1、Designation: E 2510 07Standard Test Method forTorque Calibration or Conformance of Rheometers1This standard is issued under the fixed designation E 2510; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A
2、number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This test method describes the calibration or perfor-mance conformance for the torque signal generated by com-mercial or custom-built
3、rheometers. The specific range of thetest depends upon the torque range of the rheometer.1.2 SI units are the standard.1.3 There is no ISO standard equivalent to this test method.1.4 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is therespon
4、sibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2E4 Practices for Force Verification of Testing MachinesE 473 Terminology Relating to Thermal
5、Analysis and Rhe-ologyE 617 Specification for Laboratory Weights and PrecisionMass StandardsE 1142 Terminology Relating to Thermophysical Properties3. Terminology3.1 Specific technical terms used in this test method aredefined in Terminologies E 473 and E 1142. These termsinclude angular frequency,
6、frequency, loss modulus, rheometer,storage modulus, strain, stress, viscoelasticity, viscometer,viscometry, and viscosity.3.2 Definitions:3.2.1 torque, nforce applied through a moment arm thatproduces or tends to produce rotation (N m)4. Summary of Test Method4.1 A known force is applied to a rheome
7、ter coupling shaftthrough a moment arm to produce a torque. The torque thusapplied is measured and compared to the measured torque. Theratio between indicated and applied torque is used to create acalibration coefficient that may be used in future determina-tions.4.2 The known force generated by sus
8、pended precisionmass or masses is transmitted to the rheometer coupling shaftby a line and an appropriate series of pulleys.4.3 Torque is mathematically defined by Eq 1:t5dFsinF (1)where:t = torqued = the length of the moment arm (m)F = the applied force (N)F = the angle to the moment arm over which
9、 the force isapplied ()4.3.1 If the force is applied tangentially at right angles (thatis, F = 90) to the moment arm, then sinF = 1 and Eq 1reduces to Eq 2:t5dF (2)4.4 The moment arm in this test method is created byattaching a fixture of known radius to the rheometer couplingshaft in lieu of a geom
10、etry, tool or plate. The radius of thefixture is the value of d in Eq 2.4.5 A force is applied to the fixture at a tangent by asuspended mass through a thin wire and a suitable pulleyarrangement (see, for example, Fig. 1).4.6 For a mass or masses of known value, the applied forceis given by Eq 3:F 5
11、 Mgf (3)where:M = the suspended mass (kg)g = standard acceleration due to gravity (= 9.8065 m s2)f = correction factor for local gravity and air buoyancytaken from Table 1 (dimensionless)1This test method is under the jurisdiction ofASTM Committee E37 on ThermalMeasurements and is the direct respons
12、ibility of Subcommittee E37.08 on Rheom-etry Methods and Practices.Current edition approved Feb. 1, 2007. Published March 2007.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information
13、, refer to the standards Document Summary page onthe ASTM website.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.5. Significance and Use5.1 The test method calibrates or demonstrates conformityof the torque signal of a rheometer at
14、ambient temperature.5.2 A calibration factor thus determined may be used toobtain correct torque values.5.3 This test method may be used in research, development,specification acceptance, and quality control or assurance.6. Apparatus6.1 RheometerThe essential instrumentation required pro-viding the
15、minimum rheological analytical capabilities include:6.1.1 Drive Actuator, to apply torque or angular displace-ment to the specimen in a periodic manner capable of frequen-cies of oscillation from 0.001 to 100 rad/s. This actuator mayalso be capable of providing static torque or displacement onthe sp
16、ecimen.6.1.2 Coupling Shaft, or other means to transmit the torqueor displacement from the motor to the specimen.6.1.3 Geometry or Tool, to fix the specimen between thedrive shaft and a stationary position.6.1.4 Sensor, to measure the torque developed by thespecimen, a position sensor to measure the
17、 angular displace-ment of 50 nanoradians of the test specimen, or both.6.1.5 Temperature Sensor, to provide an indication of thespecimen temperature to within 60.1C.FIG. 1 Example of Suspended Mass .TABLE 1 Unit Force Exerted by a Unit Mass in Air at Various Latitudes and ElevationsAElevation Above
18、Sea Level, m (ft)Latitude, 30.5 to 152(100 to 500)152 to 457(500 to 1500)457 to 762(1500 to 2500)762 to 1067(2500 to 3500)1067 to 1372(3500 to 4500)1372 to 1676(4500 to 5500)20 0.9978 0.9977 0.9976 0.9975 0.9975 0.997425 0.9981 0.9980 0.9979 0.9979 0.9978 0.997730 0.9985 0.9984 0.9983 0.9982 0.9982
19、0.998135 0.9989 0.9988 0.9987 0.9987 0.9986 0.998540 0.9993 0.9993 0.9992 0.9991 0.9990 0.998945 0.9998 0.9997 0.9996 0.9996 0.9995 0.999450 1.0003 1.0002 1.0001 1.0000 0.9999 0.999955 1.0007 1.0006 1.0005 1.0005 1.0004 1.0003ATaken from Practice E4.E25100726.1.6 Furnace, or Heating/Cooling Element,
20、 to providecontrolled heating or cooling of a specimen at a constanttemperature or at a constant rate within the temperature rangeof interest.6.1.7 Temperature Controller, capable of executing a spe-cific temperature program by operating the furnace or heating/cooling element between selected temper
21、ature limits constantto within 60.1C.6.1.8 Recording Device, capable of recording and display-ing on the Y-axis any fraction of the measured signal (hereapplied torque) or calculated signal (such as viscosity, storageand loss modulus, etc.) including signal noise using a linear orlogarithmic scale a
22、s a function of any fraction of the indepen-dent experimental parameter (such as temperature, time) orcalculated signals (such as stress or strain) on the X-axisincluding signal noise.6.1.9 Auxiliary instrumentation considered necessary oruseful in conducting this method includes:6.1.9.1 Cooling Cap
23、ability, to hasten cool down from el-evated temperatures, to provide constant cooling rates, or tosustain an isothermal sub-ambient temperature.6.1.9.2 Data Analysis Capability, to provide viscosity, stor-age and loss modulus, stress, strain, etc. or other usefulparameters derived from the measured
24、signals.6.1.10 A test fixture of known radius to attach a tangentiallyapplied load to the coupling shaft in lieu of the geometry, tool,or plate.NOTE 1Test fixtures of appropriate design may be obtained from themanufacture of the rheometry apparatus.6.1.11 Mass or Masses, with a suspending hook, the
25、massvalue for which are known to within 60.1 % (see E 617). Thevalue of the required mass or masses depends upon the nominaltorque range of the rheometer and is given by Eq 4:M 5 80 to 90 % oftadng!(4)where:ta= maximum measuring torque of the rheometerdn= nominal radius of the test fixture (m)6.1.12
26、 Line or Lines, composed of a non-elastic materialsuch as monofilament line of suitable length to connect thecalibration mass or masses to the test fixture at its tangent.6.1.13 An arrangement of pulleys over which the line maybe strung so that the force of the suspended mass is transmittedtangentia
27、lly to the test fixture.NOTE 2The friction of the pulley(s) shall be sufficiently small that itwill not significantly contribute to the torque measurement.6.1.14 Calipers, or other length-measuring device with arange of up to 10 cm to determine length to within 60.1 m.7. Preparation of Apparatus7.1
28、Mount the test fixture to the coupling shaft in such a waythat a line or lines connected to a mass or masses transmits theforce of the suspended mass or masses tangentially to the testfixture and coupling shaft. An illustrative example is shown inFig. 1.8. Calibration and Standardization8.1 Prepare
29、the apparatus for testing according to themanufacturers recommendation as described in the operationsmanual.9. Procedure9.1 Measure the distance from the center of the connectingshaft to the edge of the test fixture to within 60.1 mm andrecord this value as d.NOTE 3The value of d is commonly 2.5 cm
30、(= 0.025 m).9.2 With no torque applied to the test fixture, observe thetorque signal and ensure that it is less than 0.1 % of the fullscale torque value.9.3 Select a precision mass the value for which is within themaximum range of the apparatus as defined by Eq 4.9.4 Apply the calibrating torque to
31、the rheometer by con-necting one end of the line to the calibration fixture, over anyneeded pulleys to the suspended mass or masses. Ensure thatthe mass(es) is (are) free hanging without obstruction and thatthe mass is steady (without swinging from side-to-side).NOTE 4The friction of the pulley(s) s
32、hall be sufficiently small that itwill not significantly contribute to the torque measurement.9.5 Measure the applied torque and record this value as ti.9.6 Calculate the calibration constant (S) using Eq 5.9.7 Calculate the percent conformance (C) using Eq 6.10. Calculation or Interpretation of Res
33、ults10.1 For the purposes of this test method, it is assumed thatthe relationship between the indicated and applied referencetorque is linear and governed by the slope (S)ofEq5:S 5Mgdfti(5)where:S = slope of the torque calibration curve (dimensionless)ti= the indicated torque (N m)10.2 The percent c
34、onformity (C) (that is, the percent differ-ence between the experimental slope and unity) of the instru-ments torque measurement is calculated using the value of Sfrom 10.1 and Eq 6:C 5 S 1.0000! 3 100 % (6)11. Report11.1 The report shall include the following information:11.1.1 Details and descript
35、ion of the rheometer includingthe manufacturer and model number.11.1.2 The value of calibration constant (S) determined insection 9.6 reported to within 60.0001.11.1.3 The conformity value (C) as described in section 9.7reported to at least two significant figures.11.1.4 The specific dated version o
36、f this method used.12. Precision and Bias12.1 Precision of the torque measurement depends upon theprecision of the moment arm, the mass and the acceleration dueto gravity. Maximum imprecision in the determination of theE2510073torque may be estimated from the imprecisions in the indi-vidual measurem
37、ents by the following equation:dt/t5dd/d!21 dM/M!21 dg/g!2#1/2(7)where:dt = imprecision in the value for torquet = torquedd = imprecision in the measurement of the moment arm,mmd = moment arm, mmdg = imprecision in the value for acceleration due togravity, m s2g = acceleration due to gravity, m s2dM
38、 = imprecision in mass value, gM = mass, g12.1.1 Example:if:dd = 60.5 mmd =25mmdg = 6 0.0026 m s2g = 9.8ms2dM = 6 0.5 gM = 500 gthen:dt/t50.5 mm/25 mm!21 0.5 g/500 g!21 0.0026 m s2/9.8 m s2!2#1/2or expressed as percent:dt/t52.0 %!21 0.1 %!21 0.27 %!2#1/2562.0 %12.2 An interlaboratory study is planne
39、d for 20072008 togenerate precision and bias information for this test method.Anyone wishing to participate in this study may contact theE37 Staff Manager at ASTM International Headquarters.12.3 Precision12.3.1 The intralaboratory repeatability standard deviationfor S for a single instrument was fou
40、nd to be 60.05.12.4 Bias12.4.1 The measurement of conformance in this test methodis a comparison of the calibration constant S with the theoreti-cal value of 1.000 and is an indicator of bias.12.4.2 Interlaboratory results indicate that the value for C isanticipated to be 65%.13. Keywords13.1 rheome
41、ter; calibration; torqueASTM International takes no position respecting the validity of any patent rights asserted in connection with any item mentionedin this standard. Users of this standard are expressly advised that determination of the validity of any such patent rights, and the riskof infringe
42、ment of such rights, are entirely their own responsibility.This standard is subject to revision at any time by the responsible technical committee and must be reviewed every five years andif not revised, either reapproved or withdrawn. Your comments are invited either for revision of this standard o
43、r for additional standardsand should be addressed to ASTM International Headquarters. Your comments will receive careful consideration at a meeting of theresponsible technical committee, which you may attend. If you feel that your comments have not received a fair hearing you shouldmake your views k
44、nown to the ASTM Committee on Standards, at the address shown below.This standard is copyrighted by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959,United States. Individual reprints (single or multiple copies) of this standard may be obtained by contacting ASTM at the aboveaddress or at 610-832-9585 (phone), 610-832-9555 (fax), or serviceastm.org (e-mail); or through the ASTM website(www.astm.org).E2510074
