CN109063397A - The installability quick calculation method of two hole of one kind based on equal tolerance values principle - Google Patents
The installability quick calculation method of two hole of one kind based on equal tolerance values principle Download PDFInfo
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- CN109063397A CN109063397A CN201811192408.8A CN201811192408A CN109063397A CN 109063397 A CN109063397 A CN 109063397A CN 201811192408 A CN201811192408 A CN 201811192408A CN 109063397 A CN109063397 A CN 109063397A
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Abstract
The present invention relates to computer aided measurement fields, specifically, it is related to a kind of installability quick calculation method of two holes based on mathematical computations based on equal tolerance values principle, it comprises the steps of: step 1, the adjustment amount of the geometry design parameter and measuring point of acquisition pores part and prefabricated calibration fiducial axis；Step 2, fitting diameter, the fitting orientation of each hole are asked；Step 3, using the geometric parameter for being fitted geometric parameter and standard axle in hole, the adjustment amount maximum value of standard shaft diameter is solved.
Description
Technical Field
The invention relates to the field of computer-aided measurement, in particular to a mathematical computation-based quick installability calculation method for two sections of holes based on an equal tolerance value principle.
Background
The stepped shaft and the mounting hole thereof are widely applied in the mechanical field. At present, the hole-shaft fit type part mainly controls the minimum clearance (representing assemblability) and the maximum clearance (representing assembly precision) of hole-shaft fit by controlling the dimensional tolerance of each section of hole and shaft and the coaxiality tolerance between the hole and the shaft on the same part.
If the designed dimensional tolerance and geometric tolerance are appropriate and the dimensional and geometric errors of the parts are in accordance with the designed tolerance, the assemblability and the assembly accuracy of the parts can be ensured. In this case, the parts are completely interchangeable.
If the dimensional and geometric tolerances of the design are small, the likelihood of the dimensional and geometric errors of the part being out of tolerance increases. In this case, the number of parts conforming to the design tolerance is reduced, and the cost for achieving complete interchange of parts is increased.
At present, on the premise of not increasing the manufacturing cost of parts and not reducing the assembly performance and the assembly precision, the method for improving the utilization rate of the parts mainly adopts the grading tolerance. However, the design of the present grading tolerance is mainly dependent on engineering experience. This approach increases design costs as experienced engineers are scarce. Different experienced engineers may design and approve different grading tolerance schemes, which increases communication costs between departments and enterprises.
If time or manufacturing costs can be increased appropriately, it is also possible to use a heuristic, matching approach. However, since the actual parts are not easily attached and detached, the cost increase of this method is significant.
In summary, because no installability quick calculation method is introduced, the prior art has higher cost in solving the problem of assembling high-precision coaxial parts which are difficult to completely interchange.
Disclosure of Invention
The purpose of the invention is:
aiming at the problems in the prior art, the invention realizes a mathematical calculation-based low-cost quick installability calculation method based on the principle of equal tolerance value by calculating a standard shaft part matched with two sections of holes.
The scheme adopted by the invention is as follows:
the method for quickly calculating the installability of the two sections of holes based on the principle of equal tolerance values comprises the following steps of:
step 1, acquiring geometric design parameters and measuring points of the hole part and presetting the adjustment amount of a standard axis.
The stepped hole consists of a fine hole and a coarse hole, and a section of transition hole is connected between the fine hole and the coarse hole.
Nominal diameter of pored 1Nominal length ofL 1(ii) a Nominal diameter of the transition hole isD 2Nominal length ofL 2(ii) a The nominal diameter of the coarse pores isd 3Nominal length ofL 3。
Nominal diameter of the coarse holesd 3Greater than or equal to the nominal diameter of the poresd 1(ii) a Nominal diameter of transition holeD 2Greater than the nominal diameter of the poresd 1。
By bringing the axis of the fine hole close to the measuring coordinate systemzAxis, the geometric centre of the fine hole being close to the origin of the measuring coordinate system and the geometric centre of the coarse hole being such that it is in the measuring coordinate systemzThe projection on the axis is positive.
The measuring point set of the pore isp i |p i ={x i ,y i ,z i },i=1,2,…,N 1}; the measuring point set of the coarse aperture isp i |p i ={x i ,y i ,z i },i=N 1+1,N 1+2,…,N 1+N 2}。
The standard shaft system consists of a fine shaft and a coarse shaft which are completely coaxial, and a section of transition shaft is connected between the fine shaft and the coarse shaft. The three-segment axes are all standard axes and have no geometric errors. The geometric center of the thin shaft is at the origin, and the common axis of the thin shaft and the thick shaft is atzOn the shaft.
The diameter of the thin shaft isd 1+EHas a length ofL 1(ii) a The diameter of the transition shaft isd 2Has a length ofL 2(ii) a The diameter of the thick shaft isd 3+EHas a length ofL 3. Wherein,Ean arbitrary value is preset here for the adjustment of the shaft diameter.
Diameter of transition shaftd 2Smaller than the diameter of the thin shaftd 1。
After step 1, step 2 is performed.
And 2, solving the fitting diameter and the fitting direction of each section of hole.
Solving the maximum inscribed cylinder radius of the fine hole through the formula (1)R 4,mAnd recording the optimum solution [ alpha ], [ alphad x,4,m,d y,4,m,d rx,4,m,d ry,4,m]Whereind x ,d y ,d rx ,d ry are free variables, representing edges respectivelyxA shaft,yTranslation and winding of shaftsxA shaft,yRotation of the shaft. Of fine poresxDirection inscribed translation error is-d x,4,m、yDirection inscribed translation error is-d y,4,m、xError of direction inscribed angle-d rx,4,mAnd, furthermore,ydirection inscribed rotation error is-d ry,4,m。
(1)
Solving the maximum inscribed cylinder radius of the coarse axis through the formula (2)R 6,mAnd recording the optimum solution [ alpha ], [ alphad x,6,m,d y,6,m,d rx,6,m,d ry,6,m]Whereind x ,d y ,d rx ,d ry is a free variable. Of a thick shaftxDirection inscribed translation error is-d x,6,m、yDirection inscribed translation error is-d y,6,m、xError of direction inscribed angle-d rx,6,mAnd, furthermore,ydirection inscribed rotation error is-d ry,6,m。
(2)
After step 2, step 3 is performed.
And 3, solving the maximum value of the adjustment quantity of the diameter of the standard shaft by using the fitting geometric parameters of the hole and the geometric parameters of the standard shaft.
Calculating the maximum value of the adjustment amount by the formula (3)E * 。
(3)
s.t.
Wherein,
r 1,Mis the radius of the thin axis of the shaft,r 1,M=0.5(d 1+E)；
r 4,Mis the radius of the thick axis and,r 4,M=0.5(d 3+E)；
Δ6-3,4-1,mis the minimum comprehensive gap of the coarse axis of the coarse hole, namely: after the fine hole is installed in the fine shaft, in the process of adjusting the position and the direction of the shaft part, at least an adjustment allowance (surface distance) can be kept between the coarse shaft and the coarse hole; calculating the minimum comprehensive gap delta of the coarse axis of the coarse hole by the formula (4)6-3,4-1,m。
(4)
s.t.
Wherein,
R 6,4-1,mis that the coarse holes are arranged in the mounting and adjusting processxOyMaximum inscribed projection of planeThe radius of the circle is that of the circle,
maximum value of adjustment amountE * Corresponding thin and thick shaft diametersd 1 * , d 3 * The maximum diameter of the shaft part with the same tolerance value, which can be filled in the two sections of hole parts, is calculated according to the formula (5) and the formula (6).
d 1 * =d 1+E * (5)
d 3 * =d 3+E * (6)
And finishing the calculation after the step 3 is finished.
The invention has the beneficial effects that:
1. for high-precision coaxial two-section hole parts which are difficult to completely interchange, the installability of the two-section shaft part can be calculated by measuring the equal tolerance value of data and a standard shaft. 2. The prediction and classification of the assemblability of the two-section hole part can be realized through intuitive installability indexes. 3. Only general three-coordinate measuring equipment and a computer are needed, the measuring flexibility is high, and the measuring cost is not high. 4. The requirements on hardware and mathematics are low, and the popularization is facilitated.
The industrial possibility of the invention is:
the invention provides a method for rapidly calculating the installability of two-section shafts based on coordinate measurement and mathematical calculation, which has the advantages of simple process, low cost and easy use and popularization. Therefore, the invention has the possibility of industrial production.
Drawings
FIG. 1 is a flow chart of the present invention.
FIG. 2 is a drawing showing the structure and tolerance of a suitable part of the present invention.
FIG. 3 is a schematic diagram of a detail design of an embodiment.
FIG. 4 is a schematic view of a distribution of measurement points according to an embodiment.
In the figure: 1, thin shaft; 2, a transition shaft; 3, a thick shaft; 4, fine pores; 41, measuring point set of thin axis; 5, transition holes; 6, coarse holes; 61, set of measurement points for the coarse axis.
Detailed Description
The following are specific embodiments of the present invention, and the embodiments of the present invention will be further described with reference to the drawings, but the present invention is not limited to these embodiments.
A method for rapidly calculating the installability of two sections of holes based on the principle of equal tolerance values comprises the following four steps (unit: millimeter, radian):
step 1, acquiring geometric design parameters and measuring points of the hole part and presetting the adjustment amount of a standard axis.
The two sections of holes consist of fine holes and coarse holes, and a section of transition hole is connected between the fine holes and the coarse holes.
Nominal diameter of the pores was 20 and nominal length was 30; the nominal diameter of the transition hole is 24 and the nominal length is 10; the coarse holes had a nominal diameter of 30 and a nominal length of 50.
By bringing the axis of the fine hole close to the measuring coordinate systemzAxis, the geometric centre of the fine hole being close to the origin of the measuring coordinate system and the geometric centre of the coarse hole being such that it is in the measuring coordinate systemzThe projection on the axis is positive.
The measuring point set of the pore isp i |p i ={x i ,y i ,z i },i=1,2, …, 20 }; the measuring point set of the coarse aperture isp i |p i ={x i ,y i ,z i },i=21,22,…,40}。
The standard shaft system consists of a fine shaft and a coarse shaft which are completely coaxial, and a section of transition shaft is connected between the fine shaft and the coarse shaft. The three sections of holes are all used as standard axes and have no geometric errors. The geometric center of the thin shaft is at the origin, and the common axis of the thin shaft and the thick shaft is atzOn the shaft.
The diameter of the thin shaft is 20+E 1=20+0=20, length 30; the diameter of the transition shaft is 16, and the length of the transition shaft is 10; the diameter of the thick shaft is 30+E 3=30+0=30, length 50.
The diameter 16 of the transition shaft is smaller than the diameter 20 of the thin shaft.
After step 1, step 2 is performed.
And 2, solving the fitting diameter and the fitting direction of each section of hole.
Solving the maximum inscribed cylinder radius of the fine hole through the formula (1)R 4,m=10.0503, and record the optimum solutiond x,4,m,d y,4,m,d rx,4,m,d ry,4,m]=10-3×[0.0644, -0.0328, 0.8742, -0.2680]Whereind x ,d y ,d rx ,d ry is a free variable. Of fine poresxDirection inscribed translation error is-d x,4,m、yDirection inscribed translation error is-d y,4,m、xError of direction inscribed angle-d rx,4,mAnd, furthermore,ydirection inscribed rotation error is-d ry,4,m。
Solving the maximum inscribed cylinder radius of the coarse hole through the formula (2)R 6,m=15.0598, and record the optimum solutiond x,6,m,d y,6,m,d rx,6,m,d ry,6,m]=10-3×[-0.0337, -0.0362, -0.3017, 0.2811]Whereind x ,d y ,d rx ,d ry is a free variable. Of coarse porosityxDirection inscribed translation error is-d x,6,m、yDirection inscribed translation error is-d y,6,m、xError of direction inscribed angle-d rx,6,mAnd, furthermore,ydirection inscribed rotation error is-d ry,6,m。
After step 2, step 3 is performed.
And 3, solving the maximum value of the adjustment quantity of the diameter of the standard shaft by using the fitting geometric parameters of the hole and the geometric parameters of the standard shaft.
Calculating the maximum value of the adjustment amount by the formula (3)E * =0.0989。
s.t.
Wherein,
r 1,Mis the radius of the thin axis of the shaft,r 1,M=0.5(20+E)；
r 4,Mis the radius of the thick axis and,r 4,M=0.5(30+E)；
Δ6-3,4-1,mis the minimum integrated gap of the coarse axis, and the minimum integrated gap delta of the coarse axis is calculated by the formula (4)6-3,4-1,m。
s.t.
Wherein,
R 6,4-1,mis that the coarse holes are arranged in the mounting and adjusting processxOyThe maximum inscribed circle radius of the projection of the plane,
maximum value of adjustment amountE * Corresponding thin and thick shaft diametersd 1 * , d 3 * The maximum diameter of the shaft part with the same tolerance value, which can be filled in the two sections of hole parts, is calculated according to the formula (5) and the formula (6).
d 1 * =d 1+E * =20.0989
d 3 * =d 3+E * =30.0989
And finishing the calculation after the step 3 is finished.
In the above description, the present invention has been described by way of specific embodiments, but those skilled in the art will appreciate that various modifications and variations can be made within the spirit and scope of the invention as hereinafter claimed.
Claims (1)
1. A method for rapidly calculating the installability of two sections of holes based on the principle of equal tolerance values is characterized by comprising the following steps:
step 1, acquiring geometric design parameters and measuring points of a hole part and presetting adjustment quantity of a standard axis;
the stepped hole consists of a fine hole and a coarse hole, and a section of transition hole is connected between the fine hole and the coarse hole;
nominal diameter of pored 1Nominal length ofL 1(ii) a Nominal diameter of the transition hole isD 2Nominal length ofIs composed ofL 2(ii) a The nominal diameter of the coarse pores isd 3Nominal length ofL 3；
Nominal diameter of the coarse holesd 3Greater than or equal to the nominal diameter of the poresd 1(ii) a Nominal diameter of transition holeD 2Greater than the nominal diameter of the poresd 1；
By bringing the axis of the fine hole close to the measuring coordinate systemzAxis, the geometric centre of the fine hole being close to the origin of the measuring coordinate system and the geometric centre of the coarse hole being such that it is in the measuring coordinate systemzThe projection on the axis is positive;
the measuring point set of the pore isp i |p i ={x i ,y i ,z i },i=1,2,…,N 1}; the measuring point set of the coarse aperture isp i |p i ={x i ,y i ,z i },i=N 1+1,N 1+2,…,N 1+N 2}；
The standard shaft system consists of a fine shaft and a coarse shaft which are completely coaxial, and a section of transition shaft is connected between the fine shaft and the coarse shaft; the three sections of axes are used as standard axes, and have no geometric error; the geometric center of the thin shaft is at the origin, and the common axis of the thin shaft and the thick shaft is atzOn the shaft;
the diameter of the thin shaft isd 1+EHas a length ofL 1(ii) a The diameter of the transition shaft isd 2Has a length ofL 2(ii) a The diameter of the thick shaft isd 3+EHas a length ofL 3(ii) a Wherein,Epresetting an arbitrary value for the adjustment quantity of the shaft diameter;
diameter of transition shaftd 2Smaller than the diameter of the thin shaftd 1；
After finishing the step 1, performing a step 2;
step 2, solving the fitting diameter and the fitting direction of each section of hole;
solving the maximum inscribed cylinder radius of the fine hole through the formula (1)R 4,mAnd recording the optimum solution [ alpha ], [ alphad x,4,m,d y,4,m,d rx,4,m,d ry,4,m]Whereind x ,d y ,d rx ,d ry are free variables, representing edges respectivelyxA shaft,yTranslation and winding of shaftsxA shaft,yRotation of the shaft; of fine poresxDirection inscribed translation error is-d x,4,m、yDirection inscribed translation error is-d y,4,m、xError of direction inscribed angle-d rx,4,mAnd, furthermore,ydirection inscribed rotation error is-d ry,4,m；
(1)
Solving the maximum inscribed cylinder radius of the coarse axis through the formula (2)R 6,mAnd recording the optimum solution [ alpha ], [ alphad x,6,m,d y,6,m,d rx,6,m,d ry,6,m]Whereind x ,d y ,d rx ,d ry is a free variable; of a thick shaftxDirection inscribed translation error is-d x,6,m、yDirection inscribed translation error is-d y,6,m、xError of direction inscribed angle-d rx,6,mAnd, furthermore,ydirection inscribed rotation error is-d ry,6,m；
(2)
Step 3 is carried out after step 2 is finished;
step 3, solving the maximum value of the adjustment quantity of the diameter of the standard shaft by using the fitting geometric parameters of the hole and the geometric parameters of the standard shaft;
calculating the maximum value of the adjustment amount by the formula (3)E * ；
(3)
s.t.
Wherein,
r 1,Mis the radius of the thin axis of the shaft,r 1,M=0.5(d 1+E)；
r 4,Mis the radius of the thick axis and,r 4,M=0.5(d 3+E)；
Δ6-3,4-1,mis the minimum integrated gap of the coarse axis, and the minimum integrated gap delta of the coarse axis is calculated by the formula (4)6-3,4-1,m；
(4)
s.t.
Wherein,
R 6,4-1,mis that the coarse holes are arranged in the mounting and adjusting processxOyThe maximum inscribed circle radius of the projection of the plane,
maximum value of adjustment amountE * Corresponding thin and thick shaft diametersd 1 * , d 3 * The maximum diameter of the shaft part with the equal tolerance value, which can be filled in the two sections of hole parts, is calculated according to a formula (5) and a formula (6);
d 1 * =d 1+E * (5)
d 3 * =d 3+E * (6)
and finishing the calculation after the step 3 is finished.
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111553083A (en) * | 2020-04-29 | 2020-08-18 | 中国人民解放军63653部队 | Method, system and medium for optimizing and calculating parameter adjustment quantity of common intersection point multi-hole optical axis |
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2018
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111553083A (en) * | 2020-04-29 | 2020-08-18 | 中国人民解放军63653部队 | Method, system and medium for optimizing and calculating parameter adjustment quantity of common intersection point multi-hole optical axis |
| CN111553083B (en) * | 2020-04-29 | 2022-10-11 | 中国人民解放军63653部队 | Method, system and medium for optimizing and calculating parameter adjustment quantity of common intersection point multi-hole optical axis |
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