 6049 Comparison of Two Radiative Transfer Codes with Respect to the Modeling of the Line Mixing Effect A. V. Polyakov*, B.

More information

Ordinals and Cardinals: Basic set-theoretic techniques in logic

Ordinals and Cardinals: Basic set-theoretic techniques in logic Ordinals and Cardinals: Basic set-theoretic techniques in logic Benedikt Löwe Universiteit van Amsterdam Grzegorz Plebanek Uniwersytet Wroc lawski ESSLLI 2011, Ljubljana, Slovenia This course is a foundational

More information

3. R = = on Z. R, S, A, T.

3. R = = on Z. R, S, A, T. 6 Relations Let R be a relation on a set A, i.e., a subset of AxA. Notation: xry iff (x, y) R AxA. Recall: A relation need not be a function. Example: The relation R 1 = {(x, y) RxR x 2 + y 2 = 1} is not

More information

h m h a + ρ c h c + ρ a + ρ m

h m h a + ρ c h c + ρ a + ρ m Beckenanalyse 1. Subsidenz Hohe Sediment-Akkumulation und die Bildung Sedimentärer Becken sind nicht möglich ohne entsprechenden Subsidenz. Subsidenz beschreibt die Senkung der Erdoberfläche (Landoberfläche

More information

Active Compensation of the Voltage Follower

Active Compensation of the Voltage Follower 328 Active Compensation of the Voltage Follower 36 (982) 2 Active Compensation of the Voltage Follower Aktive Kompensation des Spannungsfolgers By Ahmed M. Soliman (Senior Member IEEE)* Abstract: It is

More information

Foundations of algebra

Foundations of algebra Foundations of algebra Equivalence relations - suggested problems - solutions P1: There are several relations that you are familiar with: Relations on R (or any of its subsets): Equality. Symbol: x = y.

More information

Discharge Measurements at Niger River and its Tributaries Sota, Tinkisso and Niandan

Discharge Measurements at Niger River and its Tributaries Sota, Tinkisso and Niandan Discharge Measurements at Niger River and its Tributaries Sota, Tinkisso and Niandan Hannover, June 2012 Author: Torsten Krekeler Commissioned by: Project: Federal Ministry for Economic Cooperation and

More information

ISO INTERNATIONAL STANDARD. Metallic materials Vickers hardness test Part 3: Calibration of reference blocks

ISO INTERNATIONAL STANDARD. Metallic materials Vickers hardness test Part 3: Calibration of reference blocks INTERNATIONAL STANDARD ISO 6507-3 Third edition 2005-12-15 Metallic materials Vickers hardness test Part 3: Calibration of reference blocks Matériaux métalliques Essai de dureté Vickers Partie 3: Étalonnage

More information

Annex A Procedure for Determining the Uncertainty of Coordinate Measurement Using Multiple Method

Annex A Procedure for Determining the Uncertainty of Coordinate Measurement Using Multiple Method Annex A Procedure for Determining the Uncertainty of Coordinate Measurement Using Multiple Method A.1 Procedure Rules Equipment 1. Measuring tips needed for the measurement of the feature. Measuring tips

More information

Week 4-5: Binary Relations

Week 4-5: Binary Relations 1 Binary Relations Week 4-5: Binary Relations The concept of relation is common in daily life and seems intuitively clear. For instance, let X be the set of all living human females and Y the set of all

More information

Integrated System Simulation of Machine Tools

Integrated System Simulation of Machine Tools Integrated System Simulation of Machine Tools B. Kirchgäßner, A. Schünemann, R. Helfrich INTES GmbH, Stuttgart, Germany www.intes.de; info@intes.de Summary: For the development of machine tools, dynamic

More information

A deeper investigation into the thermal drift of a linear axis

A 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 information

Berechnung von Werkzeugmaschinen in der ANSYS Umgebung. Roberto Rossetti, CADFEM (Suisse) AG

Berechnung von Werkzeugmaschinen in der ANSYS Umgebung. Roberto Rossetti, CADFEM (Suisse) AG Berechnung von Werkzeugmaschinen in der ANSYS Umgebung Roberto Rossetti, CADFEM (Suisse) AG Machine tool simulation in the ANSYS environment - 1 - Overview Stiffness analysis Harmonic analysis Weight influence

More information

Static Program Analysis

Static Program Analysis Static Program Analysis Thomas Noll Software Modeling and Verification Group RWTH Aachen University https://moves.rwth-aachen.de/teaching/ws-1617/spa/ Software Architektur Praxis-Workshop Bringen Sie Informatik

More information

Static Program Analysis

Static Program Analysis Static Program Analysis Thomas Noll Software Modeling and Verification Group RWTH Aachen University https://moves.rwth-aachen.de/teaching/ws-1617/spa/ Software Architektur Praxis-Workshop Bringen Sie Informatik

More information

Distillation. Rectification and azeotropic distillation. Nicole Schai Assisted by Christoph Murer and Simon Zollinger

Distillation. Rectification and azeotropic distillation. Nicole Schai Assisted by Christoph Murer and Simon Zollinger Distillation Rectification and azeotropic distillation Nicole Schai Assisted by Christoph Murer and Simon Zollinger Report ETH Zürich 29 th of November 2011 TABLE OF CONTENT TABLE OF CONTENTS 1 ABSTRACT...

More information

Traceability of on-machine measurements under a wide range of working conditions

Traceability of on-machine measurements under a wide range of working conditions Traceability of on-machine measurements under a wide range of working conditions Frank Keller, Matthias Franke, Norbert Gerwien, Lisa Groos, Christian Held, Klaus Wendt Traceable in-process dimensional

More information

HL Test 2018 Sets, Relations and Groups [50 marks]

HL Test 2018 Sets, Relations and Groups [50 marks] HL Test 2018 Sets, Relations and Groups [50 marks] The binary operation multiplication modulo 10, denoted by 10, is defined on the set T = {2, 4, 6, 8} and represented in the following Cayley table. 1a.

More information

D-optimally Lack-of-Fit-Test-efficient Designs and Related Simple Designs

D-optimally Lack-of-Fit-Test-efficient Designs and Related Simple Designs AUSTRIAN JOURNAL OF STATISTICS Volume 37 (2008), Number 3&4, 245 253 D-optimally Lack-of-Fit-Test-efficient Designs and Related Simple Designs Wolfgang Bischoff Catholic University ichstätt-ingolstadt,

More information

DC-limiter (Chopper) (October 2012) KP-38810gb_td_dc-limiter_chopper_rev.A

DC-limiter (Chopper) (October 2012) KP-38810gb_td_dc-limiter_chopper_rev.A DC-limiter (Chopper) (October 2012) KP-38810gb_td_dc-limiter_chopper_rev.A Woodward td_dc-limiter_chopper_rev.a Woodward behält sich das Recht vor, jeden beliebigen Teil dieser Publikation jederzeit zu

More information

Supersedes: - Superseded by: -

Supersedes: - Superseded by: - Overview IF Comet SE0X0 Created:.0.0 / sm This document and the information contained herein are the property of Stadler Elektronik G ahnhofstr., 0 Littau, Checked/released:.0.0 / kth Idx.: Change No.:

More information

Covariograms of convex bodies in the plane: A remark on Nagel s theorem

Covariograms of convex bodies in the plane: A remark on Nagel s theorem Elem. Math. 57 (00) 61 65 0013-6018/0/00061-5 $ 1.50+0.0/0 c Birkhäuser Verlag, Basel, 00 Elemente der Mathematik Covariograms of convex bodies in the plane: A remark on Nagel s theorem Daniel Neuenschwander

More information

Effective Measurement Method of Thermal Deformation of Machine Tools Caused by Linear Axis Motion

Effective 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 information

Generating Permutations and Combinations

Generating Permutations and Combinations Generating Permutations and Combinations March 0, 005 Generating Permutations We have learned that there are n! permutations of {,,, n} It is important in many instances to generate a list of such permutations

More information

Holz Werkstoff by Springer-Verlag 1981

Holz Werkstoff by Springer-Verlag 1981 Holz als Roh und Werkstoff 39 (1981) 409415 alsrohund Holz Werkstoff by SpringerVerlag 1981 Predicting Shear and Internal Bond Properties of Flakeboard R. L. Geimer U.S. Department of Agriculture, Forest

More information

AGILE. Color available - A. Black White Chrome

AGILE. Color available - A. Black White Chrome AGILE AGILE-Serie sind für den Einzelhandel, Ausstellungen, Ladengeschäft, Kunstgalerien, Museen und auch in der kommerziellen Anwendung konzipiert. AGILE Wallwasher sind für Neigungswinkel von Grad und

More information

Chapter 6. Relations. 6.1 Relations

Chapter 6. Relations. 6.1 Relations Chapter 6 Relations Mathematical relations are an extremely general framework for specifying relationships between pairs of objects. This chapter surveys the types of relations that can be constructed

More information

SIM Regional Comparison on. The Calibration of Internal and External Diameter Standards SIM.L-K FINAL REPORT July 2012

SIM Regional Comparison on. The Calibration of Internal and External Diameter Standards SIM.L-K FINAL REPORT July 2012 SIM Regional Comparison on The Calibration of Internal and External Diameter Standards SIM.L-K4.2009 FINAL REPORT July 2012 Theodore Doiron (NIST), J. A. Pires Alves (INMETRO), Bruno R. Gastaldi (INTI),

More information

The application of probabilistic method in graph theory. Jiayi Li

The application of probabilistic method in graph theory. Jiayi Li The application of probabilistic method in graph theory Jiayi Li Seite 2 Probabilistic method The probabilistic method is a nonconstructive method, primarily used in combinatorics and pioneered by Paul

More information

Week 4-5: Binary Relations

Week 4-5: Binary Relations 1 Binary Relations Week 4-5: Binary Relations The concept of relation is common in daily life and seems intuitively clear. For instance, let X be the set of all living human females and Y the set of all

More information

RED. Fall 2016 Student Submitted Sample Questions

RED. Fall 2016 Student Submitted Sample Questions RED Fall 2016 Student Submitted Sample Questions Name: Last Update: November 22, 2016 The questions are divided into three sections: True-false, Multiple Choice, and Written Answer. I will add questions

More information

Noncontact-AFM (nc-afm)

Noncontact-AFM (nc-afm) Noncontact-AFM (nc-afm) Quantitative understanding of nc-afm A attractive interaction Δf Resonance frequency: f 0 Width of resonance curve (FWHM): Γ Γ+ΔΓ Γ Q-factor: Q π f Γ = 0 f 0 f Conservative forces

More information

Finite Model Theory and CSPs

Finite Model Theory and CSPs Finite Model Theory and CSPs Albert Atserias Universitat Politècnica de Catalunya Barcelona, Spain June 19, 2007 Part I FIRST-ORDER LOGIC, TYPES AND GAMES Relational Structures vs. Functional Structures

More information

Investigation of Piezoelectric Force Measuring Devices in Force Calibration and Force. Standard Machines

Investigation of Piezoelectric Force Measuring Devices in Force Calibration and Force. Standard Machines Proceedings of the 17 th International Conference on Force, Mass, Torque and Pressure Measurements, Investigation of Piezoelectric Force Measuring Devices in Force Calibration and Force Standard Machines

More information

Lecture 7: Relations

Lecture 7: Relations Lecture 7: Relations 1 Relation Relation between two objects signify some connection between them. For example, relation of one person being biological parent of another. If we take any two people at random,

More information

Discrete Structures May 13, (40 points) Define each of the following terms:

Discrete Structures May 13, (40 points) Define each of the following terms: Discrete Structures May 13, 2014 Prof Feighn Final Exam 1. (40 points) Define each of the following terms: (a) (binary) relation: A binary relation from a set X to a set Y is a subset of X Y. (b) function:

More information

Surface Roughness - Standards and Uncertainty R. Krüger-Sehm and L. Koenders

Surface Roughness - Standards and Uncertainty R. Krüger-Sehm and L. Koenders Surface Roughness - Standards and Uncertainty R. Krüger-Sehm and L. Koenders Physikalisch-Technische Bundesanstalt, Braunschweig, Germany Surfaces Generation - Grinding - Honing - Lapping Characterisation

More information

Announcements Monday, November 13

Announcements Monday, November 13 Announcements Monday, November 13 The third midterm is on this Friday, November 17. The exam covers 3.1, 3.2, 5.1, 5.2, 5.3, and 5.5. About half the problems will be conceptual, and the other half computational.

More information

Journal of Machine Engineering, 2018, Vol. 18, No. 3, 78 86

Journal of Machine Engineering, 2018, Vol. 18, No. 3, 78 86 Journal of Machine Engineering, 2018, Vol. 18, No. 3, 78 86 ISSN 1895-7595 (Print) ISSN 2391-8071 (Online) Received: 13 January 2018 / Accepted: 14 August 2018 / Published online: 28 September 2017 accuracy,

More information

1. Positive and regular linear operators.

1. Positive and regular linear operators. 1. Positive and regular linear operators. Objekttyp: Chapter Zeitschrift: L'Enseignement Mathématique Band (Jahr): 19 (1973) Heft 3-4: L'ENSEIGNEMENT MATHÉMATIQUE PDF erstellt am: 1.0.018 Nutzungsbedingungen

More information

Cloud Computing mit mathematischen Anwendungen

Cloud Computing mit mathematischen Anwendungen Cloud Computing mit mathematischen Anwendungen Dr. habil. Marcel Kunze Engineering Mathematics and Computing Lab (EMCL) Institut für Angewandte und Numerische Mathematik IV Karlsruhe Institute of Technology

More information

Fiducials for BM1 Std. Vac. Chamber

Fiducials for BM1 Std. Vac. Chamber Fiducials for BM1 Std. Vac. Chamber Date: Chamber: Operator(s): 4/30/02 C. Banuelos M. Gaydosh Notes: IN 49.002 in 124.465 cm Y (UP) e- X Z Z 2.2500º 10.5882º TB0 OUT TB9 Fiducial Coordinates for BM1 Standard

More information

Comparison of Applied Materials DPS chambers used for Poly Si etch processes by plasma parameters

Comparison of Applied Materials DPS chambers used for Poly Si etch processes by plasma parameters Page 1 Comparison of Applied Materials DPS chambers used for Poly Si etch processes by plasma parameters Das diesem Bericht zugrundeliegende Vorhaben wurde mit Mitteln des Sächsischen Staatsministeriums

More information

ISO INTERNATIONAL STANDARD

ISO INTERNATIONAL STANDARD INTERNATIONAL STANDARD ISO 21501-2 First edition 2007-05-15 Determination of particle size distribution Single particle light interaction methods Part 2: Light scattering liquid-borne particle counter

More information

Fiducials for BM1 Std. Vac. Chamber

Fiducials for BM1 Std. Vac. Chamber Fiducials for BM1 Std. Vac. Chamber Date: Chamber: Operator(s): 4\18\02 F. Gaudreault L. Griffin Notes: Z on Exit port not measured. Single support on final check measurements. IN 49.002 in 124.465 cm

More information

Experiment 1: Linear Regression

Experiment 1: Linear Regression Experiment 1: Linear Regression August 27, 2018 1 Description This first exercise will give you practice with linear regression. These exercises have been extensively tested with Matlab, but they should

More information

Relations. P. Danziger. We may represent a relation by a diagram in which a line is drawn between two elements if they are related.

Relations. P. Danziger. We may represent a relation by a diagram in which a line is drawn between two elements if they are related. - 10 Relations P. Danziger 1 Relations (10.1) Definition 1 1. A relation from a set A to a set B is a subset R of A B. 2. Given (x, y) R we say that x is related to y and write xry. 3. If (x, y) R we say

More information

Math 200 A and B: Linear Algebra Spring Term 2007 Course Description

Math 200 A and B: Linear Algebra Spring Term 2007 Course Description Math 200 A and B: Linear Algebra Spring Term 2007 Course Description February 25, 2007 Instructor: John Schmitt Warner 311, Ext. 5952 jschmitt@middlebury.edu Office Hours: Monday, Wednesday 11am-12pm,

More information

Packet #5: Binary Relations. Applied Discrete Mathematics

Packet #5: Binary Relations. Applied Discrete Mathematics Packet #5: Binary Relations Applied Discrete Mathematics Table of Contents Binary Relations Summary Page 1 Binary Relations Examples Page 2 Properties of Relations Page 3 Examples Pages 4-5 Representations

More information

Application Note LCMS-112 A Fully Automated Two-Step Procedure for Quality Control of Synthetic Peptides

Application Note LCMS-112 A Fully Automated Two-Step Procedure for Quality Control of Synthetic Peptides Application Note LCMS-112 A Fully Automated Two-Step Procedure for Quality Control of Synthetic Peptides Abstract Here we describe a two-step QC procedure for synthetic peptides. In the first step, the

More information

INTERNATIONAL STANDARD

INTERNATIONAL STANDARD INTERNATIONAL STANDARD ISO 8426 Second edition 2008-02-01 Hydraulic fluid power Positive displacement pumps and motors Determination of derived capacity Transmissions hydrauliques Pompes et moteurs volumétriques

More information

Final Report On COOMET Vickers PTB/VNIIFTRI Key Comparison (COOMET.M.H- K1.b and COOMET.M.H- K1.c)

Final Report On COOMET Vickers PTB/VNIIFTRI Key Comparison (COOMET.M.H- K1.b and COOMET.M.H- K1.c) Version 7 of 01-19-07 Final Report On COOMET Vickers PTB/VNIIFTRI Key Comparison (COOMET.M.H- K1.b and COOMET.M.H- K1.c) E. Aslanyan¹, K. Herrmann² ¹ All Russian Research Institute for Physical -Technical

More information

Transformation of Whole-Head MEG Recordings Between Different Sensor Positions

Transformation of Whole-Head MEG Recordings Between Different Sensor Positions Transformation of Whole-Head MEG Recordings Between Different Sensor Positions Transformation von Ganzkopf-MEG-Messungen zwischen verschiedenen Sensorpositionen Thomas R. Knösche Max Planck Institute of

More information

Analysis of the decay B + l + νγ, l + = e +, µ +

Analysis of the decay B + l + νγ, l + = e +, µ + Analysis of the decay B l νγ, l = e, µ Bad Liebenzell 1 Andreas Heller, Michael Feindt, Martin Heck, Anže Zupanc, Thomas Kuhr, Pablo Goldenzweig INSTITUT FÜR EXPERIMENTELLE KERNPHYSIK (EKP), KARLSRUHER

More information

Experiences with Superconducting Cable & Fault Current Limiter in a German City Center Mark Stemmle

Experiences with Superconducting Cable & Fault Current Limiter in a German City Center Mark Stemmle Experiences with Superconducting Cable & Fault Current Limiter in a German City Center Mark Stemmle mark.stemmle@nexans.com i-pcgrid Workshop San Francisco, CA March 30 th, 2017 Agenda Introduction - Basics

More information

Announcements Monday, November 13

Announcements Monday, November 13 Announcements Monday, November 13 The third midterm is on this Friday, November 17 The exam covers 31, 32, 51, 52, 53, and 55 About half the problems will be conceptual, and the other half computational

More information

DEUTSCHER KALIBRIERDIENST

DEUTSCHER KALIBRIERDIENST DEUTSCHER KALIBRIERDIENST Abschlussbericht DKD-Ringvergleich konventioneller Wägewert 2003 Herausgegeben von der Akkreditierungsstelle des Deutschen Kalibrierdienstes (DKD) bei der Physikalisch- Technischen

More information

MIXING STATIONS VOLUMETRIC MIXING STATIONS GRAVIMETRIC MIXING STATIONS GRAVIMETRIC DOSING-/MIXING STATIONS

MIXING STATIONS VOLUMETRIC MIXING STATIONS GRAVIMETRIC MIXING STATIONS GRAVIMETRIC DOSING-/MIXING STATIONS MIXING STATIONS VOLUMETRIC MIXING STATIONS GRAVIMETRIC MIXING STATIONS GRAVIMETRIC DOSING-/MIXING STATIONS Subject to alterations, even without advance notice. Measurements and data without obligation.

More information

Analyses of driving performance in mechanized tunnelling Determination model and actual examples

Analyses of driving performance in mechanized tunnelling Determination model and actual examples Analyses of driving performance in mechanized tunnelling Determination model and actual examples Rainer Stempkowski Technical University of Vienna, Austria ABSTRACT: This paper presents a determination

More information

DS 300. Electronic Pressure Switch. with IO-Link interface. Stainless Steel Sensor. accuracy according to IEC 60770: 0.35 % FSO.

DS 300. Electronic Pressure Switch. with IO-Link interface. Stainless Steel Sensor. accuracy according to IEC 60770: 0.35 % FSO. DS 00 Electronic Pressure Switch with IO-Link interface Stainless Steel Sensor accuracy according to IEC 60770: 0.5 % FSO Nominal pressure from 0... 00 mbar up to 0... 600 bar Digital output signal IO-Link

More information

A simple method for solving the diophantine equation Y 2 = X 4 + ax 3 + bx 2 + cx + d

A simple method for solving the diophantine equation Y 2 = X 4 + ax 3 + bx 2 + cx + d Elem. Math. 54 (1999) 32 36 0013-6018/99/010032-5 $ 1.50+0.20/0 c Birkhäuser Verlag, Basel, 1999 Elemente der Mathematik A simple method for solving the diophantine equation Y 2 = X 4 + ax 3 + bx 2 + cx

More information

2.1 Notes: Simplifying Radicals (Real and Imaginary)

2.1 Notes: Simplifying Radicals (Real and Imaginary) Chapter 2 Calendar Name: Day Date Assignment (Due the next class meeting) Friday Tuesday Wednesday Thursday Friday Monday Tuesday Wednesday Thursday Friday Monday Tuesday Wednesday Thursday 8/30/13 (A)

More information

Guidelines on the Calibration of Static Torque Measuring Devices

Guidelines on the Calibration of Static Torque Measuring Devices European Association of National Metrology Institutes Guidelines on the Calibration of Static Torque Measuring Devices EURAMET/cg-14/v.01 Previously EA-10/14 July 2007 Calibration Guide EURAMET/cg-14/v.01

More information

Data mining using Rough Sets

Data mining using Rough Sets Data mining using Rough Sets Alber Sánchez 1 alber.ipia@inpe.br 1 Instituto Nacional de Pesquisas Espaciais, São José dos Campos, SP, Brazil Referata Geoinformatica, 2015 1 / 44 Table of Contents Rough

More information

About the gap between the optimal values of the integer and continuous relaxation one-dimensional cutting stock problem

About the gap between the optimal values of the integer and continuous relaxation one-dimensional cutting stock problem Operations Research Proceedings 1991, Springer-Verlag Berlin Heidelberg (1992) 439 444 About the gap between the optimal values of the integer and continuous relaxation one-dimensional cutting stock problem

More information

EAS 535 Laboratory Exercise Weather Station Setup and Verification

EAS 535 Laboratory Exercise Weather Station Setup and Verification EAS 535 Laboratory Exercise Weather Station Setup and Verification Lab Objectives: In this lab exercise, you are going to examine and describe the error characteristics of several instruments, all purportedly

More information

ON SOME PROPERTIES OF ROUGH APPROXIMATIONS OF SUBRINGS VIA COSETS

ON SOME PROPERTIES OF ROUGH APPROXIMATIONS OF SUBRINGS VIA COSETS ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS N. 39 2018 (120 127) 120 ON SOME PROPERTIES OF ROUGH APPROXIMATIONS OF SUBRINGS VIA COSETS Madhavi Reddy Research Scholar, JNIAS Budhabhavan, Hyderabad-500085

More information

POWER UNDERSTANDING MEASUREMENT UNCERTAINTY IN DP FLOW DEVICES

POWER UNDERSTANDING MEASUREMENT UNCERTAINTY IN DP FLOW DEVICES Proceedings of the ASME 2014 Power Conference POWER2014 July 28-31, 2014, Baltimore, Maryland, USA POWER2014-32205 UNDERSTANDING MEASUREMENT UNCERTAINTY IN DP FLOW DEVICES Michael S. Hering Rosemount DP

More information

HCL Series Miniature compensated low pressure sensors

HCL Series Miniature compensated low pressure sensors FEATURES 0... 5 to 0... 5, differential or gage Calibrated and temperature compensated Matched pressure volumes Miniature SMT and SIL housings RoHS compliant SPECIFICATIONS Maximum ratings EQUIVALENT CIRCUIT

More information

1. Einleitung. 1.1 Organisatorisches. Ziel der Vorlesung: Einführung in die Methoden der Ökonometrie. Voraussetzungen: Deskriptive Statistik

1. Einleitung. 1.1 Organisatorisches. Ziel der Vorlesung: Einführung in die Methoden der Ökonometrie. Voraussetzungen: Deskriptive Statistik 1. Einleitung 1.1 Organisatorisches Ziel der Vorlesung: Einführung in die Methoden der Ökonometrie Voraussetzungen: Deskriptive Statistik Wahrscheinlichkeitsrechnung und schließende Statistik Fortgeschrittene

More information

Locating RFID Tags. Matthias Benesch, Siegfried Bublitz Siemens AG. C-LAB Report. Vol. 8 (2009) No. 3

Locating RFID Tags. Matthias Benesch, Siegfried Bublitz Siemens AG. C-LAB Report. Vol. 8 (2009) No. 3 Locating RFID Tags Matthias Benesch, Siegfried Bublitz Siemens AG C-LAB Report Vol. 8 (009) No. 3 Cooperative Computing & Communication Laboratory ISSN 1619-7879 C-LAB ist eine Kooperation der Universität

More information

Binary Relations Part II

Binary Relations Part II Binary Relations Part II Outline for Today Finish from Last Time Pt. 3 of our proof that ~ is an equivalence relation Properties of Equivalence Relations What s so special about those three rules? Strict

More information

David Martin High Precision Beamline Alignment at the ESRF IWAA, Grenoble 3-7 October 2016

David Martin High Precision Beamline Alignment at the ESRF IWAA, Grenoble 3-7 October 2016 David Martin High Precision Beamline Alignment at the ESRF IWAA, Grenoble 3-7 October 2016 OVERVIEW The ESRF has just completed the Phase I Upgrade programme. The Phase I Upgrade programme was centered

More information

Three Axis Magnetic Field Transducer x-h3x-xx_e3d-2.5khz-1-0.2t

Three Axis Magnetic Field Transducer x-h3x-xx_e3d-2.5khz-1-0.2t DESCRIPTION: TYPICAL APPLICATIONS: The is a high accuracy magnetic flux density-toanalogue-voltage transducer with a highlevel and temperature compensated output signal for each of the three components

More information