Analysis of a shrink-fit failure on a gear hub/shaft assembly
Introduction
A shrink-fit is a semi-permanent assembly system that can resist the relative movement or transmit torque between two components through the creation of high radial pressures at the interface of its constituent parts. It provides a low cost joining method and is widely used in industry, with applications to cutting tool holders, wheels and bands for railway stock, turbine disks, rotors for electric motors and for locating ball and roller bearings. Shrink-fits are also an effective way of assembling machine elements such as a gear to a shaft to transmit torque. The underlying principle involves establishing a pressure between the inside diameter of the gear hub and the outside diameter of a shaft through interference in dimensions at their radial interface. Commonly, expansion of the external part by heating, or cooling of the shaft is employed, the part located and then the whole assembly returned to operating temperature where upon the pressure maintains part location to allow transmission of a torque [1], [2].
Shrink-fits must be properly designed and produced in order to achieve the required functionality in a consistent manner, particularly with reference to the following:
Interference: Reference to standards [3] and/or design guidelines [4] is required in order to determine the optimum interference between the shaft and inner diameter of the gear hub for a given nominal dimension and resultant radial pressure at the interface.
Component dimensions: Very low dimensional variation or precise dimensional control through inspection of the component parts is required.
Surface finish: Surface roughness values should range from 0.4 to 1.6 μm rad in order to provide adequate frictional adhesion between the shaft and hub bore [5], [6].
Working stresses: Stresses due to the shrink-fit pressure and additional stresses when the assembly is in use must not exceed strength of the parts.
Stress concentrations: These are created in the shaft and hub due to the abrupt transition from uncompressed to compressed material [1], [7].
Fretting: Present where the contacting surfaces of mechanical parts are subjected to rubbing and an alternating stress. A shrink-fit assembly carries a torque by virtue of the radial pressure between the two contacting component surfaces, so self-evidently, fretting may occur if the interface pressure is not sufficient to prevent relative circumferential slip between the shaft and the hub. Depending on the magnitude of the slip, both fretting wear and fatigue may be potential causes of premature failure.
Assembly requirements: Component surfaces must be cleaned thoroughly and rapid assembly achieved after component heating/cooling, with the avoidance of misalignment.
The failure under consideration in this paper concerns several of the above, interrelated, items. The influences of interference pressure, component dimensions and applied loads on an apparent fretting failure of a gear hub/shaft shrink-fit assembly is investigated. A mechanistic approach is adopted which, in essence, determines which combinations of the above parameters lead to conditions where subsequent fretting damage is likely, and correlates these predictions to observations made on the failed gear hub/shaft.
Section snippets
Failure details
The research presented in this paper was initiated by a need to determine the cause of a shrink-fit failure on a gear hub/shaft assembly. The gear hub/shaft shrink-fit was contained within a gearbox employed in a large industrial application. After a relatively short working period, the gear proved incapable of transmitting the applied operating torque and had to be removed from service, causing significant financial loss due to prolonged downtime and failure investigation costs. The need to
Solution methodology
This section describes the analytical and finite element models used to determine the likelihood of fretting along the gear hub/shaft assembly. The key mechanistic variable required to assess the likelihood of fretting damage is the magnitude and extent of relative circumferential slip between the hub and shaft, or micro-slip. Predictions of micro-slip are principally made using a novel analytical approach [10], [11], with validations being provided by finite element analysis. The basic
Simulation 1: Standstill analysis
Fig. 2 shows the calculated contact pressure along the gear hub/shaft interface in the standstill condition, i.e., immediately after assembly but prior to the shaft spinning and neglecting any thermal gradients which may be present. This formulation was referred to as the ‘baseline’ case. Three lines are shown. The line labeled ‘Analytical pressure, constant’ represents the constant value of interference pressure determined using Eq. (3) and assuming a constant outer hub diameter of 3.84a. This
Micro-slip assessment using post-failure dimensions, assumed load parameters and measured coefficient of friction
The coefficient of friction is one of the key parameters which influence the extent and magnitude of slip in the gear hub/shaft assembly. The uncertainty of using an assumed friction coefficient was removed by undertaking friction measurements on samples extracted from the failed gear hub and shaft. The value of friction measured was then used in the most severe micro-slip model, i.e., the spinning model. After this analysis, the measured, post-failure internal gear hub diameter (0.00115a
Estimation of torque required to produce observed damage
Finally, the assumption that the shaft was loaded in torsion to a maximum value of T/a3σ0 = 0.14 was relaxed and estimates of the torque required to produce the observed damage were made. The final set of analyses was thus conducted in order to determine the applied torque necessary to produce the extent of damage observed (≈0.75a), and to check for consistency in the earlier results. Fig. 12 shows a graph of predicted slip length versus applied torque for four of the models previously
Conclusions
A series of conclusions concerning the failure of the gear hub/shaft shrink-fit assembly were subsequently drawn after considering the results presented in the previous sections:
- 1.
The gear hub/shaft assembly would not experience significant micro-slip (and subsequent fretting damage) if the original on-assembly dimensions were maintained and the maximum operating torque was restricted to T/a3σ0 = 0.14.
- 2.
The predicted magnitude of relative circumferential slip at the gear hub/shaft interface entrance
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