12.3Yield Load Controlled Tightening

12.3.1 Introduction

Yield load or gradient controlled tightening techniques are based on the fact that when the yield load of the fastener material is reached, the tightening torque, Mapp ceases to increase linearly with the angle of rotation. That is when,

dM app ceases to be constant, d θ

or equivalently,

[12.3.1]

When this condition is detected, a control system automatically stops the tightening process. Proprietary fastener tightening systems based on this yield controlled tightening are available and they are claimed to reduce the preload scatter to less than ±8%.

Since each fastener is treated as unique by the control system, this technique is largely independent of the factors that contribute to high values of preload scatter when using other assembly methods. However, the method is susceptible to variations in the fastener’s yield stress and stress section area. Variations in the proportions of these stresses, which might as arise due to effects such as variations in friction conditions, can change the value of axial tensile stress at which yield occurs and hence the observed fastener preload. This is examined theoretically in 12.3.2 and12.3.3.

12.3.2 Method of Operation

The basis of the method is an algorithm that accurately detects the occurrence of yield in the fastener. Typical curves illustrating the system characteristics are shown in Figure 12-1 and Figure 12-2. It is seen that the gradient of the torque-rotation curve has a characteristic shape with a peak or plateau followed by a marked reduction in magnitude, to about 20 - 30% of the maximum value. This feature is observed under varying friction conditions and for different joint materials and hardness. The rapid drop in gradient corresponds to the onset of yield and provides the basis on which yield is detected.

From Figure 12-1 it is apparent that the complete torque-rotation curve includes an initial zone of low gradient corresponding to embedding. It is important to eliminate this by tightening the fastener to a predetermined torque before commencing automated measurement of the torque-rotation gradient.

Figure description:

Fastener Tightening Characteristics: Torque, Preload, and Angle Relationship

Applied Tightening Torque and Preload vs. Angle of Rotation

Legend

• TIGHTENING TORQUE — color: black; symbol: Solid line
• PRE-LOAD — color: black; symbol: Hatched area between dashed lines

Annotations

• SCATTER OF FASTENER YIELD LOAD (shaded_area - position: Region where curves plateau and yield)
• PRE-TIGHTENING TORQUE (horizontal_line - position: y-axis (torque constant baseline))
• (dM_app / dtheta = n * (dM_app / dtheta_max (text_label - position: Point on the torque curve indicating specific yield criteria)))
• (dM_app / dtheta_max (text_label - position: Tangent line indicating the maximum slope of the tightening torque curve))

| Angle of Rotation (theta (arbitrary units)) | Applied Tightening Torque (Mtot (arbitrary units)) | Preload Fv - Lower Bound (arbitrary units) | Preload Fv - Upper Bound (arbitrary units) | |:---|:---|:---|:---| | 0 | 0 | 0 | 0 | | 1 | 1 | 5 | 7 | | 2 | 2 (Pre-tightening Level) | 12 | 16 | | 3 | 5 | 35 | 45 | | 4 | 9 | 65 | 80 | | 5 | 11.5 (Yield Region) | 80 | 100 | | 6 | 12.5 (Peak) | 85 | 108 | | 7 | 12.4 | 84 | 107 | | 8 | 12.0 | 80 | 104 |

Notes: This diagram illustrates the torque-angle relationship during the tightening process of a fastener, specifically identifying the yield point and the resulting preload. The pre-tightening torque level is marked as a threshold. The formula shown is a common method for determining the yield point based on the gradient of the torque-angle curve.

Figure 12-1 - Yield Load Controlled Tightening

Figure description:

APPLIED TORQUE / TORQUE GRADIENT vs ANGLE OF ROTATION

Applied Torque and Torque Gradient vs. Angle of Rotation

Legend

• Mapp (Applied Torque — color: black; symbol: solid line
• (dMapp/dθ (Torque Gradient — color: black; symbol: solid line

From this point the control algorithm is as follows:

Figure description:

The image outlines a four-step control algorithm for tightening:

• a. Determine the torque-rotation gradient: $[\frac{dM_{app}}{d\theta}$
• b. Detect and store the maximum value of: $[\frac{dM_{app}}{d\theta}$
• c. Compare current value of $[\frac{dM_{app}}{d\theta}$ with $[\frac{dM_{app}}{d\theta}_{max}$
• d. Cease tightening when: $[\frac{dM_{app}}{d\theta} \leq n [\frac{dM_{app}}{d\theta}_{max}$

A typical range of values for $n$ is 0,5 to 0,7.

12.3.3 Preload Developed in Fastener

For yield controlled tightening the Von Mises Yield criterion is adopted,

where; $\sigma_{y}$ and $\tau$ are the axial and torsional stresses at the smallest cross-section of the fastener respectively, and $\sigma_{y}$ is the axial yield stress of the fastener.

In Equation [12.3.2] the cross-section at which the stresses are computed usually corresponds to the thread minor diameter, $d_{3}$, unless reduced diameter shank fasteners are used, in which case $d_{o}$ is used.

Rearranging Equation [12.3.2] yields,

Thus,

[12.3.4]

where Mth is the thread torque (transmitted by the fastener shank), which from Section 6.4.2 is given by,

[12.3.5]

From Equation [12.3.4] it is clear that the ratio $\sigma_{0.2}/\sigma_{V}$ is always greater than 1, and thus the preload stress developed in a fastener tightened to yield, $\sigma_{V}$, is less than that corresponding to the axial yield stress, $\sigma_{0.2}$.

Since Mth is function of the thread friction coefficient variations in the friction conditions lead to preload scatter. However, assuming lubrication and other factors are controlled, the variation is considerably less than that observed for torque-tightened fasteners.

Significant differences in preload are expected between lubricated and unlubricated fasteners. This is illustrated in Table 12-1 where σ V is calculated for a range of metric fastener sizes and lubrication conditions.

NOTE 1: Assumes θ = 30°; NOTE 2: It is important for MJ fasteners that M8 has p=1,0mm and M10 has p=1,25mm