Введение
Другие представления о кручении.
Twisting of an object due to an applied torque
In the field of solid mechanics, torsion is the twisting of an object due to an applied torque. Torsion is expressed in either the pascal (Pa), an SI unit for newtons per square metre, or in pounds per square inch (psi) while torque is expressed in newton metres (N·m) or foot pound force (ft·lbf). In sections perpendicular to the torque axis, the resultant shear stress in this section is perpendicular to the radius. In non circular cross sections, twisting is accompanied by a distortion called warping, in which transverse sections do not remain plane. For shafts of uniform cross section unrestrained against warping, the torsion is:
where:
T is the applied torque or moment of torsion in Nm. (tau) is the maximum shear stress at the outer surface
JT is the torsion constant for the section. For circular rods, and tubes with constant wall thickness, it is equal to the polar moment of inertia of the section, but for other shapes, or split sections, it can be much less. For more accuracy, finite element analysis (FEA) is the best method. Other calculation methods include membrane analogy and shear flow approximation. r is the perpendicular distance between the rotational axis and the farthest point in the section (at the outer surface). ℓ is the length of the object to or over which the torque is being applied. φ (phi) is the angle of twist in radians. G is the shear modulus, also called the modulus of rigidity, and is usually given in gigapascals (GPa), lbf/in2 (psi), or lbf/ft2 or in ISO units N/mm2. The product JTG is called the torsional rigidity wT.
Кручение – это деформация объекта под действием крутящего момента.
Twisting of an object due to an applied torque
In the field of solid mechanics, torsion is the twisting of an object due to an applied torque. Torsion is expressed in either the pascal (Pa), an SI unit for newtons per square metre, or in pounds per square inch (psi) while torque is expressed in newton metres (N·m) or foot pound force (ft·lbf). In sections perpendicular to the torque axis, the resultant shear stress in this section is perpendicular to the radius. In non circular cross sections, twisting is accompanied by a distortion called warping, in which transverse sections do not remain plane. For shafts of uniform cross section unrestrained against warping, the torsion is:
where:
T is the applied torque or moment of torsion in Nm. (tau) is the maximum shear stress at the outer surface
JT is the torsion constant for the section. For circular rods, and tubes with constant wall thickness, it is equal to the polar moment of inertia of the section, but for other shapes, or split sections, it can be much less. For more accuracy, finite element analysis (FEA) is the best method. Other calculation methods include membrane analogy and shear flow approximation. r is the perpendicular distance between the rotational axis and the farthest point in the section (at the outer surface). ℓ is the length of the object to or over which the torque is being applied. φ (phi) is the angle of twist in radians. G is the shear modulus, also called the modulus of rigidity, and is usually given in gigapascals (GPa), lbf/in2 (psi), or lbf/ft2 or in ISO units N/mm2. The product JTG is called the torsional rigidity wT.
В области механики твердых тел кручение определяется как скручивание объекта под действием крутящего момента. Кручение выражается в паскалях (Па), единице СИ, равной ньютонам на квадратный метр, или в фунтах на квадратный дюйм (psi), в то время как крутящий момент выражается в ньютон-метрах (Н·м) или фут-фунтах силы (ft·lbf). В сечениях, перпендикулярных оси крутящего момента, результирующее напряжение сдвига в этом сечении перпендикулярно радиусу. В сечениях некруглой формы скручивание сопровождается деформацией, называемой кручением, при которой поперечные сечения не остаются плоскими. Для валов с однородным поперечным сечением, не зафиксированных от кручения, кручение определяется следующим образом:
Twisting of an object due to an applied torque
In the field of solid mechanics, torsion is the twisting of an object due to an applied torque. Torsion is expressed in either the pascal (Pa), an SI unit for newtons per square metre, or in pounds per square inch (psi) while torque is expressed in newton metres (N·m) or foot pound force (ft·lbf). In sections perpendicular to the torque axis, the resultant shear stress in this section is perpendicular to the radius. In non circular cross sections, twisting is accompanied by a distortion called warping, in which transverse sections do not remain plane. For shafts of uniform cross section unrestrained against warping, the torsion is:
where:
T is the applied torque or moment of torsion in Nm. (tau) is the maximum shear stress at the outer surface
JT is the torsion constant for the section. For circular rods, and tubes with constant wall thickness, it is equal to the polar moment of inertia of the section, but for other shapes, or split sections, it can be much less. For more accuracy, finite element analysis (FEA) is the best method. Other calculation methods include membrane analogy and shear flow approximation. r is the perpendicular distance between the rotational axis and the farthest point in the section (at the outer surface). ℓ is the length of the object to or over which the torque is being applied. φ (phi) is the angle of twist in radians. G is the shear modulus, also called the modulus of rigidity, and is usually given in gigapascals (GPa), lbf/in2 (psi), or lbf/ft2 or in ISO units N/mm2. The product JTG is called the torsional rigidity wT.
где:
T – приложенный крутящий момент или момент кручения в Н·м.
τ (тау) – максимальное напряжение сдвига на внешней поверхности.
J – постоянная кручения для сечения. Для круглых стержней и труб с постоянной толщиной стенки она равна полярному моменту инерции сечения, но для других форм или разделенных сечений может быть значительно меньше. Для повышения точности наилучшим методом является метод конечных элементов (МКЭ). Другие методы расчета включают аналогию мембраны и приближение потока сдвига.
r – перпендикулярное расстояние между осью вращения и наиболее удаленной точкой в сечении (на внешней поверхности).
ℓ – длина объекта, к которому или вдоль которого прикладывается крутящий момент.
φ (фи) – угол скручивания в радианах.
G – модуль сдвига, также называемый модулем упругости при сдвиге, и обычно указывается в гигапаскалях (ГПа), фунтах силы на квадратный дюйм (psi) или фунтах силы на квадратный фут, или в единицах ISO Н/мм². Произведение JTG называется крутильной жесткостью wT.
Twisting of an object due to an applied torque
In the field of solid mechanics, torsion is the twisting of an object due to an applied torque. Torsion is expressed in either the pascal (Pa), an SI unit for newtons per square metre, or in pounds per square inch (psi) while torque is expressed in newton metres (N·m) or foot pound force (ft·lbf). In sections perpendicular to the torque axis, the resultant shear stress in this section is perpendicular to the radius. In non circular cross sections, twisting is accompanied by a distortion called warping, in which transverse sections do not remain plane. For shafts of uniform cross section unrestrained against warping, the torsion is:
where:
T is the applied torque or moment of torsion in Nm. (tau) is the maximum shear stress at the outer surface
JT is the torsion constant for the section. For circular rods, and tubes with constant wall thickness, it is equal to the polar moment of inertia of the section, but for other shapes, or split sections, it can be much less. For more accuracy, finite element analysis (FEA) is the best method. Other calculation methods include membrane analogy and shear flow approximation. r is the perpendicular distance between the rotational axis and the farthest point in the section (at the outer surface). ℓ is the length of the object to or over which the torque is being applied. φ (phi) is the angle of twist in radians. G is the shear modulus, also called the modulus of rigidity, and is usually given in gigapascals (GPa), lbf/in2 (psi), or lbf/ft2 or in ISO units N/mm2. The product JTG is called the torsional rigidity wT.
Режим отказа
Напряжение сдвига в валу может быть разложено на главные напряжения с помощью круга Мора. Если вал нагружен только кручением, то одно из главных напряжений будет растягивающим, а другое – сжимающим. Эти напряжения ориентированы под углом 45 градусов по спирали вокруг вала. Если вал изготовлен из хрупкого материала, то разрушение произойдет из-за трещины, возникающей на поверхности и распространяющейся к центру вала, образуя излом по спирали под углом 45 градусов. Это часто демонстрируется, скручивая кусок мела между пальцами. В случае тонкостенных полых валов чрезмерная крутящая нагрузка может привести к выпучиванию с образованием складок под углом 45° к оси вала.