Nut Threads Research Articles

Friction-Induced Vibration in Lead Screw Systems: Mathematical Modeling and Experimental Studies

Lead screw mechanisms are used to convert rotary to linear motion. The velocity-dependent coefficient of friction at the contact between lead screw and nut threads can lead to self-excited vibrations, which may result in excessive noise generated by the system. In this paper, based on a practical example of a powered automotive seat adjuster, the nonlinear dynamics of lead screw systems is studied. A test setup is developed to perform experiments on the horizontal motion drive. The experimental results are used in a novel two-step identification approach to estimate friction, damping, and stiffness parameters of the system. The identified parameters together with other known system parameters are used in the numerical simulations. The accuracy of the mathematical model is validated by comparing numerical simulation results with actual measurements in cases where limit cycles are developed. Using simulation results for a range of lead screw angular velocities and axial forces, regions of stability were found. Also, the effects of damping and stiffness parameters on the steady-state amplitude of vibration were investigated.

Continuous-Thread Model of Load Distribution and Nut Wear in Grease-Lubricated Lead Screws

Even under constant operating conditions, greases lubricating lead screw assemblies, as well as materials comprising their nut and screw threads, must perform over a range of contact pressures that not only varies from thread to thread but also evolves with the sliding distance as most heavily loaded threads wear most rapidly. An example modeled here, consisting of a nut whose bulk body is rigid and an elastic screw body having continuous elastic meshed threads, reveals the broad distribution of load along the length of the nut threads in an unworn lead screw assembly, as well as the distribution of wear depth that must accompany an eventual steady-state of uniform rate of nut thread wear. Thread load redistributions brought on by changes in operating conditions such as applied load, or even temperature in the case of a nut/screw pair of dissimilar materials, are similarly modeled. Such load redistributions in worn lead screws may cause either the top or the bottom positions of the nut thread to become most heavily loaded, depending on whether an operating condition is increased or decreased. Most importantly, the extent of these redistributions using this continuous thread model can significantly exceed those predicted by an earlier preliminary model where threads were considered as discrete turns and contact pressures could only be described as an average value over each turn. The operating condition changes are shown capable of causing worn threads at either extreme of the nut to become momentarily unloaded and removed from the contact, and this continuous-thread model indicates that even smaller changes in the operating condition can initiate such unloading, as compared to predictions from the discrete-thread model.

Fatigue Crack Growth Analyses of Aerospace Threaded Fasteners—Part III: Experimental Crack Growth Behavior

Abstract Because fatigue crack growth in a threaded fastener can cause the loss of an aircraft, damage tolerant analyses are required. Because designers commonly perform crack growth analyses on stainless steel fasteners with scant data or simplifying assumptions, or both, the objective of this research was to determine the stress intensity multiplication factor (Y) in the threads of a nut loaded, stainless steel, aerospace, roll-threaded bolt under tensile fatigue conditions as the nondimensionalized crack depth (a/d) approaches zero. Y(a/d) can then be used to improve the accuracy of fatigue crack growth life estimations. Unflawed and flawed aerospace bolts were fatigue tested at a maximum stress (S) ranging from the ultimate tensile strength (UTS) to the surface endurance limit of the test bolt and at several loading ratios of 0.1⩽R⩽0.9. Data collection from the fracture surfaces yielded crack front shape characterization and striation spacing. The shape of the crack front in the unflawed and flawed test bolts was different and both changed as the crack grew. Fifty-one striation spacing measurements ranging from 5.6×10−5 to 7.9×10−4 mm were found at crack depths of a/d>0.035. These striation measurements were directly related to crack growth rates so that stress intensity factor ranges (ΔK) and in turn Y(a/d) could be estimated.

A Study of Self-Loosening of Bolted Joints Due to Repetition of Small Amount of Slippage at Bearing Surface

This paper deals with the mechanism and relating matters on self-loosening rotation of bolted joints in the cases when very small slippages occur repeatedly at bearing surfaces under transverse loads. It can be supposed that accumulation of this kind of loosening finally produces serious states for bolted joints. Based on an assumption that a restoring force caused by an elastic torsion of a bolt shank which arises from a relative displacement between bolt and nut threads drives loosening rotation, a theoretical explanation is presented about how loosening rotation occurs and grows larger. Experiments in quasi-static states show results which agree with the theory of this paper. Additionally, consumption of transverse work and anti-loosening performance being taken up as relating subjects, more information about self-loosening is shown through examinations on some kinds of test samples.

Coupled Evolution of Load Distribution and Wear on Grease-Lubricated Lead Screw Threads

Even under constant operating conditions, greases lubricating lead screw assemblies, as well as materials comprising their nut and screw threads, must perform over a range of contact pressures that not only varies from thread-to-thread, but also evolves with the sliding distance as the most-heavily loaded threads wear most rapidly. An example modeled here, consisting of a rigid nut and elastic screw body having flexible meshed thread pairs, describes a broad distribution of loads thread-to-thread on a new lead screw assembly that gradually evolves towards uniformity as the coupled consideration of thread loading and wear depth approaches a steady-state of equal rates of thread wear. Thread load redistributions brought on by changes in the operating conditions such as applied load, or even temperature in the case of a nut/screw pair of dissimilar materials, are similarly modeled. Such load redistributions in pre-worn lead screws may cause either the top or the bottom nut threads to become most heavily loaded, depending on whether an operating condition is increased or decreased. Sufficiently large magnitudes of such operating condition change are shown to cause pre-worn threads at either extreme of the nut to become momentarily unloaded and removed from contact. Review led by Al Segall

Study of the Effect of Hole Clearance and Thread Fit on the Self-Loosening of Threaded Fasteners

This study provides an experimental and theoretical investigation of the effect of hole clearance and thread fit on the self-loosening of tightened threaded fasteners that are subjected to a cyclic transverse service load. An experimental procedure and test setup are developed in order to collect real-time data on the rate of clamp load loss per cycle as well as the loosening rotation of the bolt head. Three levels of hole clearance are investigated; namely, 3%, 6%, and 10% of the bolt nominal diameter. For the commonly used 2A thread fit for a selected bolt size, three classes of the nut thread fit are considered; namely, 1B, 2B, and 3B. A simplified mathematical model is used for the analytical investigation of the effect of the hole clearance and thread fit on threaded fasteners self-loosening. The experimental and theoretical results are presented and discussed.

Influence of Two Hexavalent Chromium-Free Coating types on Mechanical Behavior of Bolted Joints

Abstract The goal of this work is to evaluate the performance of two different coating technologies for bolts. They are based on zinc and aluminum with no hexavalent chromium in their composition. These technologies were implemented because international laws for environmental and human health protection are limiting the use of the hexavalent form of chromium because it causes different cancer types in workers, mainly in recycling processes. The experimental tests were performed using M12x1.25–10.9 bolts that were submitted to the test of torsion-tension. The clamping load, total torque, torque on thread, torque on the bolt head, and twist angle were measured. The friction coefficients between the nut and bolt threads, between the face of the nut and its bearing surface, the global coefficients of friction, and the nut factor were also measured and analyzed.

Investigation into the Effect of the Nut Thread Run-Out on the Stress Distribution in a Bolt Using the Finite Element Method

By means of comparing results from finite element analysis and photoelasticity, the salient characteristics of a finite element model of a nut and bolt have been established. A number of two-dimensional and three-dimensional models were created with varying levels of complexity, and the results were compared with photoelastic results. It was found that both two-dimensional and three-dimensional models could produce accurate results provided the nut thread run-out and friction were modeled accurately. When using two-dimensional models, a number of models representing different positions around the helix of the thread were created to obtain more data for the stress distribution. This approach was found to work well and to be economical.

ボルト・ナット結合体のゆるみに関する研究（第３報）―作用荷重が小さい場合のボルト・ナットの変形量を考慮した検討―

Bolt nut units sometimes loosen due to a rotation of the screw thread under repeated axial loading. In the previous paper, the authors demonstrated that the self-loosening was caused by a relative slip between the expanded nut threads and the contracted bolt threads. In addition, it was shown that a tendency of the numerical results on the thread loosening showed good agreement with the experimental results. However, , the estimated values were not well agreed with the experimental values since the load distributions at the engaged screw thread were assumed to be uniform.In the previous paper, an amouunt of the loosening angle was measured by a microscope. In this paper, an amount of the loosening angle could be measured continuously by using an electric micrometer. In addition, by measuring the friction coefficients of the screw thread and the bearing surfaces an estimation whether loosening angle is occurred or not is made. As a result, it is shown that the estimated loosening angle of screw thread, taking the load distribution at the engaged screw threads in an initial clamping state and the bolt and nut deformations into consideration, are fairly consistent with the experimental results.

Finite Element Analysis Of Thread Stripping Of A Threaded Assembly

In this paper, we study the nut thread stripping of a loaded threaded assembly by using finite element modeling and a criterion of damage. The aim is to envisage the appearance of the macroscopic fissure which characterizes the beginning of stripping. We compare that result with those obtained by tests and other formulations existing in the literature. We carried out tests of stripping of threads. The threaded assembly is composed of an M10 bolt and a round nut of which we will vary the height. The materials used are steel class 12.9 for the bolt, copper and the AU4G for the nuts. In this work, we considered that the material presents an irreversible damage just before the macroscopic fissure occurs. We used the expression suggested by LEMAITRE and CHABOCHE in their theory of the damage in mechanics of the continuous mediums, for the calculation of the plastic deformation due to rupture. By using the results of simulation given by ABAQUS for various levels of load, we calculated the maximum plastic deformation due to the rupture at the place considered as being deformed the most. We carried out an analysis that represents in a satisfactory way the reality of the phenomenon of thread stripping of a nut screwed in an M10 bolt. We validated this model by carrying out tests of thread stripping for various materials. The results obtained by our model, are very close to those obtained by the tests and not very far away from the other authors. This is of great importance for the continuation of our work because this model should enable us to envisage the behavior of all possible couples of ductile metallic materials without having to use to systematic tests.

Tension Control Bolts: Strength and Installation

Tension control bolts are a type of alternative design fastener, permitted by the Research Council on Structural Connections. The bolt has a splined end that extends beyond the threaded portion of the bolt and an annular groove between the threaded portion of the bolt and the splined end. The special wrench required to install these bolts has two coaxial chucks—an inner chuck that engages the splined end and an outer chuck that envelopes the nut. The two chucks turn opposite to one another to tighten the bolt. At some point, the torque developed by the friction between the nut and bolt threads and at the nut-washer interface equals the shear resistance of the bolt material at the annual groove. The splined end of the bolt then shears off at the groove. If the system has been properly manufactured and calibrated, bolt pretension is achieved at this point. Factors that control the pretension are material strength, thread conditions, the diameter of the splined end, and the surface conditions at the nut-washer-joint interface. The program reported here investigated the pretension of production tension control bolts as it varies from manufacturer to manufacturer and under different aging, weathering, and thread conditions.

Stiffness of a Ball Screw Including with Consideration to Deformation of the Screw, Nut and Screw Thread. 4th Report, Effect of Preloading Method and Load Condition.

The axial stiffness of a preloaded double nut is examined for preloading styles, preloading methods and various states of externally applied load. The axial stiffness under constant preloading (small value of spacing disc rigidity) separates into two groups following the direction of the external load regardless of other conditions. When the external load acts towards the preload relief, the stiffness decreases rapidly and the preload is lost just after the external force arrives at the preload value. Under the fixed position of preloading (large value of spacing disc rigidity), the stiffness varies following preloading conditions and external load positions. The maximum stiffness is obtained under the conditions of tension or compression in both the screw shaft and nuts, and the external force acts on the other side nut against the screw shaft on the supporting side. When the length of the screw shaft between double nuts becomes longer, the stiffness difference due to external load combination becomes larger as the spacing disc rigidity increases. The experimental values obtained under two representative external load conditions are slightly different from the calculated values, but their magnitude and behavior against the external load show a similar tendency.

Stiffness of a Ball Screw Including with Consideration to Deformation of the Screw, Nut and Screw Thread. 3rd Report, Effect of Contact Angle Change.

The contact angle between the ball and thread groove in ball screws changes following the Hertzian contact deformation and elastic deformation of the thread. Hence, how the contact angle changes with the axial load is calculated, and the effect of it both on load distribution in the screw thread and on axial stiffness is examined for the single nut and the preloaded double nut. An increase in contact angle of some 2° is calculated under basic dynamic load rating. The nonuniformity of load distribution is not influenced by the contact angle change. However, the normal load of a ball at a contact point between the ball and thread groove decreases slightly. The axial stiffness of the ball screws, consequently, rises as the contact angle increases. The measured values of axial displacement are in approximate agreement with the calculated results.

セラミック製空気静圧送りねじの開発

An air bearing lead screw and nut have been developed for application to ultra-precise positioning over long strokes. The design features are : (1) Porous restrictors made of ceramic materials with surface plating are applied to the flanks of the nut threads. (2) The thread profile is square to improve its machining accuracy and this minimizes bearing clearance. Performances of the air bearing lead screw and nut were examined with a fully air-lubricated one-dimensional linear table. Primary results for a lead screw with a nominal diameter of 25mm are : (1) The axial stiffness is over 30N/μm with 0.5 MPa supply pressure. (2) Precision of the nut linear motion is evaluated to be 5 nm. (3) Lead accuracy is improved more than 10 times compared to the machining accuracy of lead screws. These results demonstrate that the air bearing lead screw and nut is a practical approach for micropositioning with ultra-fine accuracy.

Stiffness of a ball screw including with consideration to deformation of the screw, nut and screw thread. (2nd Report, Preloaded double nuts).

The stiffness in the axial direction a preloaded ball screw constructed from a double nut is calculated considering the elastic deformation of the screw shaft, the nut itself, and the screw thread, in addition to deformation due to Hertzian contact. The basic equations derived here could be applied in many cases to preloading methods and the various states of an externally applied load. Moreover, the calculation can be carried out both for single and double circuit nuts. The calculated stiffness is low compared with the one obtained when Hertzian contact alone is considered. The difference between the two calculated values becomes large as the spacing disc rigidity increases. The externally applied load which releases a preload decreases at a higher rigidity of the spacing disc than the one calculated according to Hertzian contact. The calculated values of both the stiffness and the releasing load approximately agree with the experimental results.

Stiffness of a ball screw including the deformation of screw, nut and screw thread. 1st report. Single nut.

The stiffness of a ball screw is dominated roughly be Heatzian contact between the balls and the guiding grooves. However, the calculated values are always higher compared with experimental values. hence, to derive more exact values, the elastic deformation of the screw shaft, the nut itself and screw thread are taken up in addition to the deformation due to Hertzian contact. The load distribution in a ball screw is also examined. The load distribution changes with the load condition of the screw and the row number of thread turn. However, nonuniformity of the load distribution is not so remarkable. The deformation of a screw thread has a slight influence on the load distribution, but it gives a certain effect on the stiffness. The stiffness obtained here approaches experimental values compared with the values based on Hertzian contact.

Stress analysis of some nut-bolt connections with modifications to the external shape of the nut

The effect on the stress levels in an axially loaded bolt has been investigated for the case where a nut which incorporated a circumferential groove in its outer surface was used. It was found from a three-dimensional photoelastic frozen stress study that the modified nut reduced the maximum stress in the bolt by 5 per cent. The addition of a bevel to the load bearing face of this nut further reduced the maximum stress to 74 per cent of its value in a standard connection. It has been established that these modifications reduce the maximum shear stress in the roots of the nut threads, and that the stress concentration associated with the groove was smaller than the maximum stress concentration in both the nut and bolt thread roots. The increase indicated by photoelastic analyses in the strength of the connection produced by these modifications, has also been substantiated by fatigue tests of steel connections, but these results are not reported in this paper.

Stress in bolt and nut (Effects of contact condition at the first ridge)

Effects of the contact condition at the first ridge on mechanical behaviors of threaded portions are analysed by an axi-symmetric FEM which can deal with the three-body elastic contact problem including the effects of friction on two contact surfaces between threads of bolt and nut, and between fastened plate and nut. Since the cross sectional shape of nut at the first ridge changes circumferentially due to the lead angle of thread, it causes non-symmetric mechanical behaviors concerning the ratio of flank load and the stress concentration at the root of bolt. Four types of models are used to estimate these non-symmetric properties approximately. Each of them represents the cross section rotated one fourth revolution around the axis. The analytical object is composed of bolt, nut and fastened plate, and only the shape of nut is changed. The analysis is done by the axi-symmetric FEM ignoring the effects of lead angle. The ratio of flank load and the stress concentration at each cross section show some remarkable effects of the non-symmetric behaviors.

Stresses in Bolt and Nut : Effects of Contact Conditions at the First Ridge

Effects of the contact condition at the first ridge on mechanical behaviors of threaded portions were analysed using an axi-symmetric FEM which is appropriate for the three-body elastic contact problem including the effects of friction on two contact surfaces between threads of bolt and nut, and between fastened plate and nut. The cross sectional shape of nut at the first ridge changes circumferentially due to the lead angle of thread, which causes non-symmetric mechanical behaviors concerning the ratio of flank loads and the stress concentration at the root of bolt. Four types of models were used to estimate these non-symmetric behaviors approximately. Each of them represents the cross section rotated one fourth revolution around axis. The analytical members are bolt, nut and fastened plate, and only the shape of nut is changed. The analysis is done by the axi-symmetric FEM without considering the effects of lead angle. The ratio of flank loads and the stress concentration at each cross section show some remarkable effects of the non-symmetric behaviors.

Load and stress distribution in screw threads

The load distribution and the normalized stress distribution in the threads of an ISO metric nut and bolt were found by frozen-stress photoelastic analysis employing a fringe-multiplying polariscope in conjunction with a recording microdensitometer. Previous investigators assumed that these distributions were identical, whereas the present study shows that this is not the case. It has been further shown that deducing the load distribution from measurements of the nut deformation is unsatisfactory. The results of the reported method correlate closely with Sopwith's theoretical load distribution. Three recent finite-element analyses of nut-bolt systems have been compared indirectly to the experimental load distribution. That of Bretl and Cook was found to give the best comparison.