TORQUE CALCULATION OF TORQUE OF A SCREW OR. SUNDIAL
Saturday, January 22, 2011
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TORQUE CALCULATION OF THE TORQUE OF A SCREW OR.
formulas for the torque. Material of screws at various temperatures. Coefficients of friction.
Eventually we present the case of having to "torque" in particular a screw that is not within the conventional torque tables available, either by the diameter of the screw or the material itself. In these cases gives us no choice but to make our own calculations to determine the set torque value or theoretical torque "required by our new case.
This situation I was presented with many opportunities to work in a garage repair of hydraulic cylinders for the steel industry where many opportunities are needed to determine the settings for screws up to 95 mm in diameter or determine torque values \u200b\u200bfor temperatures above 100 ° C. On the other hand due to the large variety of screws used for the repair of over 4,000 hydraulic cylinders according to the statistics of the workshop was necessary to perform a series of tables with theoretical values \u200b\u200bcoincide with the tables of torque available at the workshop, which not covered the screws over 42 mm in diameter. From this experience it is clear that the calculation of the torque of a screw is not as simple as it looks.
While the most popular method for adjusting screws and nuts is by controlling torque and torque due to its simplicity and economy, is also one of the most uncertain as to ensuring the unifying force in a bolted assembly.
The torque control is usually achieved by adjusting a torque wrench to a specified value by either the computer manufacturer or by the values \u200b\u200bshown in the tables of torque. Recall that the torque wrench not measure the tension or preload on the screw but the value of torque applied. This value is practically a product of the friction between the flanks of the screw-thread nut and the friction between the screw head and washer, only 10% of the total torque applied setting corresponds to the generation of the preload. The problem arises when this method is used indiscriminately without taking into account the implementation of the bolted joint.
In the technical literature we can find a simple empirical formula that relates the pair of us set the preload force generated by the screw on the diameter of the same and constant dimensionless proportionality.
This simple equation valid in the elastic material of the screw is:
MA = K XDx FM .... [1]
Where "MA" is the torque or torque applied to the screw (Nm, lbs.in), "d" is the nominal diameter of screw (mm, inches), "FM" is the preload screw (N, lb) and "K" constant of proportionality is usually determined experimentally.
This factor "K" is often referred to as "nut factor" with a value like very low friction coefficient, however not confuse the "K" factor with the coefficient of static friction material.
The following table shows typical values \u200b\u200bof the factor "K" for steel screws.
The above equation can be used as long as the value of "K" is properly determined by the user. However, experience has shown that taking a value of "K" is risky, according to the application of the screw and should not be over-estimated the importance of tightening torque in those critical elements of great responsibility.
From the formula MA = K XDx FM, the value of the preload "FM" of the screw is determined by the value of allowable tensile stress on the screw material in most cases are based in 90% of the value of proportional yield point "Rp" or lower yield "REL" for metric screws and between 70% and 90% of the test voltage for imperial screws.
For example, a screw has a value as 5.6 Rp = 30 N/mm2 (nominal) with the calculation of the preload is done with 90% of this value, ie 27 N/mm2 tension.
The formula for determining the preload for the case of 90% of the yield strength (Rp or REL) of the material of the screw is:
FM = 0.9 x Rp x As .... [2]
For purposes of calculating the force, the area that is used to determine the value of the resistant strain is the nominal section of the thread, which is calculated by:
.... [3] Where:
As = area or section effective resistance.
d2 = pitch diameter of the thread. (ISO 724)
d3 = core diameter of the thread.
values \u200b\u200bd2 and d3 are available in the tables of the threads.
As d2 and d3 depend on the pace and profile of the thread, the resistant section for metric screws can be determined by:
.... [4] Where "d" is the nominal diameter of the screw thread and "P" passing of the thread.
The group presents a more extensive and complex formulas where they relate to the geometry of the screw and the hole, the material, the friction coefficients thread-thread-seat head and allowing us to calculate the values \u200b\u200bof torque for any type of screw.
These formulas are based on the principle that the rated torque or torque applied to create total bolt preload is a product of the partial sum of pairs created by the friction of both the screw and the screw head.
MA = MG + MK .... [5]
"MG" is the torque or torque generated by the thread and "MK" the moment produced by the friction of the head or nut Product bolt preload force "FM."
The adjustment time is caused by the preload on the screw can be determined, regardless of analytical development, using the formula:
.... [6] Where:
G M = Moment or torque applied to the thread. M F
= preload force on the thread.
d2 = pitch diameter of the thread.
P = Pitch of the thread.
UG = coefficient of friction screw-thread.
The number 1.155 is the drying of semi-angle flank of the thread. For the tortilla measure the angle of the thread flank is 60 °. Hence, Sec (60 / 2) = 1.155 rounded.
The torque created by friction in the screw head is determined by:
.... [7] Where:
KR M = Moment or torque applied to bolt head or nut. M F
= preload force on the head or nut. KM
D = Mean diameter of friction ring sliding area of \u200b\u200bthe head or nut.
uK = coefficient of friction of the head or nut against the seat.
The average diameter of slip "DKM" is determined by:
.... [8] Where "dW" settlement is the diameter of the head or nut that appears on the standards of the screws and is approximate to the hexagon nut or bolt head (dW = s) or the diameter of the allen head screw and "dh" is the diameter of the hole where sits the head or nut, DIN normally average 69.
Adding both expressions we have that the torque setting is determined by:
.... [9] letters used in the formulas correspond to those given in VDI 2230.
This last formula allows us to determine the torque applied to the screw or nut to obtain the value of the preload on the basis of physical and mechanical parameters of the screw as the screw hole of the settlement nut or the head, the friction coefficient between the materials of the bolted connection and thread pitch.
Interestingly, the expression enclosed in parentheses in the formula [9] to be divided by the nominal diameter "d" of the thread gets the value of the nut factor "K" used in the formula [1]:
.... [10] maximum preload force on the core of the screw within the elastic material is obtained when the tensions caused by the preload reached the value of the material yield point or point of proportionality Rp0.2 . This tension is defined final or reduced by the simultaneous presence of tensile stresses product of preload and torsional shear stresses caused by torque.
According to the theories on the strength of the materials when a bar is subjected to combined efforts, the resulting stress is calculated by:
.... [11] Regardless of the analytic proof of the formula [11] that the preload "FM", is calculated by:
.... [12] Section resistant "AS" or the effective area of \u200b\u200bthe screw submitted to the efforts and determined by the formula [3] which can be written
.... [13] and "dS" is determined by:
.... [14] 's constant The number 0.9 is the indicator of 90% of the yield point, this value can be replaced according to the application of the screw into another value.
With formulas [9] and [12] and we are able to calculate the preload and tightening torque applied to any joint bolted or develop our torque tables for our needs.
To clarify a bit more use of the formulas [9] and [12] calculate the torque or preload and tightening torque required for a hexagonal screw DIN / EN / ISO 4014, M 30 8.8 quality coarse thread , laminated, blackened and dry without lubrication mounted at 20 ยบ C.
screw parameters M 30:
Step = 3.5 (As standard)
d2 = 27.727 (As standard)
d3 = 25.706 (As standard) dW = 42.75
(As standard)
Rp02 = 660 N/mm2. (Quality 8.8 and d \u0026lt;16 to 20 ° C, ISO 898. See table below)
UG = uK = 0.12 (See tables at end of article) dS = 26.7165
calculation by [14]
AS = 560.595 Calculation of [3]
dh = 33 ( On average DIN 273 - Hole)
D KM = 37.875 Calculation of [8]
Solving the formula [12] obtain the value of preload:
M F = 300
kN With the value of the calculated torque preload adjustment required by the equation [9]:
M A = 1425 Nm
Another example:
Hex Screw M8 quality 12.9 coarse thread according to DIN / EN / ISO 4014, oil lubricated during assembly.
Step = 1.25 (according to standards)
d2 = 7.188 (As standard)
d3 = 6.466 (As standard)
dW = 11.63 (As standard)
Rp02 = 1,100 N / mm2. (Quality 12.9 to 20 ° C, ISO 898. See table below)
UG = uK = 0.1 (See tables at end of article) dS = 6.827
calculation by [14]
AS = 36, 61 Calculation of [3]
dh = 9 (On average DIN 273 - Hole)
D KM = 10.315 Calculation of [8]
Solving the formula [12] obtain the value of preload:
F M = 32.8 kN
With the value of the calculated torque preload adjustment required by the equation [9]:
M A = 37.1 Nm
We can compare these values \u200b\u200bwith those indicated by the table set out in the entry VDI How to handle the torque tables?, values \u200b\u200bare very next.
If we make the same steps for M8 hexagonal twang quality 12.9 fine thread and get the following values:
M F = 35.6 kN
M A = 39.2 Nm
We can confirm that the fine thread screws are able to generate higher preloads and support a greater tightening torque than normal or coarse thread, it is clear the main reason why the torques tables are not "extrapolate" the different types of threads or manufacturing standards for the screw. For each case there the respective tables.
I must warn that these results are valid only for new screws that meet the parameters set by the rules otherwise it may be "over torque" to the screws. It emphasizes new screws as it has been found that the coefficient of friction varies considerably when adjusted several times and loosening a screw, showed variations of friction coefficient by a factor of at least 3. This is one reason why it is always advisable not to reuse the hardware and the same should be changed every time you remove the union, especially due to the use of the screw, and inaccuracies in adjustment to the labor force and the fact that they use 90% of the yield point, no wonder the same to be removed and is "meaningless."
It should also be noted that this calculation is showed as valid for metal-metal joints, soft seamless through where it should be considered as the application. For example, it is said that the pair of adjustment screws for the pylons is approximately half that calculated for the sole purpose of preventing the galvanized coating crack structure by adjusting the screws. In the end, each case must be studied.
As explanatory Finally, when using a torque wrench torque value applied to the screw going to depend on the speed of adjustment is made, indicating the instrument arrived early to set value when this is done quickly so that the values \u200b\u200bof closest to the torque indicated by the instrument is obtained by performing a slow, steady squeeze. It is generally recommended when several bolts torqued to make the cross or "X" and beginning with a percentage of the required final value, such as first adjusting screws 30%, then 60% and finally to 100% torque required. This gives a better guarantee of the final adjustment of hardware.
The following four tables show certain information necessary to know when "Torque" a screw, such as reducing the carrying capacity of the material as a function of temperature, resistance and friction material .
coefficients of friction in the head.
coefficients of friction in the thread.
material steel screws.
limit function creep on air temperature.
I hope this post will be helpful to those who are seeking information about the couple or torque adjustment screws according to their mechanical and material parameters.
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