CN112464412A - Method for designing arc-shaped anti-backlash torsion spring of servo mechanism - Google Patents
Method for designing arc-shaped anti-backlash torsion spring of servo mechanism Download PDFInfo
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Abstract
An optimized design method of an arc-shaped backlash torsion spring of a servo mechanism comprises the steps of parameterizing the overall dimension of the arc-shaped backlash torsion spring, extracting design parameters and building a parameterized geometric model on a CAD platform; importing the parameterized geometric model into a CAE analysis platform to calculate the torsional rigidity of the arc-shaped anti-backlash torsion spring; extracting samples in the neighborhood of the initial values of the design parameters, and calculating torsional rigidity corresponding to all the sample values to form a rigidity sample set; analyzing the sensitivity of each parameter at the initial value; and updating design parameters according to the sensitivity analysis result, calculating the updated torsional rigidity, and performing iterative calculation to obtain the optimized size parameters of the arc anti-backlash torsion spring. The torsional rigidity of the torsion spring with any size can be rapidly modeled and calculated, the influence degree of each size parameter of the torsion spring on the rigidity of the torsion spring is quantized, the arc-shaped backlash eliminating torsion spring is refined, the extensive experience design is avoided, the torsional rigidity is more matched with the mechanism load, and the performance of a gear transmission chain can be effectively improved.
Description
Technical Field
The invention relates to the technical field of backlash elimination of transmission sprockets, in particular to a design method of an arc backlash elimination torsion spring.
Background
The working mode of the intermittent irradiation of the seeker requires that a servo mechanism has a structure with high transmission rigidity to realize rapid, stable and reliable tracking. And the high-precision anti-backlash spring is a key factor for determining the rigidity of a power chain of the servo mechanism. Under the double-plate gear backlash elimination scheme, the backlash elimination spring inside the gear must be matched with the mechanism load. If the supplied pre-tightening torque is too small, the pre-tightening torque cannot play a role in eliminating backlash, and if the pre-tightening torque is too large, gear meshing is too tight, so that tooth surfaces are abraded easily. At present, the arc-shaped anti-backlash torsion spring is mainly designed according to engineering experience and then verified through tests. The torsional stiffness of the arc backlash torsion spring cannot be directly estimated from the overall dimensions, which makes it difficult for designers to determine the optimal design dimensions for matching the design requirements of the mechanism.
Disclosure of Invention
The invention provides a method for designing an arc-shaped backlash eliminating torsion spring of a servo mechanism, which can be used for quickly modeling and calculating torsional rigidity of the torsion spring with any size, quantifying the influence degree of each size parameter of the torsion spring on the rigidity of the torsion spring, refining the design of the arc-shaped backlash eliminating torsion spring, getting rid of extensive empirical design, enabling the torsional rigidity to be more matched with the mechanism load, and effectively improving the performance of a gear transmission chain.
In order to achieve the aim, the invention provides an optimal design method of an arc-shaped anti-backlash torsion spring of a servo mechanism, which comprises the following steps:
s1, parameterizing the shape and size of the arc-shaped anti-backlash torsion spring, and extracting design parameters to build a parameterized geometric model on a CAD platform;
step S2, importing the parameterized geometric model into a CAE analysis platform to calculate torsional rigidity of the arc anti-backlash torsion spring;
s3, extracting samples in the neighborhood of the initial values of the design parameters, and calculating torsional rigidity corresponding to all the sample values to form a rigidity sample set;
step S4, analyzing the sensitivity of each parameter at the initial value based on the calculation result in the stiffness sample set, thereby obtaining the sensitivity degree of the stiffness to each design parameter in the initial value neighborhood;
and step S5, updating design parameters according to the sensitivity analysis result, calculating the updated torsional rigidity, and performing iterative calculation to obtain the optimized size parameters of the arc-shaped anti-backlash torsion spring.
The design parameters are mutually independent geometric parameters and comprise: the outer diameter of the torsion spring R1, the inner diameter of the torsion spring R2, the distance between the pin hole and the center of the torsion spring R0, the aperture of the pin hole D, the included angle alpha between the pin hole and the center connecting line, the included angle beta between the end part of the torsion spring and the center connecting line and the thickness t of the torsion spring.
The ratio of torque to twist angle is the torsional stiffness.
And extracting samples by adopting a Latin super-legislation method, substituting the samples into the parameterized geometric model to generate an analysis model, and calculating torsional rigidity corresponding to all sample values.
And sequentially updating the design parameters of the torsion springs according to the sequence of the sensitivity from high to low, calculating the torsional rigidity after the parameters are updated, and repeating the step S3 to the step S5 to carry out iterative calculation until the new torsional rigidity is less than or equal to the original torsional rigidity, wherein the design parameters at the moment are the optimal design parameters.
Compared with the prior art, the method has the following technical effects or advantages:
1. the parameterized geometric model and the analysis model can be used for rapidly modeling and calculating the torsional rigidity of the torsion spring with any size.
2. Through parameter sensitivity analysis, the influence degree of each size parameter of the torsion spring on the rigidity of the torsion spring is quantized, the design of the arc-shaped anti-backlash torsion spring is refined, and the extensive experience design is avoided.
3. The torsional rigidity of the optimized torsion spring is more matched with the mechanism load, and the performance of the gear transmission chain can be effectively improved.
Drawings
FIG. 1 is a schematic diagram of the design parameters of an arc-shaped anti-backlash torsion spring.
Fig. 2 is a schematic diagram of an analytical model of a torsion spring assembly.
FIG. 3 is a flow chart of a design method of an arc-shaped anti-backlash torsion spring of a servo mechanism provided by the invention.
Fig. 4 is a graph showing the results of sensitivity analysis of the torsional spring stiffness at the initial point.
Detailed Description
The preferred embodiment of the present invention will be described in detail below with reference to fig. 1 to 4.
The arc-shaped anti-backlash torsion spring is used as a key part in a precision servo mechanism, and a universal design method is lacked at present. Therefore, the design method of the arc-shaped anti-backlash torsion spring with universality and high precision needs to be researched so as to be applied to the design of a high-precision servo mechanism transmission chain.
As shown in fig. 3, the present invention provides an optimized design method for an arc-shaped anti-backlash torsion spring of a servo mechanism, which comprises the following steps:
s1, parameterizing the overall dimension of the arc anti-backlash torsion spring, extracting 7 independent design parameters, and building a parameterized geometric model on a CAD platform;
step S2, importing the parameterized geometric model into a CAE analysis platform to calculate the rigidity of the arc-shaped anti-backlash torsion spring;
s3, extracting samples in the neighborhood of the initial values of the design parameters, and calculating the corresponding rigidity of all sample values to form a rigidity sample set;
step S4, analyzing the sensitivity of each parameter at the initial value based on the calculation result in the stiffness sample set, thereby obtaining the sensitivity degree of the stiffness to each design parameter in the initial value neighborhood;
and step S5, updating the more sensitive design parameters according to the sensitivity analysis result, and calculating the updated torsional rigidity.
The optimized size parameters of the arc-shaped anti-backlash torsion spring can be obtained through several iterations, so that the design of the arc-shaped anti-backlash torsion spring is completed.
Step S1 is to simplify the shape of the arc-shaped anti-backlash torsion spring into 7 independent geometric parameters, as shown in the figure1, respectively, is an outer diameter R1Inner diameter R2Distance R between pin hole and torsional spring center0The diameter D of the pin hole, the included angle alpha between the pin hole and the central connecting line, the included angle beta between the end part of the torsion spring and the central connecting line and the thickness t of the torsion spring. In any CAD platform, a parameterized geometric model can be generated from these 7 independent parameters. Different size design conditions are correspondingly provided for different arc-shaped anti-backlash torsion springs, so that the value range of design parameters is correspondingly expanded. And determining a design initial value in a value range, and generating a parameterized geometric model on a CAD modeling platform.
Step S2 is further to calculate the torsional rigidity of the arc-shaped anti-backlash torsion spring on the CAE analysis platform, and the parameterized geometric model of the arc-shaped anti-backlash torsion spring is generated by the step S1. Under the actual working state, the two ends of the arc-shaped anti-backlash torsion spring are respectively connected with the two gears through pins, and the two gears are meshed with the next-stage gear after rotating for a certain angle relatively. The deformation of the torsion spring is driven by the movement of the pin, and the two gears are not in direct contact with the torsion spring. The invention combines the pin and the torsion spring into an assembly body for analysis and calculation, and the model of the torsion spring assembly body is shown in figure 2. A virtual tool is also introduced into the model to eliminate rigid displacement. The torsion spring assembly needs to meet the following constraint conditions before submitting the torsion spring assembly for analysis and calculation.
And a revolute pair is restrained between the torsion spring and the pin. The pin 2 rotates around the center along with the loading gear and performs planar motion. Firstly, the out-of-plane displacement of the two pins is restrained, and the pins are ensured to do plane motion. The pin 1 is connected with the fixed gear, and the in-plane movement of the pin 1 is restrained to keep the pin still. The pin 2 rotates along with the loading gear, the in-plane motion track of the pin 2 is restrained, and the pin is ensured to rotate around the center and not to radially displace. The virtual tool is set as a simple rigid body in the model and cannot be deformed. The surface of the torsion spring is attached to the surface of the tool, so that the torsion spring only generates in-plane displacement.
The torque of the torsion spring is equal to the moment of the pin concentrated force to the center. Through the model calculation, the relation between the stress of the pin and the torsion angle can be obtained, the relation between the torsion of the torsion spring and the torsion angle can be further obtained, and the ratio of the torsion to the torsion angle is the torsional rigidity.
Step S3, more than one hundred groups of samples are extracted from the neighborhood of the initial parameter value determined in step S1, the samples can be extracted by adopting a Latin ultralaw, the samples are substituted into a parameterized geometric model to generate an analysis model, and torsional rigidity corresponding to all sample values is calculated to form a rigidity sample set.
Step S4 is to perform parameter sensitivity analysis at the initial value based on the stiffness sample set calculated in step S3, and obtain a geometric parameter with higher sensitivity in the initial value neighborhood. The influence of the parameters with higher adjustment sensitivity on the rigidity is larger.
And step S5, according to the sensitivity analysis result, sequentially updating the design parameters of the torsion spring according to the sensitivity degree, calculating the torsional rigidity after the parameters are updated, and comparing the torsional rigidity with the original rigidity. If the difference between the two rigidities is larger, the updated design parameters are used as initial values, and the steps S3-S5 are repeated; if the difference between the two rigidities is small, the local optimum design parameter is obtained.
The following describes the design method of the arc-shaped anti-backlash torsion spring in detail in combination with the design example.
The arc-shaped anti-backlash torsion spring is made of chrome vanadium steel 50CrVa and is used for a final-stage gear of a certain guide head servo mechanism. The gear is a sector gear and limited by the mechanism moving space, and the double-piece gear can rotate 7 degrees relatively at most. The load value of the channel is measured to be 0.75N · m, so that the pretensioning moment of the torsion spring is above 1.5N · m when the torsion spring is deformed by 7 °, and the design target stiffness of the torsion spring is 0.214N · m/° with K being 1.5/7. The envelope of the inner space of the double-piece gear is a concentric cylindrical space with the outer diameter of 26mm, the inner diameter of 14mm and the thickness of 2 mm.
According to the space envelope, a group of torsion spring geometric parameters meeting the conditions are given as design initial values, and the sizes are R respectively1＝12、R2＝9.5，R0＝10.5、D＝1.5、α＝90°、β＝74°、t＝1.5。
At this initial value, the torsion spring is deformed by 7 ° with a torque of 0.959N · m and a stiffness of 0.137N · m/°. The pre-tightening torque is less than 1.5 Nm, and cannot reach the design index. Therefore, parameters need to be adjusted to improve stiffness. The maximum stress of the torsion spring in the working state is less than 920MPa corresponding to the torsion spring material.
Samples were taken in the neighborhood of the initial value, and the stiffness and stress at a torque of 1.5N · m were calculated, respectively, and the stiffness sensitivity at the initial value was calculated, and the result is shown in fig. 4. In this example, torsional stiffness of the torsion spring is most sensitive to the thickness t of the torsion spring, and then the outer circle radius R1And inner circle radius R2The remaining 4 design parameters had essentially no effect on stiffness. Wherein the thickness t of the torsion spring and the radius R of the outer circle1Positive correlation with stiffness, inner circle radius R2Is inversely related to stiffness.
According to the sensitivity analysis result, updating the sensitivity design parameters, and obtaining the optimal sizes R respectively after multiple iterations1＝12.4、R2＝9，R010.5, D1.5, α 90 °, β 74 °, t 1.7. Through design optimization, torsional rigidity of the torsion spring is improved from an initial value state by 53 percent to 0.225 N.m/°. The torque corresponding to a deformation of 7 ° was 1.58N · m. The maximum stress of the steel plate is 694MPa when the steel plate is deformed at 7 degrees, and the use requirement of the material is met.
The existing arc-shaped anti-backlash torsion spring is designed by experience and is verified by subsequent tests. Compared with the prior art, the method has the following technical effects or advantages:
1. the parameterized geometric model and the analysis model can be used for rapidly modeling and calculating the torsional rigidity of the torsion spring with any size.
2. Through parameter sensitivity analysis, the influence degree of each size parameter of the torsion spring on the rigidity of the torsion spring is quantized, the design of the arc-shaped anti-backlash torsion spring is refined, and the extensive experience design is avoided.
3. The torsional rigidity of the optimized torsion spring is more matched with the mechanism load, and the performance of the gear transmission chain can be effectively improved.
While the present invention has been described in detail with reference to the preferred embodiments, it should be understood that the above description should not be taken as limiting the invention. Various modifications and alterations to this invention will become apparent to those skilled in the art upon reading the foregoing description. Accordingly, the scope of the invention should be determined from the following claims.
Claims (5)
1. An optimal design method of an arc-shaped anti-backlash torsion spring of a servo mechanism is characterized by comprising the following steps:
s1, parameterizing the shape and size of the arc-shaped anti-backlash torsion spring, and extracting design parameters to build a parameterized geometric model on a CAD platform;
step S2, importing the parameterized geometric model into a CAE analysis platform to calculate torsional rigidity of the arc anti-backlash torsion spring;
s3, extracting samples in the neighborhood of the initial values of the design parameters, and calculating torsional rigidity corresponding to all the sample values to form a rigidity sample set;
step S4, analyzing the sensitivity of each parameter at the initial value based on the calculation result in the stiffness sample set, thereby obtaining the sensitivity degree of the stiffness to each design parameter in the initial value neighborhood;
and step S5, updating design parameters according to the sensitivity analysis result, calculating the updated torsional rigidity, and performing iterative calculation to obtain the optimized size parameters of the arc-shaped anti-backlash torsion spring.
2. The method for optimally designing the arc-shaped backlash torsion spring of the servo mechanism as claimed in claim 1, wherein the design parameters are mutually independent geometric parameters and comprise: the outer diameter of the torsion spring R1, the inner diameter of the torsion spring R2, the distance between the pin hole and the center of the torsion spring R0, the aperture of the pin hole D, the included angle alpha between the pin hole and the center connecting line, the included angle beta between the end part of the torsion spring and the center connecting line and the thickness t of the torsion spring.
3. The method for optimally designing the arc-shaped backlash torsion spring of the servo mechanism as claimed in claim 2, wherein the ratio of the torque to the torsion angle is the torsional rigidity.
4. The method for optimally designing the arc-shaped backlash torsion spring of the servo mechanism as claimed in claim 3, wherein a Latin super-legislation method is adopted to extract samples, the samples are substituted into a parameterized geometric model to generate an analysis model, and torsional rigidity corresponding to all sample values is calculated.
5. The method for optimally designing the arc-shaped backlash torsion spring of the servo mechanism according to claim 3, wherein the design parameters of the torsion spring are updated in sequence from high sensitivity to low sensitivity, the torsional rigidity after the parameters are updated is calculated, and the steps S3 to S5 are repeated for iterative calculation until the new torsional rigidity is less than or equal to the original torsional rigidity, and the design parameters at the moment are the optimal design parameters.
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