THE CALIBRATED LENGTH OF RAIL METHOD FOR MEASURING RAIL TEMPERATURE STRESS Xing-han Liu Xian Institute of Railway Science and Technology, China ABSTRACT Continuous Welded Rail (CWR) has been widely used all over the world. The key issue of CWR technology is to accurately measure actual rail temperature stress through rail neutral temperature or rail anchored temperature. This is a tough issue in the world. The traditional length concept was formed and evolved in the past thousands of years, whereas the meter standard system was established several hundred years ago. Based on discussion of the traditional length concept and meter standard system, we proposed a new concept, instantaneous natural length, and founded a new method, Calibrated Length of Rail (CLR). Consequently, we solved the issue of accurately measuring temperature stress of CWR. The Calibrated Length of Rail method was first used and succeeded in Guo-zhen Railway Track Engineering Division (China) on March 23, 1982. In the past 18 years, the CLR method has been successfully used in installation of CWR for nearly 2,000 kilometers (1,240 miles). The results have been excellent.
KEYWORDS Continuous Welded Rail (CWR), rail neutral temperature, rail anchored temperature, instantaneous natural length, Calibrated Length of Rail (CLR). 1. INTRODUCTION At present, great efforts are being made all over the world to develop Continuous Welded Rail (CWR). The length of rail that is installed without joints ranges from hundreds of meters to hundreds of kilometers. The character of CWR is that rail is neither expanded nor contracted. Its restrained extending and contracting values may all turn into temperature stress. If the temperature stress is not controlled well, in hot days, CWR will be buckled, whereas in cold days, CWR will be pulled apart. Today, there are several types of methods in measuring rail temperature stress. In general, there are stress methods, energy-release methods and strain methods. Examples of stress methods are acousto-elastic wave method, magnetic coercion method, and electromagnetic-acoustic transducer method. The result of stress method measurement is influenced by rail microstructure, and interfered by non-temperature stress. Examples of energy-release methods are rail push-aside method and rail uplift method. To use energy-release method, not only transportation must be interrupted, but track is damaged as well. Strain method is based on the following idea: rail temperature stress comes from the restrained values of rail length change, which comes from extending and contracting. Thus it makes sense to measure rail temperature stress by measuring the restrained values of strain. Strain value, in
fact, is a question of length change. Limitations and misunderstandings with the traditional conception of length prohibit it from being used to accurately measure rail temperature stress. Field applications support this point. Through long-term researches (1961 1997), we proposed the concept of instantaneous natural length (L i n ) to replace the traditional concept of length. With this new concept, we can successfully employ strain method to accurately measure the anchored temperature of CWR, hence, neutral temperature, rail temperature change and temperature stress. 2. DISCUSSION ON TRADITIONAL CONCEPTION OF LENGTH Measurement of length is influenced by many factors. Some of the influences come from measuring instruments; some come from the measured object. 2.1 Meter Definition and Meter Standard 2.1.1 Meter Definition One meter, simply speaking, is the length, at 0 C, of the Meter Bar kept in Paris, France, since 1791. It equals one-forty-millionth of the meridian through Paris. Although the length of the meridian through Paris was corrected later, the length of the Meter Bar remains unchanged. In 1960, the meter definition was revised to be 1650763.73 times of the wavelength of Krypton- 86 in vacuum. In 1983, the meter definition was revised to be the distance that light passes
through in 1/299792458 seconds in vacuum. Once we come to railroad, how do we handle the 0 C condition? How to handle the vacuum condition? 2.1.2 Meter Standard In 1889, the International Measurement Bureau made a group of new meter standards. The one closest to the 1791 Meter Bar among these new rules was chosen to be the international meter standard, the rest ones were sent to other countries as national meter standards. It is easily seen that errors exist at every step from the Meter Bar to the international meter standard to national meter standards. This chain goes all the way to end users, to every measuring instrument. Then, how much is the error? 2.2 A 50-meter Steel Tape Measure There are all kinds of measuring instruments. People usually use a rule right away without thinking about whether it is made with steel, or wood, or cloth. Many scientists and engineers are interested in In-steel rules, because their thermal expansion coefficient is very small. In fact, even we eliminated the thermal expansion coefficient of a measuring instrument, we cannot eliminate the thermal expansion coefficient of the measured object. Now let us forget about short steel rules or In-steel rules, just focus on a 50-meter (164-ft.) steel tape measure. 2.2.1 The Error Tolerance of Steel Tape Measures
In China, JJG4-89 Examination Regulation for Steel Tape Measure specifies that the error tolerance of steel tape measures are: Grade I steel tape measures, = ± (0.1 + 0.1L) mm or ± (0.004 + 0.1L) in. Grade II steel tape measures, = ± (0.3 + 0.2L) mm or ± (0.012 + 0.1L) in. where is the error tolerance, L is the length (in meters or inches, respectively). The Regulation also says the error tolerance of the standard steel tape measure should be less than 1/5 of that of the steel tape measure being examined. The standard steel tape measure has such a big error tolerance that it is unimaginable. 2.2.2 Examination of Temperature Measurement Is Not Strict In China, JJG4-89 Examination Regulation for Steel Tape Measure also says that the examination temperature is: for grade I steel tape measure, 20 ± 5 C (68 ± 9 F); for grade II steel tape measure, 20 ± 8 C (68 ± 14 F). The allowable range is too tolerant! 2.2.3 Tension of Measurement Is Confusing When a steel tape measure is examined, tension must be set. Chinese standard JJG4-89 uses 50N (11 lbf.). There are two reports regarding this. One report says 5 kg (11 lbs.) of tension is used in measurement. The other report says 10kg (22 lbs.) is used. While Chinese standard TBJ101-85 Regulation for Railway Measurement uses tension of 98 and 147N (22 and 33 lbf.). The standards are confusing.
In the case of a 50-meter (164-ft.) steel tape measure, we concluded from an experiment that for 1kg extra tension, the length of the steel tape measure increases 0.5 0.6mm (0.0197 0.0236in.). 2.2.4 Influence of the Weight of Steel Tapes When a steel tape measure is examined for its accuracy, it is suspended levelly in mid air. When it is used to measure the length of rail, it is put right on the rail. These two different ways of using the steel tape measure introduce considerable discrepancy. The regulations never say anything about this discrepancy. 2.2.5 The Thermal Expansion Coefficient of the Tape In China, 11.8 10-6 / C is used as the thermal expansion coefficient of steel tape measure. But some books about railway surveying use 12.5 10-6 / C or 11.5 10-6 / C. 2.2.6 Stress Is Directly Proportional to Strain The widths and thickness of the tapes are different. Even though the tension put on the tapes is constant, the stresses and strains are different. So the results of measured length are different, too. 2.3 A 50-meter Rail Speaking of measuring a 50-meter (164-ft.) rail with a 50-meter (164-ft.) steel tape measure, let us assume the length of a 50-meter (164-ft.) steel tape measure is accurate, there are several
issues to be discussed: 2.3.1 The Temperature of the Rail The cross-section of rail is complicated. Rail is massive. Temperatures of points on the surface of the rail or inside the rail are different. How can we accurately measure the temperature? From our long-term research, we concluded that it is impossible to measure the effective temperature (see 4.1) of rail. If you cannot get the temperature of the rail, how can you get its length? 2.3.2 The Force Condition of the Rail The rail expands when heated and contracts when cooled. Under force-free condition, it can expand or contract in a regular way. If not under force-free condition, there is no regular way to tell how the rail will expand or contract. Our experiments proved that even there are gaps left beforehand, a well-anchored rail cannot expand or contract any more. When a rail is unanchored from the track or put on the ballast shoulder, it cannot freely expand or contract either. Even a rail setting on smooth rollers cannot freely expand or contract, due to very little friction. If the rail is not under force-free condition due to friction, how can you tell its exact length? 2.3.3 The Thermal Expansion Coefficient of the Rail In Russia, 11.8 10-6 / C is used as the thermal expansion coefficient of the rail. In China, regardless of steel material, 11.8 10-6 / C is also used. Occasionally, the rounded-up value 12.0 10-6 / C is used. In other countries, 11.8 10-6 / C is used somewhere, 11.4 10-6 / C or 11.5
10-6 / C are used somewhere else. Do we need to take into account the rail steel material? Which value of thermal expansion coefficient among these is accurate? If the thermal expansion coefficient is inaccurate, how to calculate the length change due to change of temperature? 2.4 Summary To measure the rail of non-deterministic length with a steel tape measure of inaccurate length, the conclusion is clear it is impossible. 3. INSTANTANEOUS NATURAL LENGTH The neutral temperature of CWR (see 4.2) is the critical point between the tensile and compressive conditions of the rail. It is required that the actual rail neutral temperature remains within ±3 5 C (±5 9 F) range around its designed value. From meter definition, through meter standards, to all sorts of field length measurement, errors exist more or less due to the traditional conception of length. In particular, when you measure a 50-meter (164-ft.) rail with a 50-meter (164-ft.) steel tape measure, the summation of all the errors far exceeds the requirement of measuring neutral temperature of CWR. Let us merely take the example of a 50-meter (164- ft.) grade I steel tape measure. The error tolerance is ±(0.1 + 0.1L) = ±5.1 mm (±0.20 in.). This error range is equivalent to ±8.6 C (±15.5 F) in rail temperature change, which far exceeds the design requirement of rail neutral temperature ±3 5 C (±5 9 F). So it is quite understandable that we cannot solve this problem by using the traditional conception of length.
In the above section 2, we concluded that it is actually impossible to measure the length of the rail. Is it right that there isn t a real length of the rail? Of course there is. Under constantly changing rail temperature and force condition, there is the instantaneous length of the rail at any particular time. We name this length the instantaneous natural length. According to the CWR theory, a rail segment in stabilizing zone neither extends nor contracts. We also call the fixed length of the segment of CWR at a certain time its instantaneous natural length by that time. Our definition: the actual length of an object at a certain time is called its instantaneous natural length. 4. RAIL TEMPERATURE AND ITS CHANGE The formula to calculate rail temperature stress is: σ T = Eα T... (1) where: E modulus of elasticity of rail steel α thermal expansion coefficient of rail steel T change of rail temperature among which E and α are constants, T can be decided as the following: 4.1 Rail Effective Temperature, T e The so-called rail temperature should be the simplified name of rail effective temperature. Rail
temperature is measured in order to determine the extension or contraction of the rail due to temperature changes. The extension or contraction of the rail is not determined by the temperature of any individual point on the rail surface (top of head, web or base), but determined by the synthesized temperature from those of various parts of the whole rail cross-section. This synthesized temperature is what we call as rail effective temperature. 4.2 Rail Neutral Temperature, T n Rail neutral temperature is the rail effective temperature that measured when T( C) there is neither compressive nor tensile stress in the rail. For a new rail, during the initial period of transportation, a certain degree of decrease of rail neutral T a T n t 1 Q(Ton) temperature will occur due to the rollingout of rail. As shown in Fig. 1, the rail Figure 1 Relationship between T a and T n neutral temperature will not decrease any more if well anchored after a certain transportation quantity. 4.3 Rail Anchored Temperature, T a The new concept proposed by us is that the rail effective temperature when anchored under force free condition is defined as the anchored temperature of CWR. That is the rail neutral temperature by the time of anchoring. As shown in Fig. 1, if only when the rail is loaded by
trains (including the first train), rail neutral temperature will not be the same as rail anchored temperature. If poorly anchored, non-uniform rail longitudinal displacement will occur. In that case, rail anchored temperature will change along with the rail neutral temperature. If the steel quality is uniform, the difference between the rail anchored temperature and the stabilized rail neutral temperature will be a constant. That is: T a - T n = t 1... (2) We usually use t 1 = 6 8 C (11 14 F). 4.4 Rail Operation Temperature, T o When installing continuous welded rails, we measure the rail laying temperature; to maintain CWR, we measure rail temperature before and after maintenance; when measuring rail temperature stress in CWR at a certain time, we measure rail temperature. In these cases, we mean the operation temperature at that particular time. Rail operation temperature should be the effective temperature at a particular time. Due to limited equipment, at present, we can only get the rail operation temperature from the surface of rail. We recommend it is better to measure rail operation temperature from the sunlight-facing side of rail web. 4.5 Rail Temperature Change, T By saying rail temperature change, we mean the change of CWR operation temperature from its neutral temperature under good anchorage. To measure temperature stress in CWR, there are
direct and indirect methods. To use indirect method, rail temperature change must be known, that is: T = T o - T n... (3) When T is positive, there is compressive stress in the rail; when T is negative, there is tensile stress in the rail. 5. THE THEORY OF CALIBRATED LENGTH OF RAIL (CLR) Based on our concept of instantaneous natural length and definition of rail anchored temperature, we established a new theory named Calibrated Length of Rail (CLR) through researches and experiments. Our main instrument is a CWR calibrating tape (hereinafter tape ). While: 1) the thermal expansion coefficients of rail and tape are equal 2) the rail effective temperature and the temperature of the tape are equal 3) the rail is under force-free condition, and the tape is under certain tension then, under normal temperature, the instantaneous natural length of a certain rail segment and the instantaneous natural length of the tape are always equal. We name this certain rail segment as Calibrated Length of Rail (CLR) and denote it as L c. That is: α tape = α rail (under normal temperature) T tape = T rail = T e L i n tape L i n rail σ tape = constant, σ rail = 0 = L c L c.c where: L i n tape - the instantaneous natural length of the calibrating tape
L i n rail - the instantaneous natural length of the rail segment L c.c - the calculated length (rounded approximate value) of CLR Field applications have proved that our instruments and technique can satisfy the preceding requirements. 6. THE PRINCIPLE OF MEASURING RAIL ANCHORED TEMPERATURE BY CLR METHOD As shown in Fig. 2(a), under the condition of T tape = T e, when a force-free L c rail has just been set in the railseat of the tie, we can assume that it is set on (a) absolute smooth rollers. And the instantaneous natural length of the rail L c ± l segment between a certain pair of set points calibrated by the tape surely equals (b) the instantaneous natural length of the tape. After the rail has been anchored, as Figure 2 Principle of CLR Method shown in Fig. 2(b), compare the instantaneous natural length of the rail segment and the tape, we get (1) While the instantaneous natural length of the rail segment equals the instantaneous natural
(2) length of the tape, the anchored temperature T a equals the tape s temperature T tape, that is: T a = T tape ; (2) While the instantaneous natural length of the rail segment is less than the instantaneous natural length of the tape: where: l T a = T tape - α rail L c α rail - the thermal expansion coefficient of the rail l - the difference between the instantaneous natural lengths of the rail segment and the tape; (3) While the instantaneous natural length of the rail segment is greater than the instantaneous natural length of the tape: l T a = T tape +. α rail L c Hence, the theoretical rail anchored temperature calculating formula is: l T a = T tape ±.... (4) α rail L c The practical rail anchored temperature calculating formula is: l T a = T tape ±.... (5) α rail L c.c
7. CONCLUSION The Calibrated Length of Rail method was first used and succeeded in Guo-zhen Railway Track Engineering Division (China) on March 23, 1982. In the past 18 years, the CLR method has been successfully used in installation of CWR for nearly 2,000 kilometers (1,240 miles). The results have been excellent. Among all measurement methods of CWR temperature stress, neutral and anchored temperature in the world, only the new CLR theory has no fatal shortcomings. It can be operated widely.