What is torque controlled preloading
Torque controlled preloading is a method for preloading threaded connections by a use of a torque wrench. The torque wrench measures the torque, and gives a feedback when the set torque is reached. This method is by far the most popular way of preloading bolts due to simplicity and easy available tools. Hand operated torque wrenches are most popular up to M18 massive bolts, while hydraulic operated torque wrenches are used for larger dimensions due to high torque requirements. Disadvantages by torque controlled preloading are introduction of torsion stresses in the bolt and dependency of correct friction values to get the correct relation between the applied make-up torque and the preload force. All abbreviations and formulas in this document are in according to the rules given in VDI 2230, Blatt 1.
Make-up torque
The applied make-up torque can be expressed as:
Where:
| MA |
= Applied make-up torque |
| MK |
= Head torque |
| MG |
= Thread torque |
The head torque is a friction torque. The thread torque consists of two parts. Part one is the friction torque in the threads. Part two is the resistance from the pitch, which is the part that actually makes the desired preload force FM. The mathematic relationship between the applied make-up torque MA and the preload force FM is:
Where:
| MA |
= Applied make-up torque |
| FM |
= Preload force |
| P |
= Pitch |
| d2 |
= Pitch diameter |
| dw |
= Outer head frictions diameter |
| dh |
= Inner head friction diameter |
| β |
= Angle of thread |
| γ |
= Angle of head |
| μG |
= Coefficient of friction in threads |
| μK |
= Coefficient of friction under head |
The deduction of the above expression is described in appendix A. Examples of threaded connection and specific equations for the make-up torque follow.
Example 1: Bolt with flat head and metric threads
The make-up equation for bolts with flat head (γ=0º) and metric threads (β=60º), where dimensions are given in millimetres [mm] and applied torque in Newton-metres [Nm] is:
Figure 1: Example of a bolt with flat head
Example 2: Bolt with conical head and metric threads
The make-up equation for bolts with conical head (γ=60º) and metric threads (β=60º), where dimensions are given in millimetres [mm] and applied torque in Newton-metres [Nm] is:
Figure 2: Example of a bolt with conical head
Example 3: Pipeline connection with flat head and metric stub acme threads
The make-up equation for straight pipeline threaded connection (pin and box) with flat head (γ=0º) and stub acme threads (β=29º), where dimensions are given in millimetres [mm] and applied torque in Newton-metres [Nm] is:
Figure 3: Example of a pipeline thread with flat head
The above formula can also be applied for conical threads, but the diameter d2 is then replaced with the diameter Rt as described in API RP 7G, section A.8.1 and A.8.2.
Example 4: Plug with conical head and stub acme threads
The make-up equation for plugs with conical head (γ=60º) and stub acme threads (β=29º) and where all dimensions are given in millimetre [mm] and applied torque is wanted in Newton metres [Nm] is:
Figure 4: Conical plugs
Breakout torque
The theoretical breakout torque is:
The theoretical breakout torque is thus lower than the makeup torque since the pitch now will assist during breakout. Practical experience is however that the breakout torque is higher. Reasons for this are:
- Static friction is higher that dynamic
- Bad lubrication making metal to metal contacts
- Corrosion
- Aging of the lubrication
Preloading accuracy
Accuracy of the above make-up torques is influenced by the following conditions:
- Coefficient of friction under the bolt head
- Coefficient of friction in the bolt threads
- Accuracy of torque wrench
- Human accuracy
Variations due to these factors are illustrated in the figure below:
Figure 5: Variations in the preload force during torque controlled make-up
Typical accuracy for the preload force (ΔF) by use of a normal torque wrench is ±23%. Experiences show that this value may be reduced to ±17% for well known connection where actions are taken to provide an accurate preload force. Note that air controlled ‘hammer’ tools have very poor preload accuracy (typical ± 42% to ±60%). Recommended actions to achieve preload accuracy when applying torque controlled preloading are:
Lubrication
Use lubrication from suppliers where friction is determined by use of an Erichsen machine. This machine makes accurate measurement of the applied torque and the preload force, puts these values into the formulas given in this document and finally calculates the friction values. The test is repeated several times to provide scatter data. Only serious lubrication suppliers have the knowledge and takes the effort to do this. Other methods will give wrong values for threaded connections. Use lubrications with documented mean value and standard deviations of friction coefficient both under the bolt head and in the threads. Finally, select lubrications with low standard deviations of friction coefficient if there is no conflict with other lubrication requirements. API RP 7G recommends a coefficient of friction of 0.08 for both the head and threads when applying a thread compounds containing 40-60% by weight of finely powdered metallic zinc. A good source for coefficient of friction for bolts is the Molykote lubrication book.
Torque wrench
Use a torque wrench with documented low standard deviations and calibrate the wrench in intervals recommended by the supplier. Use wrenches with a distinct stop signal then applied torque is reached. It is normal to use an accuracy of ± 5% for high quality torque wrenches during preloading calculations.
Human factors
Applied torque must be calculated with the right input and with the right equations. Selecting makeup torques from general tables without knowledge about friction values will probably give wrong preload values. Use trained staff only when preloading threaded connections. Human factors during make-up itself are probably the most important factor to achieve correct preload values.
Another condition for correct preload force is adequate tolerances and surface finish. When a threaded connection is preloaded, the pitch of the internal thread (pin) shrinks and the external threads (box) expands. If the tolerances are insufficient or the radial support of the external threads are insufficient, thread interference may lock during preloading, and the pin is twisted instead of being preloaded.
Preload losses
Time related mechanisms for preload reduction are:
- Relaxion
- Temperature expansion
- Changed material properties
- Unscrewing
- Stress relieving
All threaded connections will have some relaxion due to plastic deformation in preloaded interfaces (setting). The most efficient measure is to increase the distance between the threads and head of the pin/bolt for increased elasticity. Another type of relaxion is creep, but this will only take place at very high temperatures. A typical example of preload losses due to temperature expansion is the use of a pin/bolt with high thermal expansion (like stainless steel) and a box/flange with low thermal expansion (like carbon steel). That will cause a preload loss if the connection is preloaded at ambient temperature and exposed to high temperature during operation. Changed material properties could be reduced E-modulus during a fire. Unscrewing is typical a problem when exposed to high amplitude vibrations. High preload is one of the most effective measures to prevent unscrewing. If high preload is not practical, other unscrewing preventing measures should be applied, like Loctite, locking pins, etc. Stress relieving inside the material itself must normally be taken into account for large dimensions.
Preload stresses
The stresses in a preloaded bolt/pin of a threaded connection can be expressed by the von Mises' criteria.
Where:
| σVME |
= Von-Mises equivalent stress |
| σM |
= Tensile stress during make-up |
| τ |
= Torsion stress during make-up |
| RP0.2 |
= Yield stress |
| ν |
= Percentage of yield strength in pin/bolt to be utilized during make-up |
The mathematic relationship between the preload force FM and maximum von-Mises equivalent stresses can be expressed as:
Where:
| FM |
= Preload force |
| ν |
= Percentage of yield strength in pin/bolt to be utilized during make-up |
| RP0.2 |
= Yield stress |
| P |
= Pitch |
| db |
= Hole diameter |
| d0 |
= Smallest outside diameter |
| d2 |
= Pitch diameter |
| β |
= Angle of thread |
| μG |
= Coefficient of friction in threads |
The above expression is deducted in appendix B. This expression can be used together with equation (2) to find the relation between the applied make-up torque and the percentage of yield in the bolt/pin. The smallest outside diameter d0 for a standard bolt will be:
The diameter d3 in the above expression is the minor thread diameter. The above expression is given for the smallest diameter in the thread cross section. If any outside section of the bolt/pin is smaller than the above expression, this diameter shall be used.
During the preloading there is force equilibrium between the bolt/pin and the flange/box. When the preloaded connection is exposed to an external load, there is deformation equilibrium between the bolt/pin and the flange/box as long as there is full contact between the preloaded parts. The major benefit of the above fact is the possibility of small variations in the bolt/pin stresses, even if the connection is highly loaded. A condition is to achieve small stress variation in the bolt/pin during external loading is to use as elastic bolt/pin and a stiff flange/box. How much a preloaded bolt/pin is loaded when exposed to an external load can be illustrated in a defection diagram for simple threaded connections. More complex cases must be calculated by the finite element (FE) method. The basic formula for axial strain in a cylinder exposed to a force F is:
Where:
| f |
= Elongation |
| l |
= Length |
| E |
= Youngs modulus |
| σ |
= Stress |
The elongation can be expressed as:
The resilience can further be expressed by (elongation per force unit)
The resilience equation above is used as basis for making more complex estimates for the resilience of the bolt and the flange in bolted connections. Resilience expressions for standard bolts and flanges are given in VDI 2230 Blatt 1. Some data used in these the VDI formulas is based on experimental research and is thus only valid for standard bolted connections. However, the principle can be used for all threaded connection, including plugs and pipeline threads. When the resilience for both the bolt/pin and the flange/box is known, it is possible to find the force relation Ф and thus the following expressions:
Where:
| FA |
= External load |
| FSA |
= Part of the external load taken by the bolt/pin |
| FPA |
= Part of the external load taken by the flange/box |
Example 5: Defection diagram for simple bolted connection
A deflection diagram for a simple bolted connection is given below:
Figure 6: Defection diagram for a bolted connection
This example has an elastic bolt (large fSM) and stiff flange (small fPM) in the preloaded area between the threads and the bolt head.
Example 6: Defection diagram for a plug with a check valve
A deflection diagram for a compression plug with a check valve closing with pressure from below is given below:
Figure 7: Defection diagram for a compression plug
This example assumes that the plug is twice as elastic as the loaded part of the flange, which will be a conservative estimate when the plug is connected to a massive flange. The stressed flange area is indicated in the figure above. To prevent through valve leakage, the compression stresses in the plug seat should be higher than the pressure from below. The seal stresses may be increased without changing the preload, by use of slightly different plug seat angle vs. flange seat angle.
Control calculations
Before the calculation of a threaded connection can be finalized, the following control calculations must be performed:
- Max stresses in the bolt/pin when exposed to an external load
- Max stresses in the flange/box when exposed to an external load
- Max stresses in the bolt/pin head contact area
- Max tension stress amplitude in the bolt/pin
- Shear strength of the threads
Maximum stresses in the bolt/pin are normally kept blow yield when applying torque controlled preloading. Yield control preloading used of long and critical bolts are however in the yield zone during preloading. Maximum stresses in the flange/box itself should also be below the yield strength. Maximum stresses in the head contact area should be below the lowest yield limit for both the bolt and the flange to prevent excessive setting (relaxion). Stress amplitude calculations are only required if the threaded connection is exposed to dynamic external loads, with the intention to prevent fatigue fracture. The stress amplitude in the bolt must be less than the fatigue strength of the material. Note that the fatigue strength for threads normally is 4 to 10 times below a sample with polished surface of the same material. Finally, calculate the shear stresses in the threads and verify that these are below the fracture strength of the materials of both the bolt/pin and the flange/box/nut. Adequate formulas for the above control calculations are given in VDI 2230 Blatt 1.
Updated: 07.01.2013
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