CN114962448B - Pre-tightening method of ball linear guide rail - Google Patents
Pre-tightening method of ball linear guide rail Download PDFInfo
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
- F16C29/00—Bearings for parts moving only linearly
- F16C29/04—Ball or roller bearings
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
- F16C29/00—Bearings for parts moving only linearly
- F16C29/12—Arrangements for adjusting play
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- G—PHYSICS
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- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
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- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
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Abstract
A ball linear guide rail pre-tightening method comprises the following steps: step 1, determining structural parameters of a ball linear guide rail pair; step 2, establishing a deformation equivalent model of the skirt part of the sliding block, and equivalent the skirt part of the sliding block into a fixed cantilever beam; step 3, establishing a relation between single ball pre-tightening force and pre-tightening amount of the ball linear guide rail pair; step 4, establishing the relation between the single ball pre-tightening amount of the ball linear guide rail pair and the curvature center of the rollaway nest; and 5, establishing a balance equation of the ball linear guide rail pair. According to the invention, balls with different diameters are used for the same guide rail, so that each row of balls can obtain a preset pretightening force, and the problems that the pretightening force of the guide rail is smaller than expected and the pretightening forces of all the raceways are unequal due to the deformation of the linear rolling guide rail are solved.
Description
Technical Field
The invention relates to the technical field of mechanical guide, in particular to a ball linear guide rail pre-tightening method.
Background
The ball linear guide rail pair is widely applied to various automatic equipment, in particular to a high-grade numerical control machine tool by virtue of the advantages of strong bearing capacity, low friction loss, high motion sensitivity and the like. The pretightening force is a key factor which directly influences the comprehensive performance of the ball linear guide rail pair, and influences the rigidity, the service life and the like of the ball linear guide rail pair. When the pretightening force is too small, the rigidity of the guide rail pair is insufficient, and when the pretightening force is too large, the abrasion among the balls, the sliding blocks and the guide rail is increased, so that the service life is reduced. This is a hidden cause of poor practical use effect of the ball linear guide pair.
At present, the method for applying the pre-tightening force of the ball linear guide rail pair is to select a ball slightly larger than the nominal ball diameter so that the contact between the ball and the rollaway nest has certain interference, thereby generating vertical pre-tightening force and lateral pre-tightening force. The total pretightening force with different sizes can be generated by selecting balls with different diameters, so that the pretightening force is convenient, but the problem is also caused because the pretightening force is applied by properly increasing the diameters of the balls of each row of raceways by the same increment: the pretightening force enables the slider to deform under the force of the force, so that the actual pretightening force is smaller than the ideal pretightening force, and pretightening forces generated by channels at different positions are inconsistent, so that the actual use effect of the ball linear guide rail pair is affected.
The deformation of the sliding block is as follows: will not be generated when loaded or when preloaded, and therefore will often be ignored. This makes it difficult to find the cause of the problem when the actual use effect of the ball linear guide pair is found to be poor.
The pretightening force of the ball linear guide rail pair is the contact force between the ball and the rollaway nest, the ball and the rollaway nest are deformed and spread towards two sides under the pretightening force, namely the distance between the guide rail and the slider is increased, the diameter of the rollaway nest where the ball is located is increased, the actual contact force between the ball and the rollaway nest is always smaller than the required contact force, and the contact force of the ball of different rollaway nest of the same slider is different due to different deformation of different positions of the slider, or the pretightening force of different rollaway nest is different, which is obviously not the desired result.
Taking a square equal-load ball linear guide pair as an example, if balls slightly larger than the nominal ball diameter are selected and the diameters of the ball bearings of the ball tracks are the same, certain vertical and lateral pretightening forces are generated. Under the action of the pretightening force, the sliding block can generate certain skirt deformation, and as shown in figure 1, the opening distances of the upper roller path and the lower roller path of the sliding block are different. Specifically, the upper two raceways are more preloaded than the lower raceway.
In terms of lateral pre-tightening force (pre-tightening force in the horizontal direction in fig. 1), the skirt portion of the slider deforms, so that the actual pre-tightening force in the horizontal direction between the left and right two raceways of the lower row and the balls is smaller than the actual pre-tightening force in the horizontal direction between the left and right two raceways of the upper row and the balls.
In the case of vertical pre-tightening force (pre-tightening force in the vertical direction in fig. 1), because the pre-tightening force in the vertical direction between the left and right two raceways of the upper row and the balls is a pair of balance forces, the two are mutually connected, and the two are equal in size and opposite in direction. Therefore, the skirt part of the sliding block deforms, so that the actual pretightening force between the left and right two rolling ways of the lower row and the balls in the vertical direction is reduced, and the actual pretightening force between the left and right two rolling ways of the upper row and the balls in the vertical direction is also reduced.
Disclosure of Invention
In order to overcome the problems, the invention provides a pre-tightening method of a ball linear guide rail, which can use balls with different diameters for the same guide rail, so that each row of balls can obtain a preset pre-tightening force.
The technical scheme adopted by the invention is as follows: a ball linear guide rail pre-tightening method comprises the following steps:
Step 1, determining structural parameters of a ball linear guide rail pair; let ball linear guide pair total 4 rows of balls, be 1,2,3,4 respectively, alpha 0 is the nominal contact angle of ball and raceway in the guide pair, unit: degree (°), O is the ball center, d is the nominal ball diameter, unit: millimeter (mm), n is the number of loaded balls in a single row, O c and O r are the nominal raceway curvature centers of the sliding block and the guide rail respectively, and r c and r r are the raceway curvature radii of the sliding block and the guide rail respectively, and the unit is: millimeter (mm);
step 2, establishing a deformation equivalent model of the skirt part of the sliding block; the skirt part of the sliding block is equivalent to a fixed cantilever beam, in the equivalent cantilever beam schematic diagram, a fixed point A is an intersection point of the central line and the vertex of the section of the sliding block, and l 1,l4 is the vertical distance from the contact point of the groove of the sliding block to the fixed end face, and the unit is: rice (m); under the action of contact force, the deformation of the skirt part of the sliding block at the groove is respectively
Wherein F 1,F4 is the component force in the horizontal direction of the contact force of the balls in the rollaway nest 1 and rollaway nest 4 on the sliding block, E is the elastic modulus, and I is the moment of inertia;
step 3, establishing a relation between single ball pre-tightening force and pre-tightening amount of the ball linear guide rail pair; the single ball pre-tightening force of the ball linear guide rail pair is the contact force between the ball and the single-side rollaway nest, and the pre-tightening amount is the elastic deformation amount between the ball and the single-side rollaway nest; from the Hertz theory, the relation expression between the contact force and the elastic deformation is known
Wherein Q is the contact force applied, in units of: cattle (N); delta is elastic deformation, unit: millimeter (mm); v 1、υ2 is poisson's ratio of the contact 1 and contact 2 materials, and E 1、E2 is elastic modulus of the contact 1 and contact 2 materials, respectively, in units: ji Pa (GPa); δ * is a coefficient related to the geometric relationship, Σρ is the combined curvature of contact 1 and contact 2, unit: mm -1;
Since δ *、E1、E2、υ1、υ2 and Σρ are constant for a specific ball linear guide pair, the relationship between the individual ball pretension and the pretension of the ball linear guide pair can be simplified as
Where k h describes the relationship between the preload Q and the preload δ applied to an individual ball of a ball linear guide pair, referred to as the like stiffness coefficient, in units: cow mm (N mm);
Step 4, establishing the relation between the single ball pre-tightening amount of the ball linear guide rail pair and the curvature center of the rollaway nest; in the ball linear guide pair curvature center azimuth graph, the u axis is the lateral direction, the v axis is the vertical direction, alpha i is the actual contact angle between the ith row of balls and the rollaway nest, O' ci is the actual rollaway nest curvature center of the sliding block on the corresponding side of the ith row of balls, when the rollaway nest curvature center of the sliding block is changed, deltau i and Deltav i are the lateral and vertical change distance amounts of the sliding block curvature center on the corresponding side of the ith row of balls respectively, and the positive and negative of the values depend on a corresponding local coordinate system u iOcivi respectively; in the nominal contact state, the nominal raceway curvature center distance of the sliding block and the guide rail on the corresponding side of the ith row of balls
Actual contact angle alpha of ith row of balls and rollaway nest i
The actual contact angle alpha is known from symmetry 1＝α2,α3＝α4
The actual track curvature center distance si after changing the curvature center of the slide block can be obtained by Pythagorean theorem
From the geometric relationship, the relationship between the individual ball preload delta i and the center of curvature of the raceway can be determined
rc+rr-Si＝di-2δi (8)
Step 5, establishing a balance equation of the ball linear guide rail pair; under the action of pretightening force, the static balance relation of the ball linear guide rail in the vertical direction is that
n·(Q1+Q2)sinα1＝n·(Q3+Q4)sinα4
Wherein n is the number of steel balls in a bearing area in the rollaway nest; from symmetry, the contact force has the following relationship
Q1＝Q2
Q3＝Q4
Thus, the above can be written as
Q1 sinα1＝Q4 sinα4 (9)
According to the above derivation process, the calculation process of the diameter of the lower row of balls of the guide rail pair is as follows
Step 5.1, determining various parameters of the guide rail pair, including
A dimension parameter l 1,l4,α0,rc,rr,n,S0;
the required pretightening force is the contact force Q of the ball;
elastic modulus E and moment of inertia/;
And 5.2, solving the nominal diameter d 1,d4 of the ball by the combined type (1), (2), (4), (6), (7), (8) and (9).
The principle of the invention is as follows: in order to ensure that the actual pretightening force between the left and right two raceways of the upper row of the ball linear guide rail pair and the balls in the horizontal direction is consistent with the pretightening force between the left and right two raceways of the lower row and the balls in the horizontal direction; the actual pretightening force in the vertical direction between the left and right two raceways of the upper row and the balls and the pretightening force in the vertical direction between the left and right two raceways of the lower row and the balls can be large enough. The invention provides a method for realizing pretension of a ball linear guide rail, namely, the pretension is realized by using balls with different diameters for the same guide rail pair, namely, the way of applying pretension force is realized by properly increasing the diameters of the balls of each row of rollaway nest in different increments, the increment of increasing the diameters of the balls on the left rollaway nest and the right rollaway nest of the upper row is smaller, and the increment of increasing the diameters of the balls on the left rollaway nest and the right rollaway nest of the lower row is larger. (the increment of ball diameter increase on all raceways of the same slider is consistent in the prior art). Therefore, the ball linear guide rail pair has an ideal pre-tightening effect in actual use.
The beneficial effects of the invention are as follows: the rolling balls with different diameters are used for the same guide rail, so that the preset pretightening force can be obtained for each row of rolling balls, and the problems that the pretightening force of the guide rail is smaller than expected and the pretightening forces of all the rolling paths are unequal due to the deformation of the linear rolling guide rail are solved.
Drawings
FIG. 1 is a schematic illustration of a slider skirt deformation.
Fig. 2a is a front view of a ball linear guide pair.
Fig. 2b is a partial enlarged view at a in fig. 2 a.
Fig. 3 is a schematic diagram of an equivalent cantilever beam.
Fig. 4 is a view showing the direction of the center of curvature of the ball linear guide pair.
Detailed Description
The following description of the embodiments of the present invention will be made more apparent and fully hereinafter with reference to the accompanying drawings, in which some, but not all embodiments of the invention are shown. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
In the description of the present invention, it should be noted that, as the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," "outer," and the like are used for convenience in describing the present invention and simplifying the description based on the azimuth or positional relationship shown in the drawings, it should not be construed as limiting the present invention, but rather should indicate or imply that the devices or elements referred to must have a specific azimuth, be constructed and operated in a specific azimuth. Furthermore, the terms "first," "second," "third," and the like, as used herein, are used for descriptive purposes only and are not to be construed as indicating or implying any relative importance.
In the description of the present invention, it should be noted that unless explicitly stated and limited otherwise, the terms "mounted," "connected," and "connected" should be construed broadly, and may be, for example, fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; can be directly connected or indirectly connected through an intermediate medium, and can be communication between two elements. The specific meaning of the above terms in the present invention will be understood in specific cases by those of ordinary skill in the art.
Referring to the drawings, a ball linear guide pretensioning method comprises the following steps:
1. and determining structural parameters of the ball linear guide rail pair.
Fig. 2a is a front view of the ball linear guide pair, wherein the X axis is lateral and the Y axis is vertical. Let ball linear guide pair total 4 rows of balls, be 1,2,3,4 respectively, alpha 0 is the nominal contact angle of ball and raceway in the guide pair, unit: degree (°), O is the ball center, d is the nominal ball diameter, unit: millimeter (mm), n is the number of loaded balls in a single row, O c and O r are the nominal raceway curvature centers of the sliding block and the guide rail respectively, and r c and r r are the raceway curvature radii of the sliding block and the guide rail respectively, and the unit is: millimeter (mm).
2. Establishing a deformation equivalent model of a skirt part of the sliding block
Since deformation of the guide rail pair after the action of the sagging pretightening force is mainly expressed as the external expansion of the skirt portion of the sliding block, in order to calculate the deformation amount of the skirt portion of the sliding block, the geometric dimension and the loading condition of the skirt portion of the sliding block are considered, and the symmetry of two sides of the sliding block are combined, so the skirt portion of the sliding block is equivalent to a fixed cantilever beam, as shown in fig. 3, a fixed point A is the intersection point of the central line and the vertex of the section of the sliding block, l 1,l4 is the vertical distance from the contact point of the groove of the sliding block to the fixed end face, and the unit is: rice (m), slider skirt deformation model
Under the action of contact force, the deformation of the skirt part of the sliding block at the groove is respectively
Wherein F 1,F4 is the component force in the horizontal direction of the contact force of the balls in the rollaway nest 1 and rollaway nest 4 on the slide block, E is the elastic modulus, and I is the moment of inertia.
3. And establishing the relation between the single ball pretightening force and pretightening quantity of the ball linear guide pair.
The single ball pre-tightening force of the ball linear guide rail pair is the contact force between the ball and the unilateral rollaway nest (the sliding block rollaway nest or the guide rail rollaway nest), and the pre-tightening amount is the elastic deformation amount between the ball and the unilateral rollaway nest (the sliding block rollaway nest or the guide rail rollaway nest). From the Hertz theory, the relation expression between the contact force and the elastic deformation is known
Wherein Q is the contact force applied, in units of: cattle (N); delta is elastic deformation, unit: millimeter (mm); v 1、υ2 is poisson's ratio of the contact 1 and contact 2 materials, and E 1、E2 is elastic modulus of the contact 1 and contact 2 materials, respectively, in units: ji Pa (GPa); δ * is a coefficient related to the geometric relationship, Σρ is the combined curvature of contact 1 and contact 2, unit: mm -1.
Since δ *、E1、E2、υ1、υ2 and Σρ are constant for a specific ball linear guide pair, the relationship between the individual ball pretension and the pretension of the ball linear guide pair can be simplified as
Where k h describes the relationship between the preload Q and the preload δ applied to an individual ball of a ball linear guide pair, referred to as the like stiffness coefficient, in units: cow mm (N mm).
4. And establishing the relation between the single ball pre-tightening amount of the ball linear guide rail pair and the curvature center of the rollaway nest.
Fig. 4 shows a graph of the direction of the center of curvature of the ball linear guide pair, the u-axis is the lateral direction, the v-axis is the vertical direction, α i is the actual contact angle between the ith row of balls and the raceway, O' ci is the actual center of curvature of the raceway of the slider on the side corresponding to the ith row of balls, and when the center of curvature of the raceway of the slider is changed, Δu i and Δv i are the lateral and vertical changing distance amounts of the center of curvature of the slider on the side corresponding to the ith row of balls, respectively, the positive and negative of which depend on the corresponding local coordinate system (u iOcivi) in fig. 2b, respectively.
In the nominal contact state, the nominal track curvature center distance s of the sliding block and the guide rail on the corresponding side of the ith row of balls 0
Actual contact angle alpha of ith row of balls and rollaway nest i
The actual contact angle alpha is known from symmetry 1＝α2,α3＝α4
The actual track curvature center distance s after changing the curvature center of the slide block can be obtained by Pythagorean theorem i
From the geometric relationship, the relationship between the individual ball preload delta i and the center of curvature of the raceway can be determined
rc+rr-Si＝di-2δi (8)
5. And establishing a balance equation of the ball linear guide rail pair.
Under the action of the pretightening force, the static balance relation of the ball linear guide rail in the vertical direction is as follows:
n·(Q1+Q2)sinα1＝n·(Q3+Q4)sinα4
Wherein n is the number of steel balls in the bearing area in the raceway.
From symmetry, the contact force has the following relationship:
Q1＝Q2
Q3＝Q4
Thus, the above formula can be written as:
Q1 sinα1＝Q4 sinα4 (9)
According to the above deduction process, since the guide rail pair has symmetry, we only need to calculate one side of balls, and the calculation process of the diameter of the balls in the lower row of the guide rail pair is as follows:
1. Determining various parameters of the guide rail pair, including:
(1) Dimensional parameter l 1,l4,α0,rc,rr,n,S0
(2) The desired preload, i.e. the ball contact force Q
(3) Elastic modulus E and moment of inertia of equivalent cantilever beam model of sliding block
2. Solving d 1,d4 by using a simultaneous equation set;
The combined type (1), (2), (4), (6), (7), (8), (9) solves the nominal diameter d 1,d4 of the ball.
The square equal-load type ball linear guide pair is widely used because the capacity of bearing loads in all directions is the same, so a common square equal-load type ball linear guide pair with a certain specification is used for example, and the specific calculation process of the lower row ball diameter of the guide pair is as follows:
1. Determining various parameters of the guide rail pair, including:
(1) Dimensional parameters
l1＝8.028732×10-3m
l4＝19.203732×10-3m
α0＝45°
rc＝rr＝3.302mm
n＝12
S0＝0.254mm
(2) Determining the required preload, i.e. contact force Q 1、Q4
Some automatic equipment requires that the ball linear guide rail pair applies 1200N pretightening force in the lateral direction and the vertical direction, and then the contact force of a single ball:
The class stiffness coefficient k can be obtained by taking in data h＝7.3899×105N·mm-3/2
From the following componentsThe method can obtain:
(3) Elastic modulus E and moment of inertia I of equivalent cantilever beam model of sliding block
The elastic modulus of the slider is e=206 Gpa
Moment of inertia of
2. Simultaneous equation system for solving nominal diameter d 1,d4
Simultaneous equations:
wherein: f 1＝Q1 cosα1,F4＝Q4 cosα4
Bringing and solving the above data
And (3) solving to obtain:
d1＝6.3575mm
d4＝6.8617mm
in practical application, only the required transverse and lateral pretightening forces are brought into an equation to be solved.
The embodiments described in the present specification are merely examples of implementation forms of the inventive concept, and the scope of protection of the present invention should not be construed as being limited to the specific forms set forth in the embodiments, and the scope of protection of the present invention and equivalent technical means that can be conceived by those skilled in the art based on the inventive concept.
Claims (1)
1. The pre-tightening method of the ball linear guide rail is characterized by comprising the following steps of:
step 1, determining structural parameters of a ball linear guide rail pair; the ball linear guide rail pair is provided with 4 rows of balls which are respectively 1,2,3 and 4 rows, The nominal contact angle of the ball and the rollaway nest in the guide rail pair is as follows: degree (°),The nominal raceway curvature center distance of the slider and the guide rail on the corresponding side of the ball is shown,The ball center, d is the nominal ball diameter, in units: millimeter (mm), n is the number of loaded balls in a single row,AndThe nominal rollaway nest curvature centers of the slide block and the guide rail respectively,AndThe track curvature radius of the sliding block and the track are respectively as follows: millimeter (mm);
step 2, establishing a deformation equivalent model of the skirt part of the sliding block; the skirt part of the sliding block is equivalent to a fixed cantilever beam, in the equivalent cantilever beam schematic diagram, the fixed point A is the intersection point of the central line and the vertex of the section of the sliding block, ，The vertical distance from the contact point of the groove of the sliding block to the fixed end surface is respectively as follows: rice (m); under the action of contact force, the deformation of the skirt part of the sliding block at the groove is respectively
Wherein,，The horizontal component of the contact force of the balls in the raceways 1 and 4 on the slider,Is the modulus of elasticity of the material,Is the moment of inertia;
step 3, establishing a relation between single ball pre-tightening force and pre-tightening amount of the ball linear guide rail pair; the single ball pre-tightening force of the ball linear guide rail pair is the contact force between the ball and the single-side rollaway nest, and the pre-tightening amount is the elastic deformation amount between the ball and the single-side rollaway nest; from the Hertz theory, the relation expression between the contact force and the elastic deformation is known
In the method, in the process of the invention,Units of contact force: cattle (N); is elastically deformed, unit: millimeter (mm); 、 Poisson's ratio of the materials of contact 1 and contact 2, 、The elastic modulus of the materials of the contact body 1 and the contact body 2 are respectively as follows: ji Pa (GPa); as coefficients related to the geometric relationship, For the combined curvature of contact 1 and contact 2, units:；
Due to 、、、、、Is constant for a specific ball linear guide pair, so that the relation between the single ball pre-tightening force and the pre-tightening amount of the ball linear guide pair can be simplified to
In the method, in the process of the invention,Describes the pretightening force exerted by a single ball of a ball linear guide pairAnd the pre-tightening amountThe relationship between these is called stiffness like coefficient, unit: cow mm (N mm);
Step 4, establishing the relation between the single ball pre-tightening amount of the ball linear guide rail pair and the curvature center of the rollaway nest; in the direction diagram of the curvature center of the ball linear guide rail pair, the u axis is lateral, the v axis is vertical, For the actual contact angle of the ith row of balls with the raceway,The actual center of curvature of the raceway of the slider on the side corresponding to the ith row of balls, when the center of curvature of the raceway of the slider is changed,AndThe lateral and vertical change distance amounts of the curvature center of the slide block at the corresponding side of the ith row of balls are respectively determined by the corresponding local coordinate system; In the nominal contact state, the nominal raceway curvature center distance of the sliding block and the guide rail on the corresponding side of the ith row of balls
Wherein,Nominal ball diameter for the ith row of balls; actual contact angle of ith row ball and rollaway nest
The actual contact angle is known from symmetry，The actual track curvature center distance after changing the curvature center of the slide block can be obtained by Pythagorean theorem
From the geometrical relationship, the amount of individual ball pretension can be determinedRelationship to the centre of curvature of the raceway
Step 5, establishing a balance equation of the ball linear guide rail pair; under the action of pretightening force, the static balance relation of the ball linear guide rail in the vertical direction is thatWherein n is the number of steel balls in a bearing area in the rollaway nest;、、、 Balls in 1 st, 2 nd, 3 rd and 4 th rows respectively contact force with the track; from symmetry, the contact force has the following relationship Thus, the above can be written as
According to the above derivation process, the calculation process of the diameter of the lower row of balls of the guide rail pair is as follows
Step 5.1, determining various parameters of the guide rail pair, including size parameters，，，，，n，；
The required pre-tightening force, i.e. the contact force of the balls；
Elastic modulus of equivalent cantilever beam model of sliding blockAnd moment of inertia；
Step 5.2, the nominal diameter of the balls is solved by the combined type (1), (2), (4), (6), (7), (8) and (9)，。
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| CN113792451B (en) * | 2021-08-16 | 2022-11-11 | 东南大学 | Rolling linear guide rail pair static rigidity calculation and structural parameter design method |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN110725861A (en) * | 2019-09-17 | 2020-01-24 | 浙江工业大学 | A method of applying preload force of ball linear guide pair |
Non-Patent Citations (1)
| Title |
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| 一种计及滑块裙部变形的滚珠直线导轨副垂直刚度模型;陈汀;黄其柏;;中国机械工程(13);第1546-1549页及图1-7 * |
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