自动化系统中振动控制吸收器设计的实现外文文献

ScienceDirect Available online at Available online at ScienceDirect Procedia Manufacturing 00 2017 000 000 Paulo Afonso Tel 351 253 510 761 fax 351 253 604 741 E mail address psafonso dps uminho pt 2351 9789 2017 The Authors Published by Elsevier B V Peer review under responsibility of the scientific committee of the Manufacturing Engineering Society International Conference 2017 Procedia Manufacturing 32 2019 578 584 2351 9789 2019 The Authors Published by Elsevier Ltd This is an open access article under the CC BY NC ND license https creativecommons org licenses by nc nd 4 0 Selection and peer review under responsibility of the 12th International Conference Interdisciplinarity in Engineering 10 1016 j promfg 2019 02 255 2019 The Authors Published by Elsevier Ltd This is an open access article under the CC BY NC ND license https creativecommons org licenses by nc nd 4 0 Selection and peer review under responsibility of the 12th International Conference Interdisciplinarity in Engineering Available online at ScienceDirect Procedia Manufacturing 00 2018 000 000 2351 9789 2018 The Authors Published by Elsevier Ltd This is an open access article under the CC BY NC ND license https creativecommons org licenses by nc nd 4 0 Selection and peer review under responsibility of the 12th International Conference Interdisciplinarity in Engineering The 12th International Conference Interdisciplinarity in Engineering Implementation of an Absorber Design for Vibration Control in Automation Systems Timber Yuena 0F Lucian Balana Moein Mehrtasha W Booth School of Engineering Practice Forced Vibrations System Response Resonance Frequencies Vibration Absorbers 1 Introduction Automation equipment in manufacturing often contains rotation components such as motors and pumps For example air pumps are commonly used to generate compressed air to run pneumatic actuators for robot grippers Corresponding author E mail address timber mcmaster ca Available online at ScienceDirect Procedia Manufacturing 00 2018 000 000 2351 9789 2018 The Authors Published by Elsevier Ltd This is an open access article under the CC BY NC ND license https creativecommons org licenses by nc nd 4 0 Selection and peer review under responsibility of the 12th International Conference Interdisciplinarity in Engineering The 12th International Conference Interdisciplinarity in Engineering Implementation of an Absorber Design for Vibration Control in Automation Systems Timber Yuena 0F Lucian Balana Moein Mehrtasha W Booth School of Engineering Practice Forced Vibrations System Response Resonance Frequencies Vibration Absorbers 1 Introduction Automation equipment in manufacturing often contains rotation components such as motors and pumps For example air pumps are commonly used to generate compressed air to run pneumatic actuators for robot grippers Corresponding author E mail address timber mcmaster ca Timber Yuen et al Procedia Manufacturing 32 2019 578 584 579 Typically air pumps are operated at 300 500 RPM When rotating mechanisms are operating at high speeds it is very important that they are balanced If any of the blades or diaphragms has slightly different weight than the others a rotating unbalance will be formed Rotating unbalance occurs when the center of mass of the rotating part does not coincide with the center of rotation Such an out of balance rotation will cause unwanted sinusoidal forcing in machines And mechanical vibration will result The issues of the mechanical vibration on automation equipment are 1 mechanical noise 2 premature failure of components and 3 yield losses in high accuracy production The best way to resolve these issues is to get to the root of the problem by replacing the defective component However at times when it is too difficult to determine the source of vibration vibration control techniques can be employed to reduce the amplitude of the vibration This paper focuses on the design and implementation of passive vibration absorbers for machines with a known vibration frequency close to one of the system resonance frequencies at the vibration modes The benefits and limitations of such vibration absorbers will be discussed as well Nomenclature M Overall mass of the system kg C Overall damping Coefficient of the system Ns m K Overall stiffness of the system N m m Unbalance mass kg R Eccentricity m n System natural frequency rad s Rotational Speed of the Unbalance mass rad s r Frequency ratio n Damping Factor x System Oscillation Amplitude m 1 1 Free Vibration When an external force is applied to a system and then this force is removed the system will undergo Free Vibration Let s just consider the case when the system has some oscillations i e when the damping factor of the system is less than 1 The system response of such a system will typically look like the graph shown in Figure 1a Note that over time the oscillations disappear and the system settles back to the original level Such a system can be modeled as single degree of freedom system Fig 1b and equation 1 can be used to describe the system 1 Fig 1 Free Vibration Response with 1 and One DOF System Model 1 2 Forced Vibration When a single degree of freedom system is subjected to a forcing function input f t Fosin t along the x axis the following differential equation can be used to describe the system 1 580 Timber Yuen et al Procedia Manufacturing 32 2019 578 584 2 For a rotating unbalance with mass m and eccentricity R the amplitude of the input forcing function is 3 Since the transient response of the system disappears quickly over time it is common to consider just the steady state response of the system The steady state response can be expressed as 1 4 The steady state response can also be expressed in an alternative form 1 5 where r is the ratio between the input frequency and the system natural frequency 6 And the steady state magnitude ratio M is often used to study the effects of r on the vibration amplitude 7 A typical graph of Magnitude verses frequency ratio is shown below with 0 1 in Fig 2 a Fig 2 Magnitude and Phase Angle versus Frequency Ratio Graphs One can see clearly that as the frequency ratio increases the magnitude ratio M goes through a peak at r 1 When r 1 the input frequency is identical to one of the system s resonance frequencies the steady state amplitude is at its maximum Figure 2 b above shows how the phase angle between the input and output oscillation versus r looks like when 0 1 Note regardless what is when r 1 the phase angle is always 90 degrees Timber Yuen et al Procedia Manufacturing 32 2019 578 584 581 2 Vibration Absorber Design Vibration absorbers can be designed to control system oscillations if the following two main criteria are met 1 When the excitation frequency is a constant For example when a pump is running at constant speed and it is the cause of system oscillation 2 When the excitation frequency is close to the system natural frequency i e when r is close to 1 A common design of a vibration absorber is shown below in Fig 3 for an exhaust pipe of a vehicle The absorber consists of a mass M2 mounted at the end of a stiffness element K2 and a clamp to mount onto the tail pipe Fig 3 Vibration Absorber on an Exhaust Pipe of a Vehicle To understand why the excitation frequency needs to be close to the system natural frequency to work it is useful to consider the phase angle information between the input and the absorber provided in Fig 4 below Fig 4 Phase Angle between Input and the Absorber Mass 2 1 Experimental Setup To illustrate the implementation of a vibration absorber a vertical cantilever aluminum beam structure has been constructed as the experimental setup A fan powered by a DC powered supply is mounted on the aluminum structure as the input or source of vibration A small clip is added onto one of the fan blades to form a rotating unbalance and to create a sinusoidal input An accelerometer mounted on the top of the aluminum structure is used to collect oscillation data for analysis Fig 5 The Experimental Setup 582 Timber Yuen et al Procedia Manufacturing 32 2019 578 584 3 Experimental Results 3 1 Case 1 Free Vibrations of the System To determine the system natural frequency an initial displacement of around 30 mm along x is applied to the tip of the system and set it into free vibrations System oscillation data is collected and the natural frequency and damping factor calculated The damping factor is calculated using the Log Decrement 1 method commonly used in the industry 8 Fig 6 Free Vibrations of the Experimental Setup Table 1 Free Vibrations Experimental Results Case 1 Case 1 Free Vibrations Natural Frequency fn Hz 2 6 Peak 1 Height X1 mm Peak 2 Height X2 mm Log Decrement 31 74 30 14 0 0517 Damping Factor 0 00823 Since the cantilever beam structure oscillates at 2 6 Hz in free vibration it is expected that mode 1 of system vibration will occur at 2 6 Hz as well Based on Euler Bernoulli beam s theory mode 2 of the system vibration is expected to be at 6 25 times the frequency of mode 1 2 Multiplying 2 6 by 6 25 mode 2 is expected to be at around 16 Hz 3 2 Case 2 Forced Vibrations of the System at 16 Hz To illustrate that passive vibration absorbers can be designed for any mode of vibration of a system as long as the excitation frequency is close to one of the modes the speed of the DC fan in the system is set to rotate at 16 Hz to align with mode 2 of the system resonance frequency Accelerometer data collected were converted into displacement and plotted in the figures below A passive vibration absorber designed for 16 Hz as shown below in Table 2 was mounted onto the system for vibration suppression Table 2 Vibration Absorber Design Absorber Vibration Absorber Natural Frequency 16 Hz Vibration Absorber Mass 0 1 Kg Vibration Absorber Stiffness 1011 N m Timber Yuen et al Procedia Manufacturing 32 2019 578 584 583 In Case 2a the system was excited with the unbalanced fan at 16 Hz without the use of any vibration absorber Then the test is repeated in Case 2b with the vibration absorber As shown in Table 3 below there is a 98 of reduction in vibration amplitude with the vibration absorber attached However it is clear that the vibration could not be completely eliminated by the vibration absorber Fig 7 Forced Response of Experimental Setup 16 Hz Input a No Absorber b with Absorber Table 3 Effects of Vibration Absorber at 16 Hz of Excitation Case 2a No Absorber Case 2b With Absorber designed for 16 Hz Steady State Vibration Amplitude 3 7 mm 0 07 mm Reduction of Amplitude 3 63 mm Reduction of Amplitude 98 3 3 Case 3 Forced Vibrations of the System at 23 Hz One limitation of a passive vibration absorber is that it is only designed for a particular excitation frequency An absorber will only be effective for vibration suppression if the excitation frequency is aligned with or very close to the designed frequency To illustrate this the DC fan was adjusted to generate an input of 23 Hz In Case 3a the system was excited by the 23 Hz input without any vibration absorber In Case 3b the test was repeated with the vibration absorber designed for 16 Hz The graphs below were generated using the experimental data collected Fig 8 Forced Response of Experimental Setup 23 Hz Input a No Absorber b with Absorber designed for 16 Hz 584 Timber Yuen et al Procedia Manufacturing 32 2019 578 584 In Fig 8 a one can see that with the excitation frequency at 23 Hz the system was operating at a frequency ratio of r 1 44 with respect to the natural frequency of 16 Hz of mode 2 The transient response of the system settled quickly over the first 7 seconds to a steady state amplitude of 0 3 mm This steady state amplitude was significantly lower than the 3 7 mm measured at before in Case 2a In Fig 8 b one can see that although the vibration absorber designed for 16 Hz did not cause any stability issues 3 when the excitation was at 23 Hz it caused an increase of 67 in vibration amplitude at steady state Table 4 Effects of Vibration Absorber at 23 Hz of Excitation Case 3a No Absorber Case 3b With Absorber designed for 16 Hz Steady State Vibration Amplitude