A synchronous belt wheel helix angle detection method

Abstract

This invention discloses a method for detecting the helix angle of a synchronous belt pulley, belonging to the field of gear measurement technology. The method includes the following steps: S1, calculating the lead of the synchronous belt pulley based on the pitch circle diameter and the helix angle at the pitch circle; S2, selecting any helix line on the synchronous belt pulley teeth as the measurement position; S3, since the lead is equal at all points along the helix line of the synchronous belt pulley, we obtain: β x =atan(tan(β)×d x / d); S4, calculate the module at the measurement position; S5, calculate the actual helix angle β obtained from the actual measurement at the measurement position. 实 With β x In comparison, this invention determines whether the helix angle of the synchronous pulley is out of tolerance. It transforms the helix angle at the pitch circle diameter, which is otherwise unmeasurable, into the helix angle at a measurable location, reducing the likelihood of out-of-tolerance synchronous pulley production and improving the yield rate of synchronous pulleys.

Description

Technical Field

[0001] This invention belongs to the field of gear measurement, specifically relating to a method for detecting the helix angle of a synchronous belt pulley. Background Technology

[0002] Synchronous belt pulleys are mechanical transmission components used in conjunction with synchronous belts. They achieve high-precision, slip-free power transmission through meshing with the teeth of the synchronous belt, ensuring a constant transmission ratio. They offer advantages such as smooth transmission, high efficiency, ease of maintenance, and a wide speed ratio range, and are widely used in various mechanical equipment requiring precise power transmission. The helix angle of a synchronous belt pulley refers to the angle between the pulley's tooth groove and the axis. Setting the helix angle is used to optimize transmission smoothness or reduce axial force. Currently, in the production and measurement of synchronous belt pulleys, theoretical design values ​​for the helix angle at the tooth profile, number of teeth, pitch, addendum circle diameter, pitch circle diameter, and pitch diameter are typically provided. However, in actual production and measurement, because tooth profile measurement is a contact measurement, and the pitch circle diameter of a synchronous belt pulley is larger than the addendum circle diameter (the pitch circle has no physical contour), the helix angle at the pitch diameter cannot be directly measured through contact. Some manufacturers use the helix angle at the pitch diameter as the helix angle at the addendum circle for production and measurement, resulting in some synchronous belt pulleys having helix angles that exceed tolerances, affecting their use. Summary of the Invention

[0003] The technical problem solved by this invention is to provide a method for detecting the helix angle of a synchronous pulley, which calculates the theoretical value of the helix angle at a contactable measurement location on the synchronous pulley, making it convenient for personnel to compare the actual measured value of the helix angle at that location with the theoretical value, thereby reducing the possibility of the synchronous pulley helix angle exceeding the tolerance.

[0004] Technical Solution: To solve the above technical problems, the present invention adopts the following technical solution: A method for detecting the helix angle of a synchronous belt pulley, comprising the following steps:

[0005] S1. Calculate the synchronous pulley lead based on the pitch circle diameter and the helix angle at the pitch circle:

[0006] L=πd / tan(β)

[0007] In the formula, d is the pitch circle diameter of the synchronous pulley, β is the helix angle at the pitch circle, and L is the lead of the synchronous pulley;

[0008] S2. Select any helix on the timing belt pulley teeth as the measurement position, and measure the lead L at that position. x Satisfy the following formula:

[0009] L x =πd x / tan(β) x )

[0010] In the formula, dx It is the diameter of the circle containing the measurement location, β x It is the theoretical helix angle at the measurement location;

[0011] S3. Since the lead is equal at all points along the helix of the synchronous belt pulley, L=L x That is, πd / tan(β) = πd x / tan(β) x ),get:

[0012] β x =atan(tan(β)×d x / d)

[0013] In the formula, β x β is the theoretical helix angle at the measurement location, β is the helix angle at the pitch circle, and d is the theoretical helix angle at the measurement location. x It is the diameter of the circle at the measurement location, and d is the pitch circle diameter of the synchronous pulley;

[0014] S4. Calculate the modulus at the measurement location:

[0015] m x =d x ×cos(β) x ) / z

[0016] In the formula, d x It is the diameter at the measurement location, β x It is the theoretical helix angle at the measurement position; z is the number of teeth on the pulley, m x It is the modulus at the measurement location;

[0017] S5. The actual helix angle β obtained from the actual measurement at the measurement location. 实 With β x In comparison, determine whether the helix angle of the synchronous pulley is out of tolerance.

[0018] Preferably, the measurement location is any spiral line between the root circle and the tip circle.

[0019] Preferably, in step S5, a deviation threshold for the helix angle at the pitch circle is preset, and β is calculated based on the deviation threshold for the helix angle at the pitch circle. x The tolerance zone, if β 实 Located in β x If it is outside the tolerance zone, it is considered out of tolerance; if it is located in β... x Within the tolerance zone, it will not exceed the tolerance.

[0020] Preferably, the deviation threshold of the helix angle at the pitch circle is e;

[0021] β x上 =atan(tan(β+e)×d) x / d)

[0022] β x下 =atan(tan(β-e)×d) x / d)

[0023] In the formula, β x上 It is the upper limit of the theoretical helix angle at the measurement location, β. x下 β is the lower limit of the theoretical helix angle at the measurement location, β is the helix angle at the pitch circle, and d is the lower limit of the theoretical helix angle at the measurement location. x d is the diameter of the circle at the measurement location, e is the pitch circle diameter of the synchronous pulley, and e is the deviation threshold of the helix angle at the pitch circle.

[0024] β x下 With β x上 Between β x The tolerance zone, if β x下 ≤β 实 ≤β x上 If the result is within tolerance, then it is determined that the error is not exceeded; otherwise, it is determined that the error is exceeded.

[0025] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0026] 1. The synchronous pulley helix angle detection method of the present invention calculates the helix angle at any measurement position on the synchronous pulley that can be measured by contact by using the existing pitch circle diameter and the helix angle at the pitch circle diameter of the synchronous pulley, and compares it with the actual measured value of the helix angle at that position to determine whether the helix angle of the synchronous pulley is out of tolerance.

[0027] 2. The helix angle at the pitch circle diameter, which cannot be measured, is transformed into the helix angle at a measurable measurement location, thereby reducing the possibility of out-of-tolerance production of synchronous pulleys and improving the production qualification rate of synchronous pulleys. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of the synchronous belt pulley structure according to an embodiment of the present invention;

[0029] Figure 2 This is a schematic diagram of the helical structure of the tooth tip and tooth root in the embodiment;

[0030] Figure 3 This is a schematic diagram of the cross-sectional structure of the synchronous belt pulley in an embodiment;

[0031] Figure 4 This is a schematic diagram of the cylindrical surface of the synchronous belt pulley in the embodiment. Detailed Implementation

[0032] The present invention will be further illustrated below with reference to specific embodiments. These embodiments are implemented based on the technical solutions of the present invention, and it should be understood that these embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention.

[0033] Example

[0034] A method for detecting the helix angle of a synchronous belt pulley includes the following steps:

[0035] S1. Calculate the synchronous pulley lead based on the pitch circle diameter and the helix angle at the pitch circle diameter:

[0036] L=πd / tan(β)

[0037] In the formula, d is the pitch circle diameter of the synchronous pulley, β is the helix angle at the pitch circle, and L is the lead of the synchronous pulley;

[0038] When manufacturing each synchronous pulley, the customer will provide drawings of the synchronous pulley according to the design requirements, and provide the number of teeth, pitch, tip circle diameter, pitch diameter (pitch circle diameter), and the helix angle corresponding to the pitch diameter.

[0039] S2. Select any helix line on the sidewall of the timing belt pulley teeth as the measurement position, and measure the lead L at that position. x Satisfy the following formula:

[0040] L x =πd x / tan(β) x )

[0041] In the formula, d x It is the diameter of the circle at the measurement location, which is the first virtual circle. The first virtual circle is concentric with the nodal circle, β x It is the theoretical helix angle at the measurement location;

[0042] like Figure 1 , Figure 2 and Figure 3 As shown, in this embodiment, the spiral line used as the measurement position is located between the tooth tip circle and the tooth root circle. In this embodiment, a spiral line located in the middle between the tooth tip and the tooth root is selected as the measurement position.

[0043] S3. Since the lead is equal at all points along the helix of the synchronous belt pulley, L=L x That is, πd / tan(β) = πd x / tan(β) x ),get:

[0044] β x =atan(tan(β)×d x / d)

[0045] In the formula, β x β is the theoretical helix angle at the measurement location, β is the helix angle at the pitch circle, and d is the theoretical helix angle at the measurement location. x d is the diameter of the circle at the measurement location, and d is the pitch circle diameter of the synchronous pulley.

[0046] In this embodiment, β = 5°, d x =78.958, d=80.214;

[0047] β x =atan(tan(5°)×78.958 / 80.214)

[0048] =4.9221°

[0049] =4°55′19.6″.

[0050] like Figure 4 As shown, the horizontal right-angled side is the circumference of the end face of the synchronous pulley. The circumference of the pitch circle > the circumference of the addendum circle > the circumference of the circle where the measurement position is located > the circumference of the root circle. The vertical right-angled side is the lead. The lead of the helix at different positions is equal. The helix angle gradually increases from the tooth root to the tooth tip, with β > β. x .

[0051] S4. Calculate the modulus at the measurement location:

[0052] m x =d x ×cos(β) x ) / z

[0053] In the formula, d x It is the diameter at the measurement location, β x It is the theoretical helix angle at the measurement position; z is the number of teeth on the pulley, m x The modulus at the measurement location.

[0054] The module at the measurement position of the synchronous belt pulley can be obtained by calculation. The module at the measurement position is used to input the gear measuring equipment. In this embodiment, the gear measuring equipment is the TTI-300H gear tester manufactured by Tokyo Tech Co., Ltd. of Japan.

[0055] S5. The actual helix angle β obtained from the actual measurement at the measurement location. 实 Compared with the theoretical value β x In comparison, to determine whether the helix angle of the synchronous pulley is out of tolerance, a deviation threshold for the helix angle at the pitch circle is preset (provided by the design drawings), and β is calculated based on the deviation threshold for the helix angle at the pitch circle. x The tolerance zone, if β 实 Located in β x If it is outside the tolerance zone, it is considered out of tolerance; if it is located in β... x Within the tolerance zone, it will not exceed the tolerance; specifically, the deviation threshold for the helix angle at the pitch circle is e;

[0056] β x上 =atan(tan(β+e)×d) x / d)

[0057] β x下 =atan(tan(β-e)×d) x / d)

[0058] In the formula, β x上 It is the upper limit of the theoretical helix angle at the measurement location, β. x下 β is the lower limit of the theoretical helix angle at the measurement location, β is the helix angle at the pitch circle, and d is the lower limit of the theoretical helix angle at the measurement location. x d is the diameter of the circle at the measurement location, e is the pitch circle diameter of the synchronous pulley, and e is the deviation threshold of the helix angle at the pitch circle.

[0059] β x下 With β x上 Between β x The tolerance zone, if β x下 ≤β 实 ≤β x上 If the result is within tolerance, then it is determined that the error is not exceeded; otherwise, it is determined that the error is exceeded.

[0060] In this embodiment, the helix angle deviation threshold e at the pitch circle is set to 6′, β=5°, dx=78.958, d=80.214, and the upper limit β of the helix angle at the pitch circle is... 上 =5°06′; Lower limit of helix angle β at the pitch circle 下 =4°54′;

[0061] β x =atan(tan(β)×d x / d)

[0062] β x上 =atan(tan(5°06′)×78.958 / 80.214)

[0063] =5.0201°

[0064] =5°01′14″

[0065] β x下 =atan(tan(4°54′)×78.958 / 80.214)

[0066] =4.8236°

[0067] =4°49′25.1″

[0068] β x下 (4°49′25.1″) and β x上 The tolerance zone of βx is between (5°01′14″). If β 实 If it is located outside the tolerance zone, it is considered out of tolerance. If β 实 If it is within the tolerance zone, it is determined that it is not out of tolerance.

[0069] In this embodiment, the actual measurement was performed using a TTI-300H gear measuring instrument manufactured by Tokyo Tech Co., Ltd., Japan. Measurement method: Basic parameters such as the module, number of teeth, pressure angle, helix angle, and tip diameter of the synchronous pulley at the measurement location were input. The measuring software built into the gear measuring instrument generated a standard synchronous pulley profile, scanned the helix at the measurement location, and output the deviation value of the actual helix angle from the theoretical helix angle. Based on the output deviation value, β can be obtained. 实 (β) 实 =β x + Deviation value), based on the tolerance zone calculated above, determine β 实 Is it within the tolerance zone β? x下 (4°49′25.1″) and β x上 Between (5°01′14″), if β 实 If it is located outside the tolerance zone, it is considered out of tolerance. If β 实 If the deviation is within the tolerance zone, it is considered within tolerance. Another comparison method is to directly compare the deviation value output by the gear testing instrument with the upper and lower tolerances at the measurement position. The upper tolerance is equal to β. x上 Subtract β x In this embodiment, the upper tolerance = 5°01′14″ - 4°55′19.6″ = 0°5′54.4″, and the lower tolerance is equal to β. x下 Subtract β x In this embodiment, the lower tolerance is 4°49′25.1″-4°55′19.6″=-0°5′54.5″. If the deviation value is within the upper and lower tolerances, it is not out of tolerance; if it is outside the upper and lower tolerances, it is out of tolerance.

[0070] Terminology Definition: The standard (National Standard, Standard No.: GB / T 11361-2018) defines the "pitch diameter" of a pulley as the pitch circle diameter (represented by "d"). This is the basic dimension for design calculations, located at the point where the pulley teeth mesh with the belt's pitch line. The normal geometric relationship is: pitch diameter (working diameter) > outer diameter (critical diameter). This is determined by the principle of synchronous belt drives, where the belt's pitch line (core layer) is located above the tooth tip, meaning there are tooth grooves on the pulley rim that mesh with the belt teeth. Pulley Dimensions (Values): A table usually provides the specific corresponding values ​​for the pitch diameter "d" and the outer diameter "d0". Pitch diameters with different numbers of teeth can be found in the pulley diameters provided in GB / T 11361-2018 (usually listing multiple pitch models, such as MXL, XL, etc.).

[0071] Helix angle: The acute angle between the tangent of the helix line where the tooth profile surface of a synchronous pulley intersects its pitch cylinder surface and the axis of the synchronous pulley. The helix angle of a synchronous pulley gradually increases from the tooth root to the tooth tip.

[0072] Lead definition: The distance the tooth surface of a synchronous pulley moves axially after one revolution of the helix on the tooth surface. Synchronous pulleys have equal leads; the lead of the helix corresponding to every point on the tooth surface is equal.

[0073] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for detecting the helix angle of a synchronous belt pulley, characterized in that, Includes the following steps: S1. Calculate the synchronous pulley lead based on the pitch circle diameter and the helix angle at the pitch circle: L = πd / tan(β); In the formula, d is the pitch circle diameter of the synchronous pulley, β is the helix angle at the pitch circle, and L is the lead of the synchronous pulley; S2. Select any helix on the timing belt pulley teeth as the measurement position, and measure the lead L at that position. x Satisfy the following formula: L x =πd x / tan(β) x ); In the formula, d x It is the diameter of the circle containing the measurement location, β x It is the theoretical helix angle at the measurement location; S3. Since the lead is equal at all points along the helix of the synchronous belt pulley, L=L x That is, πd / tan(β) = πd x / tan(β) x ),get: b x =atan (tan (β) × d) x / d); In the formula, β x β is the theoretical helix angle at the measurement location, β is the helix angle at the pitch circle, and d is the theoretical helix angle at the measurement location. x It is the diameter of the circle at the measurement location, and d is the pitch circle diameter of the synchronous pulley; S4. Calculate the modulus at the measurement location: m x =d x ×cos(β x ) / z; In the formula, d x It is the diameter at the measurement location, β x It is the theoretical helix angle at the measurement position; z is the number of teeth on the pulley, m x It is the modulus at the measurement location; S5. The actual helix angle β obtained from the actual measurement at the measurement location. 实 With β x In comparison, determine whether the helix angle of the synchronous pulley is out of tolerance.

2. The method for detecting the helix angle of a synchronous belt pulley according to claim 1, characterized in that, The measurement location is any spiral line between the root circle and the tip circle of the tooth.

3. The method for detecting the helix angle of a synchronous belt pulley according to claim 1, characterized in that, In step S5, a deviation threshold for the helix angle at the pitch circle is preset, and β is calculated based on this deviation threshold. x The tolerance zone, if β 实 Located in β x If it is outside the tolerance zone, it is judged as out of tolerance; if it is located in β... x Within the tolerance zone, it will not exceed the tolerance.

4. The method for detecting the helix angle of a synchronous belt pulley according to claim 3, characterized in that, The deviation threshold of the helix angle at the pitch circle is e; β x上 =tan(tan(β+e)×d x / d); β x下 =tan(tan(β-e)×d x / d); In the formula, β x上 It is the upper limit of the theoretical helix angle at the measurement location, β. x下 β is the lower limit of the theoretical helix angle at the measurement location, β is the helix angle at the pitch circle, and d is the lower limit of the theoretical helix angle at the measurement location. x d is the diameter of the circle at the measurement location, e is the pitch circle diameter of the synchronous pulley, and e is the deviation threshold of the helix angle at the pitch circle. β x下 With β x上 Between β x The tolerance zone, if β x下 ≤β 实 ≤β x上 If the result is within tolerance, then it is determined that the error is not out of tolerance; otherwise, it is determined that the error is out of tolerance.

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