Instruction Manual
Model 4200ER
Extended Range
Vibrating Wire Strain Gage
No part of this instruction manual may be reproduced, by any means, without the written consent of Geokon, Inc.
The information contained herein is believed to be accurate and reliable. However, Geokon, Inc. assumes no responsibility for errors, omissions or misinterpretation. The information herein is subject to change without notification.
Copyright ©2016 by Geokon, Inc.
(Doc Rev. Initial, 03-16)
Warranty Statement
Geokon, Inc. warrants its products to be free of defects in materials and workmanship, under normal use and service for a period of 13 months from date of purchase. If the unit should malfunction, it must be returned to the factory for evaluation, freight prepaid. Upon examination by Geokon, if the unit is found to be defective, it will be repaired or replaced at no charge. However, the WARRANTY is VOID if the unit shows evidence of having been tampered with or shows evidence of being damaged as a result of excessive corrosion or current, heat, moisture or vibration, improper specification, misapplication, misuse or other operating conditions outside of Geokon's control. Components which wear or which are damaged by misuse are not warranted. This includes fuses and batteries.
Geokon manufactures scientific instruments whose misuse is potentially dangerous. The instruments are intended to be installed and used only by qualified personnel. There are no warranties except as stated herein. There are no other warranties, expressed or implied, including but not limited to the implied warranties of merchantability and of fitness for a particular purpose. Geokon, Inc. is not responsible for any damages or losses caused to other equipment, whether direct, indirect, incidental, special or consequential which the purchaser may experience as a result of the installation or use of the product. The buyer's sole remedy for any breach of this agreement by Geokon, Inc. or any breach of any warranty by Geokon, Inc. shall not exceed the purchase price paid by the purchaser to Geokon, Inc. for the unit or units, or equipment directly affected by such breach. Under no circumstances will Geokon reimburse the claimant for loss incurred in removing and/or reinstalling equipment.
Every precaution for accuracy has been taken in the preparation of manuals and/or software, however,
Geokon, Inc. neither assumes responsibility for any omissions or errors that may appear nor assumes liability for any damages or losses that result from the use of the products in accordance with the information contained in the manual or software.
TABLE of CONTENTS
Extended Range ......................................................................................................1
Vibrating Wire Strain Gage ...............................................................................1
1. INTRODUCTION ......................................................................................................1
2. GAGE INSTALLATION ...........................................................................................2
2.1. Adjusting the Desired Range .......................................................................2
2.2. Placing the Gage in Concrete .......................................................................2
Alternative Method ..........................................................................................................4
2.3. Using Pre-cast Briquettes or Grouting .........................................................4
2.4. Cable Protection and Termination ...............................................................4
2.5. Lightning Protection ....................................................................................5
3. TAKING READINGS ................................................................................................6
3.1. Operation of the GK-403 Readout Box .......................................................6
3.2. Operation of the GK-404 Readout Box .......................................................7
3.3. Operation of the GK-405 Readout Box .......................................................7
3.4. MICRO-6000 Datalogger ............................................................................8
3.5. Measuring Temperatures ............................................................................9
4.DATA REDUCTION FOR THE GK-403, GK-404 or GK-405 in POSITION D ......9
4.1. Conversion of Readings to Strain Changes .................................................9
4.2. Temperature Corrections .............................................................................9
4.3. Shrinkage Effects .........................................................................................11
4.4. Creep Effects ................................................................................................11
4.5. Effect of Autogenous Growth ......................................................................12
5. TROUBLESHOOTING ..............................................................................................12
APPENDIX A - SPECIFICATIONS ...............................................................................13
A.1 4200ER Strain Gage......................................................................................13
A.2 Thermistor (see Appendix C also) ................................................................13
APPENDIX B - THERMISTOR TEMPERATURE DERIVATION .............................14
APPENDIX C - HIGH-TEMPERATURE THERMISTOR LINEARIZATION ............15
LIST of FIGURES, TABLES and EQUATIONS
Figure 1 - Model 4200ER Vibrating Wire Strain Gage .................................................................. 1
Figure 3 - Attaching VCE-4200X Strain Gages to Rebar............................................................... 3
Figure 3B - Alternative Method for attaching VCE 4200X straingages to rebar. .......................... 4
Figure 4 - Lightning Protection Scheme ......................................................................................... 6
Table 1 - Embedment Strain Gage Readout Positions .................................................................... 6
Figure 5 GK405 Readout Unit ....................................................................................................... 8
Table 2 - Embedment Strain Gage Datalogger Parameters ............................................................ 8
Equation 1 - Strain Calculation, channel D .................................................................................... 9
Table A-1 Strain Gage Specifications.......................................................................................... 13
Equation C-1 Convert Thermistor Resistance to Temperature .................................................... 14
Table C-1 Thermistor Resistance versus Temperature ................................................................ 14
Table B-2: High Temperature Thermistor Resistance versus Temperature. ................................ 15
1. INTRODUCTION
The Geokon Model 4200ER Vibrating Wire Strain Gage is designed primarily for high range strain measurements in mass concrete, in structures such as foundations, piles, bridges, dams, containment vessels, tunnel liners, etc. See Figure 1. Strains as high as 10,000 mirostrain can be accomodated
1
Figure 1 - Model 4200ER Vibrating Wire Strain Gage
Note the small collar under the shrink tube at one end.
The primary means of gage placement is direct embedment in concrete by pre-attaching the gage to rebar or tensioning cables, pre-casting the gage into a concrete briquette which is subsequently cast into the structure, or grouting into boreholes in the concrete.
Strains are measured using the vibrating wire principle: a length of steel wire is tensioned between two end blocks that are firmly in contact with the mass concrete. Deformations in the concrete will cause the two end blocks to move relative to one another, altering the tension in the steel wire. This change in tension is measured as a change in the resonant frequency of vibration of the wire. Electromagnetic coils that are located close to the wire accomplish excitation and readout of the gage frequency.
Portable readouts or dataloggers available from Geokon, such as the model, GK-403, GK
404 or MICRO-6000 datalogger, used in conjunction with any of these vibrating wire strain gages, will provide the necessary voltage pulses to pluck the wire and convert the measured frequencies so as to display the reading directly in digits which can then be converted into microstrain using the calibration coefficients supplied.
This manual contains installation instructions, readout and data reduction procedures, and troubleshooting guidelines.
PLEASE NOTE THE FOLLOWING:
Do not rotate or pull on the gage end blocks as this will alter the readings and may cause permanent damage.
2
2. GAGE INSTALLATION
The 4200ER strain gages are supplied fully sealed and pre-tensioned with the plucking coil mounted. A preliminary check is advisable and this is made by connecting to the readout box and observing the displayed readout (see readout instructions, Section 3). The observed reading should be around the mid-range position (see Table 1). Pressure on the gage ends should make this reading decrease.
Check the resistance between the two lead wires (usually red and black). For the model
4200ER it should be around 180 ohms. Remember to add the cable resistance at approximately 14.7
/1000' or 48.5
/km (at 20°C, multiply by 2 for both directions). If the gage contains a thermistor, check its resistance (usually the white and green lead wires) with an ohmmeter. Check the reading against that which should be obtained at the existing ambient temperature. See Appendix B for the resistance to temperature conversion and resistance v. temperature table.
Return any faulty gages to the factory. Gages should not be opened in the field.
2.1. Adjusting the Desired Range
Gages are supplied with the wire tension set in approximate rmid-range If the range needs to be at some other position this is accomplished by the following procedure: Attach the red and black leeds to a readout box with the channel position set in the D and the mode for microstrain. Grip the small collar under the shrink tube and rotate the end flange adjacent to it as shown in Figure 2
Figure 2 Adjusting the range
Rotate clockwise to decrease the initial reading and counter-clockwise to increase the reading. Please remember that although the readings are taken on Channel D, in the digits output mode, the digits shown are not directly in microstrain but must be converted to microstrain by multiplying the observed digits change by the gage factor given on the calibration sheet.
2.2. Placing the Gage in Concrete
3
The Model 4200ER strain gages are normally set into the concrete structure in one of two ways: either by casting the unit(s) into the concrete mix directly or by pre-casting the unit(s) into briquettes that are subsequently cast into the structure.
When casting the gage directly into the structure care must be taken to avoid applying any large forces to the end blocks during installation. The model 4200ERcan be wired into position by wiring directly to the tube (see Figure 3). The wires should not be tied too tightly since rebar and/or tension cables tend to move during concrete placement and vibration.
Care should be taken not to damage the cable with the vibrator. The gage can also be placed directly into the mix if it can be assured that the orientation will be correct after the gage placement.
Nylon Ty-rap
Instrument Cable
Rebar or Tensioned Cable
Wire Tie
Wire Tie
Nylon Ty-rap
Instrument Cable
Coil Assembly
(VCE-4200)
Wire Tie
Wire Tie
Coil Assembly
(VCE-4200)
Rubber Tape
Wood or
Styrofoam
Block
Rubber Tape
Attached to rebar with blocking Suspended between rebars
Figure 3 - Attaching VCE-4200X Strain Gages to Rebar
Note the following instructions to suspend the model VCE-4200X strain gage between rebar:
1. Wrap a layer of self-vulcanizing rubber tape around the gage in the two places
shown in Figure 3 (around the tie points). The rubber layer serves as a shock absorber, dampening any vibrations of the suspension system. Sometimes, without the rubber layers, as the tie wires are tightened the resonant frequency of the tie wires interferes with the resonant frequency of the gage. This results in unstable readings or no readings at all. This effect disappears once the
concrete has been placed.
2. Select a length of soft iron tie wire, the kind normally used for tying rebar cages together. Twist it 2 times around the body of the strain gage, over the rubber strips, about 3 cm from the gage ends.
3. Twist two loops in the wire, one on either side of the gage, at a distance of about
3cm
from the gage body. Repeat this process at the other end of the gage.
4. Position the gage between the rebar and twist the wire ends twice around the rebar, then around itself.
5. Tighten the wire and orient the gage by twisting on the loops.
6. Slip on the plucking coil and affix using a hose clamp. Tie the instrument cable off to one of the rebar using nylon Ty-Raps™.
4
Alternative Method
Tie two short pieces of steel rebar to the existing rebar using nylon Tie-wraps, as shown in
Figure 3B. Then tie the strain gage to the short pieces of rebar again using nylon tie wraps.
This method avoids the resonance problems associated with the previous method.
Figure 3B - Alternative Method for attaching VCE 4200X straingages to rebar.
2.3. Using Pre-cast Briquettes or Grouting
An alternate method to the above is to pre-cast the gages into briquettes of the same mix as the mass concrete and then place these in the structure prior to concrete placement. The briquettes should be constructed not more than 3 days and not less than 1 day prior to installation. The briquettes should be continuously cured with water prior to placement in the mass concrete.
Embedment gages can also be used in shotcrete and in drilled holes in rock or concrete that are subsequently grouted. When used in shotcrete special care should be taken to protect the lead wires. Encasing them in conduit or heavy tubing has been used effectively to protect the cable. The gages can be placed by packing the immediate area around the gage by hand and then proceeding with the shotcrete operation.
2.4. Cable Protection and Termination
The cable from the strain gages can be protected by the use of flexible conduit, which can be supplied by Geokon.
Terminal boxes with sealed cable entries and covers are also available, allowing many gages to be terminated at one location with complete protection of the lead wires. The panel can have built-in jacks or a single connection with a rotary position selector switch.
5
Cables may be spliced to lengthen them, without affecting the gage readings. Always maintain polarity by connecting color to color. Always waterproof the splice completely, preferably using a splice kit (epoxy based) such as the 3M Scotchcast
kit, model 82-A1.
Cables may be terminated by stripping and tinning and connected by clipping to the patch cord from the readout box. Alternatively, a plug may be used which will connect directly into the readout box or to a receptacle on a special patch cord.
2.5. Lightning Protection
The 4200ER Embedment Strain Gage, unlike numerous other types of instrumentation available from Geokon, does not have any integral lightning protection components, i.e. transzorbs or plasma surge arrestors. Usually this is not a problem as the gages are installed within concrete or grout and somewhat isolated from potentially damaging electrical transients. However, there may be occasions where some sort of lightning protection is desirable, for example where the gage is in contact with rebar that may be exposed to direct or indirect lightning strikes. Also, if the instrument cable is exposed, it may be appropriate to install lightning protection components, as the transient could travel down the cable to the gage and possibly destroy it.
Note the following suggestions:
If the gage is connected to a terminal box or multiplexer components such as plasma surge arrestors (spark gaps) may be installed in the terminal box/multiplexer to provide a measure of transient protection. Terminal boxes and multiplexers available from
Geokon provide locations for installation of these components.
Lighting arrestor boards and enclosures are available from Geokon that install at the exit point of the instrument cable from the structure being monitored. The enclosure has a removable top so, in the event the protection board (LAB-3) is damaged, the user may service the components (or replace the board). A connection is made between this enclosure and earth ground to facilitate the passing of transients away from the gage.
See Figure 4. Consult the factory for additional information on these or alternate lightning protection schemes.
Plasma surge arrestors can be epoxy potted into the gage cable close to the sensor. A ground strap would connect the surge arrestor to earth ground, either a grounding stake or the rebar itself.
6
Terminal Box/Multiplexer
Instrument Cable
(usually buried)
Structure
Rebars
VCE-4200
LAB-3 Enclosure LAB-3 Board
Surface
Ground Connections
Figure 4 - Lightning Protection Scheme
3. TAKING READINGS
The following three sections describe how to take readings using readout equipment available from Geokon. Table 1 shows a 10,000 microstrain range gage, Other ranges are avialbale on request.
Model:
Readout Position:
Display Units:
Frequency Range:
Mid-Range Reading:
Minimum Reading:
Maximum Reading:
4200ER - 10,000
D
Readout units
400-1200 Hz
2000
1000
3000
Table 1 - Embedment Strain Gage Readout Positions
3.1. Operation of the GK-403 Readout Box
The GK-403 can store gage readings and also apply calibration factors to convert readings to engineering units. Consult the GK-403 Instruction Manual for additional information on
Mode "G" of the Readout. The GK-403 reads out the thermistor temperature directly in degrees C.
Connect the Readout using the flying leads or in the case of a terminal station, with a connector. The red and black clips are for the vibrating wire gage; the white and green leads are for the thermistor and the blue for the shield drain wire.
1. Turn the display selector to position ""D".
2. Turn the unit on and a reading will appear in the front display window. The last digit may change one or two digits while reading. Press the "Store" button to record the value displayed. If the no reading displays or the reading is unstable see section 5 for troubleshooting suggestions. The thermistor will be read and displayed on the screen above the gage reading in degrees centigrade.
7
3. The unit will automatically turn itself off after approximately 2 minutes to conserve power.
3.2. Operation of the GK-404 Readout Box
The GK404 is a palm sized readout box which diplays the Vibrating wire value and the temperature in degrees centigrade.
The GK-404 Vibrating Wire Readout arrives with a patch cord for connecting to the vibrating wire gages. One end will consist of a 5-pin plug for connecting to the respective socket on the bottom of the GK-404 enclosure. The other end will consist of 5 leads terminated with alligator clips. Note the colors of the alligator clips are red, black, green, white and blue.
The colors represent the positive vibrating wire gage lead (red), negative vibrating wire gage lead (black), positive thermistor lead (green), negative thermistor lead (white) and transducer cable drain wire (blue). The clips should be connected to their respectively colored leads from the vibrating wire gage cable.
Use the POS (Position) button to select position D and the MODE button to select
μE
(Note that the display, although marked
μE is not directly in microstrains. The change in digits diplayed must be multiplied by the gage factor given on the calibration sheet to get the true microstrains)
The GK-404 will continue to take measurements and display the readings until the OFF button is pushed, or if enabled, when the automatic Power-Off timer shuts the GK-404 off.
The GK-404 continuously monitors the status of the (2) 1.5V AA cells, and when their combined voltage drops to 2V, the message Batteries Low is displayed on the screen. A fresh set of 1.5V AA batteries should be installed at this point
3.3. Operation of the GK-405 Readout Box
The GK-405 Vibrating Wire Readout is made up of two components:
the Readout Unit, consisting of a Windows Mobile handheld PC running the GK-405
Vibrating Wire Readout Application
the GK-405 Remote Module which is housed in a weather-proof enclosure and connects to the vibrating wire sensor by means of:
1) Flying leads with alligator type clips when the sensor cable terminates in bare wires or,
2) by means of a 10 pin connector..
The two components communicate wirelessly using Bluetooth
®
, a reliable digital communications protocol. The Readout Unit can operate from the cradle of the Remote
Module (see Figure 5) or, if more convenient, can be removed and operated up to 20 meters from the Remote Module
8
Figure 5 GK405 Readout Unit
For further details consult the GK405 Instruction Manual.
3.4. MICRO-6000 Datalogger
The following parameters are recommended when using the strain gages with the MICRO-
1000 datalogger or any other CR1000 based datalogger:
See Table 2 for the recommended Gage Type selection and Gage Factor,G, entry to convert to microstrain when using the embedment strain gages with the MICRO-1000
Datalogger Configuration Software. Table 2 also lists the starting and ending frequency settings for the excitation sweep when writing a program for the CR1000 using the P28 vibrating wire measurement instruction. Alternately, if a calibration sheet is supplied with the strain gage the exact values can be calculated from the start and end frequencies of the calibration. To maximize the stability and resolution of the sensor a relatively narrow band of excitation frequency should be selected. One could calculate these settings by taking an initial reading and then setting the starting frequency to 200 Hz below and the ending frequency 200 Hz above.
Model:
MICRO-6000 Gage
Type:
4200ER
4200
Gage Factor G: Shown on cal sheet
Start Frequency
(P28):
4 (400 Hz)
End Frequency
(P28):
12 (1200 Hz)
Table 2 - Embedment Strain Gage Datalogger Parameters
9
3.5. Measuring Temperatures
All Vibrating Wire Strain Gages are equipped with a thermistor for reading temperature. The thermistor gives a varying resistance output as the temperature changes. Usually the white and green leads are connected to the internal thermistor.
Note: All readout boxes will read the thermistor and display temperature in
C.
4.DATA REDUCTION FOR THE GK-403, GK-404 or GK-405 in POSITION D
4.1. Conversion of Readings to Strain Changes
Readings on channel D of all Readout Box are set up to display microstrain when used with a 6 inch long strain gage . But the 4200X strain gage is special in that it has unusually large range so that the displayed readout units, R, must be multiplied by the gage factor, G, on the calibration sheet to obtain true values of microstrain,
.
= G(R
1
R
0
)
Equation 1 - Strain Calculation, channel D
Where R0 and R1 are the readout box readings in Pos D.
Note: when (R1
R0) is positive, the strain is tensile.
A typical calibration sheet is shown in Figure 6
It will be noted that the 4200Er output is not very linear varying as much a +/- 3%FS.
Therefor it is advisable to use the polynomial expression to aceive greater accuracy.
4.2. Temperature Corrections
Temperature variations of considerable magnitude are not uncommon, particularly during concrete curing; therefore it is always advisable to measure temperatures along with the measurement of strain. Temperature induced expansions and contractions can give rise to real changes of stress in the concrete if the concrete is restrained in any way, and these stresses are superimposed on any other load related stresses.
Temperature can also affect the strain gage itself since increasing temperatures will cause the vibrating wire to elongate and thus to go slack indicating what would appear to be a compressive strain in the concrete. This effect is balanced to some degree by a
10
Figure 6 - Typical Calibration Sheet for the 4200ER Strain Gage
11 corresponding stretching of the wire caused by expansion of the concrete in which the gage is embedded or to which the gage is attached. If the concrete expanded by exactly the same amount as the wire then the wire tension would remain constant and no correction would be necessary.
The effect of temperature on the 4200ER strain gage is complex - it varies depending on the strain level.A Typical temperature correction factor to be applied to the 4200ER-10,000 is as follows:
Temperature Correction Factor = +(0.000401*R1 - 1.067)(T1-T0)
Where
R1 is the current gage reading,.
T1 is the current temperature in degrees C,
T0 is the initial temperature in degrees C.
This correction factor was developed by testing four gages at three different parts of their range (i.e., at microstrain levels of 4000, 8000 and 12000), at five different temperature levels, i.e., -40, -20, 0, 20, 40, and 60 degrees C).
When using the polynomial expression to calculate the strain, this correction factor must be applied to the current reading R1. The modified value of R1 is then inserted into the polynomial.
Thus the modified value of R1 to be inserted into the polynomial is
R1+ (0.000401*R1
– 1.067) x (T1 - T0)
4.3. Shrinkage Effects
A well know property of concrete is its propensity to shrink as the water content diminishes, or for the concrete to swell as it absorbs water. This shrinkage and swelling can give rise to large apparent strain changes that are not related to load or stress changes. The magnitude of the strains can be several hundred microstrain.
It is difficult to compensate for these unwanted strains. An attempt may be made, or it may occur naturally, to keep the concrete under a constant condition of water content. But this is frequently impossible on concrete structures exposed to varying weather conditions.
Sometimes an attempt is made to measure the shrinkage and/or swelling effect by casting a strain gage inside a concrete block that remains unloaded but exposed to the same moisture conditions as the active gages. Strains measured on this gage may be used as a correction.
4.4. Creep Effects
It is also well known that concrete will creep under a sustained load. What may seem to be a gradually increasing load as evidenced by a gradually increasing strain may, in fact, be strain due to creeping under a constant sustained load.
12
On some projects, gages have been cast into concrete blocks in the laboratory and then kept loaded by means of springs inside a load frame so that the creep phenomenon can be quantified.
4.5. Effect of Autogenous Growth
In some old concrete, with a particular combination of aggregates and alkaline cements, the concrete may expand with time as it undergoes a chemical change and recrystallization.
This expansion is rather like creep but in the opposite direction. It is difficult to account for.
5. TROUBLESHOOTING
Maintenance and troubleshooting of embedment strain gages are confined to periodic checks of cable connections and maintenance of terminals. Once installed, the gages are usually inaccessible and remedial action is limited.
Consult the following list of problems and possible solutions should difficulties arise.
Consult the factory for additional troubleshooting help.
Symptom: Strain Gage Readings are Unstable
Is the readout box position set correctly? If using a datalogger to record readings automatically are the swept frequency excitation settings correct?
Is the strain reading outside the specified range (either compressive or tensile) of the instrument?
Is there a source of electrical noise nearby? Most probable sources of electrical noise are motors, generators and antennas. Move the equipment away from the installation or install electronic filtering. Make sure the shield drain wire is connected to ground whether using a portable readout or datalogger.
Does the readout work with another gage? If not, the readout may have a low battery or be malfunctioning.
Symptom: Strain Gage Fails to Read
Is the cable cut or crushed? This can be checked with an ohmmeter. Nominal resistance between the two gage leads (usually red and black leads) is 180
,
10
.
Remember to add cable resistance when checking (22 AWG stranded copper leads are approximately 14.7
/1000' or 48.5
/km, multiply by 2 for both directions). If the resistance reads infinite, or very high (megohms), a cut wire must be suspected. If the resistance reads very low (
100
) a short in the cable is likely. Splicing kits and instructions are available from the factory to repair broken or shorted cables. Consult the factory for additional information.
Does the readout or datalogger work with another strain gage? If not, the readout or datalogger may be malfunctioning.
13
APPENDIX A - SPECIFICATIONS
A.1 4200ER Strain Gage
Model: 4200ER
Range (nominal):
10,000
Resolution:
5.0
¹
Calibration
Accuracy
0.5%FSR
Sytem Accuracy: 2.0% FSR²
Stability: 0.1%FS/yr
Linearity: +/-3.0% FSR
Thermal
Coefficient: variable
Frequency Range
Hz:
400-1200
Dimensions (gage): 6.00 x 0.750"
(Length
Diameter)
153
19 mm
Dimensions (coil):
0.875
0.875"
22
22 mm
Coil Resistance:
50
Temperature
Range:
-20 to +80
C
Table A-1 Strain Gage Specifications
Notes:
¹ Depends on the readout; figures in Table A-1 pertain to the GK-403 or GK-404 Readout.
² System Accuracy takes into account hysteresis, non-linearity, misalignment, batch factor variations, and other aspects of the actual measurement program.
A.2 Thermistor (see Appendix C also)
Range: -80 to +150° C
Accuracy: ±0.5° C
14
APPENDIX B - THERMISTOR TEMPERATURE DERIVATION
Thermistor Type: YSI 44005, Dale #1C3001-B3, Alpha #13A3001-B3
Resistance to Temperature Equation:
T
1
( )
( )
3
.
Equation C-1 Convert Thermistor Resistance to Temperature
Where: T
Temperature in
C.
LnR
Natural Log of Thermistor Resistance
A
1.4051
10-3 (coefficients calculated over the
50 to +150
C. span)
B
2.369
10-4
C
1.019
10-7
Ohms
201.1K
88.46K
82.87K
77.66K
72.81K
68.30K
64.09K
60.17K
56.51K
53.10K
49.91K
46.94K
44.16K
41.56K
39.13K
36.86K
34.73K
32.74K
30.87K
29.13K
27.49K
25.95K
24.51K
23.16K
21.89K
20.70K
19.58K
18.52K
17.53K
187.3K
174.5K
162.7K
151.7K
141.6K
132.2K
123.5K
115.4K
107.9K
101.0K
94.48K
Temp
-50
-24
-23
-22
-21
-20
-29
-28
-27
-26
-25
-19
-18
-17
-16
-15
-14
-13
-12
-11
-38
-37
-36
-35
-34
-33
-32
-31
-30
-44
-43
-42
-41
-40
-39
-49
-48
-47
-46
-45
Ohms
16.60K
5692
5427
5177
4939
4714
4500
4297
4105
3922
3748
3583
3426
3277
3135
3000
2872
2750
2633
2523
8851
8417
8006
7618
7252
6905
6576
6265
5971
15.72K
14.90K
14.12K
13.39K
12.70K
12.05K
11.44K
10.86K
10.31K
9796
9310
56
57
58
59
60
51
52
53
54
55
61
62
63
64
65
66
67
68
69
46
47
48
49
50
42
43
44
45
Temp
30
31
32
33
34
35
36
37
38
39
40
41
Ohms
2417
1040
1002
965.0
929.6
895.8
863.3
832.2
802.3
773.7
746.3
719.9
694.7
670.4
647.1
624.7
603.3
582.6
562.8
543.7
1475
1418
1363
1310
1260
1212
1167
1123
1081
2317
2221
2130
2042
1959
1880
1805
1733
1664
1598
1535
Temp
-10
11
12
13
14
15
6
7
8
9
10
-4
-3
-2
-1
0
1
2
3
4
5
-9
-8
-7
-6
-5
21
22
23
24
25
26
27
28
29
16
17
18
19
20
96
97
98
99
100
91
92
93
94
95
101
102
103
104
105
106
107
108
109
86
87
88
89
90
82
83
84
85
Temp
70
71
72
73
74
75
76
77
78
79
80
81
Ohms
525.4
266.6
258.6
250.9
243.4
236.2
229.3
222.6
216.1
209.8
203.8
197.9
192.2
186.8
181.5
176.4
171.4
166.7
162.0
157.6
353.4
342.2
331.5
321.2
311.3
301.7
292.4
283.5
274.9
507.8
490.9
474.7
459.0
444.0
429.5
415.6
402.2
389.3
376.9
364.9
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
122
123
124
125
126
127
128
129
130
Temp
110
111
112
113
114
115
116
117
118
119
120
121
150
Ohms
153.2
87.9
85.7
83.6
81.6
79.6
77.6
75.8
73.9
72.2
70.4
68.8
67.1
65.5
64.0
62.5
61.1
59.6
58.3
56.8
110.8
107.9
105.2
102.5
99.9
97.3
94.9
92.5
90.2
149.0
145.0
141.1
137.2
133.6
130.0
126.5
123.2
119.9
116.8
113.8
55.6
Table C-1 Thermistor Resistance versus Temperature
15
APPENDIX C - HIGH-TEMPERATURE THERMISTOR LINEARIZATION
High Temperature Thermistor Linearization using SteinHart-Hart Log Equation
Thermistor Type: Thermometrics BR55KA822J
Basic Equation:
T
A
B
(
LnR
)
1
C
(
LnR
)
3
273 .
2
Where: T
Temperature in
C
LnR
Natural Log of Thermistor Resistance
A
1.02569
10-3
B
2.478265
10-4
C
1.289498
10-7
Note: Coefficients calculated over -30
to +260
C. span.
Temperature Calculation and Error Table
Temp R
(ohms)
LnR LnR
3
Calculated
Temp
Diff FS
Error
Temp R
(ohms)
LnR LnR
3
Calculated
Temp
Diff FS
Error
-30 113898 11.643 1578.342 -30.17 0.17 0.06 120 407.62 6.010 217.118 120.00 0.00 0.00
.-25 86182 11.364 1467.637 -25.14 0.14 0.05 125 360.8 5.888 204.162 125.00 0.00 0.00
-20 65805 11.094 1365.581 -20.12 0.12 0.04 130 320.21 5.769 191.998 130.00 0.00 0.00
-15 50684.2 10.833 1271.425 -15.10 0.10 0.03 135 284.95 5.652 180.584 135.00 0.00 0.00
-10 39360 10.581 1184.457 -10.08 0.08 0.03 140 254.2 5.538 169.859 140.01 -0.01 0.00
-5 30807.4 10.336 1104.068 -5.07
0 24288.4 10.098 1029.614 -0.05
0.07 0.02 145 227.3 5.426 159.773 145.02 -0.02 -0.01
0.05 0.02 150 203.77 5.317 150.314 150.03 -0.03 -0.01
5 19294.6 9.868 960.798
10 15424.2 9.644 896.871
4.96
9.98
15 12423 9.427 837.843 14.98
0.04 0.01 155 183.11 5.210 141.428 155.04 -0.04 -0.01
0.02 0.01 160 164.9 5.105 133.068 160.06 -0.06 -0.02
0.02 0.01 165 148.83 5.003 125.210 165.08 -0.08 -0.03
20 10061.4 9.216 782.875 19.99
25 8200 9.012 731.893 25.00
0.01
0.00
0.00
0.00
170
175
134.64
122.1
4.903
4.805
117.837
110.927
170.09
175.08
-0.09
-0.08
-0.03
-0.03
30 6721.54 8.813 684.514 30.01 -0.01 0.00 180 110.95 4.709 104.426 180.07 -0.07 -0.02
35 5540.74 8.620 640.478 35.01 -0.01 0.00 185 100.94 4.615 98.261 185.10 -0.10 -0.04
40 4592 8.432 599.519 40.02 -0.02 -0.01 190 92.086 4.523 92.512 190.09 -0.09 -0.03
45 3825.3 8.249 561.392 45.02 -0.02 -0.01 195 84.214 4.433 87.136 195.05 -0.05 -0.02
50 3202.92 8.072 525.913 50.01 -0.01 -0.01 200 77.088 4.345 82.026 200.05 -0.05 -0.02
55 2693.7 7.899 492.790 55.02 -0.02 -0.01 205 70.717 4.259 77.237 205.02 -0.02 -0.01
60 2276.32 7.730 461.946 60.02 -0.02 -0.01 210 64.985 4.174 72.729 210.00 0.00 0.00
65 1931.92 7.566 433.157 65.02 -0.02 -0.01 215 59.819 4.091 68.484 214.97 0.03 0.01
70 1646.56 7.406 406.283 70.02 -0.02 -0.01 220 55.161 4.010 64.494 219.93 0.07 0.02
75 1409.58 7.251 381.243 75.01 -0.01 0.00 225 50.955 3.931 60.742 224.88 0.12 0.04
80 1211.14 7.099 357.808 80.00 0.00 0.00 230 47.142 3.853 57.207 229.82 0.18 0.06
85 1044.68 6.951 335.915 85.00 0.00 0.00 235 43.673 3.777 53.870 234.77 0.23 0.08
90 903.64 6.806 315.325 90.02 -0.02 -0.01 240 40.533 3.702 50.740 239.69 0.31 0.11
95 785.15 6.666 296.191 95.01 -0.01 0.00 245 37.671 3.629 47.788 244.62 0.38 0.13
100 684.37 6.528 278.253 100.00 0.00 0.00 250 35.055 3.557 45.001 249.54 0.46 0.16
105 598.44 6.394 261.447 105.00 0.00 0.00 255 32.677 3.487 42.387 254.44 0.56 0.19
110 524.96 6.263 245.705 110.00 0.00 0.00 260 30.496 3.418 39.917 259.34 0.66 0.23
115 461.91 6.135 230.952 115.00 0.00 0.00
Table B-2: High Temperature Thermistor Resistance versus Temperature.
