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Accurate transmission performance evaluation of servo-mechanisms for robots

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Highlights

  • Methods employed to assess the performance of modern servo-mechanisms are reported.

  • Practical guidelines for improving the measurements quality are proposed.

  • The effect of oil temperature and input speed on the reducer is assessed.

  • A model of the reducer transmission error is derived from the measured data.

Abstract

The Servo-Mechanisms (SMs) mounted in industrial robots joints are a major source of positioning accuracy errors. To improve robots precision performance, researchers have been focusing on the development of novel SMs design and control strategies, which need extensive experimental analyses to tune their parameters. In this context, the scope of this paper is double: first, to present the novel experimental apparatus and methods designed to improve the accuracy of the transmission performance evaluation of high dynamics SMs and, secondly, to report and discuss the achieved experimental results. In the first part, a description of the test rig tuning operations is given, primarily focusing on the signals synchronization and on the elimination of the measuring errors caused by the mechanical transmission elasticity and the servomotor torque ripples. Then, control strategies for compensating the torque ripples and input speed errors are defined. It is shown that speed oscillations can be reduced of 70% when rotating the servomotor up to 2000 rpm, improving the measurement quality of the reducer performance. In the second part, a set of experiments is carried out to assess the combined effect of input speed and lubricant temperature on the reducer behavior. The system sensitivity to the variation of the input parameters is confirmed by the dynamic lost motion curves, whose mean value equals 16.8 and 35.4 when the reducer is operated at its minimum and maximum friction load respectively. At last, the extrapolated harmonic content is used to build a simple mathematical model of the reducer transmission error.

Introduction

In the last years, to comply with the growing demand of modern markets, Industrial Robots (IRs) have become the central elements of many automated production plants owing to their high operational effectiveness, large degree of flexibility and extended workspace [1], [2]. To perform precise operations, ensure a high quality of the manufactured parts and reduce the waste of material, much attention has been recently placed on the IRs positioning performance [3], [4], [5], [6], [7], [8]. This is primarily governed by the Servo-Mechanisms (SMs) embedded in the robots joints, consisting of a servomotor and a speed reducer [2], [9]. The major problems with the servomotors and related drive systems are: (i) curve tracking error [10], [11], (ii) unmodeled high order electromechanical effects [12] and (iii) torque ripples [13]. The first can partially be addressed by implementing adaptive control laws [14], whereas the remaining ones require the definition of proper compensation strategies [15]. From the control point of view, one must also deal with the nonlinearities introduced by the gear transmission [16]. Among the existing classes available in the market (see [17] for a review), cycloidal reducers are getting much more attention from IR manufacturers due to their compact size and higher robustness. The most used option, named Rotate Vector (RV) reducer, is a two stages solution consisting of a planetary gear followed by a cycloid-pin gear [18]. Both stages cause undesired hysteretic behavior as a result of the transmission backlash and compliance [19], [20]. The so-called “double valued nonlinearity” originated from the backlash directly affects the robot accuracy and creates important control challenges [21]. The combined effect of backlash and compliance is evaluated through the Transmission Error (TE) and the Lost Motion (LM) [22], [23], i.e. the industry-accepted standard performance indexes for the reducers accuracy. It should be noted that well-behaved reducers would present minimum (ideally null) values of TE and LM.

To overcome the above discussed SMs limitations, previous studies have been focused on the redesign of the reducer internal parts (e.g. tooth shape optimization [24], [25], [26] and machining/assembly tolerances correction [27], [28]), the implementation of load-side feedback sensors [29] or the definition of model-based feedforward compensations [30], [31]. The first approach has led to a number of promising design concepts. The proposed solutions, actually tested on research lab prototypes, support the development of new reducers but cannot be applied to the existent industrial plants as each IR would need to be disassembled to enable parts substitution. The second approach is simple and intuitive but, similarly to the first one, it would raise the plant setup time and cost considerably. The latter approach is less expensive during the implementation phase even though, for definition, it necessarily requires the development of high fidelity behavioral models. Previous research works have formulated either theoretical [32], [33], [34] or simulation-based [35], [36] models capable of capturing the reducers nonlinearities. However, the inherent complexity of the reducer assembly and the rather limited availability of detailed drawings (tolerances and installation aspects, normally hidden from vendors) make it difficult to develop exact correlations between geometric/functional parameters and output performance. A crucial point, usually missed in merely kinematic analyses, is the lubrication state of the transmission [26], [37]. In fact, the RV reducers case is filled with great amount of lubricant (accurately chosen and specified by manufacturers), which aids in reducing parts wear but also introduces non-negligible speed and temperature dependent viscous friction effects that impact the TE [38].

For a deep understanding of the RV reducer dynamics, experimental campaigns become essential, also in view of determining accurate empirical models which can be readily exploited for compensation purposes. The transmission performance of precision reducers has been already tested, investigating the influence of speed [39], external load [22] and state of degradation [40]. Other studies have defined practical strategies for compensating manufacturing and assembly errors of the measuring system [41], [42], [43]. The referenced works have provided valuable standards and metrics for the performance testing of precision reducers, though a series of important aspects have not been yet sufficiently discussed. First of all, these works lack of accurate descriptions regarding the adopted measuring methods and tools. There is no mention of the rig tuning process, and the speed state at the reducer input side is claimed constant because the servomotor is controlled in speed mode. However, this may not be always the case since proper actions must be taken to suppress the servomotor disturbs and avoid the shaft vibrations [44]. These phenomena strongly compromise the TE measurement and deserve consideration. Other research gaps can be noticed in terms of parameters selection and results interpretation. For example, the influence of lubricant temperature on the reducer behavior is not appropriately documented neither in previous studies nor in product catalogs. Even so, the relevant impact of such parameter on the performance of heavy duty IRs has been shown experimentally in [45].

Based on these considerations, the novel contributions of this paper are as follows:

  • To provide a detailed description of the instrumentation and experimental methods employed to assess the SMs performance.

  • To report practical guidelines and compensation approaches for stabilizing the reducer input speed and thus extending the measurement accuracy.

  • To quantitatively assess the effect of the lubricant temperature and input speed on the reducer behavior.

The extrapolated data will support the validation of existing methods and tools aimed at optimizing the SMs performance [46], and the development of new kinematic compensation models.

The remaining of the paper is structured as follows: Section 2 describes the utilized experimental equipment, Section 3 deals with the rig performance identification and tuning, whereas Section 4 reports the RV reducer experimental results. The concluding remarks are given in Section 5.

Section snippets

Experimental setup

This section provides a detailed description of the test equipment utilized for the experimental characterization of industrial SMs.

Input transmission elasticity

IRs present compact and highly integrated SMs where the reducer is directly keyed on the servomotor shaft. On the other hand, the mechanical transmission typically seen in testing platforms comprises additional elements, namely a strain gauge torquemeter and a multi-plate coupling. Compared to the servomotor shaft and the reducer input shaft, such elements have relatively low torsional stiffness. Fig. 4 shows a simplified lumped parameters model of the system consisting of two inertias

RV reducer experimental analysis

This section discusses the results of the experimental campaign, carried out after the rig tuning process, with the aim of characterizing the RV reducer performance. The main value of interest is the reducer TE function [22], defined as: TE(θ)=θoutθinτAs discussed earlier, to exclude unwanted effects from the TE evaluation, e.g. the torsional compliance of the input transmission, θin and θout are directly read at the input and output side of the RV reducer. The TE is measured during forward

Conclusions

This paper reports about the performance evaluation of SMs employed in modern IRs. It has been conceived to reach a double scope: (i) to present in details the developed measuring system and methods, and (ii) to share and discuss the results achieved during the first experimental campaign. Hence, the first part of the work focuses on the description of the employed hardware and software tools, with particular emphasis placed on the data synchronization and on the effects introduced by the input

Declaration of Competing Interest

No author associated with this paper has disclosed any potential or pertinent conflicts which may be perceived to have impending conflict with this work. For full disclosure statements refer to https://doi.org/10.1016/j.rcim.2022.102400.

Funding sources

This research was funded by the European Community’s HORIZON 2020 programme under grant agreement No. 958303 (PENELOPE).

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