JP4960857B2 - Calculation method of worm gear tooth profile with diagonally misaligned shaft machining - Google Patents

Description

  In the present invention, the two planes including the respective axial core lines of the worm and the wheel share a perpendicular line from each other's axial core line and are in a parallel relationship with a predetermined interval, and the respective axial core lines are viewed from the perpendicular direction, The present invention relates to a tooth profile calculation method for a worm and a wheel having a predetermined oblique angle relationship (both are collectively referred to as a “worm gear”), that is, an oblique misalignment shaft machining type worm gear tooth profile calculation method.

The present invention also provides a method for calculating the tooth contact clearance between the worm and the wheel obtained from the tooth profile data obtained from the above calculation method, the tooth profile data obtained in this way, and the tooth contact clearance data. In addition, regarding the wheel manufacturing method, the worm gear reducer including the worm and the wheel manufactured by the manufacturing method, the electric steering device using the worm gear reducer, and the like enjoy the effects of the manufacturing method.

  The worm gear reducer is small in size, has a high reduction ratio, is quiet in rotation, and has low noise. Therefore, the worm gear reducer is used in various industrial fields, and provides an auxiliary steering force for an electric steering system of an automobile and a steering input / output. It is also used between the shafts.

  By the way, a worm and a wheel (generally referred to as “worm wheel”, but simply referred to as “wheel” in the present application) used in a worm gear reducer are formed into four types 1 to 4 depending on the processing method. There are various types of worms (JIS B 1723).

  The worm gear is roughly classified into two types, a cylindrical worm gear and a hourglass worm gear. Here, the case of a cylindrical worm gear will be dealt with. The above JIS standard also relates to a cylindrical worm gear.

As shown in FIG. 7 (a), the type 1 worm 1I is configured to attach a machining tool (bite) WS in parallel with the worm shaft section, and the shape of the worm tooth surface in the shaft section is a straight line. Is. In the figure, symbol α _a indicates the pressure angle of the axial cross section.

As shown in FIG. 7 (b), the type 2 worm 1II attaches a machining tool (bite) WT in the direction perpendicular to the worm's tooth groove, and the shape of the worm tooth surface in the section perpendicular to the tooth groove is a straight line. It is what has become. In addition, the code | symbol (alpha) _c in a figure shows the pressure angle of the tool for a process (bite).

As shown in FIG. 1 (a), 3 form worm 1III is for machining by tilting the working tools (milling or grinding) WP pressure angle alpha _c only advance angle beta _c of the worm 1III conical surface, the teeth The worm tooth surface of the cross section perpendicular to the groove is not a straight line.

As shown in FIG. 4 (a), (b), 4 form worm 1IV is machining tool having a flat working surface (milling (b) or the grinding wheel (a)) WR, the diameter _{d g} of WQ basis It is processed by decentering a circle, and the worm tooth surface becomes an involute curve in a cross section perpendicular to the axis. In addition, the code | symbol (beta) g in a figure is a basic circle advance angle.

  Here, in the industry, the type 1 worm and the type 2 worm are rarely used, and the type 3 worm and the type 4 worm, in particular, the type 3 worm is used in particular. Implementation, research and development are active.

  By the way, with respect to the worm gear, it has been conventionally demanded to take as many meshing contact surfaces as possible between the worm and the wheel so as to reduce the smooth contact and the transmission force per unit contact area.

  In order to solve this problem, a method of adjusting a good combination of tooth flank afterwards by combining a worm and a wheel manufactured separately according to conventional intuition and experience was used. Non-Patent Document 1 proposes a calculation method capable of calculating each tooth surface shape (tooth shape) completely with a mathematical formula and obtaining a desired tooth surface gap between the worm and the wheel. Yes.

  This Non-Patent Document 1 is excellent in that the ideal meshing of the worm gear is achieved mathematically, but relates to a worm gear of a three-type axis-right cross-over type.

  On the other hand, in recent years, there has been an increasing demand for the worm and wheel shafts to be obliquely inclined at a certain angle, particularly in automobile-related electric steering devices that have a large space limit in the surrounding environment. The calculation method disclosed in Non-Patent Document 1 cannot deal with such a case.

  Although there is no description of the calculation method for the obliquely staggered shaft type worm gear, Patent Documents 1 and 2 describe the embodiments and the effects thereof, and are industrially useful. It turns out that it is.

  Further, Patent Document 3 particularly relates to a worm gear reducer in an electric steering apparatus, by making the wheel advance angle smaller than the worm advance angle, thereby increasing the wheel tooth module and increasing the strength of the worm gear, or It is possible to reduce the size by reducing the distance between the shafts of the worm gear reducer (paragraph [0015] of Patent Document 3).

  FIG. 9 is a diagram showing a main part of a worm gear speed reducer that is a background art of the present invention, and is described in Patent Document 3. As shown in FIG. FIG. 9 shows a worm 11 and a wheel 12 that meshes with the worm 11 as the main part. Here, the worm 11 and the wheel 12 are collectively referred to as a worm gear 15.

  In the case of this worm gear 15, as can be seen from FIG. 9, in order to make the advance angle of the wheel 12 smaller than the advance angle of the worm 11, the axis of the worm 11 and the axis of the wheel 12 are perpendicular to the drawing. As shown in FIG. 2, the diagonal arrangement is not orthogonal but with a constant oblique angle Γo. That is, this patent document 3 also relates to an obliquely misaligned shaft type worm gear.

  By the way, in this patent document 3, generally, paragraph [0007], “In consideration of strength, it is necessary to use a large-diameter hob cutter, and in this case, the meshing area between the worm and the wheel becomes small. There is a description that "the surface pressure load increases", and problems of large-diameter hob cutters (processing tools) have been pointed out.

  Further, Patent Document 3 has a statement that the paragraph [0008] generally indicates that it was difficult for the conventional orthogonal worm gear reducer to ensure sufficient wheel tooth surface strength. In order to ensure the tooth surface strength, it has been suggested that the obliquely staggered shaft worm gear is advantageous.

  Furthermore, Patent Document 3 generally describes in paragraph [0009], “When a tooth surface of a wheel is formed with a large diameter hob cutter, an interference problem occurs in order to eliminate the problem of the advance angle, and this interference is avoided. Therefore, an oblique worm gear reducer has been proposed. In this case, however, there is a problem in that contact between the tooth surfaces becomes point contact, and the mesh portion surface pressure increases and durability decreases. ”And a problem in the case of using a large-diameter hob cutter (processing tool) and a staggered shaft worm gear has been pointed out.

  Here, in order to solve the above-described problem, Patent Document 3 proposes a “diagonally staggered shaft worm gear reducer in which the advance angle of the wheel is smaller than the advance angle of the worm” as described above. is there.

However, according to the present inventor and the applicant, with a technique different from the technique described in Patent Document 3, a smooth contact with a slanting misalignment shaft type worm gear can be ensured by ensuring a good meshing contact surface. It seemed that a worm gear with reduced transmission force per contact area and improved durability was possible.
"Study on tooth surface modification method of type 3 worm gear (1st report, analysis of calculation method of hob basic thread surface)" (The Japan Society of Mechanical Engineers, Vol. 52, No. 481, No. 61-9). .85-1312B) JP-A-61-37581 (FIG. 2) JP 2000-219140 A (FIG. 1) JP 2007-239849 A (FIG. 4)

  The present invention is intended to ameliorate the above-mentioned problem, and makes it possible to ensure a good meshing contact surface in terms of design and manufacture for an obliquely staggered shaft worm gear using a large-diameter machining tool. An object of the present invention is to provide a worm gear tooth profile calculation method for obliquely misaligned shaft machining.

The present invention also provides a method for calculating the tooth contact clearance between the worm and the wheel using the above calculation method, and a method for manufacturing a worm and a wheel using the tooth profile data thus obtained and data on the tooth contact clearance. By providing the worm gear speed reducer including the worm and the wheel manufactured by the manufacturing method, and the electric steering apparatus using the worm gear speed reducer, the effects of the manufacturing method can be enjoyed. I am doing so.

The oblique staggered shaft machining type worm gear tooth profile calculation method of the present invention is such that two planes including the respective axial core lines of the worm and the wheel share a perpendicular from each other's axial core lines and are in a parallel relationship with a predetermined interval, A method for calculating a tooth profile of a 3-type worm and the same wheel, or a 4-type worm and the same wheel, in which each axial center line has a predetermined oblique angle relationship when viewed from the perpendicular direction,
And expressions of AA or 4 forms a worm tooth profile is processed by a warm working tool having a desired pressure angle,
A worm cutting wheel tooth profile obtained by machining the wheel by tilting the tool having the worm tooth profile by the predetermined oblique angle with respect to the axis of the wheel while maintaining the predetermined distance; ,
Wherein a worm and a same worm type, the large diameter machining tool having a larger pitch radius than the pitch circle radius of the worm, large obtained by common expression that defines the relationship between the expression of the worm cutting wheel tooth The formula of the tooth profile of the diameter tool,
A large diameter obtained when machining a large-diameter machining tool having the tooth shape of the large-diameter tool by tilting the wheel at a predetermined tool attachment angle with respect to the wheel axis while maintaining the predetermined interval. Using the tool cutting wheel tooth profile formula,
The worm tooth profile is calculated from the worm tooth profile equation, and the wheel tooth profile is calculated from the large-diameter tool cutting wheel tooth profile equation.

  The tooth gap clearance calculation method between the diagonally misaligned shaft machining worm and the wheel of the present invention is based on the simultaneous contact line between the worm tooth profile and the wheel tooth profile obtained by the oblique misalignment shaft machining worm gear tooth profile calculation method of the present invention. A gap is calculated along the surface, and a clearance distribution on the meshing surface between the worm and the wheel is obtained to calculate a tooth contact state.

  The manufacturing method of the worm and wheel of the diagonally misaligned shaft machining type of the present invention includes the tooth profile data of the worm and the wheel obtained by the diagonally misaligned shaft machining type worm gear tooth profile calculation method of the present invention and the diagonal misalignment of the present invention. A worm and a wheel are manufactured using data on a tooth contact clearance obtained by a method for calculating a tooth contact clearance between a shaft-working worm and a wheel.

The worm gear reducer provided with the worm and the wheel manufactured by using the manufacturing method of the obliquely staggered shaft type worm and wheel of the present invention is characterized by receiving the effect of the manufacturing method.

The wheel and the worm of the worm gear reducer having the worm and the wheel manufactured by using the manufacturing method of the obliquely staggered shaft processing type worm and wheel of the present invention are connected to the input / output shaft and the electric motor of the electric steering device , respectively. It is characterized by that.

According to the diagonally misaligned shaft machining type worm gear tooth profile calculation method of the present invention, the two planes including the axis lines of the worm and the wheel share a perpendicular from each other and have a parallel relationship with a predetermined interval. The tooth shape calculation method of the 3-type worm and the same wheel, or the 4-type worm and the same wheel , in which each axial center line has a predetermined oblique angle relationship when viewed from the perpendicular direction,
A formula of type 3 or type 4 worm tooth machined by a worm machining tool having a desired pressure angle;
A worm cutting wheel tooth profile obtained by machining the wheel by tilting the tool having the worm tooth profile by the predetermined oblique angle with respect to the axis of the wheel while maintaining the predetermined distance; ,
Wherein a worm and a same worm type, the large diameter machining tool having a larger pitch radius than the pitch circle radius of the worm, large obtained by common expression that defines the relationship between the expression of the worm cutting wheel tooth The formula of the tooth profile of the diameter tool,
A large diameter obtained when machining a large-diameter machining tool having the tooth shape of the large-diameter tool by tilting the wheel at a predetermined tool attachment angle with respect to the wheel axis while maintaining the predetermined interval. Using the tool cutting wheel tooth profile formula,
Wherein calculating the worm tooth profile by the expression of the worm tooth profile, so to calculate the equation by wheel tooth profile of the large-diameter tool cutting wheel teeth, good for definitive diagonally staggered shaft-type worm gear with working tools of large diameter even on a mesh designed contact surface make it possible also to ensure the production, also contributes to the durability of the machining.

  According to the method of calculating the contact gap between the diagonally misaligned shaft machining worm and the wheel of the present invention, simultaneous contact between the worm tooth profile and the wheel tooth profile obtained by the oblique misalignment shaft machining worm gear tooth profile calculation method of the present invention. Since the clearance is calculated along the line, the clearance distribution on the meshing surface between the worm and the wheel is obtained to calculate the tooth contact state, the calculation of the tooth contact clearance can be accurately calculated in advance, and at that time, the tooth profile of the present invention described above The effect of the shape calculation method is demonstrated.

  According to the manufacturing method of the worm and wheel of the diagonally misaligned shaft machining type of the present invention, the tooth profile data of the worm and the wheel obtained by the diagonally misaligned shaft machining worm gear tooth profile calculation method of the present invention, Since the worm and the wheel are manufactured using the data of the tooth contact clearance obtained by the method of calculating the tooth contact clearance between the obliquely misaligned shaft worm and the wheel, the tooth profile calculation method and the tooth contact clearance calculation method of the present invention The effect is demonstrated as a manufacturing method.

The worm gear reducer provided with the worm and the wheel manufactured by using the manufacturing method of the oblique staggered shaft type worm and wheel of the present invention enjoys and exhibits the effects of the manufacturing method of the present invention.

When employed in the electric steering apparatus worm gear speed reducer having a worm and a wheel that is manufactured by the method diagonal staggered axes machining type worm and wheel of the present invention, the input and output shaft of the electric steering apparatus worm gear connecting the wheel of the reduction gear, by connecting the worm of the worm gear reducer to the motor of the electric steering system, it exerts enjoyed the effects of the production method of the present invention.

Below, the basic idea and embodiment of this invention are demonstrated using drawing.
<Basic idea of the present invention relating to an obliquely misaligned shaft type worm gear>
1. Basic idea The present invention idea diagonally staggered axis machining type worm gear tooth profile calculation method, the parallel relationship between the worm and the respective predetermined intervals share a normal of the two planes containing the axial line from the axial line of each other the wheel In addition, there is a method for calculating the tooth profile of a 3-type worm and the same wheel, or a 4-type worm and the same wheel , in which each axial center line has a predetermined oblique angle relationship when viewed from the perpendicular direction,
A formula of type 3 or type 4 worm tooth machined by a worm machining tool having a desired pressure angle;
A worm cutting wheel tooth profile obtained by machining the wheel by tilting the tool having the worm tooth profile by the predetermined oblique angle with respect to the axis of the wheel while maintaining the predetermined distance; ,
Wherein a worm and a same warm form, the large-diameter machining tool having a larger pitch radius than the pitch circle radius of the worm, obtained by common expression that defines the relationship between expression of the worm cutting wheel tooth Formula of tooth profile shape of large diameter tool,
A large diameter obtained when machining a large-diameter machining tool having the tooth shape of the large-diameter tool by tilting the wheel at a predetermined tool attachment angle with respect to the wheel axis while maintaining the predetermined interval. Using the tool cutting wheel tooth profile formula,
The worm tooth profile is calculated from the worm tooth profile equation, and the wheel tooth profile is calculated from the large-diameter tool cutting wheel tooth profile equation.

  This calculation method is further improved and utilized by the calculation method described in Non-Patent Document 1 so that it can be applied to the case where the axis line of the worm and the wheel is obliquely crossed. It is characterized in that a predetermined oblique angle (Γ) of both axis core wires is introduced therein.

Next, this calculation method is characterized in that a large-diameter machining tool having a pitch circle radius larger than the worm is used for machining the wheel. In this way, especially when the worm gear is small, such as a worm gear reducer for an electric steering apparatus of an automobile, the gear cutting of the wheel is made more stable and reliable while extending the life of the machining tool. Can be practically used.

  Next, this calculation method uses a large-diameter machining tool, and in order to form a wheel that intersects the worm at the predetermined oblique angle, the large-diameter machining tool should be tilted with respect to the axis of the wheel. The common formula for calculating the tool mounting angle is used.

  In this way, the obliquely misaligned shaft machining type worm gear tooth profile calculation method of the present invention can accurately calculate the tooth profile profile of the worm gear while using a large-diameter machining tool, thereby calculating an appropriate tooth contact clearance as will be described later. Thus, the tooth gap distribution can be designed and analyzed in advance, and a worm gear that ensures a good meshing contact surface can be manufactured.

  In addition, according to this calculation method, it is possible to freely control a good tooth contact design such as a tooth profile shape and a tooth surface clearance, and to obtain a worm gear excellent in durability.

  That is, according to the above calculation method of the present invention, with respect to the obliquely staggered shaft type worm gear, the meshing contact surface between the worm and the wheel is taken as much as possible to reduce the smooth contact and the transmission force per unit contact area, Durability can be improved.

2. A calculation method in which the tooth profile calculation method of the present invention is applied to a type 3 worm gear. In this calculation method, the formula of the worm tooth profile is the formula of the type 3 worm tooth profile (formula (1.7) in FIG. 2 (c)),
The formula of the worm cutting wheel tooth profile is the formula of the type 3 worm cutting wheel tooth profile (formula (1.16) in FIG. 3 (e)) corresponding to the formula of the type 3 worm,
The formula of the tooth shape of the large-diameter tool is obtained from a common formula (formula (3.1) in FIG. 6 (d)) that defines the relationship with the formula of the tooth shape of the 3-type worm cutting wheel. satisfy the (formula (1.7) in FIG. 2 (c)) wherein the tooth profile,
The formula for the large-diameter tool cutting wheel tooth profile when the large-diameter machining tool having a large-diameter tool tooth shape according to the formula for the large-diameter tool tooth shape is used. It is characterized by satisfying the expression (1.16) in FIG.

  In this calculation method, the tooth profile calculation method of the present invention is specifically applied to a JIS standard type 3 worm, and the detailed calculation process will be described later. The tooth profile calculation method of the present invention can be applied to the present invention, and the operational effects of the above tooth profile calculation method can be specifically demonstrated for the 3-type worm.

3. A calculation method in which the tooth profile calculation method of the present invention is applied to a type 4 worm gear. In this calculation method, the equation of the worm tooth profile is the equation of the type 4 worm tooth profile (the equation (2.5) in FIG. 5A).
The formula of the worm cutting wheel tooth profile is the formula of the 4 worm cutting wheel tooth profile corresponding to the formula of the 4 worm (formula (2.13) in FIG. 5 (j)),
The formula of the tooth shape of the large-diameter tool is obtained from a common formula (formula (3.1) in FIG. 6 (d)) that defines the relationship with the formula of the tooth shape of the 4-type worm cutting wheel. satisfy the (formula (2.5) in FIG. 5 (a)) wherein the tooth profile,
The formula of the large-diameter tool cutting wheel tooth profile when the large-diameter machining tool having a large-diameter tool tooth profile according to the formula of the large-diameter tool tooth shape is used. It is characterized by satisfying the expression (2.13)) of FIG.

  In this calculation method, the tooth profile calculation method of the present invention is specifically applied to a JIS standard type 4 worm, and the detailed calculation process will be described later. The tooth profile calculation method of the present invention can be applied to the present invention, and the operational effects of the above-described tooth profile calculation method of the present invention can be specifically demonstrated with respect to the 4-type worm.

4). Worm gear tooth gap clearance calculation method using data obtained by the tooth profile calculation method of the present invention This calculation method is a simultaneous contact line between the worm tooth profile obtained by the tooth profile calculation method of the present invention and the wheel tooth profile. , And the tooth contact state is calculated by calculating the gap distribution on the meshing surface between the worm and the wheel.

  In other words, as long as the tooth profile data is obtained, it is possible to calculate the worm gear contact gap to be obtained by appropriately selecting various related data (the above-mentioned predetermined interval, etc.) and applying it to the manufacturing method as follows. Thus, a worm and a wheel with a desired tooth contact gap can be manufactured, and the effect of the tooth profile calculation method of the present invention can be exhibited as an actual worm gear.

5. Manufacturing method for manufacturing a worm gear using the obtained tooth profile data and tooth contact clearance data This manufacturing method is a method for calculating the tooth profile of a worm and a wheel, obtained by the method of calculating the tooth profile of the obliquely misaligned shaft machining worm gear according to the present invention. The worm and the wheel are manufactured using the above data and the data on the tooth contact clearance obtained by the tooth contact clearance calculation method.

  According to this manufacturing method, an oblique staggered shaft type worm gear that ensures an appropriate tooth contact clearance can be designed and manufactured in advance, and the effects of the tooth profile calculation method of the present invention can be exhibited as a manufacturing method. Can do.

  In addition, since a large-diameter machining tool is used, the machining speed can be increased and the tool life can be increased compared to a small-diameter machining tool, which is excellent in practicality.

For worm gear speed reducer using a worm gear obtained by the production method of the present invention <br/> worm gear speed reducer effect of the worm gear of the prior SL present invention, i.e., effects of the tooth profile calculation method of the present invention Can be enjoyed and used as a worm gear reducer.

The worm gear obtained by the production method of the present invention when used in the electric steering system <br/> The electric steering apparatus as worm gear reducer, in its output shaft a wheel for worm gear reducer of the present invention, the same worm By being connected to the electric motor, the effect of the tooth profile calculation method of the present invention can be enjoyed and exhibited as an electric steering device.

Furthermore, as in Patent Document 2, the degree of freedom in the layout of the electric steering apparatus can be improved, for example, by making use of the worm gears and making the arrangement of the electric motor parallel to the steering rack shaft.
<Embodiment 1>
FIG. 1 shows an example of a method for calculating an obliquely misaligned shaft machining type worm tooth profile according to the present invention. (A) is an explanatory diagram of a machining method for a 3-type worm that is the object of the calculation method, and (b) The figure which shows the tool shape of (a), (c) is a figure which shows Formula (1.1) used with the calculation method, (d) is a figure which shows the coordinate system of the worm | warm and tool of (a), (e ) To (g) are diagrams showing Expressions (1.2) to (1.4) used in the calculation method.

2 (a) to (h) (excluding (f)) is a diagram showing equations (1.5) to (1.11) used in the calculation method of FIG. 1, and (f) is this calculation. It is a figure which shows mesh | engagement of the tool and wheel which have a worm | worm and a wheel or a worm tooth profile when the axis | shaft core line of the 3 type | mold worm obtained by the method is inclined Γ.

  FIGS. 3A to 3E are diagrams showing Expressions (1.12) to (1.16) used in the calculation method of FIG. In addition, about the part already demonstrated from this, the duplication description is abbreviate | omitted using the same code | symbol.

From this, an embodiment in which the obliquely misaligned shaft machining type worm gear tooth profile calculation method of the present invention is applied to a 3-type worm will be described. In the following description, terms and symbols as described in the description of symbols are used corresponding to the terms in the claims.
1. Basic formula of type 3 worm gear 1.1 Basic formula of thread surface of type 3 worm
As in JIS B 1723, 3 form worm 1III is the rotation axis of the milling or grinding of the conical surface (warm working tools WP) relative to the worm shaft, a threaded surface which is processed by tilting advance angle beta _c. [Fig. 1 (a)]
For the tool (milling cutter or grindstone) WP, take the tool axis as the Z axis on the coordinate system O-XYZ [Fig. 1 (b)],
ρ _a : tooth tip radius ρ _c : pitch circle radius α _c : pressure angle
W: Blade width at ρ _c ρ: Radius of an arbitrary tool surface (point A) Θ: Deflection angle on the XY plane of an arbitrary tool surface (point A). With respect to the Z axis, the negative side is the [1] plane and the positive side is the [2] plane.

The coordinate (point A) of any tool surface is
The equation (1.1) in FIG. In decoding, negative is the [1] plane and positive is the [2] plane.

For the worm 1III, the axis is taken as the z-axis on the coordinate system o-xyz [FIG. 1 (d)],
r _c : pitch circle radius β _c : advance angle of pitch circle
L: Lead L = 2πr _c tanβ _c
λ: Rotation angle
z _c : groove width in pitch circle
a: Distance between worm and tool axis a = r _c + ρ _c
And

Consider a case in which the worm coordinate system o-xyz is fixed and the tool is ground by rotating the tool clockwise with a rotation angle λ with respect to the worm axis. Any tool surface coordinate (A point), when viewed from the worm coordinate system o-xyz, the angle λ is rotated right-hand threads, becomes a z-axis in .lambda.r _c tan _c translational position,
The equation (1.2) in FIG.

The thread surface of the worm 1III (contact surface between the worm and the tool) is formed by the envelope surface of the moving tool surface (coordinate group), and the conditional expression of this envelope surface is the following Jacobian:
Calculate (1.3) in Fig. 1 (f)
It is given as (1.4) in Fig. 1 (g).

When equation (1.4) holds, the coordinates (x, y, z) expressed by equation (1.2) become the coordinates of the screw surface of the worm, and the radius r is expressed by equation (1.5) in Fig. 2 (a). The axial cross-sectional profile of the thread surface (contour in the xz plane) is y = 0,
(1.6) in Fig. 2 (b).

Since the general formula representing the thread surface of the worm 1III is translated by θr _c tanβ _{c in the} z-axis direction when the shaft cross-sectional profile is rotated by an angle θ with respect to the worm axis,
The equation (1.7) in FIG.

In addition, the angle α (pressure angle of the screw surface) formed by the tangent at the arbitrary radius r on the axial cross section contour of the worm 1III and the x axis is:
The formula (1.8) in Fig. 2 (d) is obtained, and the tooth width W of the tool is
The equation (1.9) in FIG.
1.2 Basic formula of wheel tooth surface meshing with type 3 worm with angle Γ tilted The axis is set on o-xyz with the axis as z-axis for type 3 worm 1III, and the axis with respect to wheel 2III The coordinate system is taken on O-ξηζ as the ζ axis. Mount the worm shaft at an angle Γ with respect to the plane perpendicular to the wheel shaft [Fig. 2 (f)],
r _c: worm pitch circle radius β _c: worm lead angle
L: Worm lead L = 2πr _c tanβ _c
n: Number of worms Γ: Worm tilt angle ψ: Worm rotation angle
R _c : Wheel pitch circle radius γ _c : Wheel advance angle γ _c = β _c + Γ

Z: Number of teeth on the wheel
u: Teeth ratio u = Z / n
c: Distance between worm and wheel axis c = r _c + R _c
And

When the worm 1III is rotated about the z axis by an angle ψ, the thread surface of the worm at an arbitrary radius r does not move in the z axis direction (the wheel rotates).
(1.10) in Fig. 2 (g). However, as a conditional expression,
Equation (1.11) in Fig. 2 (h) holds.

When this is expressed by a wheel coordinate system O-ξηζ that rotates by an angle ψ / u left-hand screw according to the gear ratio u,
It becomes (1.12) formula of Fig.3 (a).

The thread surface of the wheel 2III (the contact surface between the worm 1III and the wheel 2III) is formed by the envelope surface of the moving worm surface (coordinate group), and the conditional expression of this envelope surface is the following Jacobian:
Calculate (1.13) in Fig. 3 (b)
It is given as (1.14) in Fig. 3 (c). Here, γ = θ + ψ.

When equation (1.14) in Fig. 3 (c) holds, the coordinates (ξ, η, ζ) represented by equation (1.12) in Fig. 3 (a) become the coordinates of the wheel tooth surface, and the radius R, ξη plane The angle τ with respect to the ξ axis is
The equation (1.15) in Fig. 3 (d)
The equation (1.16) in FIG.
<Embodiment 2>
FIG. 4 shows another example of the method of calculating the obliquely misaligned shaft machining type worm gear tooth profile according to the present invention. FIG. 4A is an explanatory view of a machining method (grinding) of a 4-type worm that is the object of the calculation method. (B) is explanatory drawing of the processing method (cutting) of the 4 form worm used as the calculation method, (c) is a figure which shows the involute helicoid which is a tooth profile shape of the 4 form worm of (a), (b). (D) is a figure which shows the involute curve on plane [S] in (c), (e)-(g) shows Formula (2.1)-Formula (2.3) used with the calculation method. (H) is a diagram showing an axial cross-sectional contour used in this process, and (i) is a diagram showing an equation (2.4) used in the calculation method.

FIGS. 5A to 5J (excluding (d)) are diagrams showing formulas (2.5) to (2.13) used in the calculation method of FIG. 4, and (d) is this calculation. It is a figure which shows mesh | engagement of the tool and wheel which have a worm | worm and a wheel or a worm tooth profile when the axis | shaft core line of the 4 type | mold worm obtained by the method is inclined Γ.

In the following, an embodiment in which the obliquely misaligned shaft machining type worm gear tooth profile calculation method of the present invention is applied to a 4-type worm will be described.
2. Basic formula of type 4 worm gear 2.1 Basic formula of thread surface of type 4 worm
As described in JIS B 1723, the 4-type worm 1IV (involute worm) is a threaded surface that is machined so as to be straight on a plane that is in contact with the basic cylinder with a flat surface milling WR or grinding wheel WQ. It becomes an involute curve on a plane perpendicular to the axis, and can be cut with a cutting tool or an involute hob. [Fig. 4 (a), (b)]
When a cylinder of radius r _g rolls on the plane [P], the thread surface drawn in space by the straight line G with the inclination angle β _g in the [P] plane is an involute helicoid, and the curve A ₀ A is unwound from the base circle. Involute curve [FIG. 4 (c) (d)].

The 4-type worm 1IV is formed by progressively moving an involute curve with a lead L in the screw axis direction. At this time,
L: Lead
L = 2πr _g tanβ _g = 2πr _c tanβ _c
r _g : Foundation cylinder radius β _g : Lead angle of foundation chord winding
r _c : Pitch circle radius β _c : Lead angle of pitch circle radius.

In FIG. 4D, since A ₀ D (arc length) = CD (linear length), the curve A ₀ A on the cross section perpendicular to the axis is expressed in polar coordinates.
The equation (2.1) in FIG. Here, inv is called an involute function.

When the right-handed movement of the curve A ₀ A around the worm axis with a declination φ is
Equation (2.2) in Fig. 4 (f) is obtained.

The axial cross-sectional contour of the screw surface (contour on the xz plane) is set to φ = 0,
If the coordinate transformation is performed so that the groove width in the pitch circle is z _c and the center of the groove width is z = 0 [FIG. 4 (h)], the equation (2.3) in FIG. Is
Equation (2.4) in Fig. 4 (i) is obtained. For the double sign, the negative side is the [1] plane and the positive side is the [2] plane with respect to the z-axis.

Since the general formula representing the thread surface of the worm 1IV is translated by θr _c tanβ _{c in the} z-axis direction when the shaft cross-sectional profile is rotated by an angle θ with respect to the worm axis,
It becomes (2.5) Formula of Fig.5 (a).

In addition, the angle α (pressure angle of the thread surface) formed by the tangent at an arbitrary radius r on the axial cross-sectional contour of the worm 1IV and the x axis is:
In FIG. 5 (b), equation (2.6) is obtained. When the pressure angle at the pitch circle radius r _c is α _a ,
Equation (2.7) in Fig. 5 (c) holds.
2.2 Fundamental formula of wheel tooth surface meshing with 4-type worm with angle Γ inclined The coordinate system is taken on o-xyz with the axis as z-axis for 4-type worm 1IV, and the axis with respect to wheel 2IV The coordinate system is taken on O-ξηζ as the ζ axis. Mount the worm shaft at an angle Γ with respect to the plane perpendicular to the wheel shaft [Fig. 5 (d)]
r _g : Worm base circle radius β _g : Lead angle of worm base circle
r _c : Worm pitch circle radius β _c : Lead angle of worm pitch circle
z _c : Groove width in the pitch circle of the worm
L: Worm lead L = 2πr _c tanβ _c
n: Number of worms Γ: Worm tilt angle ψ: Worm rotation angle
R _c : Wheel pitch circle radius γ _c : Wheel advance angle γ _c = β _c + Γ

Z: Number of teeth on the wheel
u: Teeth ratio u = Z / n
c: Distance between worm and wheel axis c = r _c + R _c
And

When the worm 1IV is rotated about the z-axis by an angle ψ, the thread surface of the worm 1IV at an arbitrary radius r does not move in the z-axis direction (the wheel 2IV rotates).
Equation (2.8) in Fig. 5 (e) is obtained.

When this is expressed by a wheel coordinate system O-ξηζ that rotates by an angle ψ / u left-hand screw according to the gear ratio u,
Equation (2.9) in FIG.

The thread surface of the wheel 2IV (the contact surface between the worm 1IV and the wheel 2IV) is formed by the envelope surface of the moving worm surface (coordinate group), and the conditional expression of this envelope surface is the following Jacobian:
Calculate (2.10) in Fig. 5 (g),
This is given as equation (2.11) in Fig. 5 (h). Here, γ = θ + ψ.

When equation (2.11) in Fig. 5 (h) holds, the coordinates (ξ, η, ζ) represented by equation (2.9) in Fig. 5 (f) become the coordinates of the wheel tooth surface, and the radius R, ξη plane The angle τ with respect to the ξ axis is
(2.12) in Fig. 5 (i)
Equation (2.13) in Fig. 5 (j) is obtained.
<Description of common formula>
FIG. 6 is a diagram for explaining a common formula showing the relationship between a worm for optimizing meshing and a tool for large-diameter machining, which is commonly used in the method of calculating the worm gear tooth profile shape of the obliquely misaligned shaft machining method of the present invention. (A) is a figure which shows mesh | engagement with a worm | warm and a wheel, (b) is a figure which shows mesh | engagement with the tool for large diameter machining, and a wheel, (c) is used by (a), (b). The figure which shows the table | surface of the relationship of a code | symbol, (d) is a figure which shows the common formula (3.1) which shows the relationship between the worm | warm which optimizes meshing, and the tool for large diameter processing.

The worm inclination angle (oblique angle) in each of the formulas 3 and 4 is changed to Γ, and the advance angle of the worm gear is set to a predetermined oblique angle Γw, and a large diameter machining tool ( (Including hob cutter, single cutter, grindstone, etc.) For 1PH , 1QH, and 1RH, if the tooth profile is calculated with the predetermined tool mounting angle Γh obtained by the common formula (3.1), the desired worm 1 with the oblique misalignment shaft machining type The tooth profile shapes of (1III, 1IV ) and wheel 2 (2III, 2IV) can be obtained, and this tooth profile shape optimizes the meshing.
3. Relational expression between worm and large-diameter tool for optimum meshing ( common to 3 and 4 types )
The ideal mesh between the worm and the wheel is to process the wheel in the same posture as the meshed state using a hob with the same specifications as the worm. However, when the hob diameter is small, the hob wears rapidly and the life is shortened, which is not practical in production. Therefore, a tool for large diameter machining (such as a large diameter hob) is used.

Here, reference numeral 2 '(2III', 2IV ') denotes each wheel when the hob diameter is small, that is, when the wheel is machined with the hob (1P, 1Q, 1R) having the same diameter as the worm meshing with the wheel. Is shown.

Therefore, the large-diameter machining tools 1PH, 1QH, and 1RH are made in the same shape as the worm and have a large diameter [FIG. 6 (b)]
In order to distinguish between a worm and a large-diameter machining tool, a suffix is added to the symbol to make a table in FIG.

Relationship worm and the large-diameter machining tool to optimize the engagement, in a pitch circle radius R _c of the wheel,
This is to set the equation (3.1) in FIG.
<Embodiment 3>
FIG. 7A is a diagram showing a machining method for a single worm to which the obliquely misaligned shaft machining type worm gear tooth profile calculation method of the present invention can be applied, and FIG. 7B is a diagonally misaligned shaft machining worm gear tooth profile of the present invention. It is a figure which shows the processing method of 2 type | mold worm which can apply the calculation method.

  Since these worm gear processing methods have been described in the background art of the specification, they are omitted here.

The concept derived from the calculation methods and the common formulas of the first and second embodiments described above can also be applied to the type 1 worm 1I and type 2 worm 1II described in FIG. The effects similar to those of the type 3 worm 1II and type 4 worm 1IV by the staggered shaft machining type worm tooth profile calculation method can also be exhibited in the type 1 worm 1I and type 2 worm 1II .

Similarly, AA worm group III, 4 form worm 1IV, worm and tooth contact gap calculation method the wheel for, a method of manufacturing the worm and wheel, as well as the worm gear of the worm and wheel manufactured by the manufacturing method The application to the speed reducer and the electric steering device using the worm gear speed reducer can also be applied to the type 1 worm 1I and the type 2 worm 1II . effects on, those capable of also exerting Oite one form worm 1I, 2 form worm 1II.

  As shown in FIG. 8 (b), the electric steering device 10 of FIG. 8 (a) assists steering of wheels (tires) T of a vehicle such as an automobile, and is connected to a handle HD operated by a driver. The input / output shaft 3 includes an input shaft 3A, and an output shaft 3B connected to the input shaft 3A via a torque sensor 6, and an electric motor 4 that generates an auxiliary steering force.

  The electric steering device 10 also includes a worm gear speed reducer 5 including a worm 1 of the present invention connected to the electric motor 4, a wheel 2 connected to the output shaft 3B of the input / output shaft 3, and an output shaft 3B. A pinion 3a provided on the input shaft 3A side and a steering rack shaft 7 linearly driven by the pinion 3a are provided.

  According to the electric steering device 10 having such a configuration, when the driver steers the handle HD, the steering force is detected by the torque sensor 6, and the electric motor 4 is driven in accordance with the steering force, and the driving force Is transmitted from the worm 1 to the wheel 2, the output shaft 3B, the pinion 3a, and the steering rack shaft 7 to assist the steering of the wheels (tires) T.

  At this time, the electric steering device 10 (10I, 10II, 10III, 10IV) is manufactured by the worm 1 (1I, 1II, 1III, 1IV) and worm gear reducer 5 (5I, 5II, 5III, 5IV) equipped with wheels 2 (2I, 2II, 2III, 2IV) are used, and these effects can be applied to worm gear reducers and electric steering devices. In particular, in the case of an oblique misalignment axis, it is advantageous in terms of in-vehicle layout.

  In addition, the method of calculating the worm gear tooth profile of the obliquely misaligned shaft machining method of the present invention is not limited to the above-described embodiment, and various modifications and combinations are possible within the scope described in the claims and the scope of the embodiment These modifications and combinations are also included in the scope of the right.

  In addition, the tooth contact clearance calculation method, the manufacturing method for manufacturing a worm and a wheel, the worm gear reducer, and the electric steering device of the present invention are not limited to the above-described embodiments, but are described in the claims. Various modifications and combinations are possible within the scope described above, and these modifications and combinations are also included in the scope of the right.

  In addition, the oblique staggered shaft machining type worm gear tooth profile calculation method of the present invention has been described for the case of machining by tilting to a relatively non-orthogonal angle, but also when the axial center line of the worm and the wheel is in an orthogonal relationship, Of course, the wheel is formed for this purpose by using a tool for large-diameter machining.

  The oblique misalignment shaft machining worm gear tooth profile calculation method of the present invention ensures a good meshing contact surface for the oblique misalignment shaft worm gear using a large-diameter machining tool, and the design analysis of the tooth profile can be freely performed. Can be used in industrial fields that require

1 shows an example of a method for calculating an obliquely staggered shaft machining type worm gear tooth profile according to the present invention, wherein (a) is an explanatory diagram of a machining method for a 3-type worm that is the object of the calculation method, and (b) is a diagram of (a). The figure which shows a tool shape, (c) is a figure which shows Formula (1.1) used with the calculation method, (d) is a figure which shows the coordinate system of the worm | warm and tool of (a), (e)-(g ) Is a diagram showing equations (1.2) to (1.4) used in the calculation method. (A) to (h) (excluding (f)) are diagrams showing the equations (1.5) to (1.11) used in the calculation method of FIG. 1, and (f) is the calculation method. The figure which shows mesh | engagement of the tool and wheel which have a worm and a wheel, or a worm tooth shape when the axis line of the obtained 3 form worm is inclined Γ (A)-(e) is a figure which shows Formula (1.12)-Formula (1.16) used with the calculation method of FIG. The other example of the calculation method of the diagonally misaligned shaft machining type worm gear tooth profile according to the present invention is shown in FIG. FIG. 4 is an explanatory diagram of a processing method (cutting) of a 4-type worm that is a target of the calculation method, FIG. 8C is a diagram showing an involute helicoid that is a tooth-shaped shape of the 4-type worm of FIGS. Is a diagram showing an involute curve on the plane [S] in (c), (e) to (g) are equations (2.1) to (2.3) used in the calculation method, (h) ) Is a diagram showing an axial cross-sectional contour used in this process, and (i) is a diagram showing an expression (2.4) used in the calculation method (A)-(j) (except (d)) is a figure which shows Formula (2.5) -Formula (2.13) used with the calculation method of FIG. 4, (d) is this calculation method. The figure which shows mesh | engagement of the tool and wheel which have a worm and a wheel, or a worm tooth shape when the axis line of the obtained 4 form worm is inclined Γ A common formula showing a relationship between a worm for optimizing meshing and a tool for large-diameter machining, which is commonly used in the method of calculating the shape of a worm gear tooth profile with an obliquely misaligned shaft machining method according to the present invention, and (a) Is a diagram showing the meshing between the worm and the wheel, (b) is a diagram depicting the meshing between the large-diameter machining tool and the wheel, and (c) is the relationship of the symbols used in (a) and (b). The figure which shows a table | surface, (d) is a figure which shows the common formula (3.1) which shows the relationship between the worm | warm which optimizes meshing, and the tool for large diameter processing (A) is a figure which shows the processing method of 1 type | mold worm which can apply the idea of the diagonally misaligned shaft machining type worm gear tooth profile calculation form of this invention, (b) is the diagonally misaligned shaft machining type worm gear tooth profile profile of this invention. The figure which shows the processing method of the 2 type worm which can apply the idea of the calculation method (A) is sectional drawing which shows the principal part of the electrically-driven steering apparatus using the worm | warm and wheel manufactured by the example of the manufacturing method of the worm | screw and wheel of the diagonally misaligned shaft processing type of this invention, (b) is (a). The figure which shows the whole structure of an electric steering device The figure which shows the principal part of the worm gear reduction gear used as the background art of this invention

Explanation of symbols

1 (1I, 1II, 1III, 1IV) Worm 2 (2I, 2II, 2III, 2IV) Wheel z (FIGS. 6 (a), (b)) Worm shaft core ζ (FIGS. 6 (a), (b)) Wheel Axle core wire WF (FIGS. 6A and 6B) Worm plane HF (FIGS. 6A and 6B) Wheel plane straight line oO (FIGS. 6A and 6B) Perpendicular line OO (FIG. 6) (A), (b)) Predetermined interval Γ (FIG. 2 (f), FIG. 5 (d)) Predetermined oblique angle Γ _w , Γ _h tilt angle (predetermined oblique angle, predetermined tool mounting angle)
α _c (FIG. 1 (b)) Tool pressure angle WP (FIG. 1 (a)) Worm machining tool WQ (FIG. 4 (a)) Worm machining tool (grinding stone)
WR (Figure 4 (b)) Tool for worm machining (milling)
1P (FIG. 1 (a)) Tool 1Q having a worm tooth profile (FIG. 4 (a)) Tool 1R having a worm tooth profile (FIG. 4 (b)) Tool ρ _c having a worm tooth profile (FIG. 1 (b)) Pitch circle radius r _{cw of} tool for machining (FIG. 6 (c)) Pitch circle radius r _{ch of} tool for worm machining (FIG. 6 (c)) Pitch circle radius of large diameter machining tool 1PH (FIG. 2 (f)) large Diameter machining tool 1RH (Fig. 5 (d)) Large diameter machining tool 1QH (Fig. 5 (d)) Large diameter machining tool 3 (3A, 3B) I / O shaft
4 Electric motor
5 (5I, 5II, 5III, 5IV) Worm gear reducer
10 (10I, 10II, 10III, 10IV) Electric steering system

Claims (5)

The two planes including the axis lines of the worm and the wheel share a perpendicular line from each other and have a parallel relationship with a predetermined distance, and each axis line line has a predetermined oblique angle when viewed from the perpendicular direction. A tooth profile calculation method between a 3-type worm and the same wheel, or a 4-type worm and the same wheel, in an intersecting angle relationship,
A formula of type 3 or type 4 worm tooth machined by a worm machining tool having a desired pressure angle;
A worm cutting wheel tooth profile obtained by machining the wheel by tilting the tool having the worm tooth profile by the predetermined oblique angle with respect to the axis of the wheel while maintaining the predetermined distance; ,
Wherein a worm and a same warm form, the large-diameter machining tool having a larger pitch radius than the pitch circle radius of the worm, obtained by common expression that defines the relationship between expression of the worm cutting wheel tooth Formula of tooth profile shape of large diameter tool,
A large diameter obtained when machining a large-diameter machining tool having the tooth shape of the large-diameter tool by tilting the wheel at a predetermined tool attachment angle with respect to the wheel axis while maintaining the predetermined interval. Using the tool cutting wheel tooth profile formula,
A method of calculating an obliquely misaligned shaft machining type worm gear tooth profile by calculating a tooth profile of a worm by the formula of the worm tooth profile and calculating a tooth profile of the wheel by the formula of the large-diameter tool cutting wheel profile. The formula of the worm tooth profile is the formula of the type 3 worm tooth profile (formula (1.7) in FIG. 2 (c)),
The formula of the worm cutting wheel tooth profile is the formula of the type 3 worm cutting wheel tooth profile (formula (1.16) in FIG. 3 (e)) corresponding to the formula of the type 3 worm,
The formula of the tooth shape of the large-diameter tool is obtained from a common formula (formula (3.1) in FIG. 6 (d)) that defines the relationship with the formula of the tooth shape of the 3-type worm cutting wheel. satisfy the (formula (1.7) in FIG. 2 (c)) wherein the tooth profile,
The formula for the large-diameter tool cutting wheel tooth profile when the large-diameter machining tool having a large-diameter tool tooth shape according to the formula for the large-diameter tool tooth shape is used. 3. The method of calculating an obliquely staggered shaft machining type worm gear tooth profile according to claim 1, wherein the formula (1.16) in FIG. 3 (e) is satisfied . The formula of the worm tooth profile is the formula of the 4-type worm tooth profile (formula (2.5) in FIG. 5A),
The formula of the worm cutting wheel tooth profile is the formula of the 4 worm cutting wheel tooth profile corresponding to the formula of the 4 worm (formula (2.13) in FIG. 5 (j)),
The formula of the tooth shape of the large-diameter tool is obtained from a common formula (formula (3.1) in FIG. 6 (d)) that defines the relationship with the formula of the tooth shape of the 4-type worm cutting wheel. satisfy the (formula (2.5) in FIG. 5 (a)) wherein the tooth profile,
The formula of the large-diameter tool cutting wheel tooth profile when the large-diameter machining tool having a large-diameter tool tooth profile according to the formula of the large-diameter tool tooth shape is used. 5. The oblique staggered shaft machining worm gear tooth profile calculation method according to claim 1, wherein the formula (2.13)) of FIG. 5 (j) is satisfied . A gap is calculated along a simultaneous contact line between the worm tooth profile and the wheel tooth profile obtained by the method of calculating the obliquely staggered shaft machining worm gear tooth profile according to any one of claims 1 to 3, and the meshing surface of the worm and the wheel A method for calculating a tooth contact clearance between an obliquely misaligned shaft machining worm and a wheel, wherein a tooth contact state is calculated by obtaining a clearance distribution in the wheel. The data of the tooth profile shape of the worm and the wheel obtained by the oblique misalignment shaft machining worm gear tooth profile calculation method according to any one of claims 1 to 3, and the oblique misalignment shaft machining worm and wheel of claim 4 A method for manufacturing a worm and wheel of an obliquely staggered shaft machining type, wherein a worm and a wheel are manufactured using data on a tooth contact clearance obtained by a tooth contact clearance calculation method.

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