Stiffness and damping model of bolted joint based on the modified three-dimensional fractal topography

Advances in Mechanical Engineering

Cheng

et al. 2018

Self Cite

Joint flexibility has a major impact on the motion accuracy of a robotic end effector, particularly at high speeds. This work proposes a technique of precisely modeling the torsional stiffness of the rotational joints for the industrial robots. This technique considers the contacts that exist in the joint system, which can have a significant effect on the overall joint stiffness. The torsional stiffness of the connections that commonly exist in the rotational joints, such as the belt connection, the connections using key, bolts, and pins, were modeled by combining the force analysis and the fractal theory. Through modeling the equivalent stiffness for the springs in serial and in parallel, the torsional stiffness of all joints for the ER3A-C60 robot were calculated and analyzed. The results show that the estimated stiffness based on the proposed technique is closer to the actual values than that based on the previous model without considering the contacts. The analysis is useful for controlling the dynamic characteristic of the industrial robots with the rotational joints while planning the trajectory for the end effector.

“…These calculations are not the focus of this work; however, a more detailed explanation of the computing processes can be found in Zhao et al 27 Torsional stiffness for contacts…”

Section: Fractal Contact Stiffnessmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Rotation-joint stiffness modeling for industrial robots considering contacts

Advances in Mechanical Engineering

Cheng

et al. 2018

Self Cite

“…According to the fractal theory proposed in Zhao et al, 9 the pressure, the normal stiffness, and the tangential stiffness are all directly related to the largest area of one asperity. These relationships are defined as follows:…”

Section: Calculation Of Radial and Torsional Stiffnessmentioning

confidence: 99%

“…4 Majumdar and Bhushan 5 presented a classical M-B fractal theory to analyze the contact mechanism of two rough surfaces, in which the contact status is assumed as the contact between a rough surface and a rigid surface. This model was modified by other scholars [6][7][8][9] to reduce the difference between the numerical simulation and the experimental results. Zhao and Xu 9 presented a modified three-dimensional fractal theory to build the contact stiffness and damping models of joint.…”

Section: Introductionmentioning

confidence: 99%

Stiffness optimization for high-speed double-locking toolholder-spindle joint using fractal theory

Proceedings of the Institution of Mechanical Engineers, Part E:

Zhao

et al. 2017

Self Cite

The higher contact stiffness of the double-locking toolholder-spindle (BTF40-type) joint is helpful in improving the machining accuracy and cutting stability of high-speed machining center. In this article, an optimization technique is introduced to obtain the high contact stiffness of BTF40 toolholder-spindle joint at the high speed. The torsional and radial stiffness at 25,000 r/min can be obtained by using the macro-micro hybrid method. The contact ratio of taper surface and maximum nodal pressure of contact surfaces is used as constraint conditions to ensure the connection reliability and the working life of the toolholder-spindle system. The particle swarm optimization algorithm with suitable parameters for this problem is used to search the optimal stiffness of joint automatically. The optimal stiffness of joint and pressure distribution of taper surface are compared with the initial values for validating the effectiveness of the optimization results. This research is valuable for guiding the application of BTF-type toolholder-spindle system at the high speed 25,000 r/min.

“…And it is emphasized that every machined tooth surface shall be smooth on the macrolevel and rough in the microscale. To get an accurate and valid method to calculate the mesh stiffness, the Weierstrass-Mandelbort (W-M) [17][18][19] function is employed here to express the surface characters and M-B 20,21 contact model and finite element method (FEM) have been combined to calculate the local contact stiffness K h and total mesh stiffness K of the spur gear. The paper will not only focus on the model of mesh stiffness but also on the changing rule of the mesh stiffness influenced by the fractal dimension, roughness parameter, and input torque.…”

Section: Introductionmentioning

confidence: 99%

Time-varying stiffness model of spur gear considering the effect of surface morphology characteristics

Proceedings of the Institution of Mechanical Engineers, Part E:

Zhang

Zhao

et al. 2018

Self Cite

The nonuniform cantilever beam and Hertzian contact model have been widely used to derive the mesh stiffness of spur gear assuming that the contact surface is absolutely frictionless. However, studies have confirmed that machined surfaces are rough in microscale and can be simulated by the Weierstrass–Mandelbort function. In order to get a reasonable and precise mesh stiffness model, the M-B contact model and finite element method are combined to express the local contact stiffness Kh. Through the simulation and comparison, the analytical finite element method is proved to be consistent with the traditional models and introduces the roughness parameters of machined tooth surface into the meshing process. Furthermore, the results also show that it is advantageous to improve the total mesh stiffness by increasing the fractal dimension D and input torque T as well as decreasing the roughness parameter G. In this paper, a relationship is built between the total mesh stiffness of gear sets with tooth surface characters and input torque, which can be a guidance in the design of the tooth surface parameters and the choice of the processing method in the future.