{"id":15495,"date":"2025-04-17T00:24:58","date_gmt":"2025-04-17T00:24:58","guid":{"rendered":"https:\/\/www.mechstream.com\/?p=15495"},"modified":"2025-04-17T00:25:01","modified_gmt":"2025-04-17T00:25:01","slug":"shaft-stiffness-and-force-calculator","status":"publish","type":"post","link":"https:\/\/www.mechstream.com\/ar\/shaft-stiffness-and-force-calculator\/","title":{"rendered":"\u062d\u0627\u0633\u0628\u0629 \u0635\u0644\u0627\u0628\u0629 \u0627\u0644\u0639\u0645\u0648\u062f \u0648\u0627\u0644\u0642\u0648\u0629"},"content":{"rendered":"

\u0627\u0643\u062a\u0634\u0641 \u062f\u0642\u0629 \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0645\u0639 \u062d\u0627\u0633\u0628\u0629 \u0635\u0644\u0627\u0628\u0629 \u0648\u0642\u0648\u0629 \u0639\u0645\u0648\u062f \u0627\u0644\u062f\u0648\u0631\u0627\u0646. \u0635\u064f\u0645\u0645\u062a \u0647\u0630\u0647 \u0627\u0644\u0623\u062f\u0627\u0629 \u062e\u0635\u064a\u0635\u064b\u0627 \u0644\u0645\u062d\u062a\u0631\u0641\u064a \u0627\u0644\u0645\u064a\u0643\u0627\u0646\u064a\u0643\u0627\u060c \u062d\u064a\u062b \u062a\u0633\u0627\u0639\u062f\u0643 \u0639\u0644\u0649 \u062a\u062d\u062f\u064a\u062f \u0635\u0644\u0627\u0628\u0629 \u0639\u0645\u0648\u062f \u0627\u0644\u062f\u0648\u0631\u0627\u0646 \u0648\u0627\u0644\u0642\u0648\u0629 \u0627\u0644\u0645\u0637\u0644\u0648\u0628\u0629 \u0644\u0645\u062e\u062a\u0644\u0641 \u0627\u0644\u062a\u0637\u0628\u064a\u0642\u0627\u062a. \u062d\u0633\u0651\u0646 \u0639\u0645\u0644\u064a\u0629 \u0627\u0644\u062a\u0635\u0645\u064a\u0645 \u0648\u0627\u0644\u062a\u062d\u0644\u064a\u0644 \u0644\u062f\u064a\u0643\u060c \u0645\u0645\u0627 \u064a\u0636\u0645\u0646 \u0644\u0643 \u0627\u0644\u0623\u062f\u0627\u0621 \u0627\u0644\u0623\u0645\u062b\u0644 \u0648\u064a\u0642\u0644\u0644 \u0645\u0646 \u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629 \u062d\u062f\u0648\u062b \u0623\u0639\u0637\u0627\u0644 \u0645\u064a\u0643\u0627\u0646\u064a\u0643\u064a\u0629. \u0628\u0641\u0636\u0644 \u0633\u0647\u0648\u0644\u0629 \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647\u0627 \u0648\u062f\u0642\u062a\u0647\u0627 \u0627\u0644\u0639\u0627\u0644\u064a\u0629\u060c \u062a\u064f\u0639\u062f \u062d\u0627\u0633\u0628\u062a\u0646\u0627 \u0645\u0631\u062c\u0639\u064b\u0627 \u0623\u0633\u0627\u0633\u064a\u064b\u0627 \u0644\u0644\u0645\u0647\u0646\u062f\u0633\u064a\u0646 \u0648\u0627\u0644\u0645\u0635\u0645\u0645\u064a\u0646 \u0627\u0644\u0630\u064a\u0646 \u064a\u0633\u0639\u0648\u0646 \u0625\u0644\u0649 \u062a\u062d\u0633\u064a\u0646 \u0645\u0648\u062b\u0648\u0642\u064a\u0629 \u0648\u0643\u0641\u0627\u0621\u0629 \u0645\u0634\u0627\u0631\u064a\u0639\u0647\u0645. \u0643\u0646 \u0631\u0627\u0626\u062f\u064b\u0627 \u0641\u064a \u0645\u062c\u0627\u0644\u0643 \u0645\u0646 \u062e\u0644\u0627\u0644 \u062f\u0645\u062c \u0623\u062f\u0648\u0627\u062a \u062d\u0633\u0627\u0628\u064a\u0629 \u0645\u062a\u0642\u062f\u0645\u0629 \u0641\u064a \u0633\u064a\u0631 \u0639\u0645\u0644\u0643. \u0627\u0633\u062a\u0643\u0634\u0641 \u062d\u0627\u0633\u0628\u062a\u0646\u0627 \u0627\u0644\u064a\u0648\u0645!<\/p>\n\n\n

\n
\"\u062d\u0627\u0633\u0628\u0629<\/figure>\n<\/div>\n\n\n\n\n\n \n \n \u062d\u0627\u0633\u0628\u0629 \u0635\u0644\u0627\u0628\u0629 \u0627\u0644\u0639\u0645\u0648\u062f<\/title>\n <style>\n \/* \u4f7f\u7528\u7279\u5b9a\u7684\u7c7b\u540d\u524d\u7f00\uff0c\u907f\u514d\u6837\u5f0f\u51b2\u7a81 *\/\n .shaft-calculator {\n max-width: 1200px;\n margin: 0 auto;\n padding: 20px;\n font-family: inherit;\n position: relative;\n z-index: 1;\n }\n\n .shaft-calculator .section {\n margin-bottom: 30px;\n position: relative;\n }\n\n .shaft-calculator .parameters-grid {\n display: grid;\n grid-template-columns: repeat(3, 1fr);\n gap: 20px;\n margin-bottom: 20px;\n }\n\n .shaft-calculator .parameter-explanation {\n background: #f8f9fa;\n padding: 15px;\n border-radius: 4px;\n margin-bottom: 15px;\n }\n\n .shaft-calculator .parameter-explanation h3 {\n color: #333;\n margin: 0 0 10px 0;\n font-size: 16px;\n }\n\n .shaft-calculator .parameter-explanation p {\n margin: 5px 0;\n color: #666;\n font-size: 14px;\n }\n\n .shaft-calculator .unit-info {\n color: #007bff !important;\n font-size: 13px !important;\n }\n\n .shaft-calculator .calculator-inputs {\n display: grid;\n grid-template-columns: repeat(3, 1fr);\n gap: 20px;\n margin-bottom: 20px;\n }\n\n .shaft-calculator .input-group {\n display: flex;\n flex-direction: column;\n gap: 5px;\n }\n\n .shaft-calculator .input-group label {\n font-weight: 500;\n color: #333;\n }\n\n .shaft-calculator .input-group input,\n .shaft-calculator .input-group select {\n padding: 8px;\n border: 1px solid #ddd;\n border-radius: 4px;\n font-size: 14px;\n width: 100%;\n box-sizing: border-box;\n }\n\n .shaft-calculator .input-group input:focus,\n .shaft-calculator .input-group select:focus {\n border-color: #007bff;\n outline: none;\n box-shadow: 0 0 0 2px rgba(0,123,255,0.25);\n }\n\n .shaft-calculator .section h2 {\n color: #333;\n margin-bottom: 20px;\n padding-bottom: 10px;\n font-size: 1.5em;\n font-weight: 600;\n }\n\n .shaft-calculator .calculate-btn {\n background-color: #007bff;\n color: white;\n padding: 12px 24px;\n border: none;\n border-radius: 4px;\n cursor: pointer;\n font-size: 16px;\n margin: 20px auto;\n display: block;\n min-width: 200px;\n transition: background-color 0.3s;\n }\n\n .shaft-calculator .calculate-btn:hover {\n background-color: #0056b3;\n color: #ffffff;\n }\n\n .shaft-calculator .results {\n display: none;\n margin-top: 20px;\n padding: 20px;\n background-color: #f8f9fa;\n border-radius: 4px;\n box-shadow: 0 2px 4px rgba(0,0,0,0.1);\n }\n\n .shaft-calculator .result-item {\n margin: 10px 0;\n font-size: 16px;\n display: flex;\n justify-content: space-between;\n align-items: center;\n padding: 12px;\n border-bottom: 1px solid #eee;\n background-color: #fff;\n }\n\n .shaft-calculator .result-label {\n color: #333;\n font-weight: 500;\n }\n\n .shaft-calculator .result-value-container {\n display: flex;\n align-items: center;\n gap: 5px;\n }\n\n .shaft-calculator .result-value {\n font-weight: bold;\n color: #28a745;\n font-size: 1.1em;\n }\n\n @media (max-width: 768px) {\n .shaft-calculator .parameters-grid,\n .shaft-calculator .calculator-inputs {\n grid-template-columns: 1fr;\n }\n }\n <\/style>\n<\/head>\n<body>\n <div class=\"shaft-calculator\">\n <!-- Parameters Explanation Section -->\n <div class=\"section\">\n <h2>\u062d\u062f\u0648\u062f<\/h2>\n <div class=\"parameters-grid\">\n <div class=\"parameter-explanation\">\n <h3>\u0627\u0644\u0642\u0648\u0629 \u0627\u0644\u0645\u062d\u0648\u0631\u064a\u0629 (\u0642\u062f\u0645)<\/h3>\n <p>\u0627\u0644\u0642\u0648\u0629 \u0627\u0644\u0645\u0624\u062b\u0631\u0629 \u0639\u0644\u0649 \u0637\u0648\u0644 \u0645\u062d\u0648\u0631 \u0627\u0644\u0639\u0645\u0648\u062f<\/p>\n <p class=\"unit-info\">\u0627\u0644\u0648\u062d\u062f\u0629: \u0646\u064a\u0648\u062a\u0646<\/p>\n <\/div>\n <div class=\"parameter-explanation\">\n <h3>\u0627\u0644\u0642\u0648\u0629 \u0627\u0644\u0634\u0639\u0627\u0639\u064a\u0629 (Fr)<\/h3>\n <p>\u0627\u0644\u0642\u0648\u0629 \u0627\u0644\u0645\u0624\u062b\u0631\u0629 \u0639\u0645\u0648\u062f\u064a\u064b\u0627 \u0639\u0644\u0649 \u0645\u062d\u0648\u0631 \u0627\u0644\u0639\u0645\u0648\u062f<\/p>\n <p class=\"unit-info\">\u0627\u0644\u0648\u062d\u062f\u0629: \u0646\u064a\u0648\u062a\u0646<\/p>\n <\/div>\n <div class=\"parameter-explanation\">\n <h3>\u0642\u0637\u0631 \u0627\u0644\u0639\u0645\u0648\u062f (\u062f)<\/h3>\n <p>\u0642\u0637\u0631 \u0627\u0644\u0639\u0645\u0648\u062f<\/p>\n <p class=\"unit-info\">\u0627\u0644\u0648\u062d\u062f\u0629: \u0645\u0645 (\u0645\u0644\u064a\u0645\u062a\u0631)<\/p>\n <\/div>\n <div class=\"parameter-explanation\">\n <h3>\u0627\u0644\u0645\u0633\u0627\u0641\u0629 (\u0623)<\/h3>\n <p>\u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0645\u0646 \u0623\u062d\u062f \u0627\u0644\u0637\u0631\u0641\u064a\u0646 \u0625\u0644\u0649 \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u0623\u0648\u0644\u0649<\/p>\n <p class=\"unit-info\">\u0627\u0644\u0648\u062d\u062f\u0629: \u0645\u0645 (\u0645\u0644\u064a\u0645\u062a\u0631)<\/p>\n <\/div>\n <div class=\"parameter-explanation\">\n <h3>\u0627\u0644\u0645\u0633\u0627\u0641\u0629 (\u0628)<\/h3>\n <p>\u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0645\u0646 \u0623\u062d\u062f \u0627\u0644\u0637\u0631\u0641\u064a\u0646 \u0625\u0644\u0649 \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u062b\u0627\u0646\u064a\u0629<\/p>\n <p class=\"unit-info\">\u0627\u0644\u0648\u062d\u062f\u0629: \u0645\u0645 (\u0645\u0644\u064a\u0645\u062a\u0631)<\/p>\n <\/div>\n <div class=\"parameter-explanation\">\n <h3>\u0627\u0644\u0637\u0648\u0644 \u0627\u0644\u0625\u062c\u0645\u0627\u0644\u064a (\u0644\u062a\u0631)<\/h3>\n <p>\u0627\u0644\u0637\u0648\u0644 \u0627\u0644\u0625\u062c\u0645\u0627\u0644\u064a \u0644\u0644\u0639\u0645\u0648\u062f<\/p>\n <p class=\"unit-info\">\u0627\u0644\u0648\u062d\u062f\u0629: \u0645\u0645 (\u0645\u0644\u064a\u0645\u062a\u0631)<\/p>\n <\/div>\n <div class=\"parameter-explanation\">\n <h3>\u0645\u0627\u062f\u0629<\/h3>\n <p>\u0645\u0627\u062f\u0629 \u0627\u0644\u0639\u0645\u0648\u062f<\/p>\n <p class=\"unit-info\">\u064a\u0624\u062b\u0631 \u0639\u0644\u0649 \u0645\u0639\u0627\u0645\u0644 \u0627\u0644\u0645\u0631\u0648\u0646\u0629 (E)<\/p>\n <\/div>\n <\/div>\n <\/div>\n\n <!-- Calculator Section -->\n <div class=\"section\">\n <h2>\u0627\u0644\u0622\u0644\u0629 \u0627\u0644\u062d\u0627\u0633\u0628\u0629<\/h2>\n <div class=\"calculator-inputs\">\n <div class=\"input-group\">\n <label for=\"ft\">\u0642\u062f\u0645 (\u0634\u0645\u0627\u0644)<\/label>\n <input type=\"number\" id=\"ft\" step=\"0.1\" placeholder=\"\u0623\u062f\u062e\u0644 \u0627\u0644\u0642\u0648\u0629 \u0627\u0644\u0645\u062d\u0648\u0631\u064a\u0629\">\n <\/div>\n <div class=\"input-group\">\n <label for=\"fr\">\u0641\u0631\u0646\u0633\u064a (\u0646)<\/label>\n <input type=\"number\" id=\"fr\" step=\"0.1\" placeholder=\"\u0623\u062f\u062e\u0644 \u0627\u0644\u0642\u0648\u0629 \u0627\u0644\u0634\u0639\u0627\u0639\u064a\u0629\">\n <\/div>\n <div class=\"input-group\">\n <label for=\"diameter\">\u062f (\u0645\u0645)<\/label>\n <input type=\"number\" id=\"diameter\" step=\"0.1\" placeholder=\"\u0623\u062f\u062e\u0644 \u0627\u0644\u0642\u0637\u0631\">\n <\/div>\n <div class=\"input-group\">\n <label for=\"a\">\u0623 (\u0645\u0645)<\/label>\n <input type=\"number\" id=\"a\" step=\"0.1\" placeholder=\"\u0623\u062f\u062e\u0644 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0623\">\n <\/div>\n <div class=\"input-group\">\n <label for=\"b\">\u0628 (\u0645\u0645)<\/label>\n <input type=\"number\" id=\"b\" step=\"0.1\" placeholder=\"\u0623\u062f\u062e\u0644 \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\">\n <\/div>\n <div class=\"input-group\">\n <label for=\"length\">\u0644 (\u0645\u0645)<\/label>\n <input type=\"number\" id=\"length\" step=\"0.1\" placeholder=\"\u0623\u062f\u062e\u0644 \u0627\u0644\u0637\u0648\u0644 \u0627\u0644\u0625\u062c\u0645\u0627\u0644\u064a\">\n <\/div>\n <div class=\"input-group\">\n <label for=\"material\">\u0645\u0627\u062f\u0629<\/label>\n <select id=\"material\">\n <option value=\"steel\">\u0627\u0644\u0641\u0648\u0644\u0627\u0630 (E = 210 \u062c\u064a\u062c\u0627 \u0628\u0627\u0633\u0643\u0627\u0644)<\/option>\n <option value=\"aluminum\">\u0627\u0644\u0623\u0644\u0648\u0645\u0646\u064a\u0648\u0645 (E = 70 \u062c\u064a\u062c\u0627 \u0628\u0627\u0633\u0643\u0627\u0644)<\/option>\n <option value=\"brass\">\u0627\u0644\u0646\u062d\u0627\u0633 (E = 100 \u062c\u064a\u062c\u0627 \u0628\u0627\u0633\u0643\u0627\u0644)<\/option>\n <\/select>\n <\/div>\n <\/div>\n <div class=\"button-container\">\n <button class=\"calculate-btn\" onclick=\"calculateResults()\">\u0627\u062d\u0633\u0628<\/button>\n <\/div>\n <\/div>\n\n <!-- Results Section -->\n <div class=\"section results\" id=\"results\">\n <h2>\u0627\u0644\u0646\u062a\u0627\u0626\u062c<\/h2>\n <div class=\"result-item\">\n <div class=\"result-label\">\u0639\u0632\u0645 \u0627\u0644\u0642\u0635\u0648\u0631 \u0627\u0644\u0630\u0627\u062a\u064a (I):<\/div>\n <div class=\"result-value-container\">\n <span class=\"result-value\" id=\"momentOfInertia\">0<\/span>\n <span class=\"unit\">\u0645\u0645\u2074<\/span>\n <\/div>\n <\/div>\n <div class=\"result-item\">\n <div class=\"result-label\">\u0627\u0644\u0633\u0631\u0639\u0629 \u0627\u0644\u062d\u0631\u062c\u0629 (fc):<\/div>\n <div class=\"result-value-container\">\n <span class=\"result-value\" id=\"criticalSpeed\">0<\/span>\n <span class=\"unit\">\u0647\u0631\u062a\u0632<\/span>\n <\/div>\n <\/div>\n <div class=\"result-item\">\n <div class=\"result-label\">\u0627\u0644\u062a\u0631\u062f\u062f \u0627\u0644\u0637\u0628\u064a\u0639\u064a (fg):<\/div>\n <div class=\"result-value-container\">\n <span class=\"result-value\" id=\"naturalFreq\">0<\/span>\n <span class=\"unit\">\u0647\u0631\u062a\u0632<\/span>\n <\/div>\n <\/div>\n <div class=\"result-item\">\n <div class=\"result-label\">\u0645\u0631\u0628\u0639 \u0627\u0644\u0633\u0631\u0639\u0629 \u0627\u0644\u062d\u0631\u062c\u0629 (fc\u00b2):<\/div>\n <div class=\"result-value-container\">\n <span class=\"result-value\" id=\"criticalSpeedSquared\">0<\/span>\n <span class=\"unit\">\u0647\u0631\u062a\u0632\u00b2<\/span>\n <\/div>\n <\/div>\n <div class=\"result-item\">\n <div class=\"result-label\">\u0645\u0631\u0628\u0639 \u0627\u0644\u062a\u0631\u062f\u062f \u0627\u0644\u0637\u0628\u064a\u0639\u064a (fg\u00b2):<\/div>\n <div class=\"result-value-container\">\n <span class=\"result-value\" id=\"naturalFreqSquared\">0<\/span>\n <span class=\"unit\">\u0647\u0631\u062a\u0632\u00b2<\/span>\n <\/div>\n <\/div>\n <div class=\"result-item\">\n <div class=\"result-label\">\u0646\u0633\u0628\u0629 \u0627\u0644\u062a\u0631\u062f\u062f (f):<\/div>\n <div class=\"result-value-container\">\n <span class=\"result-value\" id=\"freqRatio\">0<\/span>\n <\/div>\n <\/div>\n <div class=\"result-item\">\n <div class=\"result-label\">\u0627\u0644\u0645\u0639\u0627\u0645\u0644:<\/div>\n <div class=\"result-value-container\">\n <span class=\"result-value\" id=\"coefficient\">0<\/span>\n <\/div>\n <\/div>\n <\/div>\n <\/div>\n\n <script>\n function calculateResults() {\n \/\/ Get input values\n const ft = parseFloat(document.getElementById('ft').value) || 0;\n const fr = parseFloat(document.getElementById('fr').value) || 0;\n const diameter = parseFloat(document.getElementById('diameter').value) || 0;\n const a = parseFloat(document.getElementById('a').value) || 0;\n const b = parseFloat(document.getElementById('b').value) || 0;\n const length = parseFloat(document.getElementById('length').value) || 0;\n const material = document.getElementById('material').value;\n\n \/\/ Material properties (MPa)\n const E = material === 'steel' ? 210000 : (material === 'aluminum' ? 70000 : 100000);\n\n \/\/ Calculate moment of inertia (mm\u2074)\n const I = (Math.PI * Math.pow(diameter, 4)) \/ 64;\n\n \/\/ Calculate cross-sectional area (mm\u00b2)\n const A = (Math.PI * Math.pow(diameter, 2)) \/ 4;\n\n \/\/ Calculate critical speed (Hz)\n const criticalSpeed = Math.sqrt((E * I) \/ (A * length * length * length)) \/ (2 * Math.PI);\n\n \/\/ Calculate natural frequency (Hz)\n const naturalFreq = criticalSpeed * Math.sqrt(1 - (fr \/ (E * A)));\n\n \/\/ Calculate squares\n const criticalSpeedSquared = Math.pow(criticalSpeed, 2);\n const naturalFreqSquared = Math.pow(naturalFreq, 2);\n\n \/\/ Calculate frequency ratio\n const freqRatio = naturalFreq \/ criticalSpeed;\n\n \/\/ Calculate coefficient (assuming it's based on the ratio)\n const coefficient = 1 \/ (1 - Math.pow(freqRatio, 2));\n\n \/\/ Display results\n document.getElementById('momentOfInertia').textContent = I.toFixed(2);\n document.getElementById('criticalSpeed').textContent = criticalSpeed.toFixed(2);\n document.getElementById('naturalFreq').textContent = naturalFreq.toFixed(2);\n document.getElementById('criticalSpeedSquared').textContent = criticalSpeedSquared.toFixed(2);\n document.getElementById('naturalFreqSquared').textContent = naturalFreqSquared.toFixed(2);\n document.getElementById('freqRatio').textContent = freqRatio.toFixed(4);\n document.getElementById('coefficient').textContent = coefficient.toFixed(4);\n\n document.getElementById('results').style.display = 'block';\n }\n <\/script>\n<\/body>\n<\/html>","protected":false},"excerpt":{"rendered":"<p>Discover precision engineering with our Shaft Stiffness and Force Calculator. 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