A design method of a life-based gear planetary roller screw

Abstract

The patent application discloses a kind of design method of gear planetary roller screw based on life, belong to transmission screw technical field.This method is designed by forward solution, from selecting diameter range, according to transmission ratio to determine radial dimension parameter, design gear part and thread part, determine load and utilize fixed life to carry out inverse calculation solution, system comprehensively expounds the design method of forward calculation gear planetary roller screw, has wide application prospect in transmission screw and engineering vehicle field.The beneficial effects of the present application are: abandon traditional type selection rule based on dynamic load, based on hertz theory and fatigue life theory, take life as the first consideration factor, so as to meet the practical needs of tens of thousands of life of engineering vehicle.

Description

Technical Field

[0001] This invention patent discloses a design method for a life-based gear planetary roller screw, belonging to the field of transmission screw application technology. Background Technology

[0002] Currently, planetary roller screws on the market all follow traditional theory, using the basic rated dynamic load that can be withstood when the life is exactly 1 million revolutions as the selection basis. However, in practical applications such as engineering vehicles, the number of cycles under a certain load is considered. As a result, there are working conditions with high load and low life or low load and high life. Life-based design has gradually become a demand trend, and traditional selection and theory cannot meet this requirement.

[0003] To address the aforementioned issues, this invention patent, based on Hertzian theory and fatigue life theory, and prioritizing lifespan, provides a detailed explanation of the lifespan-based design method for planetary roller screws, offering guidance for customer selection and design, supplier portfolio development, and production. Summary of the Invention

[0004] To address the aforementioned problems, this invention provides a life-based design method for a gear planetary roller screw, employing the following technical solution:

[0005] A life-based design method for a gear planetary roller screw includes the following steps:

[0006] (1) Select the diameter range;

[0007] (2) Determine the radial dimension parameters based on the transmission ratio;

[0008] (3) Design the gear section and the threaded section;

[0009] (4) Determine the load based on the design results of (3);

[0010] (5) Use lifetime for inverse calculation.

[0011] Furthermore, in step (1), the diameter range d of the lead screw designed in the forward direction is selected according to the requirements;

[0012] Furthermore, in step (2), the radial dimension parameters are designed based on the transmission ratio.

[0013] The equation for the radial dimension parameter of the lead screw is:

[0014] dS0=d, PS=LS / nS, dS1=dS0+h, dS2=dS0-h-2e,

[0015] Where dS0 is the lead screw pitch diameter, nS is the number of leads, LS is the lead screw lead, PS is the lead screw pitch, h is the thread height, dS1 is the lead screw major diameter, and dS2 is the lead screw minor diameter.

[0016] The equation for the radial dimension parameters of the roller is:

[0017] dR0=dS0 / (nS-2), nR=1, PR=LR / nR, dR1=dR0+h, dR2=dR0-h-2e,

[0018] Where dR0 is the roller pitch diameter, nR is the number of roller heads, LR is the roller lead, PR is the roller pitch, h is the tooth height, dR1 is the roller top diameter, and dR2 is the roller bottom diameter.

[0019] The equation for the radial dimension parameter of the nut is:

[0020] dN0=dS0+2dR0, nN=nS, PN=LN / nN, dN1=dN0+h+2e, dN2=dN0-h,

[0021] Wherein, dN0 is the roller pitch diameter, nN is the number of roller heads, LN is the roller lead, PN is the roller pitch, h is the tooth height, dN1 is the roller top diameter, and dN2 is the roller bottom diameter.

[0022] Furthermore, in step (3),

[0023] The basic equation relating gears is:

[0024] ZN / ZR=dN0 / dR0, (dN0-dR0) / 2=(ZN-ZR)m / 2, dR0=mZR, dN0=mZN, ha1=(ha*+x1)m, ha2= (ha*-Δha*-x2)m, hf1=(ha*+c*-x1)m, hf2=(ha*+c*+x2)m, Δha*=(ha*-x2)2 / z2tan2α

[0025] Where ZN is the number of teeth on the gear ring, ZR is the number of teeth on the roller, m is the standard module, ha is the addendum, hf is the dedendum, ha* is the addendum coefficient, x is the displacement coefficient, c* is the clearance coefficient, and α is the pressure angle.

[0026] The gear design equation is:

[0027] DR0=dR0, DR1=DR0+2ha1, DR2=DR0-2hf1, DN0=dN0, DN1=DN0+2ha2, DN2=DN0-2hf2,

[0028] Among them, DR0 is the pitch circle diameter of the roller, DR1 is the addendum circle diameter of the roller, DR2 is the dedendum circle diameter of the roller, DN0 is the pitch circle diameter of the gear ring, DN1 is the addendum circle diameter of the gear ring, and DN2 is the dedendum circle diameter of the gear ring.

[0029] The basic equation for threaded connections is:

[0030] h=0.375P / tan(θ), b=7h / 6, e=h / 6, r=dR0 / 2sin(θ / 2),

[0031] Where h is the tooth height, b is the root width, P is the pitch, θ is the tooth angle, e is the tooth crest clearance, and r is the tooth radius.

[0032] The thread design equation is:

[0033] dS1=dS0+h, dS2=dS0-h, dN1=dN0-h, dN2=dN0+h, dR1=dN0+h, dR2=dN0-h,

[0034] Wherein, dS1 is the top diameter of the lead screw, dS2 is the bottom diameter of the lead screw, dN1 is the top diameter of the nut, dN2 is the bottom diameter of the nut, dR1 is the top diameter of the roller, and dR2 is the bottom diameter of the roller.

[0035] Furthermore, in step (4),

[0036] The axial critical load equation is:

[0037] C≤π3Ed4S2 / 64(μlS)2SS

[0038] Where C is the critical axial load, E is the elastic modulus of the material, ds2 is the screw root diameter, μ is the installation coefficient, ls is the screw length, and SS is the safety factor.

[0039] The equation for thread shear strength is:

[0040] F≤πdR3b2nτp

[0041] Where F is the thread shear strength, b is the thread root width, n is the number of engagement points of a single roller, and τp is the allowable shear stress.

[0042] The equation for the number of rollers in the theory is:

[0043] C / F≤m≤0.5πarcsin-1[(dR0+2h) / (dS0+dN0)],

[0044] Where m is the theoretical number of rollers.

[0045] Furthermore, in step (5),

[0046] The rated load equation is:

[0047] C0 = C(100 / L)1 / 3,

[0048] Where C0 is the rated load and L is the predetermined service life, and 0.65C0 is used for selection.

[0049] The critical speed equation is:

[0050] nRmax≤(640EI / ρA)1 / 2,

[0051] Where nRmax is the critical maximum speed, I is the minimum cross-sectional second moment, ρ is the material density, and A is the minimum cross-sectional area.

[0052] The efficiency equation is:

[0053] η=tan(fS-fM) / tan{fS-fM-arctan[(fS-fM) / cos(α / 2)]},

[0054] Where η is the transmission efficiency, fS is the screw helix angle, and fM is the nut helix angle.

[0055] Hertz's theory and fatigue life theory equations are as follows:

[0056] σ=3Fn / 2πab, δ=K(2πab / σ)2 / 3, a=[6Fn(1-ν2) / πE(e2-e4)]1 / 3, b=a(1-e2)1 / 2, K=[9π4(e2-e4) / 4E]1 / 3,

[0057] Where σ is the contact stress, Fn is the normal force, a is the major semi-axis of the ellipse, b is the minor semi-axis of the ellipse, δ is the elastic deformation, and K is the elastic deformation coefficient.

[0058] Furthermore, in step (3), constraint equations are applied.

[0059] The constraint equation to avoid root shear is:

[0060] ZRmin≥2ha* / sin2α,

[0061] ZRmin represents the minimum number of teeth required for the roller.

[0062] The equation for the gear correction factor to avoid interference is:

[0063] mZR+2m(ha*+xR)≤dR2,

[0064] Where ZR is the number of roller teeth and xR is the gear correction factor.

[0065] In practical implementation, roller interference can be corrected using any one of the following methods: direct calculation, constraint correction, or machining correction.

[0066] Compared with the prior art, the present invention has the following advantages:

[0067] (1) In the design method of a life-based gear planetary roller screw of the present invention, the process is to select the diameter range, determine the radial dimension parameters according to the transmission ratio, design the gear part and the thread part, determine the load and use the predetermined life to perform back calculation, and systematically and comprehensively explain the forward calculation design method of gear planetary roller screw.

[0068] (2) In the design method of a life-based gear planetary roller screw of the present invention, the radial dimension parameter design equations of the screw, roller and nut are described in detail during the radial dimension parameter design process according to the transmission ratio; the basic relationship equations and design equations of gear and thread are described in detail during the gear design and thread design process; the equations of critical load, thread shear strength and theoretical number of rollers are described in detail during the load determination process; and the mutual equations of life and load are described in detail during the life back calculation process.

[0069] (3) In the design method of a life-based gear planetary roller screw of the present invention, when designing and implementing the thread and gear, the adverse conditions such as undercut and interference are fully considered, and a feasible method for correcting the interference is proposed; when implementing the life back calculation, the solution calculation method of critical speed and efficiency is considered.

[0070] (4) This invention can accurately describe the design methods and calculation equations of each stage in the design process of gear planetary roller screws, abandon the traditional selection rules based on dynamic load, and take Hertz theory and fatigue life theory as the basis, with life as the primary consideration, thereby meeting the practical requirements of engineering vehicles for tens of thousands of cycles of life. Attached Figure Description

[0071] Figure 1 This is a basic flowchart of the present invention;

[0072] Figure 2 This is a distribution diagram of the theoretical number of rollers in this invention;

[0073] Figure 3 This is a structural diagram illustrating an example of the present invention.

[0074] Figure 4 This is a schematic diagram of the Hertz contact of the present invention. Detailed Implementation

[0075] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0076] This invention discloses a life-based design method for a gear planetary roller screw, comprising the following steps:

[0077] (1) Select the diameter range;

[0078] (2) Determine the radial dimension parameters based on the transmission ratio;

[0079] (3) Design the gear section and the threaded section;

[0080] (4) Determine the load based on the design results of (3);

[0081] (5) Inverse calculations using lifetime, such as Figure 1 As shown.

[0082] Specifically, in step (1), the diameter range d of the lead screw designed in the forward direction is selected according to the requirements;

[0083] Specifically, in step (2), the radial dimension parameters are designed based on the transmission ratio.

[0084] The equation for the radial dimension parameter of the lead screw is:

[0085] dS0=d, PS=LS / nS, dS1=dS0+h, dS2=dS0-h-2e,

[0086] Where dS0 is the lead screw pitch diameter, nS is the number of leads, LS is the lead screw lead, PS is the lead screw pitch, h is the thread height, dS1 is the lead screw major diameter, and dS2 is the lead screw minor diameter.

[0087] The equation for the radial dimension parameters of the roller is:

[0088] dR0=dS0 / (nS-2), nR=1, PR=LR / nR, dR1=dR0+h, dR2=dR0-h-2e,

[0089] Where dR0 is the roller pitch diameter, nR is the number of roller heads, LR is the roller lead, PR is the roller pitch, h is the tooth height, dR1 is the roller top diameter, and dR2 is the roller bottom diameter.

[0090] The equation for the radial dimension parameter of the nut is:

[0091] dN0=dS0+2dR0, nN=nS, PN=LN / nN, dN1=dN0+h+2e, dN2=dN0-h,

[0092] Wherein, dN0 is the roller pitch diameter, nN is the number of roller heads, LN is the roller lead, PN is the roller pitch, h is the tooth height, dN1 is the roller top diameter, and dN2 is the roller bottom diameter.

[0093] Specifically, in step (3),

[0094] The basic equation relating gears is:

[0095] ZN / ZR=dN0 / dR0, (dN0-dR0) / 2=(ZN-ZR)m / 2, dR0=mZR, dN0=mZN, ha1=(ha*+x1)m, ha2= (ha*-Δha*-x2)m, hf1=(ha*+c*-x1)m, hf2=(ha*+c*+x2)m, Δha*=(ha*-x2)2 / z2tan2α

[0096] Where ZN is the number of teeth on the gear ring, ZR is the number of teeth on the roller, m is the standard module, ha is the addendum, hf is the dedendum, ha* is the addendum coefficient, x is the displacement coefficient, c* is the clearance coefficient, and α is the pressure angle.

[0097] The gear design equation is:

[0098] DR0=dR0, DR1=DR0+2ha1, DR2=DR0-2hf1, DN0=dN0, DN1=DN0+2ha2, DN2=DN0-2hf2,

[0099] Among them, DR0 is the pitch circle diameter of the roller, DR1 is the addendum circle diameter of the roller, DR2 is the dedendum circle diameter of the roller, DN0 is the pitch circle diameter of the gear ring, DN1 is the addendum circle diameter of the gear ring, and DN2 is the dedendum circle diameter of the gear ring.

[0100] The basic equation for threaded connections is:

[0101] h=0.375P / tan(θ), b=7h / 6, e=h / 6, r=dR0 / 2sin(θ / 2),

[0102] Where h is the tooth height, b is the root width, P is the pitch, θ is the tooth angle, e is the tooth crest clearance, and r is the tooth radius.

[0103] The thread design equation is:

[0104] dS1=dS0+h, dS2=dS0-h, dN1=dN0-h, dN2=dN0+h, dR1=dN0+h, dR2=dN0-h,

[0105] Wherein, dS1 is the top diameter of the lead screw, dS2 is the bottom diameter of the lead screw, dN1 is the top diameter of the nut, dN2 is the bottom diameter of the nut, dR1 is the top diameter of the roller, and dR2 is the bottom diameter of the roller.

[0106] Specifically, in step (4),

[0107] The axial critical load equation is:

[0108] C≤π3Ed4S2 / 64(μlS)2SS

[0109] Where C is the critical axial load, E is the elastic modulus of the material, ds2 is the screw root diameter, μ is the installation coefficient, ls is the screw length, and SS is the safety factor.

[0110] The equation for thread shear strength is:

[0111] F≤πdR3b2nτp

[0112] Where F is the thread shear strength, b is the thread root width, n is the number of engagement points of a single roller, and τp is the allowable shear stress.

[0113] The equation for the number of rollers in the theory is:

[0114] C / F≤m≤0.5πarcsin-1[(dR0+2h) / (dS0+dN0)],

[0115] Where m is the theoretical number of rollers, such as Figure 2 As shown.

[0116] Specifically, in step (5),

[0117] The rated load equation is:

[0118] C0 = C(100 / L)1 / 3,

[0119] Where C0 is the rated load and L is the predetermined service life, and 0.65C0 is used for selection.

[0120] The critical speed equation is:

[0121] nRmax≤(640EI / ρA)1 / 2,

[0122] Where nRmax is the critical maximum speed, I is the minimum cross-sectional second moment, ρ is the material density, and A is the minimum cross-sectional area.

[0123] The efficiency equation is:

[0124] η=tan(fS-fM) / tan{fS-fM-arctan[(fS-fM) / cos(α / 2)]},

[0125] Where η is the transmission efficiency, fS is the screw helix angle, and fM is the nut helix angle.

[0126] Hertz's theory and fatigue life theory equations are as follows:

[0127] σ=3Fn / 2πab, δ=K(2πab / σ)2 / 3, a=[6Fn(1-ν2) / πE(e2-e4)]1 / 3, b=a(1-e2)1 / 2, K=[9π4(e2-e4) / 4E]1 / 3

[0128] Where σ is the contact stress, Fn is the normal force, a is the major semi-axis of the ellipse, b is the minor semi-axis of the ellipse, δ is the elastic deformation, and K is the elastic deformation coefficient.

[0129] Specifically, in step (3), constraint equations are applied.

[0130] The constraint equation to avoid root shear is:

[0131] ZRmin≥2ha* / sin2α,

[0132] ZRmin represents the minimum number of teeth required for the roller.

[0133] The equation for the gear correction factor to avoid interference is:

[0134] mZR+2m(ha*+xR)≤dR2,

[0135] Where ZR is the number of roller teeth and xR is the gear correction factor.

[0136] In practical implementation, roller interference can be corrected using any of the following methods: direct calculation, constraint correction, and machining correction. The final structural diagram after modeling is as follows: Figure 3 As shown.

[0137] Specifically, in the implementation process, the parts concerning the verification calculation of the lead screw structure, the modeling and assembly, and the selection of coefficients in the calculation process are common knowledge to those skilled in the art, and will not be described in detail here.

[0138] Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without inventive effort, including but not limited to equivalent substitutions, modifications, or improvements, are within the scope of protection of this invention. Although various aspects are illustrated in the examples, the drawings are not necessarily drawn to scale unless specifically indicated otherwise.

Claims

1. A design method for a life-based gear planetary roller screw, characterized in that, Includes the following steps: (1) Select the diameter range; (2) Determine the radial dimension parameters based on the transmission ratio; (3) Design of gear and threaded parts: The basic equation relating gears is: Z N / Z R =d N0 / d R0 ,(d N0 -d R0 ) / 2=(Z N -Z R )m / 2,d R0 =mZ R ,d N0 =mZ N ,h a1 =(h a *+x1)m,h a2 =(h a *-∆h a *-x2)m,h f1 =(h a *+c*-x1)m,h f2 =(h a *+c*+x2)m,∆h a *=(h a *-x2)² / z N tan 2 α Where, d N0 d is the mean diameter of the nut. R0 Z is the pitch diameter of the roller. N Z represents the number of teeth on the gear ring. R Here, m is the number of roller teeth, h is the standard module, and m is the number of standard roller teeth. a Tooth tip height, h f Tooth root height, h a *Tooth tip coefficient, x-displacement coefficient, c*Clearance coefficient, αPressure angle The gear design equation is: D R0 =d R0 ,D R1 =D R0 +2h a1 ,D R2 =D R0 -2h f1 ,D N0 =d N0 ,D N1 =D N0 +2h a2 ,D N2 =D N0 -2h f2 , Among them, D R0 Roller pitch circle diameter, D R1 Roller tooth tip circle diameter, D R2 Roller tooth root circle diameter, D N0 Pitch circle diameter of gear ring, D N1 Gear ring tooth tip circle diameter, D N2 Gear root circle diameter, The basic relational equation for threaded wires is: h=0.375P / tan(θ),b=7h / 6,e=h / 6,r=d R0 / 2sin(θ / 2), Where h is the tooth height, b is the tooth root width, P is the pitch, θ is the tooth angle, e is the intercuspal clearance, and r is the tooth radius. The thread design equation is: d S1 =d S0 +h,d S2 =d S0 -h,d N1 =d N0 -h,d N2 =d N0 +h,d R1 =d R0 +h,d R2 =d R0 -h, d S1 Screw tip diameter, d S0 d is the mean diameter of the lead screw. S2 Screw root diameter, d N1 Nut top diameter, d N2 Nut root diameter, d R1 Roller tip diameter, d R2 Roller bottom diameter, (4) Based on the design results of (3), determine the load: The axial critical load equation is: C≤π 3 Ed S2 4 / 64(μl S ) 2 S S Where C is the critical axial load, E is the elastic modulus of the material, and d s2 Screw base diameter, μ installation coefficient, l s Screw length, S S Safety factor, The equation for thread shear strength is: F≤πd R2 b 2 n p Where F is the thread shear strength, b is the thread root width, n is the number of engagement points of a single roller, and τ is the thread shear strength. p Allowable shear stress, The equation for the number of rollers in the theory is: C / F≤m n ≤0.5πarcsin -1 [(is R0 +2h) / (d S0 +d N0 )], Where, m n This represents the theoretical number of rollers. (5) Inverse calculation using lifetime: The rated load equation is: C0=C(100 / L) 1 / 3 , Where C0 is the rated load and L is the intended service life, calculated as 0.65C0 during selection. The critical speed equation is: n Rmax ≤(640EI / ρA) 1 / 2 , Where, n Rmax Let I be the critical maximum rotational speed, I be the minimum cross-sectional moment, ρ be the material density, and A be the minimum cross-sectional area. The efficiency equation is: η=tan(f S -f M ) / time{f S -f M -arctane[(f S -f M ) / cos(α / 2)]}, Among them, f S f is the helix angle of the lead screw. M The helix angle of the nut. Hertz's theory and fatigue life theory equations are as follows: σ=3F n / 2πab,δ=K(2πab / σ) 2 / 3 ,a=[6F n (1-n 2 ) / πE(e 2 -e 4 )] 1 / 3 ,b=a(1-e 2 ) 1 / 2 ,K=[9π 4 (e 2 -e 4 ) / 4E] 1 / 3 Where σ is the contact stress, F n δ is the normal force, a is the major semi-axis of the ellipse, b is the minor semi-axis of the ellipse, δ is the elastic deformation, and K is the elastic deformation coefficient.

2. The design method of a life-based planetary roller screw according to claim 1, characterized in that, In step (1), the diameter d of the lead screw designed in the forward direction is selected according to the requirements.

3. The design method for a life-based planetary roller screw according to claim 1, characterized in that, In step (2), the radial dimension parameters are designed based on the transmission ratio. The equation for the radial dimension parameter of the lead screw is: d S0 =d,P S =L S / n S ,d S1 =d S0 +h,d S2 =d S0 -h-2e, Where d is the diameter of the lead screw in the forward design, d S0 n is the mean diameter of the lead screw. S L represents the number of lead screw threads. S P is the lead of the lead screw. S Where is the screw pitch, h is the thread height, and d is the thread height. S1 d is the lead screw tip diameter. S2 Where is the lead screw root diameter, and e is the tooth crest clearance. The equation for the radial dimension parameters of the roller is: d R0 =d S0 / (n S -2),n R =1,P R =L R / n R ,d R1 =d R0 +h,d R2 =d R0 -h-2e, Where, d R0 n is the pitch diameter of the roller. R L represents the number of roller heads. R For roller lead, P R Where is the roller pitch, h is the tooth profile height, and d is the thread height. R1 d is the roller tip diameter. R2 Where 'e' is the roller root diameter and 'e' is the tooth crest clearance. The equation for the radial dimension parameter of the nut is: d N0 =d S0 +2d R0 ,n N =n S ,P N =L N / n N ,d N1 =d N0 +h+2e,d N2 =d N0 -h, Where, d N0 n is the mean diameter of the nut. N L represents the number of nut heads. N For the nut lead, P N Where d is the nut pitch, h is the thread height, and d is the thread pitch. N1 d is the nut tip diameter. N2 'e' is the nut base diameter, and 'e' is the tooth crest clearance.

4. The design method of a life-based planetary roller screw according to claim 1, characterized in that, In step (3), constraint equations are applied. The constraint equation to avoid root shear is: Z Rmin ≥2h a * / sin 2 a, Among them, Z Rmin Minimum number of teeth required for rollers, The equation for the gear correction factor to avoid interference is: mZ R +2m(h a *+x R )≤d R2 , Among them, Z R x is the number of roller teeth. R This is the gear correction factor. In practical implementation, roller interference can be corrected using any one of the following methods: direct calculation, constraint correction, or machining correction.

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