CN112434447A - Time-varying reliability analysis system and method for lead screw machining - Google Patents
Time-varying reliability analysis system and method for lead screw machining Download PDFInfo
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Abstract
The invention provides a time-varying reliability analysis system for lead screw machining, which is characterized by comprising an input-response module and a reliability analysis module; wherein: the input-response module comprises an uncertainty parameter description unit and a response solving unit; the uncertainty parameter description unit describes the strength of a heat source with uncertainty and time-varying characteristics through an interval process by engineering experience, namely, expressing the heat source heat productivity in unit volume unit time into an interval process, and representing the heat source heat productivity through a median function, a radius function and a correlation coefficient function or a covariance function of the heat source heat productivity; the response solving unit solves the response samples corresponding to the uncertainty parameter samples through a deterministic calculation process, so that the problems of high cost and low efficiency caused by indiscriminately detecting all lead screws are solved; meanwhile, the time-varying reliability index of the screw in the continuous processing process can also be used as a reference index for adjusting the continuous grinding processing procedure of the screw.
Description
Technical Field
The invention relates to the technical field of analysis of screw machining reliability, in particular to a time-varying reliability analysis system and method for screw machining.
Technical Field
The screw is the most commonly used transmission element in machine tools and precision machines, and its main function is to convert the rotary motion into linear motion, it can accurately determine the position of the table coordinate, and it also needs to transmit a certain power, so it has very high requirements on precision, strength and wear resistance. Therefore, the precision of the precision lead screw needs to be checked after the precision lead screw is machined, and usually, an inspector manually checks the machining error of the lead screw to judge whether the precision of the lead screw reaches the standard or not. The inspection mode has low efficiency, consumes a large amount of manpower and material resources, and is easy to cause the inconsistency of the front and back measurement results of the workpiece due to the irregularity of the professional knowledge and the actual working experience of the inspectors, so that the error is larger, and the balance between the efficiency and the accuracy of the lead screw detection is difficult to achieve. With the increasing production task, the toggle joint is bound to be an elbow for enlarging the workpiece output.
During grinding, factors influencing the processing precision of the screw rod are many, wherein a thermal deformation error caused by temperature change is a main factor, and the thermal deformation error is embodied as an axial length error of the screw rod. Machining errors caused by thermal deformation typically account for 40% -70% of the total workpiece machining errors. In the machining process, when the thermal deformation exceeds the allowable range, the precision of the machined screw does not meet the requirement, and the machined state is considered to belong to dangerous working conditions. However, due to the non-uniformity of temperature variation of the lead screw in the machining process and some non-linear factors influencing thermal deformation, the heat source is difficult to perform deterministic mathematical description, and the internal temperature field is difficult to accurately simulate, which directly causes the difficulty in direct calculation of the thermal deformation amount or calculation of an index capable of reflecting whether the thermal deformation amount is acceptable, so that the lead screw can only be detected after machining.
Disclosure of Invention
The invention provides a time-varying reliability analysis system and method for lead screw machining, aiming at the problems that the heat deformation amount is difficult to directly calculate in the lead screw machining process, and the lead screw can only be detected after machining, so that the detection cost is high and the efficiency is low. The invention considers the time-varying uncertainty of the heat source of the screw in the grinding process, takes the main influence factor of the axial thermal deformation of the screw in the processing process as the factor for judging whether the screw is processed reliably or not, namely, the heat source strength as the judging factor for judging whether the screw is in a safe state or not in the processing process, and uses a novel time-varying reliability analysis method based on the interval process to calculate the reliability index of the screw processing. Whether the axial thermal deformation amount generated in the machining process of the screw rod is within an acceptable range can be judged through the reliability index, and then the screw rod with the reliability index meeting the requirement, namely the thermal deformation amount within the acceptable range is not detected, so that the detection cost is reduced. In addition, the reliability index provided by the invention can also provide an optimization target for the optimization of continuous grinding time length and grinding feed depth.
The technical scheme of the invention provides a time-varying reliability analysis system for lead screw processing, which comprises an input-response module and a reliability analysis module,
the input-response module comprises an uncertainty parameter description unit and a response solving unit;
the uncertainty parameter description unit describes the strength of a heat source with uncertainty and time-varying characteristics through an interval process by engineering experience, namely, expressing the heat source heat productivity in unit volume unit time into an interval process, and representing the heat source heat productivity through a median function, a radius function and a correlation coefficient function or a covariance function of the heat source heat productivity;
the response solving unit solves the response samples corresponding to the uncertain parameter samples through a deterministic calculation process, namely, the samples of the uncertain parameters are used as input, and the response samples corresponding to the input are solved to establish an input sample and a response sample set. The response solving unit takes the heat source heat productivity sample as input, solves the corresponding screw axial thermal deformation caused by the heat source heat productivity and takes the axial thermal deformation as output. Calculating the corresponding screw axial thermal deformation response through different heat source heat productivity samples, and constructing a heat source heat productivity input sample set and a screw axial thermal deformation response sample set;
the reliability analysis module is used for taking the axial thermal deformation generated by the screw in the processed process as a factor for judging whether the screw is in a safe state or not, namely, taking the axial thermal deformation as a factor for judging whether the screw precision meets the precision requirement or not based on an interval process model and input and response samples established by the uncertain parameter description unit and the response solving unit, and calculating the time-varying reliability of the screw by a time-varying reliability analysis method based on an interval process so as to judge whether the screw meets the precision requirement or not and whether follow-up precision detection is required or not.
Further, the given input is the heat source calorific value of the lead screw grinding process, and the corresponding output is the axial thermal deformation amount of the lead screw generated in the grinding process.
The technical scheme of the invention also provides a time-varying reliability analysis method for screw processing, which comprises the following steps:
and 4, judging whether the actual heat source calorific value is smaller than the maximum heat source calorific value meeting the design requirement as a standard for judging whether the lead screw is in a safe state, judging that the lead screw is in the safe state when the heat source calorific value does not exceed a design allowable value at all times in the lead screw grinding process, and judging that the lead screw is in a failure state if the heat source calorific value exceeds the design allowable value at one time in the lead screw grinding process.
And 5, analyzing the time-invariant reliability based on the step 4 so as to obtain a time-variant reliability index of the screw rod in the machining process.
Further, the minimum value of the difference value between the allowable value of the heat source heat productivity and the actual heat source heat productivity at any time in the time interval of the continuous grinding processing of the lead screw is more than 0, and the lead screw is judged to be in the safe state;
the time-varying reliability analysis is converted into the time-invariant reliability analysis only by paying attention to whether or not the minimum value of the difference value between the allowable value of the heat source heat generation amount and the actual heat source heat generation amount in the time domain is greater than 0.
Further, the method comprises establishing a median function, a radius function and a correlation coefficient function or a covariance function of the interval process to characterize the interval process.
The invention has the beneficial effects that:
the time-varying uncertainty of the heat source heat productivity is described by using an interval process, so that the fluctuation of the heat source heat productivity and the correlation of the heat source heat productivity at different moments can be considered in the subsequent reliability analysis, and the problem of inaccurate model caused by the fact that the heat source heat productivity is assumed as a deterministic factor in the traditional method is solved; the time-varying reliability index of the screw rod in the continuous machining process is calculated to reflect the machining precision of the screw rod so as to guide the whole detection, partial detection or no detection of the screw rod subsequently, so that the problems of high cost and low efficiency caused by indiscriminate detection of all the screw rods are solved; meanwhile, the time-varying reliability index of the screw in the continuous processing process can also be used as a reference index for adjusting the continuous grinding processing procedure of the screw.
Drawings
FIG. 1 is a schematic diagram of modules of a time-varying reliability analysis system for lead screw machining;
FIG. 2 is a flow chart diagram of a time-varying reliability analysis method for lead screw processing;
FIG. 3 is a schematic diagram of meshing;
FIG. 4 is a schematic diagram of a reliability index solution flow;
Detailed Description
The technical means of the present invention will be described in detail below.
As shown in fig. 1, this embodiment provides a time-varying reliability analysis system for lead screw machining, the system comprising an input-response module and a reliability analysis module, wherein:
the input-response module comprises an uncertainty parameter description unit and a response solving unit.
The uncertainty parameter description unit considers the time-varying uncertainty of the heat source heat productivity in the lead screw grinding process, processes the heat source heat productivity into an interval process, and represents the interval process through a median function, a radius function and a correlation coefficient function of the heat source heat productivity.
Processing heat value of heat source into interval process
For any time instant
The heat value of the heat source is an interval variable g (t)i). Describing the time-varying uncertainty of the heat source heat productivity through the interval process, and describing the heat source heat productivity g (t) at any timei) Are all in the interval gI(ti)＝[gL(ti),gU(ti)]Internal, i.e. g (t)i)∈gI(ti)＝[gL(ti),gU(ti)]. Meanwhile, a basic characteristic parameter for representing an interval process, namely an upper boundary function g, is given according to engineering experienceU(t), lower boundary function gL(t), median function gm(t), radius function gr(t) and autocorrelation coefficient function
The upper boundary function and the lower boundary function of the heat source calorific value are respectively gU(t) and gL(t)；
The median function of the heat value of the heat source is as follows:
the radius function of the heat source heat productivity is as follows:
heat value of heat source is tiAnd tjThe correlation coefficient function at time is:
the heat source calorific value processing of the present embodiment is a stationary interval process, in which both the value function and the radius function are constant and the autocorrelation coefficient function is only related to the time interval of two moments.
According to an empirical formula of the heat value of the heat source:
wherein u isGThe specific grinding energy consumed for cutting metal per unit volume per unit time, u, is selectedG＝30J/(cm3S); and R is the radius of the lead screw.
The heat source heating value median function can be expressed as:
gm(t)＝RuG (5)
the heat source heating value radius function can be expressed as:
gr(t)＝0.3RuG (6)
the heat source calorific value autocorrelation coefficient function can be expressed as:
wherein the time interval τ ═ ti-tjL, |; l is the correlation length.
The response solving unit is used for solving the axial thermal deformation of the lead screw caused by heat source heating corresponding to the heat source heating of the lead screw in the continuous grinding machining, namely when a determined heat source heating is given, the response solving unit can give a corresponding axial thermal deformation of the lead screw. The following basic assumptions are required to be observed in solving the response of the screw axial thermal deformation corresponding to the heat source calorific value:
a. the grinding heat source is simplified into an annular heat source and moves along the axial direction of the workpiece, the grinding depth is constant, and the input heat is equal on any section of the screw rod;
b. the lead screw is regarded as a homogeneous cylinder, and the diameter is the middle diameter of the lead screw;
c. the diameters of journal parts at two end parts of the screw rod are converted into the same diameter as the middle diameter of the screw rod;
d. the heat exchange coefficient of each part of the circumferential surface of the lead screw is the same as that of an external cooling medium;
e. the two ends of the screw rod are insulated.
Based on the basic assumption, the temperature field inside the screw can be treated as a two-dimensional problem, and the basic differential equation of the temperature distribution can be expressed as:
where r is a cylindrical radius coordinate, z is a length coordinate, T is a temperature of each point, k is a material heat transfer coefficient, α is a heat transfer coefficient, and g is a heat source calorific value per unit volume (g is 0 because there is no heat source inside the screw). Where T is the temperature difference between points relative to the calculated zero point, i.e. T ═ Tr,x,t-T∞The coolant or room temperature is taken as the zero point of calculation, i.e. T∞＝0。
In the grinding process of the screw rod, the heat exchange rule between the outer surface and the cooling medium can adopt a third type of boundary conditions:
wherein h is the surface convection heat transfer coefficient, T0Is the surface temperature of the screw.
For numerical calculation, equations (8) and (9) are discretized, discrete intervals in the radial direction, the axial direction, and time are represented by Δ r, Δ z, and Δ t, respectively, and different cells on the periphery are defined by (x, y) versus (r, z), respectively, using a rectangular area gridding method, as shown in fig. 3. As the time zero point from the start of grinding,
is the temperature at (x, y) after i time intervals, then equation (8) can be discretized as:
wherein A ═ α Δ t/Δ r2,B＝αΔt/Δz2,
Is the temperature rise caused by heat entering the (x, y) cell during the Δ t time.
The formula (9) can be simplified to
Let y be n2,
At the outer imaginary point of the circumference (y ═ n)2+1) thereon are
The joint type (10), (11), (12) can be obtained on a hypothetical cylinderTemperature of each point
The difference equation is satisfied, so that the temperature distribution of each point in the cylinder can be solved.
According to the temperature of each point on the cross section of the screw
First, the average temperature on the cross section is determined:
the total elongation Δ L of the cylinder in length is then:
wherein, gamma is the linear expansion coefficient of the material, and L is the length of the cylinder.
The reliability analysis module judges whether the lead screw is in a safe state by judging whether the difference value between the heat source heating value corresponding to the lead screw axial heat deformation allowance value obtained by the response solving unit of the input-response module and the actual heat source heating value is larger than 0, and converts the time-varying reliability analysis into the time-invariant reliability analysis by only paying attention to whether the minimum value of the difference value between the heat source heating value allowance value and the actual heat source heating value in the time domain is larger than 0.
Considering the function of the screw as:
G(t)＝g0-g(t) (15)
wherein, g0The allowable value of the thermal deformation of the screw axis is shown, g (t) is the actual heat source heating value shown by the interval process, and t is a time variable.
For this interval process, it can be expressed as a linear combination of several independent standard interval variables with deterministic functions by a truncated interval K-L expansion method [33 ]:
substituting equation (16) into equation (15) yields:
expanding by a truncation interval K-L, and enabling an interval variable vector zeta to be [ zeta ═ zeta1,ζ2,…,ζN]Representing the uncertainty in the interval process. Thus, the above formula can be abbreviated as follows:
G(t)＝h(ζ,t) (18)
wherein h (. cndot.) can be according to g0-g (-) is obtained by transformation. Let Z be ζ, then the above formula can be rewritten as follows:
G(t)＝h(Z,t) (19)
since Z is a section variable vector, g (t) is a section variable at an arbitrary time t. Next, a time-varying reliability analysis model of the lead screw is constructed based on equation (20).
For a given continuous grinding cycle [0, Γ ], the screw being in a safe state means that the following conditions are satisfied:
that is, for any time t ∈ [0, Γ ], the function g (t) is greater than 0.
As can be seen from the equation (20), when the function value of the screw is large and zero at any time in the continuous grinding period, the screw is in a safe state in the continuous grinding period, and it is only necessary to ensure that the minimum value of the function of the structure is positive at all times if it is required to ensure that the structure is in the safe state at any time. At this time, the lead screw safety only needs to satisfy the following conditions:
the time-varying reliability analysis problem is converted into a time-invariant reliability analysis problem through the above formula.
For the function h (Z, t), any one of the realized values Z of the interval variable Z is given*The function is then expressed as h (z)*T) when the function is actually a univariate function h (t) only with respect to time t, so that the realized value z for any interval variable is*Can obtain a minimum value of the function corresponding to the implementation value in the continuous grinding period
Function in continuous grinding period [0, gamma ]]Minimum value of
Changes with the change of the input interval variable Z, and it can be known that
As a function of the interval variable Z, equation (21) can then be expressed as:
as can be seen from equation (22), the time-varying reliability problem has already been transformed into the time-invariant reliability problem, and thus the time-varying reliability problem can be analyzed by the time-invariant reliability analysis method. The function H (Z) varies as the interval variable Z varies, the possible values in the uncertainty region forming an interval HI(Z) its upper boundary, lower boundary, midpoint and radius are respectively HL(Z)、HU(Z)、Hm(Z) and Hr(Z). The non-probability structure reliability index beta is:
when beta is less than-1, the upper boundary of the function value interval is less than 0, namely all possible values of the function are less than 0, so that the screw is unreliable and needs to be subsequently detected and corrected; with the increase of the beta in the interval < -1,1 >, the possible value of the function which is larger than 0 is continuously increased, so that the reliability of the screw rod is also increased, and the detection can be carried out according to the specific production requirement; when beta is larger than 1, the lower boundary of the functional function value interval is larger than 0, namely all possible values of the functional function are larger than 0, so that the screw is completely reliable, and subsequent detection and correction are not needed after the screw is ground.
From equation (23), it can be seen that the function is required to be obtained for obtaining the non-probability reliability index β
Lower boundary H ofL(Z) and an upper boundary HU(Z) and the analytical expression of the function H (Z) is difficult to obtain, so that the interval HI(Z) lower boundary HL(Z) and an upper boundary HUThe solution of (Z) is also difficult to implement. Therefore, in order to reduce the calculation cost and the solving difficulty, the extreme value prediction model of the functional function in the design reference period is established in the process of calculating the reliability index of the structure
To approximate the original surrogate model H (Z) and obtain the surrogate model
Upper boundary of (1)
And a lower boundary
And solving the reliability index. The solution of the structural reliability index mainly comprises three continuous steps: the method comprises the steps of obtaining time extreme value response of a function, establishing and updating an extreme value prediction model based on a Kriging model, and calculating a reliability index. The solving process of the reliability index is shown in fig. 4.
The embodiment also provides a time-varying reliability analysis method for lead screw processing, which specifically comprises the following steps:
in the embodiment, uncertainty with time-varying characteristics of heat source calorific value in the lead screw grinding process is considered, and an interval process model is established according to samples or engineering experience
To describe the time-varying uncertainty of the heat source heating value g (t) in the lead screw grinding process. Determining a median function gm(t)＝RuGRadius function gr(t)＝0.3RuGAnd autocorrelation coefficient function
and 5, analyzing the time-invariant reliability based on the step 4 so as to obtain a time-variant reliability index of the screw rod in the machining process.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. The details of the embodiments are not to be interpreted as limiting the scope of the invention, and any obvious changes, such as equivalent alterations, simple substitutions and the like, based on the technical solution of the invention, can be interpreted without departing from the spirit and scope of the invention.
Claims (5)
1. A time-varying reliability analysis system for lead screw processing is characterized by comprising an input-response module and a reliability analysis module; wherein: wherein:
the input-response module comprises an uncertainty parameter description unit and a response solving unit;
the uncertainty parameter description unit describes the strength of a heat source with uncertainty and time-varying characteristics through an interval process by engineering experience, namely, expressing the heat source heat productivity in unit volume unit time into an interval process, and representing the heat source heat productivity through a median function, a radius function and a correlation coefficient function or a covariance function of the heat source heat productivity;
the response solving unit solves a response sample corresponding to the uncertain parameter sample through a deterministic calculation process, namely, the sample of the uncertain parameter is used as an input, and the response sample corresponding to the input is solved to establish an input sample and a response sample set;
the response solving unit takes the heat source heat productivity sample as input, solves the corresponding screw axial thermal deformation caused by the heat source heat productivity and takes the axial thermal deformation as output; calculating the corresponding screw axial thermal deformation response through different heat source heat productivity samples, and constructing a heat source heat productivity input sample set and a screw axial thermal deformation response sample set;
the reliability analysis module is used for taking the axial thermal deformation generated by the screw in the processed process as a factor for judging whether the screw is in a safe state or not, namely, taking the axial thermal deformation as a factor for judging whether the screw precision meets the precision requirement or not based on an interval process model and input and response samples established by the uncertain parameter description unit and the response solving unit, and calculating the time-varying reliability of the screw by a time-varying reliability analysis method based on an interval process so as to judge whether the screw meets the precision requirement or not and whether follow-up precision detection is required or not.
2. The time-varying reliability analysis system for lead screw machining according to claim 1, characterized in that: the given input is the heat source calorific value of the lead screw grinding process, and the corresponding output is the axial thermal deformation amount of the lead screw generated in the grinding process.
3. A time-varying reliability analysis method for lead screw machining is characterized by comprising the following steps:
step 1, considering uncertainty of the heat source calorific value in the lead screw grinding process with time-varying characteristics, and establishing an interval process model according to a sample or engineering experience to describe the time-varying uncertainty of the heat source calorific value in the lead screw grinding process;
step 2, establishing a response solving unit, and ensuring that a corresponding response sample can be obtained for each input sample by establishing a mapping relation between input and response, namely establishing a mapping relation between heat source heat productivity in the grinding process of the screw rod and axial thermal deformation generated in the grinding process of the screw rod, so that corresponding axial thermal deformation of the screw rod can be obtained by calculating for different heat source heat productivity samples;
step 3, determining the lowest precision of the screw rod meeting the design requirement, namely determining the maximum axial thermal deformation of the screw rod meeting the design requirement, and obtaining the heat source calorific value of the screw rod under the condition of meeting the maximum axial thermal deformation of the design requirement through the inverse solution of a response solving unit;
and 4, judging whether the actual heat source calorific value is smaller than the maximum heat source calorific value meeting the design requirement as a standard for judging whether the lead screw is in a safe state, judging that the lead screw is in the safe state when the heat source calorific value does not exceed a design allowable value at all times in the lead screw grinding process, and judging that the lead screw is in a failure state if the heat source calorific value exceeds the design allowable value at one time in the lead screw grinding process.
And 5, analyzing the time-invariant reliability based on the step 4 so as to obtain a time-variant reliability index of the screw rod in the machining process.
4. The time-varying reliability analysis method for lead screw machining according to claim 3, wherein in step 4, the lead screw is determined to be in the safe state only if the minimum value of the difference between the allowable value of the heat source calorific value and the actual heat source calorific value at any time in the time interval of the continuous grinding of the lead screw is greater than 0;
the time-varying reliability analysis is converted into the time-invariant reliability analysis only by paying attention to whether or not the minimum value of the difference value between the allowable value of the heat source heat generation amount and the actual heat source heat generation amount in the time domain is greater than 0.
5. The time-varying reliability analysis method for lead screw processing according to claim 3, wherein the step 1 further comprises establishing a median function, a radius function and a correlation coefficient function or a covariance function of an interval process to characterize the interval process.
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| 李金武: "《不确定性时变参数下结构的响应边界计算与可靠性分析》", 《中国优秀硕士学位论文全文库》 * |
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| CN112434447B (en) | 2022-04-26 |
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