CN115795926A - Method for constructing barreling and polishing machining test model based on similarity theory - Google Patents

Method for constructing barreling and polishing machining test model based on similarity theory Download PDF

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CN115795926A
CN115795926A CN202310082882.XA CN202310082882A CN115795926A CN 115795926 A CN115795926 A CN 115795926A CN 202310082882 A CN202310082882 A CN 202310082882A CN 115795926 A CN115795926 A CN 115795926A
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barreling
model
test model
polishing
acting force
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CN115795926B (en
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李文辉
温学杰
李秀红
杨胜强
田涛
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Taiyuan University of Technology
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Abstract

The invention belongs to the technical field of barreling and burnishing, provides a method for constructing a barreling and burnishing test model based on a similar theory, and solves the problem that an actual model test is difficult to perform due to high test cost, high operation difficulty and the like in the research process of a barreling and burnishing process. The invention calculates the similarity factor related to physical quantity in the barreling and polishing process based on the dimension analysis method; considering the influence of the gravity acceleration, constructing a barreling and polishing processing test model of the gravity acceleration distortion, and deducing a distortion coefficient calculation formula according to a similar theory; calculating a distortion coefficient by using a discrete element simulation method; and predicting the actual model result according to the test model result, calculating a prediction error, and verifying the effectiveness of the test model design method. The test model constructed by the method has higher similarity with the actual model, and the purpose of reflecting the actual model result by the test model result is realized.

Description

Method for constructing barreling and polishing machining test model based on similar theory
Technical Field
The invention belongs to the technical field of barreling and polishing processing, and particularly relates to a method for constructing a barreling and polishing processing test model based on a similar theory.
Background
The tumbling and polishing processing technology has the advantages of strong adaptability, good processing effect, economy and bearability and the like, simultaneously has the functions of removing trace materials, polishing the surface and strengthening the surface, and becomes a finished manufacturing technology with great development potential. The method aims at the problems of high test cost, high operation difficulty and the like in the process research of the tumbling and polishing machining process of large high-performance parts such as blisks, casings, gears, crankshafts and the like, so that the actual model test is difficult to perform. A test model construction method is found, the test model result reflects the actual model result, and the method has significant meaning for the research and development of the barreling and polishing processing technology of large parts.
The similarity theory aims at establishing similar sufficient necessary conditions between an actual model and a test model, and predicting the result of the actual model by constructing the test model to replace the actual model test so as to achieve the aim of reducing the test cost. At present, a design method of a similar theoretical model is applied to the fields of aerospace, structural engineering, mining engineering and the like. Chinese patent CN113761669A provides a method for designing the shrinkage ratio of a curved beam structure of an airplane, in which similar distortion caused by a strain rate effect and a strain hardening effect is considered; chinese patent CN111695207A provides a method for designing a crane test model according to a similar theory and a dimension analysis method, and is verified by finite element simulation, and the design of the crane test model can be realized by applying the method; the Chinese patent CN112610230A utilizes a similar theory to construct an indoor model of the tunnel boring machine, and is used for predicting large-size boring of an engineering site; these examples all demonstrate the validity of a similar theory.
A barrel polishing finishing process research based on a discrete element method belongs to the field of discrete element research, and the methods do not relate to the design of a test model in the field of discrete elements and do not consider similar distortion caused by gravity acceleration. Therefore, the method for constructing the barreling and burnishing test model based on the similar theory is developed to solve the problem that the actual model test is difficult to perform due to high test cost, high operation difficulty and the like in the research process of the barreling and burnishing process, and the constructed barreling and burnishing test model is used for guiding the construction of a test device.
Disclosure of Invention
The invention provides a method for constructing a barreling and polishing test model based on a similar theory in order to solve at least one technical problem in the prior art.
The invention is realized by adopting the following technical scheme: a method for constructing a barreling and polishing test model based on a similar theory comprises the following steps:
s1: analyzing the principle of barreling and burnishing, and extracting the dependent variable and the physical quantity influencing the dependent variable in the process of barreling and burnishing, wherein the dependent variable is the speed of a barreling and burnishing block in a container
Figure SMS_2
And the acting force of the rolling and polishing grinding block on the workpiece
Figure SMS_3
(ii) a The physical quantities affecting the dependent variable are specifically: dimensional parameters of workpiece, barrel polishing grinding block and container
Figure SMS_4
(ii) a Material parameters, including density, of the workpiece, barrel polishing pad and container
Figure SMS_5
Shear modulus
Figure SMS_6
Poisson ratio
Figure SMS_7
(ii) a The motion parameters are determined according to a specific barreling and polishing processing technology; other parameters, including simulation time
Figure SMS_8
Acceleration of gravity
Figure SMS_1
；
S2: by density
Figure SMS_9
Size parameter of
Figure SMS_10
Simulation time
Figure SMS_11
Obtaining a similar proportional relation related to physical quantity in the barreling and polishing processing technology by using a dimension analysis method as a basic dimension;
s3: ensuring the same material parameters of the test model and the actual model, and setting the size parameters between the test model and the actual model
Figure SMS_12
Is a similarity factor of
Figure SMS_13
Obtaining similar factors of other physical quantities;
s4: estimated gravitational acceleration
Figure SMS_14
The similarity factor is difficult to satisfy under the actual test condition, and the gravity acceleration between the test model and the actual model is determined
Figure SMS_15
The similarity factor of the gravity acceleration distortion is changed into 1, and a barreling and polishing processing test model of the gravity acceleration distortion is obtained;
s5: correcting the speed and the acting force of the barrel polishing grinding block by adopting an analog simulation numerical fitting method, and deducing a calculation formula of a distortion coefficient;
s6: establishing discrete element simulation of the actual model and the test model obtained in the step S4; arranging data blocks in the test model and the actual model, and respectively extracting the test model of the tumbling and polishing processing of the gravity acceleration distortion, the speed of a tumbling and polishing grinding block in a container in each data block in the actual model and the acting force of the tumbling and polishing grinding block on a workpiece; calculating the distortion coefficient of the speed and the acting force in each data block, and averaging the distortion coefficients to obtain an overall distortion coefficient;
s7: and respectively predicting the actual model result in each data block by using the test model result and the overall distortion coefficient, calculating the prediction error in each data block, calculating the overall prediction error, and judging the effectiveness of the test model.
Preferably, in step S2, the similar proportional relation between the test model and the actual model is shown as the following formula:
Figure SMS_16
in the formula (I), the compound is shown in the specification,
Figure SMS_18
shear modulus of test model and actual model respectively
Figure SMS_19
Acceleration of gravity
Figure SMS_21
Density, density
Figure SMS_22
Size parameter of
Figure SMS_23
Simulation time
Figure SMS_24
Acting force
Figure SMS_25
And velocity
Figure SMS_17
Similar proportions of (a); poisson ratio
Figure SMS_20
The motion parameters are dimensionless physical quantities, and the similar proportional relation of the relevant physical quantities of the motion parameters is determined according to a specific barreling and polishing processing technology.
Preferably, in step S3, the material parameters of the test model and the actual model are the same, i.e. the test model and the actual modelDensity of
Figure SMS_26
Shear modulus
Figure SMS_27
The similarity factor of (a) is 1; poisson ratio
Figure SMS_28
The Poisson ratio similarity factor of the test model and the actual model is 1; similar factors related to physical quantities in the barreling and polishing process are shown as follows:
Figure SMS_29
in the formula (I), the compound is shown in the specification,
Figure SMS_31
、
Figure SMS_33
、
Figure SMS_35
、
Figure SMS_37
、
Figure SMS_39
respectively shear modulus
Figure SMS_40
Acceleration of gravity
Figure SMS_41
Density, density
Figure SMS_30
Size parameter of
Figure SMS_32
Simulation time
Figure SMS_34
Acting force
Figure SMS_36
And velocity
Figure SMS_38
A similarity factor of (d); the similarity factor of the relevant physical quantity of the motion parameter is determined according to the specific barreling and polishing processing technology.
Preferably, in step S5, the distortion coefficient is calculated as follows:
Figure SMS_42
in the formula (I), the compound is shown in the specification,
Figure SMS_44
is speed
Figure SMS_46
The distortion coefficient of (a) is determined,
Figure SMS_48
the speed of the tumbling grinding block in the container in the actual model,
Figure SMS_50
to test the speed of the tumbling abrasive block in the container in the model,
Figure SMS_51
is acting force
Figure SMS_53
The distortion coefficient of (a) is determined,
Figure SMS_54
the acting force of the roll-polishing grinding block on the workpiece in the actual model,
Figure SMS_43
the acting force of the rolling polishing grinding block on the workpiece in the test model,
Figure SMS_45
、
Figure SMS_47
are respectively acting force
Figure SMS_49
And velocity
Figure SMS_52
Similar factors of (c).
Preferably, in step S6, the calculation formula of the total distortion coefficient is as follows:
Figure SMS_55
in the formula (I), the compound is shown in the specification,
Figure SMS_57
in order to be the overall velocity distortion factor,
Figure SMS_58
in order to be the overall force distortion factor,
Figure SMS_59
is as follows
Figure SMS_60
The velocity distortion factor of each data block,
Figure SMS_61
is as follows
Figure SMS_62
The force distortion factor within an individual data block,
Figure SMS_63
as to the number of the speed data blocks,
Figure SMS_56
the number of the acting force data blocks.
Preferably, in step S7, the calculation formula for predicting the actual model result in each data block by using the experimental model result and the global distortion coefficient is as follows:
Figure SMS_64
the prediction error in each data block is calculated as follows:
Figure SMS_65
the overall prediction error is calculated as follows:
Figure SMS_66
in the formula (I), the compound is shown in the specification,
Figure SMS_77
、
Figure SMS_79
、
Figure SMS_81
are respectively the first
Figure SMS_82
The speed of the roll-polishing grinding block in the container in the actual model of each data block, the speed of the roll-polishing grinding block in the container in the test model, and the speed result predicted based on the test model,
Figure SMS_83
、
Figure SMS_84
、
Figure SMS_85
are respectively the first
Figure SMS_67
The acting force of the roll-polishing grinding block on the workpiece in the actual model of each data block, the acting force of the roll-polishing grinding block on the workpiece in the test model, and the acting force result predicted based on the actual model,
Figure SMS_70
is as follows
Figure SMS_71
The speed prediction error of each data block,
Figure SMS_72
is as followsjThe force prediction error of each data block,
Figure SMS_73
in order to provide an overall speed prediction error,
Figure SMS_74
in order to predict the error for the total applied force,
Figure SMS_78
as to the number of the speed data blocks,
Figure SMS_80
the number of the acting force data blocks is,
Figure SMS_68
、
Figure SMS_69
respectively acting force
Figure SMS_75
And velocity
Figure SMS_76
Similar factors of (c).
Preferably, the tumbling finishing process is a spindle type tumbling finishing process, and the motion parameter of the spindle type tumbling finishing process comprises an angular velocity
Figure SMS_86
(ii) a In step S2, the angular velocity
Figure SMS_87
Has the similar proportional relation of
Figure SMS_88
(ii) a In step S3, the angular velocity
Figure SMS_89
Is a similarity factor of
Figure SMS_90
。
Preferably, the tumbling and polishing process is a one-dimensional horizontal vibration type tumbling and polishing process, and the motion parameters of the one-dimensional horizontal vibration type tumbling and polishing process include amplitude
Figure SMS_92
Frequency of the magnetic flux
Figure SMS_94
(ii) a In step S2, amplitude
Figure SMS_95
Frequency of
Figure SMS_96
Has the similar proportional relation of
Figure SMS_97
(ii) a In step S3, amplitude
Figure SMS_98
Frequency of the magnetic flux
Figure SMS_99
Is a similarity factor of
Figure SMS_91
、
Figure SMS_93
。
Compared with the prior art, the invention has the beneficial effects that:
when the test model is constructed, the flow field characteristics of the tumbling and polishing grinding block and the action characteristics of the tumbling and polishing grinding block on a workpiece in the tumbling and polishing process are mainly considered, namely the acting force of the tumbling and polishing grinding block on the workpiece and the speed of the tumbling and polishing grinding block in a container. Calculating similar factors related to physical quantities in the barreling and polishing system based on a dimensional analysis method; considering the influence of gravity acceleration, constructing a barreling polishing distortion model, and deducing a distortion coefficient calculation formula according to a similar theory; calculating a distortion coefficient by using a discrete element simulation method; and predicting the actual model result according to the test model result, calculating a prediction error, and verifying the effectiveness of the test model design method.
The test model constructed by the method has higher similarity with the actual model, and the purpose of reflecting the actual model result by the test model result is realized; for the research and development of the barreling and burnishing processing technology of the large-sized parts, the method can reduce the test cost, reduce the operation difficulty, shorten the test period, improve the research and development efficiency of the barreling and burnishing processing technology of the large-sized high-performance parts, and is favorable for the popularization and the application of the barreling and burnishing processing technology.
In addition, the method is not limited to the design of the barreling and burnishing test model of the large-sized part, and is also effective to the design of the barreling and burnishing test model of other parts.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required in the embodiments will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of a method for constructing a barreling and burnishing test model based on a similarity theory;
FIG. 2 is a schematic view of a main spindle type barrel polishing finishing process in embodiment 1;
FIG. 3 shows arrangement positions of barrel polishing grinding block speed and force data blocks extracted in spindle barrel polishing finishing in example 1;
FIG. 4 is the velocity distributions of the actual model, the test model, and the rolling and polishing grinding block predicted based on the test model in the spindle type barrel polishing finishing processing in example 1;
FIG. 5 shows the distribution of the acting force (normal force) of the main spindle type barrel polishing grinding block on the workpiece, which is predicted based on the test model, the test model and the actual model in the embodiment 1;
FIG. 6 shows the distribution of the acting force (tangential force) of the main spindle type barrel polishing grinding block on the workpiece, which is predicted based on the test model, the test model and the actual model in the embodiment 1;
FIG. 7 is a schematic view of one-dimensional horizontal vibration type barrel polishing and finishing processing in example 2;
FIG. 8 is a diagram showing the arrangement positions of force data blocks extracted in the one-dimensional horizontal vibration type barrel polishing in example 2;
fig. 9 is a layout position of a block of speed data of the barrel polishing block extracted in one-dimensional horizontal vibration type barrel polishing finishing processing in embodiment 2;
FIG. 10 is a graph showing the velocity distributions of the actual model, the test model, and the actual model roll-polishing block predicted based on the test model in the one-dimensional horizontal vibration type roll-polishing finishing process in example 2;
fig. 11 shows the distribution of the acting force of the actual model, the test model, and the actual model roll-polishing block predicted based on the test model on the workpiece (the normal force on the workpiece) in the one-dimensional horizontal vibration type roll-polishing finishing in embodiment 2;
fig. 12 shows the distribution of the acting force of the actual model, the test model, and the actual model roll-polishing block predicted based on the test model on the workpiece (the normal force on the lower side of the workpiece) in the one-dimensional horizontal vibration type roll-polishing finishing in embodiment 2;
fig. 13 shows the distribution of the acting force (the tangential force on the upper side of the workpiece) of the actual model, the test model, and the actual model roll-polishing block predicted based on the test model in the one-dimensional horizontal vibration type roll-polishing finishing process in embodiment 2 on the workpiece;
fig. 14 shows the distribution of the acting force of the actual model, the test model, and the actual model roll-polishing block predicted based on the test model on the workpiece (the tangential force on the lower side of the workpiece) in the one-dimensional horizontal vibration type roll-polishing finishing process in example 2.
In the figure: 1-a workpiece; 2-clamping; 3, rolling and polishing the grinding block; 4-a liquid medium; 5-a container; 6-a main shaft; 7-a vibration platform; 8-acting force data block in the main shaft type barreling and polishing process; 9-main shaft type barreling and polishing medium speed data block; 10-a workpiece upper side acting force data block in one-dimensional horizontal vibration type barreling and finishing processing; 11-a data block of acting force on the lower side of the workpiece in one-dimensional horizontal vibration type barreling and polishing processing; 12-one-dimensional horizontal vibration type barreling and finishing medium-speed data block.
Detailed Description
The technical solutions in the embodiments of the present invention are clearly and completely described with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without any creative effort, shall fall within the protection scope of the present invention.
It should be understood that the structures, ratios, sizes, and the like shown in the drawings and described in the specification are only used for understanding and reading the present disclosure, and are not used for limiting the limit of the present disclosure, which is not a technical meaning, and any structural modifications, ratio changes, or size adjustments may still fall within the scope of the present disclosure without affecting the function and the achievable effect of the present disclosure.
Example 1:
when the barreling finishing process is a spindle type barreling finishing process, the construction of the test model specifically comprises the following steps: as shown in the figure 1 of the drawings,
s1: analyzing the principle of main shaft type barreling and polishing processing, extracting dependent variables and physical quantities influencing the dependent variables in the main shaft type barreling and polishing processing technology, and integrating the physical quantities with the same physical meaning; the dependent variable in the main shaft type tumbling and polishing processing technology is the speed of the tumbling and polishing grinding block 3 in the container 5
Figure SMS_100
And the acting force of the rolling polishing grinding block 3 on the workpiece 1
Figure SMS_101
(ii) a The physical quantities affecting the dependent variable are integratedThe method comprises the following specific steps:
1) Dimensional parameters of workpiece 1, barrel polishing grinding block 3 and container 5
Figure SMS_103
(ii) a Dimensional parameters
Figure SMS_104
From the diameter of the container
Figure SMS_105
Height of the container
Figure SMS_106
Diameter of work
Figure SMS_107
Length of work piece
Figure SMS_108
Height of workpiece bottom from container
Figure SMS_109
Distance between the workpiece axis and the container wall
Figure SMS_102
Integrating the diameters of the rolling polishing grinding blocks;
2) Material parameters, including density, of the workpiece 1, the barrel polishing pad 3, and the container 5
Figure SMS_110
Shear modulus
Figure SMS_111
Poisson ratio
Figure SMS_112
；
3) Parameters of motion, including angular velocity
Figure SMS_113
(ii) a Angular velocity
Figure SMS_114
Speed of rotation of main shaft
Figure SMS_115
Workpiece rotation speed
Figure SMS_116
Integrating to obtain the product;
4) Other parameters, including simulation time
Figure SMS_117
Acceleration of gravity
Figure SMS_118
。
Speed of tumbling block 3 in container 5
Figure SMS_119
And the acting force of the rolling polishing grinding block 3 on the workpiece 1
Figure SMS_120
The functional relationship with other physical quantities is given by the formula (1-1):
Figure SMS_121
(1-1)
and (3) defining the similarity proportion of each physical quantity of the main shaft type barreling and burnishing processing test model and the actual model as a formula (1-2).
Figure SMS_123
、
Figure SMS_124
、
Figure SMS_125
、
Figure SMS_126
、
Figure SMS_127
、
Figure SMS_128
、
Figure SMS_129
、
Figure SMS_122
(1-2)
In the formula, subscript
Figure SMS_131
For test models, subscripts
Figure SMS_133
In order to be a practical model of the model,
Figure SMS_135
、
Figure SMS_136
、
Figure SMS_138
、
Figure SMS_139
、
Figure SMS_140
、
Figure SMS_130
、
Figure SMS_132
、
Figure SMS_134
、
Figure SMS_137
the density, the size parameter, the simulation time, the shear modulus, the Poisson ratio, the gravitational acceleration, the angular velocity, the acting force and the similar proportion of the speed of the test model and the actual model are respectively.
S2: by density
Figure SMS_141
And the size parameters
Figure SMS_142
Simulation time
Figure SMS_143
For basic dimension, a dimension analysis method is utilized to derive a similar proportional relation related to physical quantity in the spindle type barreling and polishing processing technology; the specific derivation process is as follows:
s201: by density
Figure SMS_144
Size parameter of
Figure SMS_145
Simulation time
Figure SMS_146
For basic dimension, the dimensional expressions related to physical quantities in the spindle type barreling and polishing process are as follows:
Figure SMS_147
s202: screening dimensionless physical quantity Poisson's ratio
Figure SMS_148
And converting the rest physical dimension expressions into dimension matrixes as shown in the following table:
Figure SMS_149
s203: transforming the dimension matrix obtained in the step S202 into a homogeneous linear equation system according to a dimension homogeneous principle, namely formula (1-3):
Figure SMS_150
(1-3)
the basic solution is obtained by the following formula (1-4):
Figure SMS_151
Figure SMS_152
(1-4)
and obtaining in spindle-type barrel-grinding finishing
Figure SMS_153
The formula (1-5):
Figure SMS_154
(1-5)
s204: according to the similarity theory, each of the test model and the actual model
Figure SMS_155
The same terms are used to derive similar proportional relational expressions of each physical quantity, see the expressions (1-6):
Figure SMS_156
(1-6)
in the formula (I), the compound is shown in the specification,
Figure SMS_158
、
Figure SMS_159
、
Figure SMS_160
shear modulus of the test model and the actual model respectively
Figure SMS_161
Acceleration of gravity
Figure SMS_162
Angular velocity
Figure SMS_163
Acting force
Figure SMS_164
And velocity
Figure SMS_157
Similar proportions of (a);
s3: ensure the balance of the workpiece 1, the rolling polishing grinding block 3 and the containerThe material parameters of the vessel 5 are all the same, i.e.
Figure SMS_165
(ii) a Setting the similarity factor of the geometric dimension between the test model and the actual model as
Figure SMS_166
(
Figure SMS_167
) And calculating respective similarity factors according to the similarity proportional relation of the physical quantities, wherein the similarity factors are as shown in the formula (1-7):
Figure SMS_168
(1-7)
in the formula (I), the compound is shown in the specification,
Figure SMS_170
、
Figure SMS_172
、
Figure SMS_174
、
Figure SMS_175
、
Figure SMS_177
respectively shear modulus
Figure SMS_178
Acceleration of gravity
Figure SMS_180
Density, density
Figure SMS_169
Size parameter of
Figure SMS_171
Simulation time
Figure SMS_173
Angular velocity
Figure SMS_176
Acting force
Figure SMS_179
And velocity
Figure SMS_181
A similarity factor of (d);
and the Poisson's ratio of the workpiece 1, the roll polishing grinding block 3 and the container 5 in the main shaft type roll polishing finishing processing technology
Figure SMS_182
Is dimensionless number, so the poisson ratio similarity factor between the experimental model and the actual model is 1.
S4: the similarity factor of the gravitational acceleration calculated in the step 3 is
Figure SMS_183
And (3) the condition is difficult to satisfy under the actual test condition (the similarity factor of the gravity acceleration under the actual condition is 1), and the similarity factor of the gravity acceleration is changed into 1 to obtain the barreling and polishing processing test model of the gravity acceleration distortion.
S5: correcting the speed and the acting force of the rolling polishing grinding block by adopting an analog simulation numerical fitting method, and deducing a calculation formula of a distortion coefficient, wherein the concrete deduction process is as follows:
s501: physical quantities of test model and actual model of barreling and polishing process of gravity acceleration distortion
Figure SMS_184
The relational expression of the formula is shown in the formula (1-8):
Figure SMS_185
(1-8)
in the formula (I), the compound is shown in the specification,
Figure SMS_202
、
Figure SMS_203
、
Figure SMS_204
、
Figure SMS_205
、
Figure SMS_206
shear modulus of the test model respectively
Figure SMS_207
Acceleration of gravity
Figure SMS_208
Angular velocity
Figure SMS_186
Acting force
Figure SMS_188
And velocity
Figure SMS_190
Is/are as follows
Figure SMS_192
The expression is given by the formula,
Figure SMS_194
、
Figure SMS_196
、
Figure SMS_198
、
Figure SMS_200
、
Figure SMS_187
is the shear modulus of the actual model
Figure SMS_189
Acceleration of gravity
Figure SMS_191
Angular velocity
Figure SMS_193
Acting force
Figure SMS_195
And velocity
Figure SMS_197
Is
Figure SMS_199
The formula of the expression is shown in the specification,
Figure SMS_201
is the distortion coefficient.
S502: according to a similar theory, the speed of the roll-polishing grinding block 3 in the container 5 in the distortion model of the spindle type roll-polishing finishing test constructed in the step 4
Figure SMS_209
And the acting force of the rolling polishing grinding block 3 on the workpiece 1
Figure SMS_210
Dimensionless functional relationships with other physical quantities are of the formula (1-9):
Figure SMS_211
(1-9)
s503: substituting the formula (1-9) into the formula (1-8) including the gravity acceleration
Figure SMS_212
The relational expression of the terms can be represented by the following formulae (1 to 10):
Figure SMS_213
(1-10)
the distortion coefficient formula for calculating the speed and the acting force of the rolling and polishing grinding block by substituting the formula (1-7) into the formula (1-10) is shown in (1-11):
Figure SMS_214
(1-11)
in the formula (I), the compound is shown in the specification,
Figure SMS_216
is speed
Figure SMS_218
The distortion coefficient of (a) is determined,
Figure SMS_220
the speed of the tumbling grinding block in the container in the actual model,
Figure SMS_222
to test the speed of the tumbling abrasive block in the container in the model,
Figure SMS_224
is acting force
Figure SMS_225
The coefficient of distortion of (a) is,
Figure SMS_226
the acting force of the roll-polishing grinding block on the workpiece in the actual model,
Figure SMS_215
the acting force of the rolling polishing grinding block on the workpiece in the test model,
Figure SMS_217
、
Figure SMS_219
are respectively acting force
Figure SMS_221
And velocity
Figure SMS_223
Similar factors of (c).
S6: in this embodiment, a similarity factor is set
Figure SMS_227
0.5, the dimensional parameters, material parameters, motion parameters and other parameters of the actual model and the experimental model are as shown in table 1:
TABLE 1 spindle-type barreling finishing actual model and test model parameters
Figure SMS_228
The discrete element simulation of the test model and the actual model is established according to the parameters in the table 1 (the actual model is 1 to the real object, and the ratio of the test model to the real object is 1
Figure SMS_229
: 1) The filling amount of the roll-polishing grinding block 3 is 50%, the number of particles is 12400, the container 5 is made of nylon, the roll-polishing grinding block 3 is made of brown corundum, and the workpiece 1 is made of stainless steel. Because the simulation aims at fitting the distortion coefficient, the simulation of simultaneous anticlockwise rotation of the main shaft 6 and the workpiece 1 is only carried out, discrete element simulation of a barreling and polishing test model and an actual model of gravity acceleration distortion in the main shaft type barreling and polishing process is respectively established according to similar factors related to physical quantities in the barreling and polishing process obtained in the S3, and the discrete element simulation is led into discrete element software EDEM for simulation, and the gravity acceleration is kept unchanged. As shown in fig. 3, after the simulation is finished, data blocks are arranged according to the size and configuration characteristics of the workpiece, the size and the number of the data blocks are determined by the specific workpiece 1, the speed of the roll-polishing grinding block in the container and the acting force of the roll-polishing grinding block on the workpiece in each data block of the test model and the actual model are respectively extracted, and data processing is performed.
Respectively calculating distortion coefficients of the speed and the acting force in each data block according to the formulas (1-11); averaging the distortion coefficients to obtain the total distortion coefficient, see formula (1-12):
Figure SMS_230
（1-12）
in the formula (I), the compound is shown in the specification,
Figure SMS_231
in order to be the overall velocity distortion factor,
Figure SMS_232
in order to have an overall force distortion coefficient,
Figure SMS_233
is as follows
Figure SMS_234
The velocity distortion factor of each data block,
Figure SMS_235
the applied force distortion coefficient in the jth data block,
Figure SMS_236
as to the number of the speed data blocks,
Figure SMS_237
the number of the acting force data blocks.
Combined with Table 1, the overall velocity distortion coefficient was calculated
Figure SMS_238
0.998, applied forces include normal forces
Figure SMS_239
And tangential force
Figure SMS_240
Wherein the coefficient of global normal force distortion
Figure SMS_241
1.299, total tangential force distortion coefficient
Figure SMS_242
1.266。
S7: in order to verify the effectiveness of the overall distortion coefficient, the test model result and the overall distortion coefficient are used for respectively predicting the actual model result in each data block, and the calculation formula is as shown in the formula (1-13):
Figure SMS_243
(1-13)
and respectively calculating the prediction error in each data block according to the formulas (1-14), and calculating the total prediction error as the formulas (1-15):
Figure SMS_244
(1-14)
Figure SMS_245
(1-15)
in the formula (I), the compound is shown in the specification,
Figure SMS_258
、
Figure SMS_260
、
Figure SMS_261
are respectively the first
Figure SMS_262
Actual model speed of the individual data blocks, test model speed, speed results predicted based on the test model,
Figure SMS_263
、
Figure SMS_264
、
Figure SMS_265
are respectively the first
Figure SMS_246
The actual model acting force of each data block, the experimental model acting force, the acting force result predicted based on the actual model,
Figure SMS_248
is as follows
Figure SMS_250
The speed prediction error of each data block,
Figure SMS_251
is as follows
Figure SMS_253
The force prediction error of each data block,
Figure SMS_255
in order to provide an overall speed prediction error,
Figure SMS_257
in order to predict the error for the total applied force,
Figure SMS_259
for the number of speed data blocks,
Figure SMS_247
the number of the acting force data blocks is,
Figure SMS_249
、
Figure SMS_252
respectively acting force
Figure SMS_254
And velocity
Figure SMS_256
The similarity factor of (c).
Fig. 4, 5, and 6 show an actual model, a test model, and a velocity distribution and an acting force distribution of each data block roll polishing grinding block predicted based on the test model in spindle type roll polishing finishing. The actual model is predicted by the test model result through calculation, the total prediction error of the speed of the rolling and polishing grinding block is 0.39%, the total prediction error of the normal force of the rolling and polishing grinding block on the workpiece is 12.92%, and the total prediction error of the tangential force of the workpiece is 13.87%; the speed data block 9 in the main shaft type barreling finishing processing is numbered from left to right in sequence from 1 to 9, as can be seen from fig. 4, the farther the speed data block 9 in the main shaft type barreling finishing processing is away from the axis of the container, the higher the speed of the barreling grinding block 3 is, the speed of the barreling grinding block 3 is approximately linearly increased along with the distance, and for the speed change of the barreling grinding block 3, a test model and an actual model show the same change rule; the acting force data blocks 8 in the spindle type barreling finishing processing are numbered from top to bottom in sequence from 1 to 8, and as can be seen from fig. 5 and 6, for the normal force and the tangential force applied to the workpiece 1, the lower the height of the acting force data block 8 in the spindle type barreling finishing processing is, the larger the acting force is, and for the acting force change of the barreling grinding block 3 to the workpiece 1, the same change rule is shown between a test model and an actual model.
The method for constructing the barreling and burnishing processing test model based on the similarity theory provided by the invention is proved to have higher precision for predicting the speed and the acting force of the barreling and burnishing block in the main shaft type barreling and burnishing processing, the test model has higher similarity with the actual model and shows the same change rule, and the test model can effectively reflect the result and the change rule of the actual model.
The distortion coefficients of the velocity and the applied force in each data block, and data such as a test model, an actual model, a prediction result of the actual model, a prediction error are shown in tables 2, 3, and 4:
TABLE 2 block velocity calculation data
Figure SMS_266
TABLE 3 data block normal force calculation data
Figure SMS_267
TABLE 4 tangential force calculation data for each data block
Figure SMS_268
FIG. 2 shows a schematic drawing of a spindle-type barreling process, in which the letters have the following meanings:
Figure SMS_270
the diameter of the container is the diameter of the container,
Figure SMS_271
the height of the container is taken as the height of the container,
Figure SMS_272
the diameter of the workpiece is taken as the diameter,
Figure SMS_273
is the length of the workpiece, and is,
Figure SMS_274
is the height of the bottom of the workpiece from the container,
Figure SMS_275
is the distance between the axis of the workpiece and the wall of the vessel,
Figure SMS_276
is the speed of the rotation of the container,
Figure SMS_269
is the workpiece rotation speed.
Example 2:
when the tumbling polishing process is one-dimensional horizontal vibration type tumbling polishing, the construction of the test model specifically comprises the following steps:
s1: analyzing the one-dimensional horizontal vibration type barreling and polishing machining principle, extracting dependent variables and physical quantities influencing the dependent variables in the one-dimensional horizontal vibration type barreling and polishing machining process, and integrating the physical quantities with the same physical significance; the dependent variable in the one-dimensional horizontal vibration type barreling and polishing processing technology is the speed of the barreling and polishing grinding block 3 in the container 5
Figure SMS_277
And the acting force of the rolling polishing grinding block 3 on the workpiece 1
Figure SMS_278
(ii) a The physical quantities affecting the dependent variable are specifically as follows after integration:
1) Dimensional parameters of workpiece 1, barrel polishing grinding block 3 and container 5
Figure SMS_280
(ii) a Dimensional parameter
Figure SMS_282
From the length of the container
Figure SMS_283
Width of container
Figure SMS_284
Height of the container
Figure SMS_285
Length of work piece
Figure SMS_286
Length of work piece
Figure SMS_287
Height of work
Figure SMS_279
Height of workpiece bottom from container
Figure SMS_281
Integrating the diameters of the rolling and polishing grinding blocks;
2) Material parameters, including density, of the workpiece 1, the barrel polishing pad 3, and the container 5
Figure SMS_288
Shear modulus
Figure SMS_289
Poisson ratio
Figure SMS_290
；
3) Parameters of motion, including amplitude
Figure SMS_291
Frequency of
Figure SMS_292
；
4) Other parameters, including simulation time
Figure SMS_293
Acceleration of gravity
Figure SMS_294
。
The speed of the tumbling grinding block 3 in the container 5
Figure SMS_295
And the acting force of the rolling polishing grinding block 3 on the workpiece 1
Figure SMS_296
The functional relationship with other physical quantities is given by the formula (2-1):
Figure SMS_297
(2-1)
and (3) defining the similarity ratio of each physical quantity of the main shaft type barreling and burnishing processing test model and the actual model as formula (2-2).
Figure SMS_299
、
Figure SMS_300
、
Figure SMS_301
、
Figure SMS_302
、
Figure SMS_303
、
Figure SMS_304
、
Figure SMS_305
、
Figure SMS_298
(2-2)
In the formula, subscript
Figure SMS_307
For test models, subscripts
Figure SMS_310
In order to be a practical model,
Figure SMS_312
、
Figure SMS_314
、
Figure SMS_315
、
Figure SMS_316
、
Figure SMS_317
、
Figure SMS_306
、
Figure SMS_308
、
Figure SMS_309
、
Figure SMS_311
、
Figure SMS_313
similar proportions of the density, the size parameter, the simulation time, the shear modulus, the Poisson ratio, the gravity acceleration, the amplitude, the frequency, the acting force and the speed of the test model and the actual model are respectively shown.
S2: by density
Figure SMS_318
And the size parameters
Figure SMS_319
Simulation time
Figure SMS_320
Deriving a similar proportional relation related to physical quantity in the one-dimensional vibration type barreling and polishing system based on a dimensional analysis method for basic dimension; the specific derivation process is as follows:
s201: by density
Figure SMS_321
Size parameter of
Figure SMS_322
Simulation time
Figure SMS_323
For basic dimensions, the dimensional expressions relating to physical quantities in the one-dimensional vibratory barreling process are as follows:
Figure SMS_324
s202: screening dimensionless physical quantity Poisson's ratio
Figure SMS_325
Converting the other physical dimension expressions into dimension matrixes as follows:
Figure SMS_326
s203: transforming the dimension matrix obtained in the step S202 into a homogeneous linear equation system according to a dimension homogeneous principle, namely formula (2-3):
Figure SMS_327
(2-3)
the basic solution is obtained by the following formula (2-4):
Figure SMS_328
Figure SMS_329
(2-4)
and obtaining in one-dimensional oscillatory type tumbling finishing
Figure SMS_330
The formula (2-5):
Figure SMS_331
(2-5)
s204: according to the similarity theory, each of the test model and the actual model
Figure SMS_332
The same terms are used, and similar proportional relational expressions of the physical quantities are obtained through derivation, which are shown in the formula (2-6):
Figure SMS_333
(2-6)
in the formula (I), the compound is shown in the specification,
Figure SMS_335
、
Figure SMS_337
、
Figure SMS_338
shear modulus of test model and actual model respectively
Figure SMS_339
Acceleration of gravity
Figure SMS_340
Amplitude of vibration
Figure SMS_341
Frequency of
Figure SMS_342
Acting force
Figure SMS_334
And velocity
Figure SMS_336
Similar proportions of (a);
s3: ensuring that the material parameters of the workpiece 1, the barrel polishing grinding block 3 and the container 5 are the same, i.e.
Figure SMS_343
(ii) a Setting the similarity factor of the geometric dimension between the test model and the actual model as
Figure SMS_344
(
Figure SMS_345
) And calculating respective similarity factors according to the similarity proportional relation of the physical quantities, wherein the similarity factors are as shown in the formula (2-7):
Figure SMS_346
、
Figure SMS_347
、
Figure SMS_348
(2-7)
in the formula (I), the compound is shown in the specification,
Figure SMS_350
、
Figure SMS_352
、
Figure SMS_354
、
Figure SMS_356
、
Figure SMS_357
respectively shear modulus
Figure SMS_359
Acceleration of gravity
Figure SMS_361
Density, density
Figure SMS_349
Size parameter of
Figure SMS_351
Simulation time
Figure SMS_353
Amplitude of vibration
Figure SMS_355
Frequency of
Figure SMS_358
Acting force
Figure SMS_360
And velocity
Figure SMS_362
A similarity factor of (d);
and because of Poisson's ratio of the workpiece 1, the roll-polishing grinding block 3 and the container 5 in the one-dimensional vibration type roll-polishing finishing processing technology
Figure SMS_363
Is a dimensionless number, so the poisson ratio similarity factor between the experimental model and the actual model is 1.
S4: the similarity factor of the gravitational acceleration calculated in the step 3 is
Figure SMS_364
And (4) the test model is difficult to satisfy under actual test conditions (the similarity factor of the gravity acceleration under the actual conditions is 1), the similarity factor of the gravity acceleration is changed into 1, and the test model of the barreling and polishing processing of the gravity acceleration distortion is obtained.
S5: correcting the speed and the acting force of the rolling polishing grinding block by adopting an analog simulation numerical fitting method, and deducing a calculation formula of a distortion coefficient, wherein the concrete deduction process is as follows:
s501: physical quantities of test model and actual model of barreling and polishing process of gravity acceleration distortion
Figure SMS_365
The relational expression of the formula is shown in the formula (2-8):
Figure SMS_366
(2-8)
in the formula (I), the compound is shown in the specification,
Figure SMS_368
、
Figure SMS_369
、
Figure SMS_371
、
Figure SMS_374
、
Figure SMS_378
shear modulus of the test model respectively
Figure SMS_380
Acceleration of gravity
Figure SMS_382
Amplitude of vibration
Figure SMS_384
Frequency of
Figure SMS_385
Acting force
Figure SMS_386
And velocity
Figure SMS_387
Is/are as follows
Figure SMS_388
The expression is given by the formula,
Figure SMS_389
、
Figure SMS_390
、
Figure SMS_391
、
Figure SMS_367
、
Figure SMS_370
is the shear modulus of the actual model
Figure SMS_372
Acceleration of gravity
Figure SMS_373
Amplitude of vibration
Figure SMS_375
Frequency of the magnetic flux
Figure SMS_376
Acting force
Figure SMS_377
And velocity
Figure SMS_379
Is/are as follows
Figure SMS_381
The formula of the expression is shown in the specification,
Figure SMS_383
is the distortion coefficient.
S502: according to a similar theory, the speed of the tumbling grinding block in the container in the one-dimensional vibration type tumbling grinding and finishing processing test distortion model constructed in the step 4
Figure SMS_392
And the acting force of the rolling and polishing grinding block on the workpiece
Figure SMS_393
Dimensionless functional relationships with other physical quantities are of the formula (2-9):
Figure SMS_394
(2-9)
s503: substituting formula (2-9) into formula (2-8) contains gravity acceleration
Figure SMS_395
The relational expression of the terms can be represented by the formula (2-10):
Figure SMS_396
(2-10)
the distortion coefficient formula of the speed and the acting force of the rolling and polishing grinding block can be obtained by substituting the formula (2-7) into the formula (2-10) and is shown in (2-11):
Figure SMS_397
(2-11)
in the formula (I), the compound is shown in the specification,
Figure SMS_399
is a speed
Figure SMS_400
The coefficient of distortion of (a) is,
Figure SMS_402
for the speed of the tumbling abrasive block in the container in the actual model,
Figure SMS_405
to test the speed of the tumbling abrasive block in the container in the model,
Figure SMS_406
is acting force
Figure SMS_407
The distortion coefficient of (a) is determined,
Figure SMS_409
the acting force of the roll-polishing grinding block on the workpiece in the actual model,
Figure SMS_398
the acting force of the rolling polishing grinding block on the workpiece in the test model,
Figure SMS_401
、
Figure SMS_403
respectively acting force
Figure SMS_404
And velocity
Figure SMS_408
The similarity factor of (c).
S6: in this embodiment, a similarity factor is set
Figure SMS_410
Is 0.8. The dimensional parameters, material parameters, motion parameters and other parameters of the actual model and the experimental model are shown in table 5:
TABLE 5 parameters of one-dimensional horizontal vibration type barreling and burnishing actual model and proportional model
Figure SMS_411
Discrete element simulation of the test model and the actual model was established according to the parameters in table 5 (the actual model is 1 to the real object, and the ratio of the test model to the real object is 1
Figure SMS_412
: 1) The filling amount of the barrel polishing abrasive block 3 is 75%, and the number of the particles is 4400. The container 5 is made of nylon, the rolling polishing grinding block 3 is made of brown corundum, and the workpiece 1 is made of titanium alloy. And respectively establishing discrete element simulation of a barreling and burnishing test model and an actual model of gravity acceleration distortion in the one-dimensional vibration type barreling and burnishing process according to the similarity factors related to physical quantities in the barreling and burnishing process obtained in the S3, and importing the discrete element simulation into discrete element software EDEM for simulation, wherein the gravity acceleration is kept unchanged. As shown in fig. 8 and 9, after the simulation is finished, data blocks are arranged according to the size and configuration characteristics of the workpiece, the size and the number of the data blocks are determined by the specific workpiece, the speed of the roll-polishing grinding block 3 in the container 5 and the acting force of the roll-polishing grinding block 3 on the workpiece 1 in each data block of the test model and the actual model are respectively extracted, and data processing is performed.
Respectively calculating the distortion coefficients of the speed and the acting force in each data block according to the formulas (2-11); the average value of the distortion coefficients is obtained by the following formula (2-12):
Figure SMS_413
（2-12）
in the formula (I), the compound is shown in the specification,
Figure SMS_415
as a result of the overall speed distortion factor,
Figure SMS_416
in order to be the overall force distortion factor,
Figure SMS_417
is a first
Figure SMS_418
The speed distortion factor of each data block,
Figure SMS_419
is a first
Figure SMS_420
The coefficient of force distortion within each data block,
Figure SMS_421
for the number of speed data blocks,
Figure SMS_414
the number of the acting force data blocks.
Combined with Table 5, the overall velocity distortion coefficient was calculated
Figure SMS_422
1.531, acting forces include normal forces
Figure SMS_423
And tangential force
Figure SMS_424
Wherein the distortion coefficient of the overall normal force on the upper side of the workpiece
Figure SMS_425
1.544, distortion coefficient of overall tangential force on the upper side of the workpiece
Figure SMS_426
1.527; distortion coefficient of total normal force at lower side of workpiece
Figure SMS_427
1.480, distortion coefficient of total tangential force of lower side of workpiece
Figure SMS_428
1.429。
S7: in order to verify the effectiveness of the overall distortion coefficient, the test model result and the overall distortion coefficient are used for respectively predicting the actual model result in each data block, and the calculation formula is as shown in the formula (2-13):
Figure SMS_429
(2-13)
and respectively calculating the prediction error in each data block according to the formula (2-14), and calculating the total prediction error as the formula (2-15):
Figure SMS_430
(2-14)
Figure SMS_431
(2-15)
in the formula (I), the compound is shown in the specification,
Figure SMS_443
、
Figure SMS_445
、
Figure SMS_446
are respectively the first
Figure SMS_448
Actual model speed of the individual data blocks, test model speed, speed results predicted based on the test model,
Figure SMS_449
、
Figure SMS_450
、
Figure SMS_451
are respectively the first
Figure SMS_432
Actual model acting force and test model of individual data blockModel forces, force outcomes predicted based on actual models,
Figure SMS_434
is as follows
Figure SMS_436
The speed prediction error of each data block,
Figure SMS_438
is as follows
Figure SMS_440
The force prediction error of each data block,
Figure SMS_442
in order to provide an overall speed prediction error,
Figure SMS_444
in order to predict the error for the total applied force,
Figure SMS_447
as to the number of the speed data blocks,
Figure SMS_433
the number of the acting force data blocks is,
Figure SMS_435
、
Figure SMS_437
are respectively acting force
Figure SMS_439
And velocity
Figure SMS_441
The similarity factor of (c).
Fig. 10, 11, 12, 13, and 14 show an actual model, a test model, and a velocity distribution and an acting force distribution of each data block roll-polishing block predicted based on the test model in spindle-type roll-polishing finishing. Calculating to obtain a result, predicting an actual model by using a test model result, wherein the total prediction error of the speed of the rolling and polishing grinding block is 1.42%, the total prediction error of the rolling and polishing grinding block on the normal force of the upper side of the workpiece is 11.78%, and the total prediction error of the rolling and polishing grinding block on the tangential force of the upper side of the workpiece is 9.22%; the overall prediction error of the roll polishing grinding block on the normal force of the lower side of the workpiece is 19.99%, and the overall prediction error on the tangential force of the lower side of the workpiece is 17.79%. The speed data block 12 in the one-dimensional horizontal vibration type tumbling and polishing processing is numbered from left to right from the left wall of the container in sequence from 1 to 10, as can be seen from fig. 10, the speed of the tumbling and polishing grinding block 3 shows a rule of firstly decreasing and then increasing along the left-to-right direction of the container 5, and is symmetrical along the central line of the container 5, and for the speed change of the tumbling and polishing grinding block, a test model and an actual model show the same change rule; as can be seen from fig. 11 to 14, the test model and the actual model also show similar variation rules for the normal force and the tangential force applied to the workpiece.
The method for constructing the barreling and burnishing test model based on the similarity theory has higher precision on the prediction of the speed and the acting force of the barreling and burnishing block in the one-dimensional vibration type barreling and burnishing, the test model has higher similarity with the actual model and shows the same change rule, and the test model can effectively reflect the result and the change rule of the actual model.
The distortion coefficient of the velocity in each data block, the test model, the actual model prediction result, the prediction error, and the like are shown in table 6. The method of calculating the force of each data block is the same as the method of calculating the velocity, and since the force data blocks are too many in the present embodiment, the description thereof will not be given.
TABLE 6 speed calculation data for each data block
Figure SMS_452
FIG. 6 shows a schematic diagram of a one-dimensional horizontal vibration type barrel polishing process, in which the meanings of the letters are as follows:
Figure SMS_454
the length of the container is taken as the length of the container,
Figure SMS_455
is the height of the container，
Figure SMS_457
Is the length of the workpiece, and is,
Figure SMS_458
is the height of the workpiece, and is,
Figure SMS_459
is the distance between the workpiece and the bottom of the container,
Figure SMS_460
is the amplitude of the vibration to be measured,
Figure SMS_461
is the frequency. In addition, the width of the container
Figure SMS_453
And width of the workpiece
Figure SMS_456
Not shown in the figure.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention should be covered within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.

Claims (8)

1. A method for constructing a barreling and polishing test model based on a similar theory is characterized by comprising the following steps:
s1: analyzing the principle of barreling and burnishing processing, and extracting the dependent variable and the physical quantity influencing the dependent variable in the barreling and burnishing processing process, wherein the dependent variable is the speed of a barreling and burnishing block in a container
Figure QLYQS_1
And the acting force of the rolling and polishing grinding block on the workpiece
Figure QLYQS_3
(ii) a The physical quantities affecting the dependent variable are specifically: dimensional parameters of workpiece, barrel polishing grinding block and container
Figure QLYQS_4
(ii) a Material parameters, including density, of the workpiece, barrel polishing pad and container
Figure QLYQS_5
Shear modulus
Figure QLYQS_6
Poisson ratio of
Figure QLYQS_7
(ii) a A motion parameter; other parameters, including simulation time
Figure QLYQS_8
Acceleration of gravity
Figure QLYQS_2
；
S2: by density
Figure QLYQS_9
And the size parameters
Figure QLYQS_10
Simulation time
Figure QLYQS_11
Obtaining a similar proportional relation related to physical quantity in the barreling and polishing processing technology by using a dimension analysis method as a basic dimension;
s3: ensuring the same material parameters of the test model and the actual model, and setting the size parameters between the test model and the actual model
Figure QLYQS_12
Is a similarity factor of
Figure QLYQS_13
Obtaining similar factors of other physical quantities;
s4: estimated gravitational acceleration
Figure QLYQS_14
The similarity factor is difficult to satisfy under the actual test condition, and the gravity acceleration between the test model and the actual model is determined
Figure QLYQS_15
The similarity factor of the gravity acceleration distortion is changed into 1, and a barreling and polishing processing test model of the gravity acceleration distortion is obtained;
s5: correcting the speed and acting force of the tumbling grinding block by adopting an analog simulation numerical fitting method, and deducing a calculation formula of a distortion coefficient;
s6: establishing discrete element simulation of the actual model and the test model obtained in the step S4; arranging data blocks in the test model and the actual model, and respectively extracting the barreling polishing processing test model with gravity acceleration distortion, the speed of the barreling polishing grinding block in a container in each data block in the actual model and the acting force of the barreling polishing grinding block on a workpiece; calculating distortion coefficients of the speed and the acting force in each data block, and averaging the distortion coefficients to obtain an overall distortion coefficient;
s7: and respectively predicting the actual model result in each data block by using the test model result and the overall distortion coefficient, calculating the prediction error in each data block, calculating the overall prediction error, and judging the effectiveness of the test model.
2. The method for constructing the barreling and burnishing processing test model based on the similarity theory as claimed in claim 1, wherein: in step S2, the similar proportional relation between the test model and the actual model is shown as follows:
Figure QLYQS_16
in the formula (I), the compound is shown in the specification,
Figure QLYQS_18
shear modulus of the test model and the actual model respectively
Figure QLYQS_20
Acceleration of gravity
Figure QLYQS_21
Density, density
Figure QLYQS_22
Size parameter of
Figure QLYQS_23
Simulation time
Figure QLYQS_24
Acting force
Figure QLYQS_25
And velocity
Figure QLYQS_17
Similar proportions of (a); poisson ratio
Figure QLYQS_19
The similar proportional relation of the relevant physical quantities of the motion parameters is determined according to the specific barreling and polishing process.
3. The method for constructing the barreling and burnishing processing test model based on the similarity theory as claimed in claim 2, wherein: in step S3, the material parameters of the test model and the actual model are the same, namely the density of the test model and the actual model
Figure QLYQS_26
Shear modulus
Figure QLYQS_27
The similarity factor of (a) is 1; poisson ratio
Figure QLYQS_28
The Poisson ratio similarity factor of the test model and the actual model is 1; similar factors related to physical quantities in the barreling and polishing process are shown as follows:
Figure QLYQS_29
in the formula (I), the compound is shown in the specification,
Figure QLYQS_31
、
Figure QLYQS_33
、
Figure QLYQS_36
、
Figure QLYQS_38
、
Figure QLYQS_39
respectively shear modulus
Figure QLYQS_40
Acceleration of gravity
Figure QLYQS_41
Density, density
Figure QLYQS_30
And the size parameters
Figure QLYQS_32
Simulation time
Figure QLYQS_34
Acting force
Figure QLYQS_35
And velocity
Figure QLYQS_37
A similarity factor of (c); the similarity factor of the relevant physical quantity of the motion parameter is determined according to the specific barreling and polishing processing technology.
4. The method for constructing the barreling and burnishing processing test model based on the similarity theory as claimed in claim 3, wherein: in step S5, a calculation formula of the distortion coefficient is shown as follows:
Figure QLYQS_42
in the formula (I), the compound is shown in the specification,
Figure QLYQS_44
is speed
Figure QLYQS_46
The distortion coefficient of (a) is determined,
Figure QLYQS_48
for the speed of the tumbling abrasive block in the container in the actual model,
Figure QLYQS_50
to test the speed of the tumbling abrasive block in the container in the model,
Figure QLYQS_52
is acting force
Figure QLYQS_53
The distortion coefficient of (a) is determined,
Figure QLYQS_54
the acting force of the roll-polishing grinding block on the workpiece in the actual model,
Figure QLYQS_43
the acting force of the rolling polishing grinding block on the workpiece in the test model,
Figure QLYQS_45
、
Figure QLYQS_47
are respectively acting force
Figure QLYQS_49
And velocity
Figure QLYQS_51
Similar factors of (c).
5. The method for constructing the barreling and burnishing processing test model based on the similarity theory as claimed in claim 4, wherein: in step S6, the calculation formula of the total distortion coefficient is shown as follows:
Figure QLYQS_55
in the formula (I), the compound is shown in the specification,
Figure QLYQS_57
in order to be the overall velocity distortion factor,
Figure QLYQS_58
in order to be the overall force distortion factor,
Figure QLYQS_59
is as follows
Figure QLYQS_60
The velocity distortion factor of each data block,
Figure QLYQS_61
is a first
Figure QLYQS_62
The force distortion factor within an individual data block,
Figure QLYQS_63
for the number of speed data blocks,
Figure QLYQS_56
the number of the acting force data blocks.
6. The method for constructing the barreling and burnishing processing test model based on the similarity theory as claimed in claim 5, wherein: in step S7, a calculation formula for predicting the actual model result in each data block using the test model result and the total distortion coefficient is as follows:
Figure QLYQS_64
the prediction error in each data block is calculated as follows:
Figure QLYQS_65
the overall prediction error is calculated as follows:
Figure QLYQS_66
in the formula (I), the compound is shown in the specification,
Figure QLYQS_78
、
Figure QLYQS_80
、
Figure QLYQS_82
are respectively the first
Figure QLYQS_83
The speed of the roll-polishing grinding block in the container in the actual model of each data block, the speed of the roll-polishing grinding block in the container in the test model, and the speed predicted based on the test modelAs a result of this the user can,
Figure QLYQS_84
、
Figure QLYQS_85
、
Figure QLYQS_86
are respectively the first
Figure QLYQS_67
The acting force of the roll polishing grinding block on the workpiece in the actual model of each data block, the acting force of the roll polishing grinding block on the workpiece in the test model, and the acting force result predicted based on the actual model,
Figure QLYQS_69
is a first
Figure QLYQS_71
The speed prediction error of each data block,
Figure QLYQS_73
is as follows
Figure QLYQS_75
The force prediction error of each data block,
Figure QLYQS_77
in order to provide an overall speed prediction error,
Figure QLYQS_79
in order to predict the error for the total applied force,
Figure QLYQS_81
for the number of speed data blocks,
Figure QLYQS_68
the number of the acting force data blocks is,
Figure QLYQS_70
、
Figure QLYQS_72
are respectively acting force
Figure QLYQS_74
And velocity
Figure QLYQS_76
Similar factors of (c).
7. The method for constructing the barreling and burnishing processing test model based on the similarity theory as claimed in claim 6, wherein: the tumbling and polishing process is a main shaft type tumbling and polishing process, and the motion parameters of the main shaft type tumbling and polishing process comprise angular velocity
Figure QLYQS_87
(ii) a In step S2, the angular velocity
Figure QLYQS_88
Is in a similar proportion of
Figure QLYQS_89
(ii) a In step S3, the angular velocity
Figure QLYQS_90
Is a similarity factor of
Figure QLYQS_91
。
8. The method for constructing the barreling and burnishing processing test model based on the similarity theory as claimed in claim 6, wherein: the tumbling and polishing process is one-dimensional horizontal vibration type tumbling and polishing process, and the motion parameters of the one-dimensional horizontal vibration type tumbling and polishing process comprise amplitude
Figure QLYQS_93
Frequency of
Figure QLYQS_95
(ii) a In step S2, amplitude
Figure QLYQS_96
Frequency of
Figure QLYQS_97
Has the similar proportional relation of
Figure QLYQS_98
(ii) a In step S3, amplitude
Figure QLYQS_99
Frequency of
Figure QLYQS_100
Is a similarity factor of
Figure QLYQS_92
、
Figure QLYQS_94
。
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