S.J. Drew

The measurement of forces in grinding in the presence of vibration

Most investigations of chatter have made the assumption that torsional vibration is not a significant factor. Some recent work has shown that chatter in grinding is affected by a change in the torsional stiffness of the workpiece drive. Also, a theoretical model of grinding chatter has been developed that confirmed the significance of torsional effects. However, the model for the grinding force was assumed to be a dynamic equivalent of a published steady-state model. This paper describes tests conducted to measure the variation in force caused by an oscillation in workpiece speed. The oscillating test results indicate that the torsional vibration of the workpiece may well be a significant effect on chatter in grinding. Moreover, as the grinding force changes with workpiece speed, it may be possible to use variation of workpiece speed at high frequency to reduce chatter.

An investigation of in-process measurement of ground surfaces in the presence of vibration

Recent work on chatter in grinding has shown that the presence of torsional vibration is potentially significant. Controlling the torsional characteristics of the workpiece drive may eliminate chatter. These findings lead to a re-examination of the fundamental grinding force equation, where the surface speeds are conventionally assumed to be constant. If torsional vibration is present for both the grinding wheel and the workpiece, there will be two extra terms in the grinding force equation. Traditionally, experimental measurements used to try and verify the cutting force model have been undertaken under non-vibrating conditions. Any attempt to verify a cutting force model under vibrating conditions requires the continuous measurement of several parameters as a function of time. One of these is the instantaneous depth of cut, δ. This paper presents experimental results for an investigation into the in-process measurement of δ under chatter conditions on a cylindrical grinding machine. This initial investigation has indicated that such a measurement is very difficult and is prone to errors if chatter is present. It is proposed and anticipated that controlled (vibration) excitation under inherently stable conditions will allow for the required measurements to be made with sufficient accuracy.

Torsional vibration effects in grinding

Abstract The vast majority of models of vibration in grinding assume that there are no torsional vibration effects. In a recent doctoral study, it was found possible to eliminate grinding chatter by changing the torsional stiffness of the workpiece drive. In that study, a frequency domain model for the grinding process was developed that included torsional effects. It was concluded that for the assumed grinding force model, chatter could be influenced by the torsional characteristics of both the workpiece and wheel systems. This paper describes experiments conducted to determine how the grinding force varies with oscillating workpiece speed and oscillating chip thickness. It concludes with the description of a time domain model of the grinding process that includes a force model consistent with the experimental force measurements.

Torsional vibration of a back-to-back gearbox rig Part 2: Time domain modelling and verification

Abstract The torsional vibration of a back-to-back gearbox system has been simulated in the time domain, using time domain receptance theory. Receptance analysis in the time domain is an extension of the frequency domain method and allows the benefits of a systems approach for modelling complicated systems. Meshing spur gears represent a complicated dynamic system. The excitation from the variation in gear mesh stiffness has been considered in the present model. A gear mesh kinematic simulation was developed to simulate the contact pattern and mesh stiffness for a spur gear pair with a contact ratio of less than 2.0. The time domain receptance model was verified using a simulated white noise input to generate frequency response functions up to 1600 Hz. The simulated torsional natural frequencies were compared with the experimentally measured results in Part 1 [1]. After the adjustment of model parameters, the first eight torsional natural frequencies were accurately matched by the predictions of the time domain model. The simulated frequency response functions of the time domain model accurately matched the frequency response functions from the frequency domain receptance model presented in Part 1 [1].

Torsional vibration of a back-to-back gearbox rig Part 1: Frequency domain modal analysis

Abstract The torsional vibration of a back-to-back gearbox system has been investigated experimentally and analytically. Gearboxes are typically part of a larger system, or drivetrain, which commonly includes electric motors, shafts, couplings, ball mills, turbines and generators. The dynamics of the system has been shown significantly to influence the gearbox response and requires inclusion in gearbox modelling. Assumptions are commonly made, however, to reduce the degrees of freedom of the model, and system dynamics is subsequently neglected. Receptance methods were applied to model a back-to-back gearbox system and were shown to be an effective modelling technique for geared system analysis. A detailed experimental modal analysis was performed using the swept-sine technique with an a.c. servomotor torsional exciter. Torsional excitation allowed for the dynamic response to be measured up to 1600 Hz. A multi-degree-of-freedom, frequency domain torsional model of the gearbox system was developed using receptances. The model included a combination of lumped-mass elements, and continuous shafts with distributed inertia and hysteretic damping. The modelled torsional natural frequencies were matched to the measured frequencies by the adjustment of system model parameters to achieve a high level of agreement. Matching of system natural frequencies resulted in the accurate prediction of the first nine associated torsional deflected shapes up to 1548 Hz. This paper presents the detailed results of a full torsional, modal analysis of a gearbox system, demonstrating receptance system modelling and an effective method for torsional excitation on rotating machines.

Torsional damping of a back-to-back gearbox rig: Experimental measurements and frequency domain modelling

Abstract This paper is concerned with the experimental measurement and modelling of the torsional damping levels of a back-to-back gearbox rig. The aims of the investigation were to experimentally measure and analyse modal damping levels for the first nine torsional natural frequencies; to optimize damping parameters for modelling and to assess any limitations of the models for future work. Standard signal processing methods were used to determine modal damping levels from measured torsional frequency responses, with good confidence in the results. A damping sensitivity analysis for the two frequency domain receptance (FDR) models was used to determine optimum damping parameter values. Damping levels for six of nine natural frequencies were well matched with the experimental data. Discrepancies at other frequencies were attributed mainly to torsional-transverse coupling, present in the rig but not the model. Analysis of results for the ninth natural frequency determined a very low level of damping for the gearbox. It was also concluded that the model parameters may be used with confidence in a time domain receptance model for future investigations related to the test gearbox damping.

Coupled Torsional and Transverse Vibration of a Back-to-Back Gearbox Rig

Abstract The coupled torsional and transverse vibration of a back-to-back gearbox system has been investigated experimentally and analytically. Receptance methods were used to model the system, and were shown to be effective. A detailed experimental modal analysis was performed using the swept-sine technique with an a.c. servomotor torsional exciter. Torsional excitation allowed for the dynamic response to be measured up to 1600 Hz. The model included a combination of lumped mass elements and continuous shafts with distributed inertia and damping. The bearings were modelled as having both radial and tilt stiffness and damping elements. The model simulated the experimental results well and predicted each of the first 11 natural frequencies to within 8 per cent. Of the 11 natural frequencies, 9 simulated deflected shapes matched very well, validating the modelling approach taken for the project together with the assumptions made in the derivation of the model. This paper presents the detailed results of a full torsional/transverse model analysis of the gearbox system.