CN113722891A - Harmonic reducer transmission system torsional rigidity fitting method - Google Patents

Harmonic reducer transmission system torsional rigidity fitting method Download PDF

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Publication number
CN113722891A
CN113722891A CN202110911816.XA CN202110911816A CN113722891A CN 113722891 A CN113722891 A CN 113722891A CN 202110911816 A CN202110911816 A CN 202110911816A CN 113722891 A CN113722891 A CN 113722891A
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torsional rigidity
model
harmonic gear
torque
torsional
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杨聪彬
张雪洋
赵永胜
刘志峰
初红艳
张彩霞
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Beijing University of Technology
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Beijing University of Technology
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
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    • G06F30/17—Mechanical parametric or variational design

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Abstract

The invention discloses a torsional rigidity fitting method of a harmonic gear transmission system, which aims at the problems that the expression of the traditional torsional rigidity model of harmonic gear transmission is complex and mutton is symmetrical, otherwise, the invention improves the torsional rigidity model as follows: the invention describes the nonlinearity of the torsional rigidity by using cubic Taylor series expansion, and describes the hysteresis characteristic of the torsional rigidity by using a hyperbolic function to obtain the relation between the torque T and the torsional angle. The torsional rigidity model established by the method ensures higher fitting precision, and parameters in the model are easy to identify.

Description

Harmonic reducer transmission system torsional rigidity fitting method
Technical Field
The invention belongs to the technical field of dynamic characteristics of harmonic gear transmission systems, and particularly relates to a torsional rigidity fitting model of a harmonic reducer transmission system
Background
The harmonic gear transmission has the advantages of large transmission ratio, small return difference, small volume, high transmission efficiency and the like, and is gradually applied to various manufacturing equipment and measuring equipment, such as industrial robots, machine tools, optical scanners, laser mirror positioning mechanisms and the like. Since harmonic drive is a key drive component of the above-described electromechanical system, its performance has a large impact on the manufacturing or measurement accuracy of the system. Harmonic gear drives, however, are driven due to nonlinear torsional stiffness. The transmission precision of the system is reduced, the transmission stability is deteriorated, and even the production can not meet the working requirement. A number of researchers have performed such as fitting using cubic odd functions, and also fitting using Maxwell hysteresis models. The former method has simple model, can not express the hysteresis characteristic of the torsional rigidity, and the latter model has the disadvantages of complexity, large calculation amount and low efficiency.
Disclosure of Invention
Based on the background technology, the invention uses cubic Taylor series expansion to describe the nonlinearity of the torsional rigidity, uses a hyperbolic function to describe the hysteresis characteristic of the torsional rigidity, and obtains the relation between the torque T and the torsional angle. And a constant is introduced into the model, so that the problem that the former model is completely symmetrical is solved, and the fitting precision is improved.
The modeling method comprises the following steps:
the model fitting process is mainly as follows:
firstly, expressing the nonlinear relation between torque and torsion angle by adopting Taylor series expansion, and in order to ensure the fitting precision and reduce the calculated amount, the invention adopts three times of Taylor expansion to express:
T＝a+b·θ+c·θ2+d·θ3
wherein T is torque, a, b, c, d are polynomial coefficients, and theta is torsion angle
The hysteresis of torsional stiffness in harmonic gear drive systems is represented by hyperbolic functions. The following were used:
T＝Atanh(B·θ)
where T is torque, A, B is coefficient, and θ is torsion angle
And superposing the two parts in the formula to obtain an integral torsional rigidity fitting model, wherein the model comprises the following steps:
T＝a+b·θ+c·θ2+d·θ3+Atanh(B·θ)
from the torsional stiffness curves of harmonic gear transmissions, it can be seen that the graph consists of two closed curves, so the expression for the two curves can be expressed as:
T1＝a1+b1·θ+c1·θ2+d1·θ3+A1 tanh(B1·θ)
T2＝a2+b2·θ+c2·θ2+d2·θ3+A2 tanh(B2·θ)
wherein, T1、T2Respectively loaded and unloaded.
The corresponding relation of various values between the torque and the torsion angle of the harmonic gear transmission system can be obtained through experiments, parameters in the model can be identified by utilizing an nlnfit function in Matlab, and the functional relation between the torque and the torsion angle can be obtained.
Because of dT/d theta, the expression obtained by the above formula is subjected to derivation to obtain an expression of torsional rigidity of the harmonic gear.
Drawings
FIG. 1 is a graph of the fitting results of torsional stiffness according to the present invention
Detailed Description
Based on the background technology, the invention uses cubic Taylor series expansion to describe the nonlinearity of the torsional rigidity, uses a hyperbolic function to describe the hysteresis characteristic of the torsional rigidity, and obtains the relation between the torque T and the torsional angle. And a constant is introduced into the model, so that the problem that the former model is completely symmetrical is solved, and the fitting precision is improved.
The modeling method comprises the following steps:
the model fitting process is mainly as follows:
firstly, expressing the nonlinear relation between torque and torsion angle by adopting Taylor series expansion, and in order to ensure the fitting precision and reduce the calculated amount, the invention adopts three times of Taylor expansion to express:
T＝a+b·θ+c·θ2+d·θ3
the hysteresis of torsional stiffness in harmonic gear drive systems is represented by hyperbolic functions. The following were used:
T＝Atanh(B·θ)
and superposing the two parts in the formula to obtain an integral torsional rigidity fitting model, wherein the model comprises the following steps:
T＝a+b·θ+c·θ2+d·θ3+Atanh(B·θ)
from the torsional stiffness curves of harmonic gear transmissions, it can be seen that the graph consists of two closed curves, so the expression for the two curves can be expressed as:
T＝a1+b1·θ+c1·θ2+d1·θ3+A1 tanh(B1·θ)
T＝a2+b2·θ+c2·θ2+d2·θ3+A2 tanh(B2·θ)
wherein, T1、T2Respectively loaded and unloaded.
The corresponding relation of various values between the torque and the torsion angle of the harmonic gear transmission system can be obtained through experiments, parameters in the model can be identified by utilizing an nlnfit function in Matlab, and the functional relation between the torque and the torsion angle can be obtained.
Because of dT/d theta, the expression obtained by the above formula is subjected to derivation to obtain an expression of torsional rigidity of the harmonic gear.

Claims (1)

1. A torsional rigidity fitting method of a harmonic gear transmission system is characterized by comprising the following steps: describing the nonlinearity of the torsional rigidity by using cubic Taylor series expansion, and describing the hysteresis characteristic of the torsional rigidity by using a hyperbolic function to obtain the relation between the torque T and the torsional angle; moreover, constants are introduced into the model, so that the problem that the former model is completely symmetrical is solved, and the fitting precision is improved;
the fitting procedure is as follows:
(1) firstly, expressing the nonlinear relation between the torque and the torsion angle by adopting Taylor series expansion, and in order to ensure the fitting precision and reduce the calculated amount, expressing by adopting three times of Taylor expansion:
T＝a+b·θ+c·θ2+d·θ3
(2) a hyperbolic function is used for expressing a hysteresis phenomenon of torsional rigidity in a harmonic gear transmission system; the following were used:
T＝A tanh(B·θ)
(3) and superposing the two parts in the formula to obtain an integral torsional rigidity fitting model, wherein the model comprises the following steps:
T＝a+b·θ+c·θ2+d·θ3+A tanh(B·θ)
(4) the torsional stiffness curve of a harmonic gear drive is composed of two closed curves, so that the expression of the two curves can be expressed as:
T＝a1+b1·θ+c1·θ2+d1·θ3+A1 tanh(B1·θ)
T＝a2+b2·θ+c2·θ2+d2·θ3+A2 tanh(B2·θ)
(5) obtaining the corresponding relation of all values between the torque and the torsion angle of the harmonic gear transmission system through experiments, and identifying parameters in the model by utilizing an nlnfit function in Matlab to obtain the functional relation between the torque and the torsion angle;
(6) because of dT/d theta, the expression obtained by the above formula is subjected to derivation to obtain an expression of torsional rigidity of the harmonic gear.
CN202110911816.XA 2021-08-10 2021-08-10 Harmonic reducer transmission system torsional rigidity fitting method Pending CN113722891A (en)

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CN202110911816.XA CN113722891A (en) 2021-08-10 2021-08-10 Harmonic reducer transmission system torsional rigidity fitting method

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Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110263492A (en) * 2019-07-15 2019-09-20 北京工业大学 A kind of harmonic speed reducer double circular arc tooth outline torsion stiffness calculation method

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110263492A (en) * 2019-07-15 2019-09-20 北京工业大学 A kind of harmonic speed reducer double circular arc tooth outline torsion stiffness calculation method

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
杨聪彬等: "谐波传动柔软变形测量误差分析与补偿", 《光学精密工程》, vol. 29, no. 4, pages 793 - 801 *

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